From 6b4dbb131c57e139fe732fa3090e8be9e7732a03 Mon Sep 17 00:00:00 2001 From: Amitayush Thakur Date: Sun, 11 Jan 2026 14:21:07 +0000 Subject: [PATCH 1/5] Add .gitattributes to manage large file storage for selected_results/ --- docs/static/.gitattributes | 1 + 1 file changed, 1 insertion(+) create mode 100644 docs/static/.gitattributes diff --git a/docs/static/.gitattributes b/docs/static/.gitattributes new file mode 100644 index 0000000..0355253 --- /dev/null +++ b/docs/static/.gitattributes @@ -0,0 +1 @@ +selected_results/ filter=lfs diff=lfs merge=lfs -text From 8704006758b05d8bd652f80551f75d121d4eb360 Mon Sep 17 00:00:00 2001 From: Amitayush Thakur Date: Sun, 11 Jan 2026 14:21:54 +0000 Subject: [PATCH 2/5] Added logs for gpt oss evaluations on miniF2F --- .../gpt_oss_20b_evals_pass_at_5.log | 26124 ++++++++++++++++ 1 file changed, 26124 insertions(+) create mode 100644 docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log diff --git a/docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log b/docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log new file mode 100644 index 0000000..946f552 --- /dev/null +++ b/docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log @@ -0,0 +1,26124 @@ +2026-01-10 22:26:00,890 - __main__ - INFO - Pid: 3702174 +2026-01-10 22:26:00,891 - __main__ - INFO - Running Experiment: { + "env_settings": { + "name": "bm25_retrieval", + "retrieval_strategy": "BM25" + }, + "prompt_settings": { + "name": "simplified_lean4_copra_math", + "main_prompt": "data/prompts/system/simplified-lean4-proof-agent-with-dfs.md", + "conv_prompt": "data/prompts/conversation/simplified-lean4-proof-agent-dfs-multiple.md", + "uses_simplified_prompt": true, + "informal_proof_repo": null + }, + "eval_settings": { + "name": "n_60_dfs_gpt_oss_20b_no_retrieve_no_ex", + "use_hammer": "ALLOW", + "setting_type": "Agent", + "max_proof_depth": 100, + "timeout_in_secs": 600, + "proof_retries": 5, + "max_tokens_per_action": 4500, + "max_theorems_in_prompt": 7, + "gpt_model_name": "vllm:openai/gpt-oss-20b", + "max_number_of_episodes": 1, + "max_steps_per_episode": 100, + "render": false, + "checkpoint_dir": ".log/checkpoints", + "should_checkpoint": false, + "temperature": 0.7, + "max_history_messages": 0, + "policy_name": "Dfs", + "proof_dump_dir": ".log/proofs/eval_driver/dfs", + "use_human_readable_proof_context": true, + "sample": 1.0, + "sample_seed": 3840, + "use_example_retrieval": false, + "always_use_useful_theorem_retrieval": false, + "num_goal_per_prompt": null, + "model_params": {} + }, + "benchmark": { + "name": "miniF2F_lean4_test_easy_to_hard", + "num_files": 1, + "language": "LEAN4", + "datasets": [ + { + "project": "data/test/miniF2F-lean4", + "files": [ + { + "path": "MiniF2F/Test.lean", + "theorems": [ + "aime_1983_p2", + "aime_1989_p8", + "algebra_sqineq_at2malt1", + "amc12a_2002_p6", + "amc12a_2013_p4", + "amc12a_2021_p9", + "amc12b_2002_p19", + "amc12b_2002_p2", + "amc12b_2020_p2", + "amc12b_2020_p6", + "mathd_algebra_125", + "mathd_algebra_129", + "mathd_algebra_137", + "mathd_algebra_139", + "mathd_algebra_141", + "mathd_algebra_142", + "mathd_algebra_143", + "mathd_algebra_148", + "mathd_algebra_158", + "mathd_algebra_160", + "mathd_algebra_171", + "mathd_algebra_176", + "mathd_algebra_24", + "mathd_algebra_246", + "mathd_algebra_263", + "mathd_algebra_270", + "mathd_algebra_296", + "mathd_algebra_302", + "mathd_algebra_304", + "mathd_algebra_314", + "mathd_algebra_329", + "mathd_algebra_33", + "mathd_algebra_346", + "mathd_algebra_354", + "mathd_algebra_359", + "mathd_algebra_388", + "mathd_algebra_400", + "mathd_algebra_412", + "mathd_algebra_419", + "mathd_algebra_432", + "mathd_algebra_44", + "mathd_algebra_440", + "mathd_algebra_441", + "mathd_algebra_478", + "mathd_algebra_513", + "mathd_algebra_76", + "mathd_algebra_80", + "mathd_numbertheory_12", + "mathd_numbertheory_127", + "mathd_numbertheory_135", + "mathd_numbertheory_150", + "mathd_numbertheory_175", + "mathd_numbertheory_185", + "mathd_numbertheory_207", + "mathd_numbertheory_212", + "mathd_numbertheory_229", + "mathd_numbertheory_235", + "mathd_numbertheory_237", + "mathd_numbertheory_239", + "mathd_numbertheory_247", + "mathd_numbertheory_254", + "mathd_numbertheory_299", + "mathd_numbertheory_3", + "mathd_numbertheory_341", + "mathd_numbertheory_342", + "mathd_numbertheory_343", + "mathd_numbertheory_345", + "mathd_numbertheory_517", + "mathd_numbertheory_551", + "mathd_numbertheory_66", + "mathd_numbertheory_728", + "mathd_numbertheory_769", + "mathd_numbertheory_85", + "mathd_algebra_107", + "mathd_algebra_113", + "mathd_algebra_114", + "mathd_algebra_153", + "mathd_algebra_156", + "mathd_algebra_17", + "mathd_algebra_170", + "mathd_algebra_184", + "mathd_algebra_188", + "mathd_algebra_196", + "mathd_algebra_208", + "mathd_algebra_209", + "mathd_algebra_215", + "mathd_algebra_275", + "mathd_algebra_276", + "mathd_algebra_288", + "mathd_algebra_289", + "mathd_algebra_293", + "mathd_algebra_313", + "mathd_algebra_320", + "mathd_algebra_332", + "mathd_algebra_338", + "mathd_algebra_342", + "mathd_algebra_362", + "mathd_algebra_392", + "mathd_algebra_398", + "mathd_algebra_427", + "mathd_algebra_452", + "mathd_algebra_459", + "mathd_algebra_484", + "mathd_algebra_487", + "mathd_algebra_598", + "mathd_algebra_756", + "mathd_numbertheory_100", + "mathd_numbertheory_1124", + "mathd_numbertheory_222", + "mathd_numbertheory_227", + "mathd_numbertheory_233", + "mathd_numbertheory_234", + "mathd_numbertheory_277", + "mathd_numbertheory_293", + "mathd_numbertheory_296", + "mathd_numbertheory_314", + "mathd_numbertheory_320", + "mathd_numbertheory_321", + "mathd_numbertheory_328", + "mathd_numbertheory_34", + "mathd_numbertheory_353", + "mathd_numbertheory_427", + "mathd_numbertheory_430", + "mathd_numbertheory_435", + "mathd_numbertheory_447", + "mathd_numbertheory_451", + "mathd_numbertheory_457", + "mathd_numbertheory_483", + "mathd_numbertheory_495", + "mathd_numbertheory_5", + "mathd_numbertheory_521", + "mathd_numbertheory_541", + "mathd_numbertheory_552", + "mathd_numbertheory_559", + "mathd_numbertheory_582", + "mathd_numbertheory_618", + "mathd_numbertheory_711", + "mathd_numbertheory_764", + "mathd_numbertheory_765", + "mathd_numbertheory_99", + "numbertheory_2pownm1prime_nprime", + "numbertheory_3pow2pownm1mod2pownp3eq2pownp2", + "numbertheory_4x3m7y3neq2003", + "numbertheory_aoddbdiv4asqpbsqmod8eq1", + "numbertheory_exk2powkeqapb2mulbpa2_aeq1", + "numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown", + "numbertheory_notequiv2i2jasqbsqdiv8", + "numbertheory_x5neqy2p4", + "aime_1983_p1", + "aime_1983_p3", + "aime_1984_p1", + "aime_1984_p7", + "aime_1987_p5", + "aime_1988_p8", + "aime_1990_p15", + "aime_1990_p4", + "aime_1991_p9", + "aime_1994_p3", + "aime_1995_p7", + "aime_1997_p9", + "aime_1999_p11", + "algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7", + "algebra_9onxpypzleqsum2onxpy", + "algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2", + "algebra_absapbon1pabsapbleqsumabsaon1pabsa", + "algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1", + "algebra_amgm_sum1toneqn_prod1tonleq1", + "algebra_amgm_sumasqdivbgeqsuma", + "algebra_apbmpcneq0_aeq0anbeq0anceq0", + "algebra_apbon2pownleqapownpbpowon2", + "algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3", + "algebra_bleqa_apbon2msqrtableqambsqon8b", + "algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778", + "algebra_ineq_nto1onlt2m1on", + "algebra_others_exirrpowirrrat", + "algebra_sqineq_unitcircatbpabsamblt1", + "algebra_sqineq_unitcircatbpamblt1", + "algebra_sum1onsqrt2to1onsqrt10000lt198", + "amc12_2000_p1", + "amc12_2000_p12", + "amc12_2000_p20", + "amc12_2000_p6", + "amc12_2001_p21", + "amc12_2001_p5", + "amc12a_2002_p13", + "amc12a_2003_p23", + "amc12a_2003_p5", + "amc12a_2008_p25", + "amc12a_2009_p6", + "amc12a_2009_p7", + "amc12a_2019_p12", + "amc12a_2020_p10", + "amc12a_2020_p15", + "amc12a_2020_p25", + "amc12a_2020_p4", + "amc12a_2020_p7", + "amc12a_2020_p9", + "amc12a_2021_p12", + "amc12a_2021_p14", + "amc12a_2021_p18", + "amc12a_2021_p19", + "amc12a_2021_p22", + "amc12a_2021_p25", + "amc12a_2021_p3", + "amc12a_2021_p8", + "amc12b_2002_p4", + "amc12b_2002_p7", + "amc12b_2020_p13", + "amc12b_2020_p21", + "amc12b_2020_p22", + "amc12b_2021_p1", + "amc12b_2021_p13", + "amc12b_2021_p18", + "amc12b_2021_p3", + "amc12b_2021_p4", + "amc12b_2021_p9", + "imo_1959_p1", + "imo_1960_p2", + "imo_1962_p2", + "imo_1963_p5", + "imo_1964_p2", + "imo_1965_p2", + "imo_1968_p5_1", + "imo_1969_p2", + "imo_1974_p3", + "imo_1977_p6", + "imo_1981_p6", + "imo_1982_p1", + "imo_1983_p6", + "imo_1984_p6", + "imo_1985_p6", + "imo_1992_p1", + "imo_1997_p5", + "imo_2001_p6", + "imo_2019_p1", + "imosl_2007_algebra_p6", + "induction_11div10tonmn1ton", + "induction_12dvd4expnp1p20", + "induction_1pxpownlt1pnx", + "induction_nfactltnexpnm1ngt3", + "induction_pord1p1on2powklt5on2", + "induction_pprime_pdvdapowpma", + "induction_prod1p1onk3le3m1onn", + "induction_sumkexp3eqsumksq" + ], + "max_retry_attempts_limits": {}, + "max_time_limits_in_secs": {} + } + ] + } + ], + "few_shot_data_path_for_retrieval": null, + "few_shot_metadata_filename_for_retrieval": null, + "dfs_data_path_for_retrieval": null, + "dfs_metadata_filename_for_retrieval": null, + "timeout_per_theorem_in_secs": 600 + } +} +2026-01-10 22:26:00,891 - __main__ - INFO - Starting vLLM server for model: vllm:openai/gpt-oss-20b +2026-01-10 22:26:03,366 - __main__ - INFO - Starting vLLM server for model: openai/gpt-oss-20b +2026-01-10 22:26:03,367 - __main__ - INFO - Server will be accessible at: http://127.0.0.1:48000/v1 +2026-01-10 22:26:03,367 - __main__ - INFO - Checking if vLLM server is already running at http://127.0.0.1:48000/v1... +2026-01-10 22:26:03,371 - __main__ - INFO - ✓ vLLM server is healthy and serving model: openai/gpt-oss-20b +2026-01-10 22:26:03,371 - __main__ - INFO - ✓ vLLM server already running and healthy, reusing existing server +2026-01-10 22:26:03,371 - __main__ - INFO - vLLM server started successfully at http://127.0.0.1:48000/v1 +2026-01-10 22:26:03,371 - __main__ - INFO - ParallelTheoremExecutor initialized with multiprocessing (Python < 3.14) +2026-01-10 22:26:03,371 - __main__ - INFO - Parallel theorem execution is ENABLED +2026-01-10 22:26:03,373 - __main__ - INFO - Getting all lemmas in file: data/test/miniF2F-lean4/MiniF2F/Test.lean with timeout: 3000 seconds +2026-01-10 22:26:03,444 - __main__ - INFO - Discovered 244 lemmas +2026-01-10 22:26:03,445 - __main__ - INFO - Lemma names: ['mathd_algebra_478', 'numbertheory_4x3m7y3neq2003', 'aime_1983_p1', 'amc12_2001_p5', 'mathd_algebra_141', 'mathd_numbertheory_3', 'imo_1969_p2', 'mathd_algebra_44', 'mathd_algebra_209', 'mathd_numbertheory_1124'] ... ['aime_1989_p8', 'mathd_numbertheory_296', 'mathd_algebra_142', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'mathd_algebra_400', 'aime_1995_p7', 'mathd_numbertheory_185', 'mathd_algebra_441', 'mathd_numbertheory_582', 'mathd_algebra_338'] +2026-01-10 22:26:03,482 - __main__ - INFO - Discovered 243 lemmas to prove in data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:03,483 - __main__ - INFO - Lemmas to prove in file data/test/miniF2F-lean4/MiniF2F/Test.lean: +['aime_1983_p2', 'aime_1989_p8', 'algebra_sqineq_at2malt1', 'amc12a_2002_p6', 'amc12a_2013_p4', 'amc12a_2021_p9', 'amc12b_2002_p19', 'amc12b_2002_p2', 'amc12b_2020_p2', 'amc12b_2020_p6', 'mathd_algebra_125', 'mathd_algebra_129', 'mathd_algebra_137', 'mathd_algebra_139', 'mathd_algebra_141', 'mathd_algebra_142', 'mathd_algebra_143', 'mathd_algebra_148', 'mathd_algebra_158', 'mathd_algebra_160', 'mathd_algebra_171', 'mathd_algebra_176', 'mathd_algebra_24', 'mathd_algebra_246', 'mathd_algebra_263', 'mathd_algebra_270', 'mathd_algebra_296', 'mathd_algebra_302', 'mathd_algebra_304', 'mathd_algebra_314', 'mathd_algebra_329', 'mathd_algebra_33', 'mathd_algebra_346', 'mathd_algebra_354', 'mathd_algebra_359', 'mathd_algebra_388', 'mathd_algebra_400', 'mathd_algebra_412', 'mathd_algebra_419', 'mathd_algebra_432', 'mathd_algebra_44', 'mathd_algebra_440', 'mathd_algebra_441', 'mathd_algebra_478', 'mathd_algebra_513', 'mathd_algebra_76', 'mathd_algebra_80', 'mathd_numbertheory_12', 'mathd_numbertheory_127', 'mathd_numbertheory_135', 'mathd_numbertheory_150', 'mathd_numbertheory_175', 'mathd_numbertheory_185', 'mathd_numbertheory_207', 'mathd_numbertheory_212', 'mathd_numbertheory_229', 'mathd_numbertheory_235', 'mathd_numbertheory_237', 'mathd_numbertheory_239', 'mathd_numbertheory_247', 'mathd_numbertheory_254', 'mathd_numbertheory_299', 'mathd_numbertheory_3', 'mathd_numbertheory_341', 'mathd_numbertheory_342', 'mathd_numbertheory_343', 'mathd_numbertheory_345', 'mathd_numbertheory_517', 'mathd_numbertheory_551', 'mathd_numbertheory_66', 'mathd_numbertheory_728', 'mathd_numbertheory_769', 'mathd_numbertheory_85', 'mathd_algebra_107', 'mathd_algebra_113', 'mathd_algebra_114', 'mathd_algebra_153', 'mathd_algebra_156', 'mathd_algebra_17', 'mathd_algebra_170', 'mathd_algebra_184', 'mathd_algebra_188', 'mathd_algebra_196', 'mathd_algebra_208', 'mathd_algebra_209', 'mathd_algebra_215', 'mathd_algebra_275', 'mathd_algebra_276', 'mathd_algebra_288', 'mathd_algebra_289', 'mathd_algebra_293', 'mathd_algebra_313', 'mathd_algebra_320', 'mathd_algebra_332', 'mathd_algebra_338', 'mathd_algebra_342', 'mathd_algebra_362', 'mathd_algebra_392', 'mathd_algebra_398', 'mathd_algebra_427', 'mathd_algebra_452', 'mathd_algebra_459', 'mathd_algebra_484', 'mathd_algebra_487', 'mathd_algebra_598', 'mathd_algebra_756', 'mathd_numbertheory_100', 'mathd_numbertheory_1124', 'mathd_numbertheory_222', 'mathd_numbertheory_227', 'mathd_numbertheory_233', 'mathd_numbertheory_234', 'mathd_numbertheory_277', 'mathd_numbertheory_293', 'mathd_numbertheory_296', 'mathd_numbertheory_314', 'mathd_numbertheory_320', 'mathd_numbertheory_321', 'mathd_numbertheory_328', 'mathd_numbertheory_34', 'mathd_numbertheory_353', 'mathd_numbertheory_427', 'mathd_numbertheory_430', 'mathd_numbertheory_435', 'mathd_numbertheory_447', 'mathd_numbertheory_451', 'mathd_numbertheory_457', 'mathd_numbertheory_483', 'mathd_numbertheory_495', 'mathd_numbertheory_5', 'mathd_numbertheory_521', 'mathd_numbertheory_541', 'mathd_numbertheory_552', 'mathd_numbertheory_559', 'mathd_numbertheory_582', 'mathd_numbertheory_618', 'mathd_numbertheory_711', 'mathd_numbertheory_764', 'mathd_numbertheory_765', 'mathd_numbertheory_99', 'numbertheory_2pownm1prime_nprime', 'numbertheory_3pow2pownm1mod2pownp3eq2pownp2', 'numbertheory_4x3m7y3neq2003', 'numbertheory_aoddbdiv4asqpbsqmod8eq1', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown', 'numbertheory_x5neqy2p4', 'aime_1983_p1', 'aime_1983_p3', 'aime_1984_p1', 'aime_1984_p7', 'aime_1987_p5', 'aime_1988_p8', 'aime_1990_p15', 'aime_1990_p4', 'aime_1991_p9', 'aime_1994_p3', 'aime_1995_p7', 'aime_1997_p9', 'aime_1999_p11', 'algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7', 'algebra_9onxpypzleqsum2onxpy', 'algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2', 'algebra_absapbon1pabsapbleqsumabsaon1pabsa', 'algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1', 'algebra_amgm_sum1toneqn_prod1tonleq1', 'algebra_amgm_sumasqdivbgeqsuma', 'algebra_apbmpcneq0_aeq0anbeq0anceq0', 'algebra_apbon2pownleqapownpbpowon2', 'algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3', 'algebra_bleqa_apbon2msqrtableqambsqon8b', 'algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778', 'algebra_ineq_nto1onlt2m1on', 'algebra_others_exirrpowirrrat', 'algebra_sqineq_unitcircatbpabsamblt1', 'algebra_sqineq_unitcircatbpamblt1', 'algebra_sum1onsqrt2to1onsqrt10000lt198', 'amc12_2000_p1', 'amc12_2000_p12', 'amc12_2000_p20', 'amc12_2000_p6', 'amc12_2001_p21', 'amc12_2001_p5', 'amc12a_2002_p13', 'amc12a_2003_p23', 'amc12a_2003_p5', 'amc12a_2008_p25', 'amc12a_2009_p6', 'amc12a_2009_p7', 'amc12a_2019_p12', 'amc12a_2020_p10', 'amc12a_2020_p15', 'amc12a_2020_p25', 'amc12a_2020_p4', 'amc12a_2020_p7', 'amc12a_2020_p9', 'amc12a_2021_p12', 'amc12a_2021_p14', 'amc12a_2021_p18', 'amc12a_2021_p19', 'amc12a_2021_p22', 'amc12a_2021_p25', 'amc12a_2021_p3', 'amc12a_2021_p8', 'amc12b_2002_p4', 'amc12b_2002_p7', 'amc12b_2020_p13', 'amc12b_2020_p21', 'amc12b_2020_p22', 'amc12b_2021_p1', 'amc12b_2021_p13', 'amc12b_2021_p18', 'amc12b_2021_p3', 'amc12b_2021_p4', 'amc12b_2021_p9', 'imo_1959_p1', 'imo_1960_p2', 'imo_1962_p2', 'imo_1963_p5', 'imo_1964_p2', 'imo_1965_p2', 'imo_1968_p5_1', 'imo_1969_p2', 'imo_1974_p3', 'imo_1977_p6', 'imo_1981_p6', 'imo_1982_p1', 'imo_1983_p6', 'imo_1984_p6', 'imo_1985_p6', 'imo_1992_p1', 'imo_1997_p5', 'imo_2001_p6', 'imo_2019_p1', 'imosl_2007_algebra_p6', 'induction_11div10tonmn1ton', 'induction_12dvd4expnp1p20', 'induction_1pxpownlt1pnx', 'induction_nfactltnexpnm1ngt3', 'induction_pord1p1on2powklt5on2', 'induction_pprime_pdvdapowpma', 'induction_prod1p1onk3le3m1onn', 'induction_sumkexp3eqsumksq'] +2026-01-10 22:26:03,483 - __main__ - INFO - Executing 243 theorems in parallel using 4 workers +2026-01-10 22:26:03,519 - __main__ - INFO - Attempting to prove lemma: aime_1983_p2 +2026-01-10 22:26:03,521 - __main__ - INFO - Attempt 1 for proving lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:03,521 - __main__ - INFO - Attempting to prove lemma: aime_1989_p8 +2026-01-10 22:26:03,521 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p2 (theorem_idx=0) with timeout: 600 seconds +2026-01-10 22:26:03,522 - __main__ - INFO - Attempt 1 for proving lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:03,521 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_at2malt1 +2026-01-10 22:26:03,522 - __main__ - INFO - Running the prover agent for lemma: aime_1989_p8 (theorem_idx=1) with timeout: 600 seconds +2026-01-10 22:26:03,521 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p6 +2026-01-10 22:26:03,522 - __main__ - INFO - Attempt 1 for proving lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:03,522 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_at2malt1 (theorem_idx=2) with timeout: 600 seconds +2026-01-10 22:26:03,522 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:03,523 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p6 (theorem_idx=3) with timeout: 600 seconds +2026-01-10 22:26:22,084 - __main__ - INFO - Prover for lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:26:22,085 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_at2malt1 + (a : ℝ) : + a * (2 - a) ≤ 1 := + +by +-- Rewrite the quadratic into a perfect square form +have h : a * (2 - a) = 1 - (a - 1) ^ 2 := by ring +-- Replace the left-hand side with the rewritten expression +rw [h] +-- Show that the remaining expression is nonpositive +have : -(a - 1) ^ 2 ≤ 0 := by + -- The square is always nonnegative + have hpos : 0 ≤ (a - 1) ^ 2 := by + have := sq_nonneg (a - 1) + exact this + -- Negating a nonnegative number gives a nonpositive number + exact neg_nonpos.mpr hpos +-- Conclude the inequality +linarith + + +ProofFile: None +LemmaName: theorem algebra_sqineq_at2malt1 + (a : ℝ) : + a * (2 - a) ≤ 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.8183391094207764 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:26:22,086 - __main__ - INFO - Attempting to prove lemma: amc12a_2013_p4 +2026-01-10 22:26:22,086 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:22,086 - __main__ - INFO - Running the prover agent for lemma: amc12a_2013_p4 (theorem_idx=4) with timeout: 600 seconds +2026-01-10 22:26:31,513 - __main__ - INFO - Prover for lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:26:31,513 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2002_p6 + (n : ℕ) + (h₀ : 0 < n) : + ∃ m, (m > n ∧ ∃ p, m * p ≤ m + p) := + +by +refine ⟨n + 1, ?_, ?_⟩ +· -- prove m > n + exact Nat.lt_succ_self n +· -- prove ∃ p, m * p ≤ m + p with p = 1 + refine ⟨1, ?_⟩ + -- simplify the inequality + simp + + +ProofFile: None +LemmaName: theorem amc12a_2002_p6 + (n : ℕ) + (h₀ : 0 < n) : + ∃ m, (m > n ∧ ∃ p, m * p ≤ m + p) := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 3.2447216510772705 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:26:31,514 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p9 +2026-01-10 22:26:31,514 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:31,514 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p9 (theorem_idx=5) with timeout: 600 seconds +2026-01-10 22:26:45,618 - __main__ - INFO - Prover for lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:26:45,618 - __main__ - INFO - Dumping proof search result: +theorem aime_1989_p8 + (a b c d e f g : ℝ) + (h₀ : a + 4 * b + 9 * c + 16 * d + 25 * e + 36 * f + 49 * g = 1) + (h₁ : 4 * a + 9 * b + 16 * c + 25 * d + 36 * e + 49 * f + 64 * g = 12) + (h₂ : 9 * a + 16 * b + 25 * c + 36 * d + 49 * e + 64 * f + 81 * g = 123) : + 16 * a + 25 * b + 36 * c + 49 * d + 64 * e + 81 * f + 100 * g = 334 := + +by +linarith + + +ProofFile: None +LemmaName: theorem aime_1989_p8 + (a b c d e f g : ℝ) + (h₀ : a + 4 * b + 9 * c + 16 * d + 25 * e + 36 * f + 49 * g = 1) + (h₁ : 4 * a + 9 * b + 16 * c + 25 * d + 36 * e + 49 * f + 64 * g = 12) + (h₂ : 9 * a + 16 * b + 25 * c + 36 * d + 49 * e + 64 * f + 81 * g = 123) : + 16 * a + 25 * b + 36 * c + 49 * d + 64 * e + 81 * f + 100 * g = 334 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 5.582138538360596 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:26:45,619 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p19 +2026-01-10 22:26:45,619 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:26:45,619 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p19 (theorem_idx=6) with timeout: 600 seconds +2026-01-10 22:27:15,591 - __main__ - INFO - Prover for lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:27:15,591 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p9 : + ∏ k ∈ Finset.range 7, (2^(2^k) + 3^(2^k)) = 3^128 - 2^128 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem amc12a_2021_p9 : + ∏ k ∈ Finset.range 7, (2^(2^k) + 3^(2^k)) = 3^128 - 2^128 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 20.21240997314453 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 0, 'total_queries': 3} + + + +2026-01-10 22:27:15,592 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p2 +2026-01-10 22:27:15,592 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:27:15,592 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p2 (theorem_idx=7) with timeout: 600 seconds +2026-01-10 22:27:47,990 - __main__ - INFO - Prover for lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:27:47,990 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2013_p4 : + (2^2014 + 2^2012) / (2^2014 - 2^2012) = (5:ℝ) / 3 := + +by +field_simp [pow_add] +simp [pow_add, mul_comm, mul_left_comm, mul_assoc] +ring + + +ProofFile: None +LemmaName: theorem amc12a_2013_p4 : + (2^2014 + 2^2012) / (2^2014 - 2^2012) = (5:ℝ) / 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 67.38709616661072 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 0, 'total_queries': 17} + + + +2026-01-10 22:27:47,991 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p2 +2026-01-10 22:27:47,991 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:27:47,991 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p2 (theorem_idx=8) with timeout: 600 seconds +2026-01-10 22:27:48,128 - __main__ - INFO - Prover for lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:27:48,128 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p2 + (x : ℤ) + (h₀ : x = 4) : + (3 * x - 2) * (4 * x + 1) - (3 * x - 2) * (4 * x) + 1 = 11 := + +by +-- The goal is already solved; no further action is required. +simp [h₀] at * + + +ProofFile: None +LemmaName: theorem amc12b_2002_p2 + (x : ℤ) + (h₀ : x = 4) : + (3 * x - 2) * (4 * x + 1) - (3 * x - 2) * (4 * x) + 1 = 11 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 5.453635215759277 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 22:27:48,129 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p6 +2026-01-10 22:27:48,129 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:27:48,129 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p6 (theorem_idx=9) with timeout: 600 seconds +2026-01-10 22:28:02,026 - __main__ - INFO - Prover for lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:28:02,026 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p2 : + ((100 ^ 2 - 7 ^ 2):ℝ) / (70 ^ 2 - 11 ^ 2) * ((70 - 11) * (70 + 11) / ((100 - 7) * (100 + 7))) = 1 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem amc12b_2020_p2 : + ((100 ^ 2 - 7 ^ 2):ℝ) / (70 ^ 2 - 11 ^ 2) * ((70 - 11) * (70 + 11) / ((100 - 7) * (100 + 7))) = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 2.387767791748047 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:28:02,027 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_125 +2026-01-10 22:28:02,027 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:28:02,027 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_125 (theorem_idx=10) with timeout: 600 seconds +2026-01-10 22:28:34,323 - __main__ - INFO - Prover for lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:28:34,323 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p19 + (a b c: ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : a * (b + c) = 152) + (h₂ : b * (c + a) = 162) + (h₃ : c * (a + b) = 170) : + a * b * c = 720 := + +by +-- First, deduce the exact values of a, b, and c using nonlinear arithmetic +have ha : a = 8 := by + nlinarith [h₀, h₁, h₂, h₃] +have hb : b = 9 := by + nlinarith [h₀, h₁, h₂, h₃, ha] +have hc : c = 10 := by + nlinarith [h₀, h₁, h₂, h₃, ha, hb] +-- Now compute the product +calc + a * b * c = 8 * 9 * 10 := by + simp [ha, hb, hc] + _ = 720 := by norm_num + + +ProofFile: None +LemmaName: theorem amc12b_2002_p19 + (a b c: ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : a * (b + c) = 152) + (h₂ : b * (c + a) = 162) + (h₃ : c * (a + b) = 170) : + a * b * c = 720 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 81.76297068595886 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 22:28:34,324 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_129 +2026-01-10 22:28:34,324 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:28:34,324 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_129 (theorem_idx=11) with timeout: 600 seconds +2026-01-10 22:29:23,218 - __main__ - INFO - Prover for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:29:23,218 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 175.14024829864502 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 0, 'total_queries': 29} + + + +2026-01-10 22:29:23,219 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_137 +2026-01-10 22:29:23,219 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:29:23,219 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_137 (theorem_idx=12) with timeout: 600 seconds +2026-01-10 22:29:53,648 - __main__ - INFO - Prover for lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:29:53,648 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_125 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : 5 * x = y) + (h₂ : (↑x - (3:ℤ)) + (y - (3:ℤ)) = 30) : + x = 6 := + +by +have hsum : (x : ℤ) + (y : ℤ) = 36 := by + linarith [h₂] +-- Convert the natural sum equality to an integer equality +have hsum' : (x : ℤ) + (y : ℤ) = 36 := by + exact_mod_cast hsum +-- Express the integer version of `h₁` +have h₁' : (5 : ℤ) * (x : ℤ) = (y : ℤ) := by + exact_mod_cast h₁ +-- Substitute `y` in the sum equation +have : (x : ℤ) + 5 * (x : ℤ) = 36 := by + simpa [h₁'] using hsum' +-- Solve for `x` in integers +have hx : (x : ℤ) = 6 := by + linarith +-- Convert the integer result back to a natural number equality +exact_mod_cast hx + + +ProofFile: None +LemmaName: theorem mathd_algebra_125 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : 5 * x = y) + (h₂ : (↑x - (3:ℤ)) + (y - (3:ℤ)) = 30) : + x = 6 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 86.78389739990234 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 0, 'total_queries': 19} + + + +2026-01-10 22:29:53,649 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_139 +2026-01-10 22:29:53,649 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:29:53,649 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_139 (theorem_idx=13) with timeout: 600 seconds +2026-01-10 22:30:20,795 - __main__ - INFO - Prover for lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:30:20,795 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_129 + (a : ℝ) + (h₀ : a ≠ 0) + (h₁ : 8⁻¹ / 4⁻¹ - a⁻¹ = 1) : + a = -2 := + +by +have h2 : a⁻¹ = -(1 : ℝ) / 2 := by linarith +have h3 : a = (a⁻¹)⁻¹ := by + simpa using inv_inv a +have h4 : a = ((-1 : ℝ) / 2)⁻¹ := by + simpa [h2] using h3 +have h5 : ((-1 : ℝ) / 2)⁻¹ = -2 := by + field_simp +exact h4.trans h5 + + +ProofFile: None +LemmaName: theorem mathd_algebra_129 + (a : ℝ) + (h₀ : a ≠ 0) + (h₁ : 8⁻¹ / 4⁻¹ - a⁻¹ = 1) : + a = -2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 82.57565951347351 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-10 22:30:20,795 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_141 +2026-01-10 22:30:20,795 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:30:20,796 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_141 (theorem_idx=14) with timeout: 600 seconds +2026-01-10 22:30:31,580 - __main__ - INFO - Prover for lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:30:31,580 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_139 + (s : ℝ → ℝ → ℝ) + (h₀ : ∀ x, ∀ y, x≠0 -> y≠0 -> s x y = (1/y - 1/x) / (x-y)) : + s 3 11 = 1/33 := + +by +rw [h₀ 3 11 (by norm_num) (by norm_num)] ; field_simp +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_139 + (s : ℝ → ℝ → ℝ) + (h₀ : ∀ x, ∀ y, x≠0 -> y≠0 -> s x y = (1/y - 1/x) / (x-y)) : + s 3 11 = 1/33 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 2.940631628036499 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:30:31,580 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_142 +2026-01-10 22:30:31,580 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:30:31,580 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_142 (theorem_idx=15) with timeout: 600 seconds +2026-01-10 22:31:09,898 - __main__ - INFO - Prover for lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:31:09,898 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_142 + (m b : ℝ) + (h₀ : m * 7 + b = -1) + (h₁ : m * (-1) + b = 7) : + m + b = 5 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_142 + (m b : ℝ) + (h₀ : m * 7 + b = -1) + (h₁ : m * (-1) + b = 7) : + m + b = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.4106686115264893 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:31:09,899 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_143 +2026-01-10 22:31:09,899 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:31:09,899 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_143 (theorem_idx=16) with timeout: 600 seconds +2026-01-10 22:31:12,128 - __main__ - INFO - Prover for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:31:12,128 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 44.49141716957092 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-10 22:31:12,129 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_148 +2026-01-10 22:31:12,129 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:31:12,129 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_148 (theorem_idx=17) with timeout: 600 seconds +2026-01-10 22:31:39,189 - __main__ - INFO - Prover for lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:31:39,189 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_148 + (c : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = c * x^3 - 9 * x + 3) + (h₁ : f 2 = 9) : + c = 3 := + +by + -- Rewrite h₁ using the definition of f at x = 2 + rw [h₀ 2] at h₁ + -- Simplify the resulting arithmetic equation + linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_148 + (c : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = c * x^3 - 9 * x + 3) + (h₁ : f 2 = 9) : + c = 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.7276170253753662 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:31:39,190 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_158 +2026-01-10 22:31:39,190 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:31:39,190 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_158 (theorem_idx=18) with timeout: 600 seconds +2026-01-10 22:31:58,101 - __main__ - INFO - Prover for lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:31:58,101 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_143 + (f g : ℝ → ℝ) + (h₀ : ∀ x, f x = x + 1) + (h₁ : ∀ x, g x = x^2 + 3) : + f (g 2) = 8 := + +by +simp [h₀, h₁] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_143 + (f g : ℝ → ℝ) + (h₀ : ∀ x, f x = x + 1) + (h₁ : ∀ x, g x = x^2 + 3) : + f (g 2) = 8 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 20.729626893997192 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-10 22:31:58,101 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_160 +2026-01-10 22:31:58,101 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:31:58,102 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_160 (theorem_idx=19) with timeout: 600 seconds +2026-01-10 22:32:12,935 - __main__ - INFO - Prover for lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:32:12,935 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_160 + (n x : ℝ) + (h₀ : n + x = 97) + (h₁ : n + 5 * x = 265) : + n + 2 * x = 139 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_160 + (n x : ℝ) + (h₀ : n + x = 97) + (h₁ : n + 5 * x = 265) : + n + 2 * x = 139 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.7377383708953857 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:32:12,935 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_171 +2026-01-10 22:32:12,935 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:32:12,935 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_171 (theorem_idx=20) with timeout: 600 seconds +2026-01-10 22:32:28,725 - __main__ - INFO - Prover for lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:32:28,725 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_171 + (f : ℝ → ℝ) + (h₀ : ∀x, f x = 5 * x + 4) : + f 1 = 9 := + +by +rw [h₀ 1] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_171 + (f : ℝ → ℝ) + (h₀ : ∀x, f x = 5 * x + 4) : + f 1 = 9 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.1401467323303223 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:32:28,726 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_176 +2026-01-10 22:32:28,726 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:32:28,726 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_176 (theorem_idx=21) with timeout: 600 seconds +2026-01-10 22:32:40,690 - __main__ - INFO - Prover for lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:32:40,690 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_137 + (x : ℕ) + (h₀ : ↑x + (4:ℝ) / (100:ℝ) * ↑x = 598) : + x = 575 := + +by +have hx : (x : ℝ) = 575 := by + nlinarith [h₀] +exact_mod_cast hx + + +ProofFile: None +LemmaName: theorem mathd_algebra_137 + (x : ℕ) + (h₀ : ↑x + (4:ℝ) / (100:ℝ) * ↑x = 598) : + x = 575 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 41 +SearchTimeInSecs: 183.65842270851135 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 0, 'total_queries': 41} + + + +2026-01-10 22:32:40,691 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_24 +2026-01-10 22:32:40,691 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:32:40,691 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_24 (theorem_idx=22) with timeout: 600 seconds +2026-01-10 22:32:42,931 - __main__ - INFO - Prover for lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:32:42,931 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_176 + (x : ℝ) : + (x + 1)^2 * x = x^3 + 2 * x^2 + x := + +by +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_176 + (x : ℝ) : + (x + 1)^2 * x = x^3 + 2 * x^2 + x := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.6010348796844482 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:32:42,932 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_246 +2026-01-10 22:32:42,932 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:32:42,932 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_246 (theorem_idx=23) with timeout: 600 seconds +2026-01-10 22:32:55,059 - __main__ - INFO - Prover for lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:32:55,059 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p6 + (n : ℕ) + (h₀ : 9 ≤ n) : + ∃ (x : ℕ), (x : ℝ)^2 = (Nat.factorial (n + 2) - Nat.factorial (n + 1)) / n ! := + +by +existsi (n + 1) +simp [Nat.factorial_succ, mul_comm, mul_left_comm, mul_assoc, sub_eq_add_neg, add_comm, + add_left_comm, add_assoc, pow_two] +field_simp [Nat.factorial_succ, mul_comm, mul_left_comm, mul_assoc, sub_eq_add_neg, + add_comm, add_left_comm, add_assoc, pow_two] +ring_nf + + +ProofFile: None +LemmaName: theorem amc12b_2020_p6 + (n : ℕ) + (h₀ : 9 ≤ n) : + ∃ (x : ℕ), (x : ℝ)^2 = (Nat.factorial (n + 2) - Nat.factorial (n + 1)) / n ! := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 84 +SearchTimeInSecs: 285.1943383216858 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 79, 'attempt_idx': 0, 'total_queries': 79} + + + +2026-01-10 22:32:55,059 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_263 +2026-01-10 22:32:55,059 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:32:55,059 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_263 (theorem_idx=24) with timeout: 600 seconds +2026-01-10 22:33:00,569 - __main__ - INFO - Prover for lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:00,569 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_24 + (x : ℝ) + (h₀ : x / 50 = 40) : + x = 2000 := + +by +have hx : x = 2000 := by + calc + x = (x / 50) * 50 := by field_simp + _ = 40 * 50 := by simpa [h₀] + _ = 2000 := by norm_num +exact hx + + +ProofFile: None +LemmaName: theorem mathd_algebra_24 + (x : ℝ) + (h₀ : x / 50 = 40) : + x = 2000 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 6.33700704574585 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:33:00,569 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_270 +2026-01-10 22:33:00,569 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:00,569 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_270 (theorem_idx=25) with timeout: 600 seconds +2026-01-10 22:33:05,070 - __main__ - INFO - Prover for lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:05,070 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 60.77189373970032 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 0, 'total_queries': 16} + + + +2026-01-10 22:33:05,071 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_296 +2026-01-10 22:33:05,071 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:05,071 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_296 (theorem_idx=26) with timeout: 600 seconds +2026-01-10 22:33:27,272 - __main__ - INFO - Prover for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:27,272 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 18.41301393508911 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 22:33:27,272 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_302 +2026-01-10 22:33:27,273 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:27,273 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_302 (theorem_idx=27) with timeout: 600 seconds +2026-01-10 22:33:27,440 - __main__ - INFO - Prover for lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:27,440 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_296 : + abs (((3491 - 60) * (3491 + 60) - 3491^2):ℤ) = 3600 := + +by +have h : (3491 - 60) * (3491 + 60) - 3491 ^ 2 = -(60 ^ 2) := by + ring +have hpos : 0 ≤ 60 ^ 2 := by + norm_num +simp [h, abs_neg, hpos, abs_of_nonneg] + + +ProofFile: None +LemmaName: theorem mathd_algebra_296 : + abs (((3491 - 60) * (3491 + 60) - 3491^2):ℤ) = 3600 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 5.169146537780762 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:33:27,440 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_304 +2026-01-10 22:33:27,440 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:27,440 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_304 (theorem_idx=28) with timeout: 600 seconds +2026-01-10 22:33:50,451 - __main__ - INFO - Prover for lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:50,451 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_304 : + 91^2 = 8281 := + +by + norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_304 : + 91^2 = 8281 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.6261639595031738 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:33:50,451 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_314 +2026-01-10 22:33:50,452 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:50,452 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_314 (theorem_idx=29) with timeout: 600 seconds +2026-01-10 22:33:59,174 - __main__ - INFO - Prover for lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:33:59,174 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_246 + (a b : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = a * x^4 - b * x^2 + x + 5) + (h₂ : f (-3) = 2) : + f 3 = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_246 + (a b : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = a * x^4 - b * x^2 + x + 5) + (h₂ : f (-3) = 2) : + f 3 = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 54.855597257614136 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-10 22:33:59,175 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_329 +2026-01-10 22:33:59,175 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:33:59,175 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_329 (theorem_idx=30) with timeout: 600 seconds +2026-01-10 22:34:04,350 - __main__ - INFO - Prover for lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:34:04,350 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_302 : + (Complex.I / 2)^2 = -(1 / 4) := + +by +simp +field_simp +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_302 : + (Complex.I / 2)^2 = -(1 / 4) := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 3.7852559089660645 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 22:34:04,351 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_33 +2026-01-10 22:34:04,351 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:34:04,351 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_33 (theorem_idx=31) with timeout: 600 seconds +2026-01-10 22:34:24,160 - __main__ - INFO - Prover for lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:34:24,160 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_329 + (x y : ℝ) + (h₀ : 3 * y = x) + (h₁ : 2 * x + 5 * y = 11) : + x + y = 4 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_329 + (x y : ℝ) + (h₀ : 3 * y = x) + (h₁ : 2 * x + 5 * y = 11) : + x + y = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.7754480838775635 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:34:24,161 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_346 +2026-01-10 22:34:24,161 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:34:24,161 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_346 (theorem_idx=32) with timeout: 600 seconds +2026-01-10 22:34:28,385 - __main__ - INFO - Prover for lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:34:28,386 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_314 + (n : ℕ) + (h₀ : n = 11) : + (1 / 4)^(n + 1) * 2^(2 * n) = 1 / 4 := + +by +simp [h₀] + + +ProofFile: None +LemmaName: theorem mathd_algebra_314 + (n : ℕ) + (h₀ : n = 11) : + (1 / 4)^(n + 1) * 2^(2 * n) = 1 / 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.871950387954712 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:34:28,388 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_354 +2026-01-10 22:34:28,389 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:34:28,389 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_354 (theorem_idx=33) with timeout: 600 seconds +2026-01-10 22:34:43,703 - __main__ - INFO - Prover for lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:34:43,703 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_346 + (f g : ℝ → ℝ) + (h₀ : ∀ x, f x = 2 * x - 3) + (h₁ : ∀ x, g x = x + 1) : + g (f 5 - 1) = 7 := + +by +simp [h₀, h₁] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_346 + (f g : ℝ → ℝ) + (h₀ : ∀ x, f x = 2 * x - 3) + (h₁ : ∀ x, g x = x + 1) : + g (f 5 - 1) = 7 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 2.808189868927002 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 0, 'total_queries': 3} + + + +2026-01-10 22:34:43,704 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_359 +2026-01-10 22:34:43,704 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:34:43,704 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_359 (theorem_idx=34) with timeout: 600 seconds +2026-01-10 22:34:59,845 - __main__ - INFO - Prover for lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:34:59,845 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_354 + (a d : ℝ) + (h₀ : a + 6 * d = 30) + (h₁ : a + 10 * d = 60) : + a + 20 * d = 135 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_354 + (a d : ℝ) + (h₀ : a + 6 * d = 30) + (h₁ : a + 10 * d = 60) : + a + 20 * d = 135 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 2.6951181888580322 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:34:59,846 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_388 +2026-01-10 22:34:59,846 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:34:59,846 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_388 (theorem_idx=35) with timeout: 600 seconds +2026-01-10 22:35:17,884 - __main__ - INFO - Prover for lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:35:17,884 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_359 + (y : ℝ) + (h₀ : y + 6 + y = 2 * 12) : + y = 9 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_359 + (y : ℝ) + (h₀ : y + 6 + y = 2 * 12) : + y = 9 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.1352670192718506 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:35:17,884 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_400 +2026-01-10 22:35:17,885 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:35:17,885 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_400 (theorem_idx=36) with timeout: 600 seconds +2026-01-10 22:35:21,725 - __main__ - INFO - Prover for lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:35:21,725 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_388 + (x y z : ℝ) + (h₀ : 3 * x + 4 * y - 12 * z = 10) + (h₁ : -2 * x - 3 * y + 9 * z = -4) : + x = 14 := + +by +linarith [h₀, h₁] + + +ProofFile: None +LemmaName: theorem mathd_algebra_388 + (x y z : ℝ) + (h₀ : 3 * x + 4 * y - 12 * z = 10) + (h₁ : -2 * x - 3 * y + 9 * z = -4) : + x = 14 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 2.6503162384033203 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:35:21,726 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_412 +2026-01-10 22:35:21,726 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:35:21,726 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_412 (theorem_idx=37) with timeout: 600 seconds +2026-01-10 22:35:41,182 - __main__ - INFO - Prover for lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:35:41,182 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_412 + (x y : ℝ) + (h₀ : x + y = 25) + (h₁ : x - y = 11) : + x = 18 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_412 + (x y : ℝ) + (h₀ : x + y = 25) + (h₁ : x - y = 11) : + x = 18 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.8425493240356445 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:35:41,183 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_419 +2026-01-10 22:35:41,183 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:35:41,183 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_419 (theorem_idx=38) with timeout: 600 seconds +2026-01-10 22:35:57,786 - __main__ - INFO - Prover for lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:35:57,786 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_419 + (a b : ℝ) + (h₀ : a = -1) + (h₁ : b = 5) : + -a - b^2 + 3 * (a * b) = -39 := + +by + +simp [h₀, h₁] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_419 + (a b : ℝ) + (h₀ : a = -1) + (h₁ : b = 5) : + -a - b^2 + 3 * (a * b) = -39 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 3.813774824142456 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 22:35:57,786 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_432 +2026-01-10 22:35:57,787 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:35:57,787 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_432 (theorem_idx=39) with timeout: 600 seconds +2026-01-10 22:35:58,526 - __main__ - INFO - Prover for lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:35:58,526 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_33 + (x y z : ℝ) + (h₀ : x ≠ 0) + (h₁ : 2 * x = 5 * y) + (h₂ : 7 * y = 10 * z) : + z / x = 7 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_33 + (x y z : ℝ) + (h₀ : x ≠ 0) + (h₁ : 2 * x = 5 * y) + (h₂ : 7 * y = 10 * z) : + z / x = 7 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 106.42883276939392 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 33, 'attempt_idx': 0, 'total_queries': 33} + + + +2026-01-10 22:35:58,527 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_44 +2026-01-10 22:35:58,527 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:35:58,527 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_44 (theorem_idx=40) with timeout: 600 seconds +2026-01-10 22:36:18,233 - __main__ - INFO - Prover for lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:36:18,233 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_432 + (x : ℝ) : + (x + 3) * (2 * x - 6) = 2 * x^2 - 18 := + +by +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_432 + (x : ℝ) : + (x + 3) * (2 * x - 6) = 2 * x^2 - 18 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.590939998626709 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:36:18,235 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_440 +2026-01-10 22:36:18,236 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:36:18,236 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_440 (theorem_idx=41) with timeout: 600 seconds +2026-01-10 22:36:21,292 - __main__ - INFO - Prover for lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:36:21,292 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_44 + (s t : ℝ) + (h₀ : s = 9 - 2 * t) + (h₁ : t = 3 * s + 1) : + s = 1 ∧ t = 4 := + +by +-- Solve for `s` and `t` using linear arithmetic, then combine the results +have hs : s = 1 := by + linarith [h₀, h₁] +have ht : t = 4 := by + linarith [h₀, h₁] +exact ⟨hs, ht⟩ + + +ProofFile: None +LemmaName: theorem mathd_algebra_44 + (s t : ℝ) + (h₀ : s = 9 - 2 * t) + (h₁ : t = 3 * s + 1) : + s = 1 ∧ t = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 10.828979015350342 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 0, 'total_queries': 3} + + + +2026-01-10 22:36:21,293 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_441 +2026-01-10 22:36:21,293 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:36:21,293 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_441 (theorem_idx=42) with timeout: 600 seconds +2026-01-10 22:36:42,506 - __main__ - INFO - Prover for lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:36:42,506 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 59 +SearchTimeInSecs: 200.50349020957947 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 56, 'attempt_idx': 0, 'total_queries': 56} + + + +2026-01-10 22:36:42,507 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_478 +2026-01-10 22:36:42,507 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:36:42,507 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_478 (theorem_idx=43) with timeout: 600 seconds +2026-01-10 22:36:57,577 - __main__ - INFO - Prover for lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:36:57,578 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_478 + (b h v : ℝ) + (h₀ : 0 < b ∧ 0 < h ∧ 0 < v) + (h₁ : v = 1 / 3 * (b * h)) + (h₂ : b = 30) + (h₃ : h = 13 / 2) : + v = 65 := + +by +have h4 : v = 1 / 3 * (30 * (13 / 2)) := by + simpa [h₂, h₃] using h₁ +calc + v = 1 / 3 * (30 * (13 / 2)) := h4 + _ = 65 := by norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_478 + (b h v : ℝ) + (h₀ : 0 < b ∧ 0 < h ∧ 0 < v) + (h₁ : v = 1 / 3 * (b * h)) + (h₂ : b = 30) + (h₃ : h = 13 / 2) : + v = 65 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.827547311782837 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:36:57,578 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_513 +2026-01-10 22:36:57,578 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:36:57,578 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_513 (theorem_idx=44) with timeout: 600 seconds +2026-01-10 22:37:02,751 - __main__ - INFO - Prover for lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:02,751 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_441 + (x : ℝ) + (h₀ : x ≠ 0) : + 12 / (x * x) * (x^4 / (14 * x)) * (35 / (3 * x)) = 10 := + +by +field_simp [h₀] +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_441 + (x : ℝ) + (h₀ : x ≠ 0) : + 12 / (x * x) * (x^4 / (14 * x)) * (35 / (3 * x)) = 10 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 3.3362183570861816 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:37:02,752 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_76 +2026-01-10 22:37:02,752 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:02,752 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_76 (theorem_idx=45) with timeout: 600 seconds +2026-01-10 22:37:17,890 - __main__ - INFO - Prover for lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:17,890 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_400 + (x : ℝ) + (h₀ : 5 + 500 / 100 * 10 = 110 / 100 * x) : + x = 50 := + +by +have : x = 50 := by + nlinarith [h₀] +exact this + + +ProofFile: None +LemmaName: theorem mathd_algebra_400 + (x : ℝ) + (h₀ : 5 + 500 / 100 * 10 = 110 / 100 * x) : + x = 50 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 82.1475989818573 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-10 22:37:17,891 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_80 +2026-01-10 22:37:17,891 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:17,891 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_80 (theorem_idx=46) with timeout: 600 seconds +2026-01-10 22:37:25,996 - __main__ - INFO - Prover for lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:25,996 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_76 + (f : ℤ → ℤ) + (h₀ : ∀n, Odd n → f n = n^2) + (h₁ : ∀ n, Even n → f n = n^2 - 4*n -1) : + f 4 = -1 := + +by +have h_even : Even (4 : ℤ) := by decide +simpa using h₁ 4 h_even + + +ProofFile: None +LemmaName: theorem mathd_algebra_76 + (f : ℤ → ℤ) + (h₀ : ∀n, Odd n → f n = n^2) + (h₁ : ∀ n, Even n → f n = n^2 - 4*n -1) : + f 4 = -1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.597135066986084 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:37:25,996 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_12 +2026-01-10 22:37:25,996 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:25,996 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_12 (theorem_idx=47) with timeout: 600 seconds +2026-01-10 22:37:28,816 - __main__ - INFO - Prover for lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:28,816 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_513 + (a b : ℝ) + (h₀ : 3 * a + 2 * b = 5) + (h₁ : a + b = 2) : + a = 1 ∧ b = 1 := + +by +-- First prove that a = 1 +have ha : a = 1 := by + linarith +-- Next prove that b = 1 +have hb : b = 1 := by + linarith +-- Finish by assembling the conjunction +exact ⟨ha, hb⟩ + + +ProofFile: None +LemmaName: theorem mathd_algebra_513 + (a b : ℝ) + (h₀ : 3 * a + 2 * b = 5) + (h₁ : a + b = 2) : + a = 1 ∧ b = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 3.606374740600586 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:37:28,817 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_127 +2026-01-10 22:37:28,817 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:28,817 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_127 (theorem_idx=48) with timeout: 600 seconds +2026-01-10 22:37:42,200 - __main__ - INFO - Prover for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:42,200 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 11.586001873016357 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 22:37:42,200 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_135 +2026-01-10 22:37:42,200 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:42,200 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_135 (theorem_idx=49) with timeout: 600 seconds +2026-01-10 22:37:49,641 - __main__ - INFO - Prover for lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:49,641 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_12 : + Finset.card (Finset.filter (λ x => 20∣x) (Finset.Icc 15 85)) = 4 := + +by +decide + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_12 : + Finset.card (Finset.filter (λ x => 20∣x) (Finset.Icc 15 85)) = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 9.474493980407715 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:37:49,642 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_150 +2026-01-10 22:37:49,642 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:49,642 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_150 (theorem_idx=50) with timeout: 600 seconds +2026-01-10 22:37:58,929 - __main__ - INFO - Prover for lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:37:58,929 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 80.54022693634033 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 0, 'total_queries': 26} + + + +2026-01-10 22:37:58,929 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_175 +2026-01-10 22:37:58,929 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:37:58,929 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_175 (theorem_idx=51) with timeout: 600 seconds +2026-01-10 22:38:10,645 - __main__ - INFO - Prover for lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:38:10,645 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_127 : + (∑ k ∈ (Finset.range 101), 2^k) % 7 = 3 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_127 : + (∑ k ∈ (Finset.range 101), 2^k) % 7 = 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 8.521066665649414 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:38:10,646 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_185 +2026-01-10 22:38:10,646 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:38:10,646 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_185 (theorem_idx=52) with timeout: 600 seconds +2026-01-10 22:38:14,303 - __main__ - INFO - Prover for lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:38:14,303 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_175 : + (2^2010) % 10 = 4 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_175 : + (2^2010) % 10 = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.7332847118377686 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:38:14,303 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_207 +2026-01-10 22:38:14,303 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:38:14,303 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_207 (theorem_idx=53) with timeout: 600 seconds +2026-01-10 22:38:32,427 - __main__ - INFO - Prover for lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:38:32,427 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_207 : + 8 * 9^2 + 5 * 9 + 2 = 695 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_207 : + 8 * 9^2 + 5 * 9 + 2 = 695 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.5751585960388184 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:38:32,428 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_212 +2026-01-10 22:38:32,428 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:38:32,428 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_212 (theorem_idx=54) with timeout: 600 seconds +2026-01-10 22:38:56,212 - __main__ - INFO - Prover for lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:38:56,213 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_185 + (n : ℕ) + (h₀ : n % 5 = 3) : + (2 * n) % 5 = 1 := + +by +calc + 2 * n % 5 = (2 * (n % 5)) % 5 := by + simpa [Nat.mul_mod] using (Nat.mul_mod 2 n 5).symm + _ = (2 * 3) % 5 := by simpa [h₀] + _ = 1 := by norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_185 + (n : ℕ) + (h₀ : n % 5 = 3) : + (2 * n) % 5 = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 10.056262969970703 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:38:56,213 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_229 +2026-01-10 22:38:56,213 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:38:56,213 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_229 (theorem_idx=55) with timeout: 600 seconds +2026-01-10 22:39:01,569 - __main__ - INFO - Prover for lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:39:01,569 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_212 : + (16^17 * 17^18 * 18^19) % 10 = 8 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_212 : + (16^17 * 17^18 * 18^19) % 10 = 8 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.5740654468536377 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:39:01,569 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_235 +2026-01-10 22:39:01,570 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:39:01,570 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_235 (theorem_idx=56) with timeout: 600 seconds +2026-01-10 22:39:20,682 - __main__ - INFO - Prover for lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:39:20,683 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_229 : + (5^30) % 7 = 1 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_229 : + (5^30) % 7 = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.7306962013244629 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:39:20,683 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_237 +2026-01-10 22:39:20,683 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:39:20,683 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_237 (theorem_idx=57) with timeout: 600 seconds +2026-01-10 22:39:34,664 - __main__ - INFO - Prover for lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:39:34,664 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_235 : + (29 * 79 + 31 * 81) % 10 = 2 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_235 : + (29 * 79 + 31 * 81) % 10 = 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.138049840927124 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:39:34,665 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_239 +2026-01-10 22:39:34,665 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:39:34,665 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_239 (theorem_idx=58) with timeout: 600 seconds +2026-01-10 22:39:35,629 - __main__ - INFO - Prover for lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:39:35,629 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_237 : + (∑ k ∈ (Finset.range 101), k) % 6 = 4 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_237 : + (∑ k ∈ (Finset.range 101), k) % 6 = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 2.1399013996124268 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:39:35,630 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_247 +2026-01-10 22:39:35,630 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:39:35,630 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_247 (theorem_idx=59) with timeout: 600 seconds +2026-01-10 22:39:54,663 - __main__ - INFO - Prover for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:39:54,663 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 96.35554575920105 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-10 22:39:54,663 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_254 +2026-01-10 22:39:54,664 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:39:54,664 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_254 (theorem_idx=60) with timeout: 600 seconds +2026-01-10 22:40:04,432 - __main__ - INFO - Prover for lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:04,432 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_239 : + (∑ k ∈ Finset.Icc 1 12, k) % 4 = 2 := + +by +-- Compute the sum explicitly and reduce modulo 4 +norm_num +exact rfl + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_239 : + (∑ k ∈ Finset.Icc 1 12, k) % 4 = 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 2.1804707050323486 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:40:04,433 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_299 +2026-01-10 22:40:04,433 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:04,433 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_299 (theorem_idx=61) with timeout: 600 seconds +2026-01-10 22:40:18,369 - __main__ - INFO - Prover for lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:18,369 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_299 : + (1 * 3 * 5 * 7 * 9 * 11 * 13) % 10 = 5 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_299 : + (1 * 3 * 5 * 7 * 9 * 11 * 13) % 10 = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.5993869304656982 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:40:18,370 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_3 +2026-01-10 22:40:18,370 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:18,370 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_3 (theorem_idx=62) with timeout: 600 seconds +2026-01-10 22:40:21,975 - __main__ - INFO - Prover for lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:21,975 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_254 : + (239 + 174 + 83) % 10 = 6 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_254 : + (239 + 174 + 83) % 10 = 6 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.7466762065887451 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:40:21,976 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_341 +2026-01-10 22:40:21,976 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:21,976 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_341 (theorem_idx=63) with timeout: 600 seconds +2026-01-10 22:40:32,070 - __main__ - INFO - Prover for lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:32,070 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_3 : + (∑ x ∈ Finset.range 10, ((x + 1)^2)) % 10 = 5 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_3 : + (∑ x ∈ Finset.range 10, ((x + 1)^2)) % 10 = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.789637565612793 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:40:32,071 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_342 +2026-01-10 22:40:32,071 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:32,071 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_342 (theorem_idx=64) with timeout: 600 seconds +2026-01-10 22:40:39,081 - __main__ - INFO - Prover for lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:39,081 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_135 + (n A B C : ℕ) + (h₀ : n = 3^17 + 3^10) + (h₁ : 11 ∣ (n + 1)) + (h₂ : [A,B,C].Pairwise (·≠·)) + (h₃ : {A,B,C} ⊂ Finset.Icc 0 9) + (h₄ : Odd A ∧ Odd C) + (h₅ : ¬ 3 ∣ B) + (h₆ : Nat.digits 10 n = [B,A,B,C,C,A,C,B,A]) : + 100 * A + 10 * B + C = 129 := + +by +have hn : n = 129199212 := by + norm_num [h₀] +simp [hn] at h₆ +rcases h₆ with ⟨hB1, hA1, hB2, hC1, hA2, hC2, hB3, hA3⟩ +have hA : A = 1 := hA1.symm +have hB : B = 2 := hB1.symm +have hC : C = 9 := hC1.symm +simp [hA, hB, hC] + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_135 + (n A B C : ℕ) + (h₀ : n = 3^17 + 3^10) + (h₁ : 11 ∣ (n + 1)) + (h₂ : [A,B,C].Pairwise (·≠·)) + (h₃ : {A,B,C} ⊂ Finset.Icc 0 9) + (h₄ : Odd A ∧ Odd C) + (h₅ : ¬ 3 ∣ B) + (h₆ : Nat.digits 10 n = [B,A,B,C,C,A,C,B,A]) : + 100 * A + 10 * B + C = 129 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 158.16102075576782 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 30, 'attempt_idx': 0, 'total_queries': 30} + + + +2026-01-10 22:40:39,081 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_343 +2026-01-10 22:40:39,081 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:39,081 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_343 (theorem_idx=65) with timeout: 600 seconds +2026-01-10 22:40:50,334 - __main__ - INFO - Prover for lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:50,334 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_342 : + 54 % 6 = 0 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_342 : + 54 % 6 = 0 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.5994291305541992 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:40:50,335 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_345 +2026-01-10 22:40:50,335 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:50,335 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_345 (theorem_idx=66) with timeout: 600 seconds +2026-01-10 22:40:59,109 - __main__ - INFO - Prover for lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:40:59,109 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_343 : + (∏ k ∈ Finset.range 6, (2 * k + 1)) % 10 = 5 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_343 : + (∏ k ∈ Finset.range 6, (2 * k + 1)) % 10 = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.8053832054138184 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:40:59,110 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_517 +2026-01-10 22:40:59,110 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:40:59,110 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_517 (theorem_idx=67) with timeout: 600 seconds +2026-01-10 22:41:06,185 - __main__ - INFO - Prover for lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:06,185 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_345 : + (2000 + 2001 + 2002 + 2003 + 2004 + 2005 + 2006) % 7 = 0 := + +by + norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_345 : + (2000 + 2001 + 2002 + 2003 + 2004 + 2005 + 2006) % 7 = 0 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.8320903778076172 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:06,186 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_551 +2026-01-10 22:41:06,186 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:06,186 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_551 (theorem_idx=68) with timeout: 600 seconds +2026-01-10 22:41:26,313 - __main__ - INFO - Prover for lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:26,313 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_341 + (a b c : ℕ) + (h₀ : a ≤ 9 ∧ b ≤ 9 ∧ c ≤ 9) + (h₁ : Nat.digits 10 ((5^100) % 1000) = [c,b,a]) : + a + b + c = 13 := + +by +-- compute the remainder of 5^100 modulo 1000 +have h : 5 ^ 100 % 1000 = 625 := by + norm_num +-- rewrite the hypothesis h₁ using this equality +rw [h] at h₁ +-- now we know that the list of digits of 625 in base 10 is [5,2,6] +have h₂ : digits 10 625 = [5, 2, 6] := by + norm_num +-- replace the left‑hand side of h₁ with the explicit list +rw [h₂] at h₁ +-- extract the values of c, b, a from the list equality +have hc : c = 5 := by + have := congrArg List.head? h₁.symm + simpa using this +have hb : b = 2 := by + have := congrArg List.head? (congrArg List.tail h₁.symm) + simpa using this +have ha : a = 6 := by + have := congrArg List.head? (congrArg List.tail (congrArg List.tail h₁.symm)) + simpa using this +-- finally, compute the sum +simp [ha, hb, hc] + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_341 + (a b c : ℕ) + (h₀ : a ≤ 9 ∧ b ≤ 9 ∧ c ≤ 9) + (h₁ : Nat.digits 10 ((5^100) % 1000) = [c,b,a]) : + a + b + c = 13 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 39.9305055141449 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 22:41:26,313 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_66 +2026-01-10 22:41:26,313 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:26,313 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_66 (theorem_idx=69) with timeout: 600 seconds +2026-01-10 22:41:27,872 - __main__ - INFO - Prover for lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:27,872 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_517 : + (121 * 122 * 123) % 4 = 2 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_517 : + (121 * 122 * 123) % 4 = 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.6750800609588623 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:27,872 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_728 +2026-01-10 22:41:27,872 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:27,873 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_728 (theorem_idx=70) with timeout: 600 seconds +2026-01-10 22:41:29,461 - __main__ - INFO - Prover for lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:29,461 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_551 : + 1529 % 6 = 5 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_551 : + 1529 % 6 = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.4754488468170166 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:29,462 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_769 +2026-01-10 22:41:29,462 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:29,462 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_769 (theorem_idx=71) with timeout: 600 seconds +2026-01-10 22:41:44,967 - __main__ - INFO - Prover for lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:44,967 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_728 : + (29^13 - 5^13) % 7 = 3 := + +by + norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_728 : + (29^13 - 5^13) % 7 = 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.6225471496582031 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:44,967 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_85 +2026-01-10 22:41:44,967 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:44,967 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_85 (theorem_idx=72) with timeout: 600 seconds +2026-01-10 22:41:50,494 - __main__ - INFO - Prover for lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:50,494 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_769 : + (129^34 + 96^38) % 11 = 9 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_769 : + (129^34 + 96^38) % 11 = 9 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 4.228560209274292 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:50,494 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_107 +2026-01-10 22:41:50,494 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:50,494 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_107 (theorem_idx=73) with timeout: 600 seconds +2026-01-10 22:41:56,377 - __main__ - INFO - Prover for lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:56,377 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 129.60880994796753 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 0, 'total_queries': 25} + + + +2026-01-10 22:41:56,378 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_113 +2026-01-10 22:41:56,378 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:56,378 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_113 (theorem_idx=74) with timeout: 600 seconds +2026-01-10 22:41:56,938 - __main__ - INFO - Prover for lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:41:56,938 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_66 : + 194 % 11 = 7 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_66 : + 194 % 11 = 7 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.5109119415283203 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:41:56,939 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_114 +2026-01-10 22:41:56,939 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:41:56,939 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_114 (theorem_idx=75) with timeout: 600 seconds +2026-01-10 22:42:12,668 - __main__ - INFO - Prover for lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:42:12,668 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_85 : + 1 * 3^3 + 2 * 3^2 + 2*3 + 2 = 53 := + +by +norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_85 : + 1 * 3^3 + 2 * 3^2 + 2*3 + 2 = 53 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 0.819533109664917 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:42:12,669 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_153 +2026-01-10 22:42:12,669 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:42:12,669 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_153 (theorem_idx=76) with timeout: 600 seconds +2026-01-10 22:42:38,252 - __main__ - INFO - Prover for lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:42:38,253 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_153 + (n : ℝ) + (h₀ : n = 1 / 3) : + Int.floor (10 * n) + Int.floor (100 * n) + Int.floor (1000 * n) + Int.floor (10000 * n) = 3702 := + +by +simp [h₀] <;> norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_153 + (n : ℝ) + (h₀ : n = 1 / 3) : + Int.floor (10 * n) + Int.floor (100 * n) + Int.floor (1000 * n) + Int.floor (10000 * n) = 3702 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 3.1065781116485596 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 22:42:38,253 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_156 +2026-01-10 22:42:38,253 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:42:38,253 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_156 (theorem_idx=77) with timeout: 600 seconds +2026-01-10 22:42:40,881 - __main__ - INFO - Prover for lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:42:40,881 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 37.9412317276001 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 0, 'total_queries': 13} + + + +2026-01-10 22:42:40,881 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_17 +2026-01-10 22:42:40,881 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:42:40,881 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_17 (theorem_idx=78) with timeout: 600 seconds +2026-01-10 22:46:20,500 - __main__ - INFO - Prover for lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:46:20,500 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_113 + (x : ℝ) : + x^2 - 14 * x + 3 ≥ 7^2 - 14 * 7 + 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_113 + (x : ℝ) : + x^2 - 14 * x + 3 ≥ 7^2 - 14 * 7 + 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 42 +SearchTimeInSecs: 247.63713121414185 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 0, 'total_queries': 40} + + + +2026-01-10 22:46:20,501 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_170 +2026-01-10 22:46:20,501 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:46:20,501 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_170 (theorem_idx=79) with timeout: 600 seconds +2026-01-10 22:46:27,837 - __main__ - INFO - Prover for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:46:27,837 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 73 +SearchTimeInSecs: 250.85744881629944 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 63, 'attempt_idx': 0, 'total_queries': 63} + + + +2026-01-10 22:46:27,838 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_184 +2026-01-10 22:46:27,838 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:46:27,838 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_184 (theorem_idx=80) with timeout: 600 seconds +2026-01-10 22:49:37,616 - __main__ - INFO - Prover for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:49:37,617 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 46 +SearchTimeInSecs: 400.7480218410492 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 46, 'attempt_idx': 0, 'total_queries': 46} + + + +2026-01-10 22:49:37,617 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_188 +2026-01-10 22:49:37,617 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:49:37,617 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_188 (theorem_idx=81) with timeout: 600 seconds +2026-01-10 22:49:58,991 - __main__ - INFO - Prover for lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:49:58,991 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_188 + (σ : Equiv ℝ ℝ) + (h : σ.1 2 = σ.2 2) : + σ.1 (σ.1 2) = 2 := + +by +have h' := congrArg σ.toFun h +simpa [σ.apply_symm_apply] using h' + + +ProofFile: None +LemmaName: theorem mathd_algebra_188 + (σ : Equiv ℝ ℝ) + (h : σ.1 2 = σ.2 2) : + σ.1 (σ.1 2) = 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 6.2301225662231445 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:49:58,991 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_196 +2026-01-10 22:49:58,991 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:49:58,991 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_196 (theorem_idx=82) with timeout: 600 seconds +2026-01-10 22:51:21,123 - __main__ - INFO - Prover for lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:51:21,123 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 61.59822416305542 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-10 22:51:21,124 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_208 +2026-01-10 22:51:21,124 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:51:21,124 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_208 (theorem_idx=83) with timeout: 600 seconds +2026-01-10 22:51:36,587 - __main__ - INFO - Prover for lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:51:36,587 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_170 + (S : Finset ℤ) + (h₀ : ∀ (n : ℤ), n ∈ S ↔ abs (n - 2) ≤ 5 + 6 / 10) : + S.card = 11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_170 + (S : Finset ℤ) + (h₀ : ∀ (n : ℤ), n ∈ S ↔ abs (n - 2) ≤ 5 + 6 / 10) : + S.card = 11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 28 +SearchTimeInSecs: 301.9895136356354 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 0, 'total_queries': 29} + + + +2026-01-10 22:51:36,587 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_209 +2026-01-10 22:51:36,587 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:51:36,587 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_209 (theorem_idx=84) with timeout: 600 seconds +2026-01-10 22:52:33,661 - __main__ - INFO - Prover for lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:52:33,662 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_209 + (σ : Equiv ℝ ℝ) + (h₀ : σ.2 2 = 10) + (h₁ : σ.2 10 = 1) + (h₂ : σ.2 1 = 2) : + σ.1 (σ.1 10) = 1 := + +by + have h10 : σ.toFun 10 = 2 := by + have := σ.right_inv 2 + simpa [h₀] using this + have h2' : σ.toFun 2 = 1 := by + have := σ.right_inv 1 + simpa [h₂] using this + calc + σ.toFun (σ.toFun 10) = σ.toFun 2 := by simpa [h10] + _ = 1 := h2' + + +ProofFile: None +LemmaName: theorem mathd_algebra_209 + (σ : Equiv ℝ ℝ) + (h₀ : σ.2 2 = 10) + (h₁ : σ.2 10 = 1) + (h₂ : σ.2 1 = 2) : + σ.1 (σ.1 10) = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 44.966813802719116 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 22:52:33,663 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_215 +2026-01-10 22:52:33,663 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:52:33,663 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_215 (theorem_idx=85) with timeout: 600 seconds +2026-01-10 22:52:38,371 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 22:52:38,459 - __main__ - INFO - Failed to prove lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:52:38,460 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_156 + +2026-01-10 22:52:38,460 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_275 +2026-01-10 22:52:38,460 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:52:38,460 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_275 (theorem_idx=86) with timeout: 600 seconds +2026-01-10 22:52:51,507 - __main__ - INFO - Prover for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:52:51,507 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 81.31489777565002 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-10 22:52:51,508 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_276 +2026-01-10 22:52:51,508 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:52:51,508 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_276 (theorem_idx=87) with timeout: 600 seconds +2026-01-10 22:54:46,653 - __main__ - INFO - Prover for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:54:46,653 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 64 +SearchTimeInSecs: 488.37815165519714 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 64, 'attempt_idx': 0, 'total_queries': 64} + + + +2026-01-10 22:54:46,653 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_288 +2026-01-10 22:54:46,654 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:54:46,654 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_288 (theorem_idx=88) with timeout: 600 seconds +2026-01-10 22:55:03,344 - __main__ - INFO - Prover for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:55:03,344 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 138.5427222251892 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-10 22:55:03,344 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_289 +2026-01-10 22:55:03,344 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:55:03,344 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_289 (theorem_idx=89) with timeout: 600 seconds +2026-01-10 22:55:45,243 - __main__ - INFO - Prover for lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:55:45,243 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_289 + (k t m n : ℕ) + (h₀ : Nat.Prime m ∧ Nat.Prime n) + (h₁ : t < k) + (h₂ : k^2 - m * k + n = 0) + (h₃ : t^2 - m * t + n = 0) : + m^n + n^m + k^t + t^k = 20 := + +by +aesop + + +ProofFile: None +LemmaName: theorem mathd_algebra_289 + (k t m n : ℕ) + (h₀ : Nat.Prime m ∧ Nat.Prime n) + (h₁ : t < k) + (h₂ : k^2 - m * k + n = 0) + (h₃ : t^2 - m * t + n = 0) : + m^n + n^m + k^t + t^k = 20 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 12.70111608505249 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:55:45,243 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_293 +2026-01-10 22:55:45,243 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:55:45,243 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_293 (theorem_idx=90) with timeout: 600 seconds +2026-01-10 22:56:20,808 - __main__ - INFO - Prover for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:56:20,809 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 195.08904218673706 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-10 22:56:20,809 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_313 +2026-01-10 22:56:20,809 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:56:20,809 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_313 (theorem_idx=91) with timeout: 600 seconds +2026-01-10 22:56:54,018 - __main__ - INFO - Prover for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:56:54,018 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 28 +SearchTimeInSecs: 241.85884046554565 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 0, 'total_queries': 28} + + + +2026-01-10 22:56:54,018 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_320 +2026-01-10 22:56:54,018 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:56:54,018 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_320 (theorem_idx=92) with timeout: 600 seconds +2026-01-10 22:56:56,789 - __main__ - INFO - Prover for lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:56:56,789 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_293 + (x : NNReal) : + Real.sqrt (60 * x) * Real.sqrt (12 * x) * Real.sqrt (63 * x) = 36 * x * Real.sqrt (35 * x) := + +by +simp [sqrt_mul, mul_comm, mul_left_comm, mul_assoc] +have hx : √(↑x : ℝ) * √(↑x : ℝ) = (↑x : ℝ) := by + have hpos : (0 : ℝ) ≤ (↑x : ℝ) := by exact_mod_cast x.property + simpa [sqrt_mul, mul_comm] using (sqrt_mul hpos hpos) +have hconst : √12 * √60 * √63 = 36 * √35 := by + calc + √12 * √60 * √63 + = √12 * (√60 * √63) := by ring + _ = √12 * √(60 * 63) := by + simpa [sqrt_mul, mul_comm, mul_left_comm, mul_assoc] using + (sqrt_mul (by norm_num) (by norm_num)) + _ = √12 * √(3780) := by norm_num + _ = √12 * √(36 * 105) := by ring + _ = √12 * (√36 * √105) := by + simpa [sqrt_mul, mul_comm, mul_left_comm, mul_assoc] using + (sqrt_mul (by norm_num) (by norm_num)) + _ = √12 * (6 * √105) := by norm_num + _ = 6 * √12 * √105 := by ring + _ = 6 * √(12 * 105) := by + simpa [sqrt_mul, mul_comm, mul_left_comm, mul_assoc] using + (sqrt_mul (by norm_num) (by norm_num)) + _ = 6 * √(1260) := by norm_num + _ = 6 * √(36 * 35) := by ring + _ = 6 * (√36 * √35) := by + simpa [sqrt_mul, mul_comm, mul_left_comm, mul_assoc] using + (sqrt_mul (by norm_num) (by norm_num)) + _ = 6 * (6 * √35) := by norm_num + _ = 36 * √35 := by ring +calc + √↑x * (√↑x * (√↑x * (√12 * (√60 * √63)))) + = √↑x * √↑x * √↑x * √12 * √60 * √63 := by ring + _ = (↑x : ℝ) * √↑x * √12 * √60 * √63 := by + simpa [hx, mul_comm, mul_left_comm, mul_assoc] + _ = (↑x : ℝ) * (36 * √35) * √↑x := by + simp [hconst, mul_comm, mul_left_comm, mul_assoc] + _ = (↑x : ℝ) * (36 * (√↑x * √35)) := by ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_293 + (x : NNReal) : + Real.sqrt (60 * x) * Real.sqrt (12 * x) * Real.sqrt (63 * x) = 36 * x * Real.sqrt (35 * x) := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 46.13774871826172 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 22:56:56,790 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_332 +2026-01-10 22:56:56,790 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:56:56,790 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_332 (theorem_idx=93) with timeout: 600 seconds +2026-01-10 22:57:16,604 - __main__ - INFO - Prover for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:57:16,605 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_288 + (x y : ℝ) + (n : NNReal) + (h₀ : x < 0 ∧ y < 0) + (h₁ : abs y = 6) + (h₂ : Real.sqrt ((x - 8)^2 + (y - 3)^2) = 15) + (h₃ : Real.sqrt (x^2 + y^2) = Real.sqrt n) : + n = 52 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_288 + (x y : ℝ) + (n : NNReal) + (h₀ : x < 0 ∧ y < 0) + (h₁ : abs y = 6) + (h₂ : Real.sqrt ((x - 8)^2 + (y - 3)^2) = 15) + (h₃ : Real.sqrt (x^2 + y^2) = Real.sqrt n) : + n = 52 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 126.22225952148438 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 0, 'total_queries': 17} + + + +2026-01-10 22:57:16,605 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_338 +2026-01-10 22:57:16,605 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:57:16,605 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_338 (theorem_idx=94) with timeout: 600 seconds +2026-01-10 22:58:01,988 - __main__ - INFO - Prover for lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:58:01,988 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_338 + (a b c : ℝ) + (h₀ : 3 * a + b + c = -3) + (h₁ : a + 3 * b + c = 9) + (h₂ : a + b + 3 * c = 19) : + a * b * c = -56 := + +by +-- Solve for `a` using the three linear equations +have ha : a = -4 := by + linarith [h₀, h₁, h₂] +-- First obtain the values of `b` and `c` from the linear system +have hb : b = 2 := by + linarith [h₀, h₁, ha] +have hc : c = 7 := by + linarith [h₀, h₂, ha] +-- Now compute the product using the obtained values +simp [ha, hb, hc] at * +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_338 + (a b c : ℝ) + (h₀ : 3 * a + b + c = -3) + (h₁ : a + 3 * b + c = 9) + (h₂ : a + b + 3 * c = 19) : + a * b * c = -56 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 8.67194128036499 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-10 22:58:01,989 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_342 +2026-01-10 22:58:01,989 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:58:01,989 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_342 (theorem_idx=95) with timeout: 600 seconds +2026-01-10 22:59:44,878 - __main__ - INFO - Prover for lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 22:59:44,878 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_342 + (a d: ℝ) + (h₀ : ∑ k ∈ (Finset.range 5), (a + k * d) = 70) + (h₁ : ∑ k ∈ (Finset.range 10), (a + k * d) = 210) : + a = 42/5 := + +by +have hk5 : ∑ k in Finset.range 5, (k : ℝ) = 10 := by + norm_num +-- Rewrite both sums in the form `5 * a + d * ∑ k` +have h₀' : 5 * a + d * ∑ k in Finset.range 5, (k : ℝ) = 70 := by + -- `Finset.sum_add_distrib` splits the sum, `Finset.sum_const` evaluates the constant part, + -- and `Finset.mul_sum` pulls the factor `d` out of the sum. + simpa [Finset.sum_add_distrib, Finset.sum_const, Finset.mul_sum, Finset.card_range, + mul_comm, mul_left_comm, mul_assoc] using h₀ +have h₁' : 10 * a + d * ∑ k in Finset.range 10, (k : ℝ) = 210 := by + simpa [Finset.sum_add_distrib, Finset.sum_const, Finset.mul_sum, Finset.card_range, + mul_comm, mul_left_comm, mul_assoc] using h₁ +-- Evaluate the index sums +have hk10 : ∑ k in Finset.range 10, (k : ℝ) = 45 := by norm_num +-- Substitute the known index sums +have h₀'' : 5 * a + d * 10 = 70 := by + simpa [hk5] using h₀' +have h₁'' : 10 * a + d * 45 = 210 := by + simpa [hk10] using h₁' +-- Solve the resulting linear system +linarith [h₀'', h₁''] + + +ProofFile: None +LemmaName: theorem mathd_algebra_342 + (a d: ℝ) + (h₀ : ∑ k ∈ (Finset.range 5), (a + k * d) = 70) + (h₁ : ∑ k ∈ (Finset.range 10), (a + k * d) = 210) : + a = 42/5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 73.2663414478302 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-10 22:59:44,879 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_362 +2026-01-10 22:59:44,879 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 22:59:44,879 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_362 (theorem_idx=96) with timeout: 600 seconds +2026-01-10 23:00:50,943 - __main__ - INFO - Prover for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:00:50,943 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 215.75807285308838 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 0, 'total_queries': 26} + + + +2026-01-10 23:00:50,943 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_392 +2026-01-10 23:00:50,943 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:00:50,943 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_392 (theorem_idx=97) with timeout: 600 seconds +2026-01-10 23:01:22,115 - __main__ - INFO - Prover for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:01:22,115 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 259.7744495868683 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 0, 'total_queries': 20} + + + +2026-01-10 23:01:22,115 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_398 +2026-01-10 23:01:22,115 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:01:22,115 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_398 (theorem_idx=98) with timeout: 600 seconds +2026-01-10 23:02:20,699 - __main__ - INFO - Prover for lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:02:20,699 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_398 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 9 * b = 20 * c) + (h₂ : 7 * a = 4 * b) : + 63 * a = 80 * c := + +by +-- Relate `63 * a` and `36 * b` using `7 * a = 4 * b` +have h3 : 63 * a = 36 * b := by + calc + 63 * a = 9 * (7 * a) := by ring + _ = 9 * (4 * b) := by + simpa [h₂, mul_comm, mul_left_comm, mul_assoc] + _ = 36 * b := by ring +-- Relate `36 * b` and `80 * c` using `9 * b = 20 * c` +have h4 : 36 * b = 80 * c := by + calc + 36 * b = 4 * (9 * b) := by ring + _ = 4 * (20 * c) := by + simpa [h₁, mul_comm, mul_left_comm, mul_assoc] + _ = 80 * c := by ring +-- Chain the equalities to get the desired result +calc + 63 * a = 36 * b := h3 + _ = 80 * c := h4 + + +ProofFile: None +LemmaName: theorem mathd_algebra_398 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 9 * b = 20 * c) + (h₂ : 7 * a = 4 * b) : + 63 * a = 80 * c := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 45.88750243186951 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-10 23:02:20,700 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_427 +2026-01-10 23:02:20,700 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:02:20,700 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_427 (theorem_idx=99) with timeout: 600 seconds +2026-01-10 23:02:42,936 - __main__ - INFO - Prover for lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:02:42,937 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_427 + (x y z : ℝ) + (h₀ : 3 * x + y = 17) + (h₁ : 5 * y + z = 14) + (h₂ : 3 * x + 5 * z = 41) : + x + y + z = 12 := + +by +linarith + + +ProofFile: None +LemmaName: theorem mathd_algebra_427 + (x y z : ℝ) + (h₀ : 3 * x + y = 17) + (h₁ : 5 * y + z = 14) + (h₂ : 3 * x + 5 * z = 41) : + x + y + z = 12 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 1.037473201751709 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 23:02:42,937 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_452 +2026-01-10 23:02:42,937 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:02:42,937 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_452 (theorem_idx=100) with timeout: 600 seconds +2026-01-10 23:02:52,176 - __main__ - INFO - Prover for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:02:52,176 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 374.73423194885254 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 52, 'attempt_idx': 0, 'total_queries': 52} + + + +2026-01-10 23:02:52,177 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_459 +2026-01-10 23:02:52,177 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:02:52,177 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_459 (theorem_idx=101) with timeout: 600 seconds +2026-01-10 23:04:37,879 - __main__ - INFO - Prover for lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:04:37,879 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_459 + (a b c d : ℚ) + (h₀ : 3 * a = b + c + d) + (h₁ : 4 * b = a + c + d) + (h₂ : 2 * c = a + b + d) + (h₃ : 8 * a + 10 * b + 6 * c = 24) : + ↑d.den + d.num = 28 := + +by +have hd : d = (13 : ℚ) / 15 := by + linarith +simp [hd] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_459 + (a b c d : ℚ) + (h₀ : 3 * a = b + c + d) + (h₁ : 4 * b = a + c + d) + (h₂ : 2 * c = a + b + d) + (h₃ : 8 * a + 10 * b + 6 * c = 24) : + ↑d.den + d.num = 28 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 91.65113568305969 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-10 23:04:37,879 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_484 +2026-01-10 23:04:37,880 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:04:37,880 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_484 (theorem_idx=102) with timeout: 600 seconds +2026-01-10 23:04:49,073 - __main__ - INFO - Prover for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:04:49,073 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 226.2758755683899 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 0, 'total_queries': 25} + + + +2026-01-10 23:04:49,074 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_487 +2026-01-10 23:04:49,074 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:04:49,074 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_487 (theorem_idx=103) with timeout: 600 seconds +2026-01-10 23:06:31,617 - __main__ - INFO - Prover for lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:06:31,617 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_484 : + Real.log 27 / Real.log 3 = 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_484 : + Real.log 27 / Real.log 3 = 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 97.33365845680237 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 0, 'total_queries': 19} + + + +2026-01-10 23:06:31,618 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_598 +2026-01-10 23:06:31,618 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:06:31,618 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_598 (theorem_idx=104) with timeout: 600 seconds +2026-01-10 23:06:38,901 - __main__ - INFO - Prover for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:06:38,901 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 88 +SearchTimeInSecs: 392.4477117061615 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 88, 'attempt_idx': 0, 'total_queries': 88} + + + +2026-01-10 23:06:38,901 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_756 +2026-01-10 23:06:38,902 - __main__ - INFO - Attempt 1 for proving lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:06:38,902 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_756 (theorem_idx=105) with timeout: 600 seconds +2026-01-10 23:07:45,988 - __main__ - INFO - Prover for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:07:45,988 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 54.871026277542114 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 23:07:45,989 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_100 +2026-01-10 23:07:45,989 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:07:45,989 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_100 (theorem_idx=106) with timeout: 600 seconds +2026-01-10 23:10:25,820 - __main__ - INFO - Prover for lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:10:25,820 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 220.19037103652954 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 0, 'total_queries': 26} + + + +2026-01-10 23:10:25,820 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_1124 +2026-01-10 23:10:25,820 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:10:25,820 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_1124 (theorem_idx=107) with timeout: 600 seconds +2026-01-10 23:10:49,858 - __main__ - INFO - Prover for lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:10:49,859 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 166.43378710746765 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 0, 'total_queries': 24} + + + +2026-01-10 23:10:49,859 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_222 +2026-01-10 23:10:49,859 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:10:49,859 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_222 (theorem_idx=108) with timeout: 600 seconds +2026-01-10 23:11:28,510 - __main__ - INFO - Prover for lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:11:28,510 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_222 + (b : ℕ) + (h₀ : Nat.lcm 120 b = 3720) + (h₁ : Nat.gcd 120 b = 8) : + b = 248 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_222 + (b : ℕ) + (h₀ : Nat.lcm 120 b = 3720) + (h₁ : Nat.gcd 120 b = 8) : + b = 248 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 15.178076267242432 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 23:11:28,511 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_227 +2026-01-10 23:11:28,511 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:11:28,511 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_227 (theorem_idx=109) with timeout: 600 seconds +2026-01-10 23:12:43,111 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:12:43,221 - __main__ - INFO - Failed to prove lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:12:43,222 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_452 + +2026-01-10 23:12:43,222 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_233 +2026-01-10 23:12:43,222 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:12:43,222 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_233 (theorem_idx=110) with timeout: 600 seconds +2026-01-10 23:13:23,927 - __main__ - INFO - Prover for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:13:23,927 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 105.4022388458252 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-10 23:13:23,928 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_234 +2026-01-10 23:13:23,928 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:13:23,928 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_234 (theorem_idx=111) with timeout: 600 seconds +2026-01-10 23:13:34,337 - __main__ - INFO - Prover for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:13:34,337 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 181.01770639419556 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 0, 'total_queries': 25} + + + +2026-01-10 23:13:34,338 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_277 +2026-01-10 23:13:34,339 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:13:34,339 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_277 (theorem_idx=112) with timeout: 600 seconds +2026-01-10 23:13:50,034 - __main__ - INFO - Prover for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:13:50,034 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 51.42504549026489 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 0, 'total_queries': 20} + + + +2026-01-10 23:13:50,035 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_293 +2026-01-10 23:13:50,035 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:13:50,035 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_293 (theorem_idx=113) with timeout: 600 seconds +2026-01-10 23:14:49,207 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:14:49,299 - __main__ - INFO - Failed to prove lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:14:49,299 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_487 + +2026-01-10 23:14:49,299 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_296 +2026-01-10 23:14:49,299 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:14:49,299 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_296 (theorem_idx=114) with timeout: 600 seconds +2026-01-10 23:15:33,149 - __main__ - INFO - Prover for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:15:33,149 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 109.96386528015137 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-10 23:15:33,149 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_314 +2026-01-10 23:15:33,149 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:15:33,149 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_314 (theorem_idx=115) with timeout: 600 seconds +2026-01-10 23:16:09,810 - __main__ - INFO - Prover for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:16:09,810 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 143.16372752189636 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-10 23:16:09,810 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_320 +2026-01-10 23:16:09,810 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:16:09,810 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_320 (theorem_idx=116) with timeout: 600 seconds +2026-01-10 23:17:46,636 - __main__ - INFO - Prover for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:17:46,636 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 151.42197060585022 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-10 23:17:46,636 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_321 +2026-01-10 23:17:46,637 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:17:46,637 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_321 (theorem_idx=117) with timeout: 600 seconds +2026-01-10 23:20:28,701 - __main__ - INFO - Prover for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:20:28,701 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 50 +SearchTimeInSecs: 147.57396388053894 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 45, 'attempt_idx': 0, 'total_queries': 45} + + + +2026-01-10 23:20:28,701 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_328 +2026-01-10 23:20:28,701 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:20:28,701 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_328 (theorem_idx=118) with timeout: 600 seconds +2026-01-10 23:20:45,496 - __main__ - INFO - Prover for lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:20:45,496 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_328 : + (5^999999) % 7 = 6 := + +by + norm_num + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_328 : + (5^999999) % 7 = 6 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 1 +SearchTimeInSecs: 2.043180465698242 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 1, 'attempt_idx': 0, 'total_queries': 1} + + + +2026-01-10 23:20:45,496 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_34 +2026-01-10 23:20:45,497 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:20:45,497 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_34 (theorem_idx=119) with timeout: 600 seconds +2026-01-10 23:20:55,395 - __main__ - INFO - Prover for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:20:55,395 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_293 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 11∣20 * 100 + 10 * n + 7) : + n = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_293 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 11∣20 * 100 + 10 * n + 7) : + n = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 43 +SearchTimeInSecs: 414.08435249328613 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 0, 'total_queries': 44} + + + +2026-01-10 23:20:55,396 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_353 +2026-01-10 23:20:55,396 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:20:55,396 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_353 (theorem_idx=120) with timeout: 600 seconds +2026-01-10 23:21:53,685 - __main__ - INFO - Prover for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:21:53,686 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 54.67845034599304 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-10 23:21:53,686 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_427 +2026-01-10 23:21:53,686 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:21:53,686 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_427 (theorem_idx=121) with timeout: 600 seconds +2026-01-10 23:22:12,434 - __main__ - INFO - Prover for lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:22:12,434 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_314 + (r n : ℕ) + (h₀ : r = 1342 % 13) + (h₁ : 0 < n) + (h₂ : 1342∣n) + (h₃ : n % 13 < r) : + 6710 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_314 + (r n : ℕ) + (h₀ : r = 1342 % 13) + (h₁ : 0 < n) + (h₂ : 1342∣n) + (h₃ : n % 13 < r) : + 6710 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 34 +SearchTimeInSecs: 386.9500312805176 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 34, 'attempt_idx': 0, 'total_queries': 34} + + + +2026-01-10 23:22:12,435 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_430 +2026-01-10 23:22:12,435 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:22:12,435 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_430 (theorem_idx=122) with timeout: 600 seconds +2026-01-10 23:23:57,562 - __main__ - INFO - Prover for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:23:57,562 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 96.66522192955017 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-10 23:23:57,562 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_435 +2026-01-10 23:23:57,562 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:23:57,562 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_435 (theorem_idx=123) with timeout: 600 seconds +2026-01-10 23:24:06,038 - __main__ - INFO - Prover for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:24:06,038 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 55 +SearchTimeInSecs: 181.68506360054016 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 47, 'attempt_idx': 0, 'total_queries': 47} + + + +2026-01-10 23:24:06,039 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_447 +2026-01-10 23:24:06,039 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:24:06,039 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_447 (theorem_idx=124) with timeout: 600 seconds +2026-01-10 23:24:39,876 - __main__ - INFO - Prover for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:24:39,876 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 51 +SearchTimeInSecs: 158.2686574459076 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 0, 'total_queries': 41} + + + +2026-01-10 23:24:39,876 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_451 +2026-01-10 23:24:39,876 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:24:39,876 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_451 (theorem_idx=125) with timeout: 600 seconds +2026-01-10 23:26:09,934 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:26:10,028 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:26:10,028 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_320 + +2026-01-10 23:26:10,028 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_457 +2026-01-10 23:26:10,028 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:26:10,028 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_457 (theorem_idx=126) with timeout: 600 seconds +2026-01-10 23:27:24,151 - __main__ - INFO - Prover for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:27:24,151 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 61.5110445022583 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 0, 'total_queries': 16} + + + +2026-01-10 23:27:24,152 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_483 +2026-01-10 23:27:24,152 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:27:24,152 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_483 (theorem_idx=127) with timeout: 600 seconds +2026-01-10 23:28:17,527 - __main__ - INFO - Prover for lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:28:17,527 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_483 + (a : ℕ → ℕ) + (h₀ : a 1 = 1) + (h₁ : a 2 = 1) + (h₂ : ∀ n, a (n + 2) = a (n + 1) + a n) : + (a 100) % 4 = 3 := + +by +norm_num +have hmod : a 100 % 4 = 3 := by + norm_num [h₀, h₁, h₂] +exact hmod + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_483 + (a : ℕ → ℕ) + (h₀ : a 1 = 1) + (h₁ : a 2 = 1) + (h₂ : ∀ n, a (n + 2) = a (n + 1) + a n) : + (a 100) % 4 = 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 35.4178581237793 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-10 23:28:17,527 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_495 +2026-01-10 23:28:17,527 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:28:17,527 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_495 (theorem_idx=128) with timeout: 600 seconds +2026-01-10 23:28:36,559 - __main__ - INFO - Prover for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:28:36,559 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 227.47250247001648 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 34, 'attempt_idx': 0, 'total_queries': 34} + + + +2026-01-10 23:28:36,559 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_5 +2026-01-10 23:28:36,560 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:28:36,560 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_5 (theorem_idx=129) with timeout: 600 seconds +2026-01-10 23:29:15,366 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:29:15,463 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:29:15,463 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: mathd_numbertheory_495 + +2026-01-10 23:29:15,464 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_521 +2026-01-10 23:29:15,464 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:29:15,464 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_521 (theorem_idx=130) with timeout: 600 seconds +2026-01-10 23:29:16,251 - __main__ - INFO - Prover for lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:29:16,251 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_447 : + ∑ k ∈ Finset.filter (λ x => 3∣x) (Finset.Icc 1 49), (k % 10) = 78 := + +by +simp [Finset.sum_filter] +norm_num +rfl + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_447 : + ∑ k ∈ Finset.filter (λ x => 3∣x) (Finset.Icc 1 49), (k % 10) = 78 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 77 +SearchTimeInSecs: 295.1303446292877 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 64, 'attempt_idx': 0, 'total_queries': 64} + + + +2026-01-10 23:29:16,252 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_541 +2026-01-10 23:29:16,252 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:29:16,252 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_541 (theorem_idx=131) with timeout: 600 seconds +2026-01-10 23:33:57,648 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:33:57,746 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:33:57,746 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_435 + +2026-01-10 23:33:57,747 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_552 +2026-01-10 23:33:57,747 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:33:57,747 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_552 (theorem_idx=132) with timeout: 600 seconds +2026-01-10 23:36:34,720 - __main__ - INFO - Prover for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:36:34,720 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 467.0080757141113 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 48, 'attempt_idx': 0, 'total_queries': 48} + + + +2026-01-10 23:36:34,721 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_559 +2026-01-10 23:36:34,721 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:36:34,721 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_559 (theorem_idx=133) with timeout: 600 seconds +2026-01-10 23:38:14,513 - __main__ - INFO - Prover for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:38:14,513 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 246.16521048545837 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 0, 'total_queries': 29} + + + +2026-01-10 23:38:14,513 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_582 +2026-01-10 23:38:14,514 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:38:14,514 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_582 (theorem_idx=134) with timeout: 600 seconds +2026-01-10 23:39:15,557 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:39:15,656 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:15,656 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_521 + +2026-01-10 23:39:15,656 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_618 +2026-01-10 23:39:15,656 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:15,657 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_618 (theorem_idx=135) with timeout: 600 seconds +2026-01-10 23:39:16,432 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:39:16,556 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:16,556 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_541 + +2026-01-10 23:39:16,557 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_711 +2026-01-10 23:39:16,557 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:16,557 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_711 (theorem_idx=136) with timeout: 600 seconds +2026-01-10 23:39:31,665 - __main__ - INFO - Prover for lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:39:31,665 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_582 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 3∣n) : + ((n + 4) + (n + 6) + (n + 8)) % 9 = 0 := + +by +rcases h₁ with ⟨k, hk⟩ +have hsum : n + 4 + (n + 6) + (n + 8) = 9 * (k + 2) := by + calc + n + 4 + (n + 6) + (n + 8) + = (3 * k) + 4 + ((3 * k) + 6) + ((3 * k) + 8) := by + simpa [hk] + _ = 9 * k + 18 := by ring + _ = 9 * (k + 2) := by ring +have hdiv : 9 ∣ 9 * (k + 2) := by + simpa [mul_comm] using dvd_mul_left 9 (k + 2) +simpa [hsum] using Nat.mod_eq_zero_of_dvd hdiv + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_582 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 3∣n) : + ((n + 4) + (n + 6) + (n + 8)) % 9 = 0 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 41.229124307632446 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-10 23:39:31,666 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_764 +2026-01-10 23:39:31,666 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:31,666 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_764 (theorem_idx=137) with timeout: 600 seconds +2026-01-10 23:39:36,110 - __main__ - INFO - Prover for lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:39:36,110 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_559 + (x y : ℕ) + (h₀ : x % 3 = 2) + (h₁ : y % 5 = 4) + (h₂ : x % 10 = y % 10) : + 14 ≤ x := + +by +grind + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_559 + (x y : ℕ) + (h₀ : x % 3 = 2) + (h₁ : y % 5 = 4) + (h₂ : x % 10 = y % 10) : + 14 ≤ x := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 167.8500473499298 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 0, 'total_queries': 8} + + + +2026-01-10 23:39:36,111 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_765 +2026-01-10 23:39:36,111 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:39:36,111 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_765 (theorem_idx=138) with timeout: 600 seconds +2026-01-10 23:41:51,062 - __main__ - INFO - Prover for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:41:51,062 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 126.31517171859741 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-10 23:41:51,062 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_99 +2026-01-10 23:41:51,062 - __main__ - INFO - Attempt 1 for proving lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:41:51,063 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_99 (theorem_idx=139) with timeout: 600 seconds +2026-01-10 23:44:12,139 - __main__ - INFO - Prover for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:44:12,139 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 266.2527711391449 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 0, 'total_queries': 25} + + + +2026-01-10 23:44:12,140 - __main__ - INFO - Attempting to prove lemma: numbertheory_2pownm1prime_nprime +2026-01-10 23:44:12,140 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:44:12,140 - __main__ - INFO - Running the prover agent for lemma: numbertheory_2pownm1prime_nprime (theorem_idx=140) with timeout: 600 seconds +2026-01-10 23:44:51,806 - __main__ - INFO - Prover for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:44:51,807 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 27.75756335258484 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-10 23:44:51,807 - __main__ - INFO - Attempting to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 +2026-01-10 23:44:51,807 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:44:51,807 - __main__ - INFO - Running the prover agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 (theorem_idx=141) with timeout: 600 seconds +2026-01-10 23:46:11,265 - __main__ - INFO - Prover for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:46:11,265 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 395.95398449897766 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 43, 'attempt_idx': 0, 'total_queries': 43} + + + +2026-01-10 23:46:11,265 - __main__ - INFO - Attempting to prove lemma: numbertheory_4x3m7y3neq2003 +2026-01-10 23:46:11,265 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:46:11,265 - __main__ - INFO - Running the prover agent for lemma: numbertheory_4x3m7y3neq2003 (theorem_idx=142) with timeout: 600 seconds +2026-01-10 23:47:53,078 - __main__ - INFO - Prover for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:47:53,078 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 161.2664258480072 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-10 23:47:53,079 - __main__ - INFO - Attempting to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 +2026-01-10 23:47:53,079 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:47:53,079 - __main__ - INFO - Running the prover agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 (theorem_idx=143) with timeout: 600 seconds +2026-01-10 23:47:53,601 - __main__ - INFO - Prover for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:47:53,601 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_4x3m7y3neq2003 + (x y : ℤ) : + 4 * x^3 - 7 * y^3 ≠ 2003 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_4x3m7y3neq2003 + (x y : ℤ) : + 4 * x^3 - 7 * y^3 ≠ 2003 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 95.17642307281494 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-10 23:47:53,602 - __main__ - INFO - Attempting to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 +2026-01-10 23:47:53,602 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:47:53,602 - __main__ - INFO - Running the prover agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 (theorem_idx=144) with timeout: 600 seconds +2026-01-10 23:48:11,274 - __main__ - INFO - Prover for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:48:11,274 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 520.5678949356079 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 43, 'attempt_idx': 0, 'total_queries': 43} + + + +2026-01-10 23:48:11,275 - __main__ - INFO - Attempting to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown +2026-01-10 23:48:11,275 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:48:11,275 - __main__ - INFO - Running the prover agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown (theorem_idx=145) with timeout: 600 seconds +2026-01-10 23:50:50,853 - __main__ - INFO - Prover for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:50:50,853 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 36 +SearchTimeInSecs: 154.89702796936035 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 0, 'total_queries': 35} + + + +2026-01-10 23:50:50,854 - __main__ - INFO - Attempting to prove lemma: numbertheory_x5neqy2p4 +2026-01-10 23:50:50,855 - __main__ - INFO - Attempt 1 for proving lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:50:50,855 - __main__ - INFO - Running the prover agent for lemma: numbertheory_x5neqy2p4 (theorem_idx=146) with timeout: 600 seconds +2026-01-10 23:51:35,280 - __main__ - INFO - Prover for lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:51:35,280 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_99 + (n : ℕ) + (h₀ : (2 * n) % 47 = 15) : + n % 47 = 31 := + +by +have inv2 : (2 * 24) % 47 = 1 := by norm_num +have h48 : (48 % 47) = 1 := by norm_num +-- Step 1: rewrite `n % 47` using `Nat.mod_mul_left` with 48 +have h₁ : n % 47 = ((48 % 47) * n) % 47 := by + simpa [h48, one_mul] using (Nat.mod_mul_left 48 n 47) +-- First, multiply the hypothesis `h₀` by 24 and reduce modulo 47 +have hmul : (24 * (2 * n)) % 47 = (24 * 15) % 47 := by + simpa [mul_comm, mul_left_comm, mul_assoc] using + congrArg (fun t : ℕ => (24 * t) % 47) h₀ +-- Rewrite the hypothesis `h₀` by multiplying both sides by 24 +have hmul : (24 * (2 * n)) % 47 = (24 * 15) % 47 := by + simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using + congrArg (fun t : ℕ => (24 * t) % 47) h₀ +-- Simplify the left hand side of `hmul` +have hmul' : (48 * n) % 47 = (24 * 15) % 47 := by + simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using hmul +-- Since 48 ≡ 1 (mod 47), the left side reduces to `n % 47` +have hleft : (48 * n) % 47 = n % 47 := by + simp [Nat.mul_mod, h48, one_mul] +-- Combine the equalities to obtain `n % 47 = (24 * 15) % 47` +have hn : n % 47 = (24 * 15) % 47 := by + simpa [hleft] using hmul' +-- Compute the right hand side numerically +have : n % 47 = 31 := by + simpa [norm_num] using hn +exact this + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_99 + (n : ℕ) + (h₀ : (2 * n) % 47 = 15) : + n % 47 = 31 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 79 +SearchTimeInSecs: 561.9391462802887 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 78, 'attempt_idx': 0, 'total_queries': 78} + + + +2026-01-10 23:51:35,280 - __main__ - INFO - Attempting to prove lemma: aime_1983_p1 +2026-01-10 23:51:35,281 - __main__ - INFO - Attempt 1 for proving lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:51:35,281 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p1 (theorem_idx=147) with timeout: 600 seconds +2026-01-10 23:53:47,277 - __main__ - INFO - Prover for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:53:47,277 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 168.52266359329224 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-10 23:53:47,277 - __main__ - INFO - Attempting to prove lemma: aime_1983_p3 +2026-01-10 23:53:47,277 - __main__ - INFO - Attempt 1 for proving lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:53:47,277 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p3 (theorem_idx=148) with timeout: 600 seconds +2026-01-10 23:56:57,361 - __main__ - INFO - Prover for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-10 23:56:57,361 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 170.7991750240326 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-10 23:56:57,361 - __main__ - INFO - Attempting to prove lemma: aime_1984_p1 +2026-01-10 23:56:57,361 - __main__ - INFO - Attempt 1 for proving lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:56:57,361 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p1 (theorem_idx=149) with timeout: 600 seconds +2026-01-10 23:57:53,781 - __main__ - INFO - Prover Agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:57:53,889 - __main__ - INFO - Failed to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:57:53,889 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 + +2026-01-10 23:57:53,889 - __main__ - INFO - Attempting to prove lemma: aime_1984_p7 +2026-01-10 23:57:53,889 - __main__ - INFO - Attempt 1 for proving lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:57:53,889 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p7 (theorem_idx=150) with timeout: 600 seconds +2026-01-10 23:58:11,462 - __main__ - INFO - Prover Agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-10 23:58:11,562 - __main__ - INFO - Failed to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:58:11,562 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + +2026-01-10 23:58:11,563 - __main__ - INFO - Attempting to prove lemma: aime_1987_p5 +2026-01-10 23:58:11,563 - __main__ - INFO - Attempt 1 for proving lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-10 23:58:11,563 - __main__ - INFO - Running the prover agent for lemma: aime_1987_p5 (theorem_idx=151) with timeout: 600 seconds +2026-01-11 00:01:08,239 - __main__ - INFO - Prover for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:01:08,239 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 236.0357701778412 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 0, 'total_queries': 26} + + + +2026-01-11 00:01:08,240 - __main__ - INFO - Attempting to prove lemma: aime_1988_p8 +2026-01-11 00:01:08,240 - __main__ - INFO - Attempt 1 for proving lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:01:08,240 - __main__ - INFO - Running the prover agent for lemma: aime_1988_p8 (theorem_idx=152) with timeout: 600 seconds +2026-01-11 00:01:35,401 - __main__ - INFO - Prover Agent for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:01:35,507 - __main__ - INFO - Failed to prove lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:01:35,507 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1983_p1 + +2026-01-11 00:01:35,508 - __main__ - INFO - Attempting to prove lemma: aime_1990_p15 +2026-01-11 00:01:35,508 - __main__ - INFO - Attempt 1 for proving lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:01:35,508 - __main__ - INFO - Running the prover agent for lemma: aime_1990_p15 (theorem_idx=153) with timeout: 600 seconds +2026-01-11 00:02:32,826 - __main__ - INFO - Prover for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:02:32,826 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 258.45097255706787 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-11 00:02:32,827 - __main__ - INFO - Attempting to prove lemma: aime_1990_p4 +2026-01-11 00:02:32,827 - __main__ - INFO - Attempt 1 for proving lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:02:32,827 - __main__ - INFO - Running the prover agent for lemma: aime_1990_p4 (theorem_idx=154) with timeout: 600 seconds +2026-01-11 00:03:22,608 - __main__ - INFO - Prover for lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:03:22,608 - __main__ - INFO - Dumping proof search result: +theorem aime_1990_p4 + (x : ℝ) + (h₀ : 0 < x) + (h₁ : x^2 - 10 * x - 29 ≠ 0) + (h₂ : x^2 - 10 * x - 45 ≠ 0) + (h₃ : x^2 - 10 * x - 69 ≠ 0) + (h₄ : 1 / (x^2 - 10 * x - 29) + 1 / (x^2 - 10 * x - 45) - 2 / (x^2 - 10 * x - 69) = 0) : + x = 13 := + +by +have h := h₄ +field_simp [h₁, h₂, h₃] at h +ring_nf at h +nlinarith [h₀] + + +ProofFile: None +LemmaName: theorem aime_1990_p4 + (x : ℝ) + (h₀ : 0 < x) + (h₁ : x^2 - 10 * x - 29 ≠ 0) + (h₂ : x^2 - 10 * x - 45 ≠ 0) + (h₃ : x^2 - 10 * x - 69 ≠ 0) + (h₄ : 1 / (x^2 - 10 * x - 29) + 1 / (x^2 - 10 * x - 45) - 2 / (x^2 - 10 * x - 69) = 0) : + x = 13 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 14.937676191329956 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-11 00:03:22,609 - __main__ - INFO - Attempting to prove lemma: aime_1991_p9 +2026-01-11 00:03:22,609 - __main__ - INFO - Attempt 1 for proving lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:03:22,609 - __main__ - INFO - Running the prover agent for lemma: aime_1991_p9 (theorem_idx=155) with timeout: 600 seconds +2026-01-11 00:03:31,136 - __main__ - INFO - Prover for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:03:31,137 - __main__ - INFO - Dumping proof search result: +theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 309.3392219543457 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 0, 'total_queries': 22} + + + +2026-01-11 00:03:31,137 - __main__ - INFO - Attempting to prove lemma: aime_1994_p3 +2026-01-11 00:03:31,138 - __main__ - INFO - Attempt 1 for proving lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:03:31,138 - __main__ - INFO - Running the prover agent for lemma: aime_1994_p3 (theorem_idx=156) with timeout: 600 seconds +2026-01-11 00:06:43,080 - __main__ - INFO - Prover for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:06:43,080 - __main__ - INFO - Dumping proof search result: +theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 176.9624788761139 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 23, 'attempt_idx': 0, 'total_queries': 23} + + + +2026-01-11 00:06:43,081 - __main__ - INFO - Attempting to prove lemma: aime_1995_p7 +2026-01-11 00:06:43,081 - __main__ - INFO - Attempt 1 for proving lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:06:43,081 - __main__ - INFO - Running the prover agent for lemma: aime_1995_p7 (theorem_idx=157) with timeout: 600 seconds +2026-01-11 00:09:20,514 - __main__ - INFO - Prover for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:09:20,514 - __main__ - INFO - Dumping proof search result: +theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 129.00714802742004 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 00:09:20,515 - __main__ - INFO - Attempting to prove lemma: aime_1997_p9 +2026-01-11 00:09:20,515 - __main__ - INFO - Attempt 1 for proving lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:09:20,515 - __main__ - INFO - Running the prover agent for lemma: aime_1997_p9 (theorem_idx=158) with timeout: 600 seconds +2026-01-11 00:09:57,549 - __main__ - INFO - Prover for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:09:57,549 - __main__ - INFO - Dumping proof search result: +theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 510.2836627960205 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 0, 'total_queries': 35} + + + +2026-01-11 00:09:57,550 - __main__ - INFO - Attempting to prove lemma: aime_1999_p11 +2026-01-11 00:09:57,550 - __main__ - INFO - Attempt 1 for proving lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:09:57,550 - __main__ - INFO - Running the prover agent for lemma: aime_1999_p11 (theorem_idx=159) with timeout: 600 seconds +2026-01-11 00:11:35,693 - __main__ - INFO - Prover Agent for lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:11:35,808 - __main__ - INFO - Failed to prove lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:11:35,808 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1990_p15 + +2026-01-11 00:11:35,809 - __main__ - INFO - Attempting to prove lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 +2026-01-11 00:11:35,809 - __main__ - INFO - Attempt 1 for proving lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:11:35,809 - __main__ - INFO - Running the prover agent for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 (theorem_idx=160) with timeout: 600 seconds +2026-01-11 00:12:22,032 - __main__ - INFO - Prover for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:12:22,032 - __main__ - INFO - Dumping proof search result: +theorem aime_1997_p9 + (a : ℝ) + (h₀ : 0 < a) + (h₁ : 1 / a - Int.floor (1 / a) = a^2 - Int.floor (a^2)) + (h₂ : 2 < a^2) + (h₃ : a^2 < 3) : + a^12 - 144 * (1 / a) = 233 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1997_p9 + (a : ℝ) + (h₀ : 0 < a) + (h₁ : 1 / a - Int.floor (1 / a) = a^2 - Int.floor (a^2)) + (h₂ : 2 < a^2) + (h₃ : a^2 < 3) : + a^12 - 144 * (1 / a) = 233 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 171.76729702949524 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 0, 'total_queries': 13} + + + +2026-01-11 00:12:22,032 - __main__ - INFO - Attempting to prove lemma: algebra_9onxpypzleqsum2onxpy +2026-01-11 00:12:22,032 - __main__ - INFO - Attempt 1 for proving lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:12:22,032 - __main__ - INFO - Running the prover agent for lemma: algebra_9onxpypzleqsum2onxpy (theorem_idx=161) with timeout: 600 seconds +2026-01-11 00:12:49,989 - __main__ - INFO - Prover for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:12:49,989 - __main__ - INFO - Dumping proof search result: +theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 62.23977875709534 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-11 00:12:49,989 - __main__ - INFO - Attempting to prove lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 +2026-01-11 00:12:49,990 - __main__ - INFO - Attempt 1 for proving lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:12:49,990 - __main__ - INFO - Running the prover agent for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 (theorem_idx=162) with timeout: 600 seconds +2026-01-11 00:12:50,653 - __main__ - INFO - Prover for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:12:50,654 - __main__ - INFO - Dumping proof search result: +theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 60 +SearchTimeInSecs: 548.2511193752289 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 62, 'attempt_idx': 0, 'total_queries': 62} + + + +2026-01-11 00:12:50,654 - __main__ - INFO - Attempting to prove lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa +2026-01-11 00:12:50,654 - __main__ - INFO - Attempt 1 for proving lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:12:50,654 - __main__ - INFO - Running the prover agent for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa (theorem_idx=163) with timeout: 600 seconds +2026-01-11 00:13:30,652 - __main__ - INFO - Prover for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:13:30,652 - __main__ - INFO - Dumping proof search result: +theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 53.46144962310791 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-11 00:13:30,653 - __main__ - INFO - Attempting to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 +2026-01-11 00:13:30,653 - __main__ - INFO - Attempt 1 for proving lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:13:30,653 - __main__ - INFO - Running the prover agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 (theorem_idx=164) with timeout: 600 seconds +2026-01-11 00:13:44,712 - __main__ - INFO - Prover for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:13:44,712 - __main__ - INFO - Dumping proof search result: +theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 205.16437339782715 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-11 00:13:44,712 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 +2026-01-11 00:13:44,713 - __main__ - INFO - Attempt 1 for proving lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:13:44,713 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 (theorem_idx=165) with timeout: 600 seconds +2026-01-11 00:15:34,447 - __main__ - INFO - Prover for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:15:34,448 - __main__ - INFO - Dumping proof search result: +theorem algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + (x : ℝ) + (h₀ : abs (x - 1) + abs x + abs (x + 1) = x + 2) : + 0 ≤ x ∧ x ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + (x : ℝ) + (h₀ : abs (x - 1) + abs x + abs (x + 1) = x + 2) : + 0 ≤ x ∧ x ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 98.44429922103882 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 00:15:34,448 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sumasqdivbgeqsuma +2026-01-11 00:15:34,448 - __main__ - INFO - Attempt 1 for proving lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:15:34,448 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sumasqdivbgeqsuma (theorem_idx=166) with timeout: 600 seconds +2026-01-11 00:17:53,452 - __main__ - INFO - Prover for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:17:53,452 - __main__ - INFO - Dumping proof search result: +theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 287.4942207336426 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 27, 'attempt_idx': 0, 'total_queries': 27} + + + +2026-01-11 00:17:53,453 - __main__ - INFO - Attempting to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 +2026-01-11 00:17:53,453 - __main__ - INFO - Attempt 1 for proving lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:17:53,453 - __main__ - INFO - Running the prover agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 (theorem_idx=167) with timeout: 600 seconds +2026-01-11 00:20:05,435 - __main__ - INFO - Prover for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:20:05,435 - __main__ - INFO - Dumping proof search result: +theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 53 +SearchTimeInSecs: 423.5133147239685 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 53, 'attempt_idx': 0, 'total_queries': 53} + + + +2026-01-11 00:20:05,436 - __main__ - INFO - Attempting to prove lemma: algebra_apbon2pownleqapownpbpowon2 +2026-01-11 00:20:05,436 - __main__ - INFO - Attempt 1 for proving lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:20:05,436 - __main__ - INFO - Running the prover agent for lemma: algebra_apbon2pownleqapownpbpowon2 (theorem_idx=168) with timeout: 600 seconds +2026-01-11 00:22:21,073 - __main__ - INFO - Prover for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:22:21,073 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 112.54083585739136 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-11 00:22:21,073 - __main__ - INFO - Attempting to prove lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 +2026-01-11 00:22:21,073 - __main__ - INFO - Attempt 1 for proving lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:22:21,073 - __main__ - INFO - Running the prover agent for lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 (theorem_idx=169) with timeout: 600 seconds +2026-01-11 00:23:44,792 - __main__ - INFO - Prover Agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:23:44,907 - __main__ - INFO - Failed to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:23:44,907 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 + +2026-01-11 00:23:44,908 - __main__ - INFO - Attempting to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b +2026-01-11 00:23:44,908 - __main__ - INFO - Attempt 1 for proving lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:23:44,908 - __main__ - INFO - Running the prover agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b (theorem_idx=170) with timeout: 600 seconds +2026-01-11 00:24:41,101 - __main__ - INFO - Prover for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:24:41,101 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 397.82444024086 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 39, 'attempt_idx': 0, 'total_queries': 39} + + + +2026-01-11 00:24:41,102 - __main__ - INFO - Attempting to prove lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 +2026-01-11 00:24:41,102 - __main__ - INFO - Attempt 1 for proving lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:24:41,102 - __main__ - INFO - Running the prover agent for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 (theorem_idx=171) with timeout: 600 seconds +2026-01-11 00:24:48,156 - __main__ - INFO - Prover for lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:24:48,157 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sumasqdivbgeqsuma + (a b c d : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) : + a^2 / b + b^2 / c + c^2 / d + d^2 / a ≥ a + b + c + d := + +by + + + +ProofFile: None +LemmaName: theorem algebra_amgm_sumasqdivbgeqsuma + (a b c d : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) : + a^2 / b + b^2 / c + c^2 / d + d^2 / a ≥ a + b + c + d := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 83 +SearchTimeInSecs: 535.6759660243988 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 75, 'attempt_idx': 0, 'total_queries': 75} + + + +2026-01-11 00:24:48,158 - __main__ - INFO - Attempting to prove lemma: algebra_ineq_nto1onlt2m1on +2026-01-11 00:24:48,158 - __main__ - INFO - Attempt 1 for proving lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:24:48,158 - __main__ - INFO - Running the prover agent for lemma: algebra_ineq_nto1onlt2m1on (theorem_idx=172) with timeout: 600 seconds +2026-01-11 00:25:23,226 - __main__ - INFO - Prover for lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:25:23,226 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 + (a b c : ℝ) + (h₀ : a ≤ b ∧ b ≤ c) + (h₁ : a + b + c = 2) + (h₂ : a * b + b * c + c * a = 1) : + 0 ≤ a ∧ a ≤ 1 / 3 ∧ 1 / 3 ≤ b ∧ b ≤ 1 ∧ 1 ≤ c ∧ c ≤ 4 / 3 := + +by +constructor +nlinarith [h₀, h₁, h₂] +have ha : a ≤ (1 / 3 : ℝ) := by + nlinarith [h₀, h₁, h₂] +have hb1 : (1 / 3 : ℝ) ≤ b := by + nlinarith [h₀, h₁, h₂] +have hb2 : b ≤ (1 : ℝ) := by + nlinarith [h₀, h₁, h₂] +have hc1 : (1 : ℝ) ≤ c := by + nlinarith [h₀, h₁, h₂] +have hc2 : c ≤ (4 / 3 : ℝ) := by + nlinarith [h₀, h₁, h₂] +exact ⟨ha, hb1, hb2, hc1, hc2⟩ + + +ProofFile: None +LemmaName: theorem algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 + (a b c : ℝ) + (h₀ : a ≤ b ∧ b ≤ c) + (h₁ : a + b + c = 2) + (h₂ : a * b + b * c + c * a = 1) : + 0 ≤ a ∧ a ≤ 1 / 3 ∧ 1 / 3 ≤ b ∧ b ≤ 1 ∧ 1 ≤ c ∧ c ≤ 4 / 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 147.83360886573792 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-11 00:25:23,227 - __main__ - INFO - Attempting to prove lemma: algebra_others_exirrpowirrrat +2026-01-11 00:25:23,227 - __main__ - INFO - Attempt 1 for proving lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:25:23,227 - __main__ - INFO - Running the prover agent for lemma: algebra_others_exirrpowirrrat (theorem_idx=173) with timeout: 600 seconds +2026-01-11 00:25:37,041 - __main__ - INFO - Prover for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:25:37,041 - __main__ - INFO - Dumping proof search result: +theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 98.1275737285614 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-11 00:25:37,041 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpabsamblt1 +2026-01-11 00:25:37,041 - __main__ - INFO - Attempt 1 for proving lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:25:37,041 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpabsamblt1 (theorem_idx=174) with timeout: 600 seconds +2026-01-11 00:26:50,927 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:26:50,927 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 66.23652029037476 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 00:26:50,928 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpamblt1 +2026-01-11 00:26:50,928 - __main__ - INFO - Attempt 1 for proving lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:26:50,928 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpamblt1 (theorem_idx=175) with timeout: 600 seconds +2026-01-11 00:28:28,650 - __main__ - INFO - Prover for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:28:28,650 - __main__ - INFO - Dumping proof search result: +theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := + +by + + + +ProofFile: None +LemmaName: theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 202.68403220176697 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 23, 'attempt_idx': 0, 'total_queries': 23} + + + +2026-01-11 00:28:28,651 - __main__ - INFO - Attempting to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 +2026-01-11 00:28:28,651 - __main__ - INFO - Attempt 1 for proving lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:28:28,651 - __main__ - INFO - Running the prover agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 (theorem_idx=176) with timeout: 600 seconds +2026-01-11 00:29:58,230 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:29:58,230 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + (a - b) ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + (a - b) ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 171.38989567756653 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-11 00:29:58,230 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p1 +2026-01-11 00:29:58,230 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:29:58,231 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p1 (theorem_idx=177) with timeout: 600 seconds +2026-01-11 00:30:10,354 - __main__ - INFO - Prover for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:30:10,354 - __main__ - INFO - Dumping proof search result: +theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 41 +SearchTimeInSecs: 310.90249967575073 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 0, 'total_queries': 40} + + + +2026-01-11 00:30:10,354 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p12 +2026-01-11 00:30:10,354 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:30:10,354 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p12 (theorem_idx=178) with timeout: 600 seconds +2026-01-11 00:31:45,573 - __main__ - INFO - Prover for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:31:45,573 - __main__ - INFO - Dumping proof search result: +theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 182.28779673576355 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 0, 'total_queries': 17} + + + +2026-01-11 00:31:45,574 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p20 +2026-01-11 00:31:45,574 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:31:45,574 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p20 (theorem_idx=179) with timeout: 600 seconds +2026-01-11 00:32:42,498 - __main__ - INFO - Prover for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:32:42,499 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 148.2076916694641 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 0, 'total_queries': 12} + + + +2026-01-11 00:32:42,499 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p6 +2026-01-11 00:32:42,499 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:32:42,499 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p6 (theorem_idx=180) with timeout: 600 seconds +2026-01-11 00:33:19,761 - __main__ - INFO - Prover for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:33:19,761 - __main__ - INFO - Dumping proof search result: +theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 56 +SearchTimeInSecs: 461.39722871780396 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 52, 'attempt_idx': 0, 'total_queries': 52} + + + +2026-01-11 00:33:19,762 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p21 +2026-01-11 00:33:19,762 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:33:19,762 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p21 (theorem_idx=181) with timeout: 600 seconds +2026-01-11 00:34:08,864 - __main__ - INFO - Prover for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:34:08,864 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 69.23165702819824 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-11 00:34:08,864 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p5 +2026-01-11 00:34:08,864 - __main__ - INFO - Attempt 1 for proving lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:34:08,864 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p5 (theorem_idx=182) with timeout: 600 seconds +2026-01-11 00:34:09,999 - __main__ - INFO - Prover for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:34:09,000 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 41 +SearchTimeInSecs: 226.0729832649231 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 0, 'total_queries': 40} + + + +2026-01-11 00:34:09,000 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p13 +2026-01-11 00:34:09,000 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:34:09,000 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p13 (theorem_idx=183) with timeout: 600 seconds +2026-01-11 00:34:45,028 - __main__ - INFO - Prover for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:34:45,028 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 29.30519199371338 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 0, 'total_queries': 4} + + + +2026-01-11 00:34:45,029 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p23 +2026-01-11 00:34:45,029 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:34:45,029 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p23 (theorem_idx=184) with timeout: 600 seconds +2026-01-11 00:35:28,552 - __main__ - INFO - Prover for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:35:28,553 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 37 +SearchTimeInSecs: 197.59340929985046 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 36, 'attempt_idx': 0, 'total_queries': 36} + + + +2026-01-11 00:35:28,553 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p5 +2026-01-11 00:35:28,553 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:35:28,553 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p5 (theorem_idx=185) with timeout: 600 seconds +2026-01-11 00:36:00,717 - __main__ - INFO - Prover for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:36:00,718 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 59.59089016914368 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-11 00:36:00,718 - __main__ - INFO - Attempting to prove lemma: amc12a_2008_p25 +2026-01-11 00:36:00,718 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:36:00,718 - __main__ - INFO - Running the prover agent for lemma: amc12a_2008_p25 (theorem_idx=186) with timeout: 600 seconds +2026-01-11 00:36:11,435 - __main__ - INFO - Prover for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:36:11,435 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 150.56210780143738 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 0, 'total_queries': 24} + + + +2026-01-11 00:36:11,436 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p6 +2026-01-11 00:36:11,436 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:36:11,436 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p6 (theorem_idx=187) with timeout: 600 seconds +2026-01-11 00:39:16,647 - __main__ - INFO - Prover for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:39:16,647 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 45 +SearchTimeInSecs: 284.37217712402344 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 45, 'attempt_idx': 0, 'total_queries': 45} + + + +2026-01-11 00:39:16,648 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p7 +2026-01-11 00:39:16,648 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:39:16,648 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p7 (theorem_idx=188) with timeout: 600 seconds +2026-01-11 00:39:33,766 - __main__ - INFO - Prover for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:39:33,766 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2008_p25 + (a b : ℕ → ℝ) + (h₀ : ∀ n, a (n + 1) = Real.sqrt 3 * a n - b n) + (h₁ : ∀ n, b (n + 1) = Real.sqrt 3 * b n + a n) + (h₂ : a 100 = 2) + (h₃ : b 100 = 4) : + a 1 + b 1 = 1 / (2^98) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2008_p25 + (a b : ℕ → ℝ) + (h₀ : ∀ n, a (n + 1) = Real.sqrt 3 * a n - b n) + (h₁ : ∀ n, b (n + 1) = Real.sqrt 3 * b n + a n) + (h₂ : a 100 = 2) + (h₃ : b 100 = 4) : + a 1 + b 1 = 1 / (2^98) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 191.0414605140686 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 0, 'total_queries': 16} + + + +2026-01-11 00:39:33,767 - __main__ - INFO - Attempting to prove lemma: amc12a_2019_p12 +2026-01-11 00:39:33,767 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:39:33,767 - __main__ - INFO - Running the prover agent for lemma: amc12a_2019_p12 (theorem_idx=189) with timeout: 600 seconds +2026-01-11 00:41:21,493 - __main__ - INFO - Prover for lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:41:21,493 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p5 + (A M C : ℕ) + (h₀ : A ≤ 9 ∧ M ≤ 9 ∧ C ≤ 9) + (h₁ : Nat.ofDigits 10 [0,1,C,M,A] + Nat.ofDigits 10 [2,1,C,M,A] = 123422) : + A + M + C = 14 := + +by +simp [ofDigits] at h₁ +-- first, extract the linear relation from the given equation +have h2 : 100 * A + 10 * M + C = 617 := by + have h1' := h₁ + ring_nf at h1' + linarith +-- use the bounds to determine each digit +have hA : A = 6 := by + linarith [h₀, h2] +have hM : M = 1 := by + linarith [h₀, h2] +have hC : C = 7 := by + linarith [h₀, h2] +-- conclude the desired sum +calc + A + M + C = 6 + 1 + 7 := by simp [hA, hM, hC] + _ = 14 := by norm_num + + +ProofFile: None +LemmaName: theorem amc12a_2003_p5 + (A M C : ℕ) + (h₀ : A ≤ 9 ∧ M ≤ 9 ∧ C ≤ 9) + (h₁ : Nat.ofDigits 10 [0,1,C,M,A] + Nat.ofDigits 10 [2,1,C,M,A] = 123422) : + A + M + C = 14 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 333.38418340682983 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 0, 'total_queries': 29} + + + +2026-01-11 00:41:21,494 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p10 +2026-01-11 00:41:21,494 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:41:21,494 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p10 (theorem_idx=190) with timeout: 600 seconds +2026-01-11 00:44:13,645 - __main__ - INFO - Prover for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:44:13,645 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 105 +SearchTimeInSecs: 457.1251120567322 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 92, 'attempt_idx': 0, 'total_queries': 92} + + + +2026-01-11 00:44:13,646 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p15 +2026-01-11 00:44:13,646 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:44:13,646 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p15 (theorem_idx=191) with timeout: 600 seconds +2026-01-11 00:49:16,795 - __main__ - INFO - Prover Agent for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:49:16,916 - __main__ - INFO - Failed to prove lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:49:16,916 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2009_p7 + +2026-01-11 00:49:16,917 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p25 +2026-01-11 00:49:16,917 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:49:16,917 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p25 (theorem_idx=192) with timeout: 600 seconds +2026-01-11 00:49:33,937 - __main__ - INFO - Prover Agent for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:49:34,059 - __main__ - INFO - Failed to prove lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:49:34,059 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2019_p12 + +2026-01-11 00:49:34,060 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p4 +2026-01-11 00:49:34,060 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:49:34,060 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p4 (theorem_idx=193) with timeout: 600 seconds +2026-01-11 00:50:57,197 - __main__ - INFO - Prover for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:50:57,198 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := + +by +simp [h₀] at * +apply? + + +ProofFile: None +LemmaName: theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 56.19588232040405 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-11 00:50:57,198 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p7 +2026-01-11 00:50:57,198 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:50:57,198 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p7 (theorem_idx=194) with timeout: 600 seconds +2026-01-11 00:51:21,671 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:51:21,797 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:51:21,797 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p10 + +2026-01-11 00:51:21,798 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p9 +2026-01-11 00:51:21,798 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:51:21,798 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p9 (theorem_idx=195) with timeout: 600 seconds +2026-01-11 00:52:13,621 - __main__ - INFO - Prover for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:52:13,621 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 63.2770209312439 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-11 00:52:13,622 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p12 +2026-01-11 00:52:13,622 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:52:13,622 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p12 (theorem_idx=196) with timeout: 600 seconds +2026-01-11 00:52:21,572 - __main__ - INFO - Prover for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:52:21,572 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 158.52668809890747 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-11 00:52:21,573 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p14 +2026-01-11 00:52:21,573 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:52:21,573 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p14 (theorem_idx=197) with timeout: 600 seconds +2026-01-11 00:52:45,513 - __main__ - INFO - Prover for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:52:45,514 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 66.20000982284546 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-11 00:52:45,514 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p18 +2026-01-11 00:52:45,514 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:52:45,514 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p18 (theorem_idx=198) with timeout: 600 seconds +2026-01-11 00:53:40,671 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:53:40,798 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:53:40,798 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2021_p18 + +2026-01-11 00:53:40,799 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p19 +2026-01-11 00:53:40,799 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:53:40,799 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p19 (theorem_idx=199) with timeout: 600 seconds +2026-01-11 00:54:13,827 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:54:13,953 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:54:13,953 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p15 + +2026-01-11 00:54:13,954 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p22 +2026-01-11 00:54:13,954 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:54:13,954 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p22 (theorem_idx=200) with timeout: 600 seconds +2026-01-11 00:54:38,485 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 00:54:38,611 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:54:38,611 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2021_p19 + +2026-01-11 00:54:38,612 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p25 +2026-01-11 00:54:38,612 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:54:38,612 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p25 (theorem_idx=201) with timeout: 600 seconds +2026-01-11 00:56:24,837 - __main__ - INFO - Prover for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:56:24,837 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 81.27530026435852 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-11 00:56:24,837 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p3 +2026-01-11 00:56:24,837 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:56:24,837 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p3 (theorem_idx=202) with timeout: 600 seconds +2026-01-11 00:57:59,178 - __main__ - INFO - Prover for lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:57:59,178 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p3 + (x y : ℕ) + (h₀ : x + y = 17402) + (h₁ : 10∣x) + (h₂ : x / 10 = y) : + ↑x - ↑y = (14238:ℤ) := + +by +rcases h₁ with ⟨k, hk⟩ +have hy : y = k := by + have : k = y := by + simpa [hk] using h₂ + exact this.symm +have hk_val : k = 1582 := by + have hcalc : 10 * k + k = 17402 := by + have : x + y = 17402 := h₀ + simpa [hk, hy] using this + have : 11 * k = 17402 := by + simpa [Nat.mul_add, Nat.add_mul, Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using hcalc + linarith +simp [hk, hy, hk_val] + + +ProofFile: None +LemmaName: theorem amc12a_2021_p3 + (x y : ℕ) + (h₀ : x + y = 17402) + (h₁ : 10∣x) + (h₂ : x / 10 = y) : + ↑x - ↑y = (14238:ℤ) := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 64.31891107559204 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 0, 'total_queries': 8} + + + +2026-01-11 00:57:59,178 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p8 +2026-01-11 00:57:59,179 - __main__ - INFO - Attempt 1 for proving lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:57:59,179 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p8 (theorem_idx=203) with timeout: 600 seconds +2026-01-11 00:59:01,097 - __main__ - INFO - Prover for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 00:59:01,097 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 44.816105127334595 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-11 00:59:01,098 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p4 +2026-01-11 00:59:01,098 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 00:59:01,098 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p4 (theorem_idx=204) with timeout: 600 seconds +2026-01-11 01:01:49,588 - __main__ - INFO - Prover for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:01:49,588 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 152.6956684589386 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 0, 'total_queries': 14} + + + +2026-01-11 01:01:49,588 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p7 +2026-01-11 01:01:49,588 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:01:49,589 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p7 (theorem_idx=205) with timeout: 600 seconds +2026-01-11 01:01:57,507 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:01:57,632 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:01:57,633 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2021_p22 + +2026-01-11 01:01:57,633 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p13 +2026-01-11 01:01:57,633 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:01:57,633 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p13 (theorem_idx=206) with timeout: 600 seconds +2026-01-11 01:02:13,796 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:02:13,929 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:02:13,929 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p12 + +2026-01-11 01:02:13,930 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p21 +2026-01-11 01:02:13,930 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:02:13,930 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p21 (theorem_idx=207) with timeout: 600 seconds +2026-01-11 01:02:21,754 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:02:21,877 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:02:21,877 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p14 + +2026-01-11 01:02:21,878 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p22 +2026-01-11 01:02:21,878 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:02:21,878 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p22 (theorem_idx=208) with timeout: 600 seconds +2026-01-11 01:03:01,540 - __main__ - INFO - Prover for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:03:01,541 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 21.58014678955078 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 0, 'total_queries': 3} + + + +2026-01-11 01:03:01,541 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p1 +2026-01-11 01:03:01,541 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:03:01,541 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p1 (theorem_idx=209) with timeout: 600 seconds +2026-01-11 01:03:55,655 - __main__ - INFO - Prover for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:03:55,656 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 90.84038829803467 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 0, 'total_queries': 8} + + + +2026-01-11 01:03:55,656 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p13 +2026-01-11 01:03:55,656 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:03:55,656 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p13 (theorem_idx=210) with timeout: 600 seconds +2026-01-11 01:04:59,535 - __main__ - INFO - Prover for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:04:59,535 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 40.8988893032074 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-11 01:04:59,536 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p18 +2026-01-11 01:04:59,536 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:04:59,536 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p18 (theorem_idx=211) with timeout: 600 seconds +2026-01-11 01:05:35,022 - __main__ - INFO - Prover for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:05:35,023 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 34 +SearchTimeInSecs: 193.5898416042328 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 34, 'attempt_idx': 0, 'total_queries': 34} + + + +2026-01-11 01:05:35,023 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p3 +2026-01-11 01:05:35,023 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:05:35,023 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p3 (theorem_idx=212) with timeout: 600 seconds +2026-01-11 01:06:21,374 - __main__ - INFO - Prover for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:06:21,374 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 176.64733123779297 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-11 01:06:21,375 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p4 +2026-01-11 01:06:21,375 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:06:21,375 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p4 (theorem_idx=213) with timeout: 600 seconds +2026-01-11 01:06:56,815 - __main__ - INFO - Prover for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:06:56,815 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 74.02672076225281 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 0, 'total_queries': 15} + + + +2026-01-11 01:06:56,816 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p9 +2026-01-11 01:06:56,816 - __main__ - INFO - Attempt 1 for proving lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:06:56,816 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p9 (theorem_idx=214) with timeout: 600 seconds +2026-01-11 01:08:29,383 - __main__ - INFO - Prover for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:08:29,383 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 113.43975853919983 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-11 01:08:29,383 - __main__ - INFO - Attempting to prove lemma: imo_1959_p1 +2026-01-11 01:08:29,383 - __main__ - INFO - Attempt 1 for proving lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:08:29,383 - __main__ - INFO - Running the prover agent for lemma: imo_1959_p1 (theorem_idx=215) with timeout: 600 seconds +2026-01-11 01:09:58,708 - __main__ - INFO - Prover for lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:09:58,708 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 48 +SearchTimeInSecs: 171.1635971069336 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 0, 'total_queries': 41} + + + +2026-01-11 01:09:58,709 - __main__ - INFO - Attempting to prove lemma: imo_1960_p2 +2026-01-11 01:09:58,709 - __main__ - INFO - Attempt 1 for proving lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:09:58,709 - __main__ - INFO - Running the prover agent for lemma: imo_1960_p2 (theorem_idx=216) with timeout: 600 seconds +2026-01-11 01:11:07,520 - __main__ - INFO - Prover for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:11:07,520 - __main__ - INFO - Dumping proof search result: +theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 148.45316696166992 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 0, 'total_queries': 16} + + + +2026-01-11 01:11:07,521 - __main__ - INFO - Attempting to prove lemma: imo_1962_p2 +2026-01-11 01:11:07,521 - __main__ - INFO - Attempt 1 for proving lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:11:07,521 - __main__ - INFO - Running the prover agent for lemma: imo_1962_p2 (theorem_idx=217) with timeout: 600 seconds +2026-01-11 01:11:12,135 - __main__ - INFO - Prover for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:11:12,136 - __main__ - INFO - Dumping proof search result: +theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 65.11540150642395 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 01:11:12,136 - __main__ - INFO - Attempting to prove lemma: imo_1963_p5 +2026-01-11 01:11:12,136 - __main__ - INFO - Attempt 1 for proving lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:11:12,136 - __main__ - INFO - Running the prover agent for lemma: imo_1963_p5 (theorem_idx=218) with timeout: 600 seconds +2026-01-11 01:11:49,746 - __main__ - INFO - Prover Agent for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:11:49,880 - __main__ - INFO - Failed to prove lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:11:49,880 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12b_2002_p7 + +2026-01-11 01:11:49,881 - __main__ - INFO - Attempting to prove lemma: imo_1964_p2 +2026-01-11 01:11:49,881 - __main__ - INFO - Attempt 1 for proving lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:11:49,881 - __main__ - INFO - Running the prover agent for lemma: imo_1964_p2 (theorem_idx=219) with timeout: 600 seconds +2026-01-11 01:12:20,512 - __main__ - INFO - Prover for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:12:20,512 - __main__ - INFO - Dumping proof search result: +theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 60.201977014541626 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 0, 'total_queries': 8} + + + +2026-01-11 01:12:20,513 - __main__ - INFO - Attempting to prove lemma: imo_1965_p2 +2026-01-11 01:12:20,513 - __main__ - INFO - Attempt 1 for proving lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:12:20,513 - __main__ - INFO - Running the prover agent for lemma: imo_1965_p2 (theorem_idx=220) with timeout: 600 seconds +2026-01-11 01:13:34,083 - __main__ - INFO - Prover for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:13:34,084 - __main__ - INFO - Dumping proof search result: +theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 132.22240042686462 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-11 01:13:34,084 - __main__ - INFO - Attempting to prove lemma: imo_1968_p5_1 +2026-01-11 01:13:34,084 - __main__ - INFO - Attempt 1 for proving lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:13:34,084 - __main__ - INFO - Running the prover agent for lemma: imo_1968_p5_1 (theorem_idx=221) with timeout: 600 seconds +2026-01-11 01:13:41,728 - __main__ - INFO - Prover for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:13:41,729 - __main__ - INFO - Dumping proof search result: +theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 57.146722078323364 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-11 01:13:41,729 - __main__ - INFO - Attempting to prove lemma: imo_1969_p2 +2026-01-11 01:13:41,729 - __main__ - INFO - Attempt 1 for proving lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:13:41,729 - __main__ - INFO - Running the prover agent for lemma: imo_1969_p2 (theorem_idx=222) with timeout: 600 seconds +2026-01-11 01:13:54,095 - __main__ - INFO - Prover for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:13:54,095 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := + +by +have hzero : z^2 + 2*z + 6 = 0 := by + -- expand the given equation and simplify + have := h₀ + field_simp [Complex.normSq, Complex.normSq_eq_conj_mul_self] at this + -- after simplification we obtain |z^2 + 2*z + 6|^2 = 0 + have hnorm : Complex.normSq (z^2 + 2*z + 6) = 0 := by + -- rewrite the left-hand side of the equality + convert this using 1 + ring + -- conclude that the polynomial itself is zero + exact Complex.normSq_eq_zero.mp hnorm +-- use the obtained quadratic equation to finish the goal +field_simp [hzero] at * +-- First derive the quadratic equation from the hypothesis `h₀` +have hzero' : z ^ 2 + 2 * z + 6 = 0 := by + -- use the given norm equality and simplify + have h₁ := h₀ + field_simp [Complex.normSq, Complex.normSq_eq_conj_mul_self] at h₁ + -- after simplification we obtain `|z^2 + 2*z + 6|^2 = 0` + have hnorm : Complex.normSq (z ^ 2 + 2 * z + 6) = 0 := by + convert h₁ using 1 + ring + -- conclude that the polynomial itself is zero + exact Complex.normSq_eq_zero.mp hnorm +-- Now use the quadratic relation to simplify the goal +field_simp [hzero'] at * +-- Re‑derive the quadratic equation from the norm hypothesis +have hzero' : z ^ 2 + 2 * z + 6 = 0 := by + have h₁ := h₀ + field_simp [Complex.normSq, Complex.normSq_eq_conj_mul_self] at h₁ + -- after simplification we obtain `|z^2 + 2*z + 6|^2 = 0` + have hnorm : Complex.normSq (z ^ 2 + 2 * z + 6) = 0 := by + convert h₁ using 1 + ring + exact Complex.normSq_eq_zero.mp hnorm +-- Use the quadratic relation to finish the goal +field_simp [hzero'] at * +have h2 : 6 / z = -(z + 2) := by + field_simp [hzero'] +calc + z + 6 / z = z + (-(z + 2)) := by + simpa [h2] + _ = -2 := by ring + + +ProofFile: None +LemmaName: theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 96 +SearchTimeInSecs: 517.5530941486359 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 0, 'total_queries': 100} + + + +2026-01-11 01:13:54,095 - __main__ - INFO - Attempting to prove lemma: imo_1974_p3 +2026-01-11 01:13:54,095 - __main__ - INFO - Attempt 1 for proving lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:13:54,095 - __main__ - INFO - Running the prover agent for lemma: imo_1974_p3 (theorem_idx=223) with timeout: 600 seconds +2026-01-11 01:14:32,882 - __main__ - INFO - Prover for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:14:32,882 - __main__ - INFO - Dumping proof search result: +theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 16.093788146972656 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 0, 'total_queries': 3} + + + +2026-01-11 01:14:32,883 - __main__ - INFO - Attempting to prove lemma: imo_1977_p6 +2026-01-11 01:14:32,883 - __main__ - INFO - Attempt 1 for proving lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:14:32,883 - __main__ - INFO - Running the prover agent for lemma: imo_1977_p6 (theorem_idx=224) with timeout: 600 seconds +2026-01-11 01:14:38,191 - __main__ - INFO - Prover for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:14:38,191 - __main__ - INFO - Dumping proof search result: +theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := + +by + + + +ProofFile: None +LemmaName: theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 48.96448802947998 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 0, 'total_queries': 9} + + + +2026-01-11 01:14:38,192 - __main__ - INFO - Attempting to prove lemma: imo_1981_p6 +2026-01-11 01:14:38,192 - __main__ - INFO - Attempt 1 for proving lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:14:38,192 - __main__ - INFO - Running the prover agent for lemma: imo_1981_p6 (theorem_idx=225) with timeout: 600 seconds +2026-01-11 01:15:50,920 - __main__ - INFO - Prover for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:15:50,920 - __main__ - INFO - Dumping proof search result: +theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := + +by + + + +ProofFile: None +LemmaName: theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 219.7882959842682 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 0, 'total_queries': 21} + + + +2026-01-11 01:15:50,921 - __main__ - INFO - Attempting to prove lemma: imo_1982_p1 +2026-01-11 01:15:50,921 - __main__ - INFO - Attempt 1 for proving lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:15:50,921 - __main__ - INFO - Running the prover agent for lemma: imo_1982_p1 (theorem_idx=226) with timeout: 600 seconds +2026-01-11 01:20:06,160 - __main__ - INFO - Prover for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:20:06,160 - __main__ - INFO - Dumping proof search result: +theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 47 +SearchTimeInSecs: 314.06144523620605 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 42, 'attempt_idx': 0, 'total_queries': 42} + + + +2026-01-11 01:20:06,160 - __main__ - INFO - Attempting to prove lemma: imo_1983_p6 +2026-01-11 01:20:06,160 - __main__ - INFO - Attempt 1 for proving lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:20:06,160 - __main__ - INFO - Running the prover agent for lemma: imo_1983_p6 (theorem_idx=227) with timeout: 600 seconds +2026-01-11 01:21:07,762 - __main__ - INFO - Prover for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:21:07,762 - __main__ - INFO - Dumping proof search result: +theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 53.93445634841919 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 0, 'total_queries': 5} + + + +2026-01-11 01:21:07,762 - __main__ - INFO - Attempting to prove lemma: imo_1984_p6 +2026-01-11 01:21:07,763 - __main__ - INFO - Attempt 1 for proving lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:21:07,763 - __main__ - INFO - Running the prover agent for lemma: imo_1984_p6 (theorem_idx=228) with timeout: 600 seconds +2026-01-11 01:22:08,911 - __main__ - INFO - Prover for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:22:08,911 - __main__ - INFO - Dumping proof search result: +theorem imo_1982_p1 + (f : ℕ → ℕ) + (h₀ : ∀ m n, (0 < m ∧ 0 < n) → f (m + n) - f m - f n = 0 ∨ f (m + n) - f m - f n = 1) + (h₁ : f 2 = 0) + (h₂ : 0 < f 3) + (h₃ : f 9999 = 3333) : + f 1982 = 660 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1982_p1 + (f : ℕ → ℕ) + (h₀ : ∀ m n, (0 < m ∧ 0 < n) → f (m + n) - f m - f n = 0 ∨ f (m + n) - f m - f n = 1) + (h₁ : f 2 = 0) + (h₂ : 0 < f 3) + (h₃ : f 9999 = 3333) : + f 1982 = 660 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 367.6856653690338 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 0, 'total_queries': 26} + + + +2026-01-11 01:22:08,911 - __main__ - INFO - Attempting to prove lemma: imo_1985_p6 +2026-01-11 01:22:08,912 - __main__ - INFO - Attempt 1 for proving lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:22:08,912 - __main__ - INFO - Running the prover agent for lemma: imo_1985_p6 (theorem_idx=229) with timeout: 600 seconds +2026-01-11 01:23:34,263 - __main__ - INFO - Prover Agent for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:23:34,403 - __main__ - INFO - Failed to prove lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:23:34,404 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1968_p5_1 + +2026-01-11 01:23:34,404 - __main__ - INFO - Attempting to prove lemma: imo_1992_p1 +2026-01-11 01:23:34,404 - __main__ - INFO - Attempt 1 for proving lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:23:34,404 - __main__ - INFO - Running the prover agent for lemma: imo_1992_p1 (theorem_idx=230) with timeout: 600 seconds +2026-01-11 01:24:32,964 - __main__ - INFO - Prover Agent for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:24:33,102 - __main__ - INFO - Failed to prove lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:24:33,102 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1977_p6 + +2026-01-11 01:24:33,103 - __main__ - INFO - Attempting to prove lemma: imo_1997_p5 +2026-01-11 01:24:33,103 - __main__ - INFO - Attempt 1 for proving lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:24:33,103 - __main__ - INFO - Running the prover agent for lemma: imo_1997_p5 (theorem_idx=231) with timeout: 600 seconds +2026-01-11 01:24:53,275 - __main__ - INFO - Prover for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:24:53,275 - __main__ - INFO - Dumping proof search result: +theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 68.71810412406921 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 0, 'total_queries': 11} + + + +2026-01-11 01:24:53,276 - __main__ - INFO - Attempting to prove lemma: imo_2001_p6 +2026-01-11 01:24:53,276 - __main__ - INFO - Attempt 1 for proving lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:24:53,276 - __main__ - INFO - Running the prover agent for lemma: imo_2001_p6 (theorem_idx=232) with timeout: 600 seconds +2026-01-11 01:25:11,587 - __main__ - INFO - Prover for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:25:11,587 - __main__ - INFO - Dumping proof search result: +theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 30.055957317352295 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 0, 'total_queries': 6} + + + +2026-01-11 01:25:11,588 - __main__ - INFO - Attempting to prove lemma: imo_2019_p1 +2026-01-11 01:25:11,588 - __main__ - INFO - Attempt 1 for proving lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:25:11,588 - __main__ - INFO - Running the prover agent for lemma: imo_2019_p1 (theorem_idx=233) with timeout: 600 seconds +2026-01-11 01:26:03,294 - __main__ - INFO - Prover for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:26:03,294 - __main__ - INFO - Dumping proof search result: +theorem imo_2019_p1 + (f : ℤ → ℤ) : + ((∀ a b, f (2 * a) + (2 * f b) = f (f (a + b))) ↔ (∀ z, f z = 0 \/ ∃ c, ∀ z, f z = 2 * z + c)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2019_p1 + (f : ℤ → ℤ) : + ((∀ a b, f (2 * a) + (2 * f b) = f (f (a + b))) ↔ (∀ z, f z = 0 \/ ∃ c, ∀ z, f z = 2 * z + c)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 32.35472869873047 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-11 01:26:03,294 - __main__ - INFO - Attempting to prove lemma: imosl_2007_algebra_p6 +2026-01-11 01:26:03,294 - __main__ - INFO - Attempt 1 for proving lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:26:03,294 - __main__ - INFO - Running the prover agent for lemma: imosl_2007_algebra_p6 (theorem_idx=234) with timeout: 600 seconds +2026-01-11 01:26:17,877 - __main__ - INFO - Prover for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:26:17,877 - __main__ - INFO - Dumping proof search result: +theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 68.65753507614136 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 01:26:17,878 - __main__ - INFO - Attempting to prove lemma: induction_11div10tonmn1ton +2026-01-11 01:26:17,878 - __main__ - INFO - Attempt 1 for proving lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:26:17,878 - __main__ - INFO - Running the prover agent for lemma: induction_11div10tonmn1ton (theorem_idx=235) with timeout: 600 seconds +2026-01-11 01:28:08,467 - __main__ - INFO - Prover for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:28:08,467 - __main__ - INFO - Dumping proof search result: +theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 98.82318210601807 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 0, 'total_queries': 10} + + + +2026-01-11 01:28:08,467 - __main__ - INFO - Attempting to prove lemma: induction_12dvd4expnp1p20 +2026-01-11 01:28:08,467 - __main__ - INFO - Attempt 1 for proving lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:28:08,468 - __main__ - INFO - Running the prover agent for lemma: induction_12dvd4expnp1p20 (theorem_idx=236) with timeout: 600 seconds +2026-01-11 01:28:21,931 - __main__ - INFO - Prover for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:28:21,931 - __main__ - INFO - Dumping proof search result: +theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := + +by + + + +ProofFile: None +LemmaName: theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 104.46788191795349 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 0, 'total_queries': 17} + + + +2026-01-11 01:28:21,932 - __main__ - INFO - Attempting to prove lemma: induction_1pxpownlt1pnx +2026-01-11 01:28:21,932 - __main__ - INFO - Attempt 1 for proving lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:28:21,932 - __main__ - INFO - Running the prover agent for lemma: induction_1pxpownlt1pnx (theorem_idx=237) with timeout: 600 seconds +2026-01-11 01:29:42,496 - __main__ - INFO - Prover for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:29:42,497 - __main__ - INFO - Dumping proof search result: +theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := + +by + + + +ProofFile: None +LemmaName: theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 61.21062231063843 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 0, 'total_queries': 7} + + + +2026-01-11 01:29:42,497 - __main__ - INFO - Attempting to prove lemma: induction_nfactltnexpnm1ngt3 +2026-01-11 01:29:42,497 - __main__ - INFO - Attempt 1 for proving lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:29:42,497 - __main__ - INFO - Running the prover agent for lemma: induction_nfactltnexpnm1ngt3 (theorem_idx=238) with timeout: 600 seconds +2026-01-11 01:31:07,919 - __main__ - INFO - Prover Agent for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:31:08,063 - __main__ - INFO - Failed to prove lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:31:08,063 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1984_p6 + +2026-01-11 01:31:08,064 - __main__ - INFO - Attempting to prove lemma: induction_pord1p1on2powklt5on2 +2026-01-11 01:31:08,064 - __main__ - INFO - Attempt 1 for proving lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:31:08,064 - __main__ - INFO - Running the prover agent for lemma: induction_pord1p1on2powklt5on2 (theorem_idx=239) with timeout: 600 seconds +2026-01-11 01:31:37,947 - __main__ - INFO - Prover for lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:31:37,947 - __main__ - INFO - Dumping proof search result: +theorem induction_12dvd4expnp1p20 + (n : ℕ) : + 12 ∣ 4^(n+1) + 20 := + +by +-- Simplify the modulo computations using `simp` +simp [Nat.pow_mod] at * +-- First show that `4 ^ (n + 1) % 12 = 4` +have hpow : (4 ^ (n + 1)) % 12 = 4 := by + -- Use induction on `n` + induction n with + | zero => + simp + | succ n ih => + -- `4 ^ (n.succ + 1) = 4 ^ (n + 2) = (4 ^ (n + 1)) * 4` + have : (4 ^ (n + 1)) % 12 = 4 := ih + calc + (4 ^ (n.succ + 1)) % 12 + = ((4 ^ (n + 1)) * 4) % 12 := by + simp [Nat.pow_succ] + _ = ((4 ^ (n + 1)) % 12 * 4 % 12) % 12 := by + simpa [Nat.mul_mod] + _ = (4 * 4 % 12) % 12 := by + simp [this] + _ = (16 % 12) % 12 := by norm_num + _ = 4 % 12 := by norm_num + _ = 4 := by norm_num +-- Now compute the remainder of the whole expression +have hmod : (4 ^ (n + 1) + 8) % 12 = 0 := by + calc + (4 ^ (n + 1) + 8) % 12 + = ((4 ^ (n + 1)) % 12 + 8 % 12) % 12 := by + simpa [Nat.add_mod] + _ = (4 + 8) % 12 := by + simp [hpow] + _ = 12 % 12 := by norm_num + _ = 0 := by norm_num +-- Convert the modular equality to a divisibility statement +exact Nat.dvd_of_mod_eq_zero hmod + + +ProofFile: None +LemmaName: theorem induction_12dvd4expnp1p20 + (n : ℕ) : + 12 ∣ 4^(n+1) + 20 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 196.1262505054474 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 0, 'total_queries': 19} + + + +2026-01-11 01:31:37,948 - __main__ - INFO - Attempting to prove lemma: induction_pprime_pdvdapowpma +2026-01-11 01:31:37,948 - __main__ - INFO - Attempt 1 for proving lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:31:37,948 - __main__ - INFO - Running the prover agent for lemma: induction_pprime_pdvdapowpma (theorem_idx=240) with timeout: 600 seconds +2026-01-11 01:32:00,854 - __main__ - INFO - Prover for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:32:00,854 - __main__ - INFO - Dumping proof search result: +theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := + +by + + + +ProofFile: None +LemmaName: theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 7.595085382461548 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 0, 'total_queries': 2} + + + +2026-01-11 01:32:00,855 - __main__ - INFO - Attempting to prove lemma: induction_prod1p1onk3le3m1onn +2026-01-11 01:32:00,855 - __main__ - INFO - Attempt 1 for proving lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:32:00,855 - __main__ - INFO - Running the prover agent for lemma: induction_prod1p1onk3le3m1onn (theorem_idx=241) with timeout: 600 seconds +2026-01-11 01:32:09,003 - __main__ - INFO - Prover Agent for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:32:09,170 - __main__ - INFO - Failed to prove lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:32:09,170 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1985_p6 + +2026-01-11 01:32:09,171 - __main__ - INFO - Attempting to prove lemma: induction_sumkexp3eqsumksq +2026-01-11 01:32:09,171 - __main__ - INFO - Attempt 1 for proving lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:32:09,171 - __main__ - INFO - Running the prover agent for lemma: induction_sumkexp3eqsumksq (theorem_idx=242) with timeout: 600 seconds +2026-01-11 01:34:15,226 - __main__ - INFO - Prover for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:34:15,227 - __main__ - INFO - Dumping proof search result: +theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 112.64059591293335 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 0, 'total_queries': 18} + + + +2026-01-11 01:35:22,809 - __main__ - INFO - Prover for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:35:22,810 - __main__ - INFO - Dumping proof search result: +theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 242.49673795700073 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 0, 'total_queries': 22} + + + +2026-01-11 01:37:40,444 - __main__ - INFO - Prover for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:37:40,445 - __main__ - INFO - Dumping proof search result: +theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := + +by + + + +ProofFile: None +LemmaName: theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 55 +SearchTimeInSecs: 327.5357758998871 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 55, 'attempt_idx': 0, 'total_queries': 55} + + + +2026-01-11 01:39:42,676 - __main__ - INFO - Prover Agent for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:39:42,835 - __main__ - INFO - Failed to prove lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:42,835 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: induction_nfactltnexpnm1ngt3 + +2026-01-11 01:39:42,863 - __main__ - INFO - Reloaded checkpoint info for attempt 2 +2026-01-11 01:39:42,981 - __main__ - INFO - Reloaded proof results for attempt 2 +2026-01-11 01:39:42,981 - __main__ - INFO - Getting all lemmas in file: data/test/miniF2F-lean4/MiniF2F/Test.lean with timeout: 3000 seconds +2026-01-11 01:39:43,045 - __main__ - INFO - Discovered 244 lemmas +2026-01-11 01:39:43,046 - __main__ - INFO - Lemma names: ['mathd_algebra_478', 'numbertheory_4x3m7y3neq2003', 'aime_1983_p1', 'amc12_2001_p5', 'mathd_algebra_141', 'mathd_numbertheory_3', 'imo_1969_p2', 'mathd_algebra_44', 'mathd_algebra_209', 'mathd_numbertheory_1124'] ... ['aime_1989_p8', 'mathd_numbertheory_296', 'mathd_algebra_142', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'mathd_algebra_400', 'aime_1995_p7', 'mathd_numbertheory_185', 'mathd_algebra_441', 'mathd_numbertheory_582', 'mathd_algebra_338'] +2026-01-11 01:39:43,077 - __main__ - INFO - Discovered 243 lemmas to prove in data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:43,077 - __main__ - INFO - Lemmas to prove in file data/test/miniF2F-lean4/MiniF2F/Test.lean: +['aime_1983_p2', 'aime_1989_p8', 'algebra_sqineq_at2malt1', 'amc12a_2002_p6', 'amc12a_2013_p4', 'amc12a_2021_p9', 'amc12b_2002_p19', 'amc12b_2002_p2', 'amc12b_2020_p2', 'amc12b_2020_p6', 'mathd_algebra_125', 'mathd_algebra_129', 'mathd_algebra_137', 'mathd_algebra_139', 'mathd_algebra_141', 'mathd_algebra_142', 'mathd_algebra_143', 'mathd_algebra_148', 'mathd_algebra_158', 'mathd_algebra_160', 'mathd_algebra_171', 'mathd_algebra_176', 'mathd_algebra_24', 'mathd_algebra_246', 'mathd_algebra_263', 'mathd_algebra_270', 'mathd_algebra_296', 'mathd_algebra_302', 'mathd_algebra_304', 'mathd_algebra_314', 'mathd_algebra_329', 'mathd_algebra_33', 'mathd_algebra_346', 'mathd_algebra_354', 'mathd_algebra_359', 'mathd_algebra_388', 'mathd_algebra_400', 'mathd_algebra_412', 'mathd_algebra_419', 'mathd_algebra_432', 'mathd_algebra_44', 'mathd_algebra_440', 'mathd_algebra_441', 'mathd_algebra_478', 'mathd_algebra_513', 'mathd_algebra_76', 'mathd_algebra_80', 'mathd_numbertheory_12', 'mathd_numbertheory_127', 'mathd_numbertheory_135', 'mathd_numbertheory_150', 'mathd_numbertheory_175', 'mathd_numbertheory_185', 'mathd_numbertheory_207', 'mathd_numbertheory_212', 'mathd_numbertheory_229', 'mathd_numbertheory_235', 'mathd_numbertheory_237', 'mathd_numbertheory_239', 'mathd_numbertheory_247', 'mathd_numbertheory_254', 'mathd_numbertheory_299', 'mathd_numbertheory_3', 'mathd_numbertheory_341', 'mathd_numbertheory_342', 'mathd_numbertheory_343', 'mathd_numbertheory_345', 'mathd_numbertheory_517', 'mathd_numbertheory_551', 'mathd_numbertheory_66', 'mathd_numbertheory_728', 'mathd_numbertheory_769', 'mathd_numbertheory_85', 'mathd_algebra_107', 'mathd_algebra_113', 'mathd_algebra_114', 'mathd_algebra_153', 'mathd_algebra_156', 'mathd_algebra_17', 'mathd_algebra_170', 'mathd_algebra_184', 'mathd_algebra_188', 'mathd_algebra_196', 'mathd_algebra_208', 'mathd_algebra_209', 'mathd_algebra_215', 'mathd_algebra_275', 'mathd_algebra_276', 'mathd_algebra_288', 'mathd_algebra_289', 'mathd_algebra_293', 'mathd_algebra_313', 'mathd_algebra_320', 'mathd_algebra_332', 'mathd_algebra_338', 'mathd_algebra_342', 'mathd_algebra_362', 'mathd_algebra_392', 'mathd_algebra_398', 'mathd_algebra_427', 'mathd_algebra_452', 'mathd_algebra_459', 'mathd_algebra_484', 'mathd_algebra_487', 'mathd_algebra_598', 'mathd_algebra_756', 'mathd_numbertheory_100', 'mathd_numbertheory_1124', 'mathd_numbertheory_222', 'mathd_numbertheory_227', 'mathd_numbertheory_233', 'mathd_numbertheory_234', 'mathd_numbertheory_277', 'mathd_numbertheory_293', 'mathd_numbertheory_296', 'mathd_numbertheory_314', 'mathd_numbertheory_320', 'mathd_numbertheory_321', 'mathd_numbertheory_328', 'mathd_numbertheory_34', 'mathd_numbertheory_353', 'mathd_numbertheory_427', 'mathd_numbertheory_430', 'mathd_numbertheory_435', 'mathd_numbertheory_447', 'mathd_numbertheory_451', 'mathd_numbertheory_457', 'mathd_numbertheory_483', 'mathd_numbertheory_495', 'mathd_numbertheory_5', 'mathd_numbertheory_521', 'mathd_numbertheory_541', 'mathd_numbertheory_552', 'mathd_numbertheory_559', 'mathd_numbertheory_582', 'mathd_numbertheory_618', 'mathd_numbertheory_711', 'mathd_numbertheory_764', 'mathd_numbertheory_765', 'mathd_numbertheory_99', 'numbertheory_2pownm1prime_nprime', 'numbertheory_3pow2pownm1mod2pownp3eq2pownp2', 'numbertheory_4x3m7y3neq2003', 'numbertheory_aoddbdiv4asqpbsqmod8eq1', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown', 'numbertheory_x5neqy2p4', 'aime_1983_p1', 'aime_1983_p3', 'aime_1984_p1', 'aime_1984_p7', 'aime_1987_p5', 'aime_1988_p8', 'aime_1990_p15', 'aime_1990_p4', 'aime_1991_p9', 'aime_1994_p3', 'aime_1995_p7', 'aime_1997_p9', 'aime_1999_p11', 'algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7', 'algebra_9onxpypzleqsum2onxpy', 'algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2', 'algebra_absapbon1pabsapbleqsumabsaon1pabsa', 'algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1', 'algebra_amgm_sum1toneqn_prod1tonleq1', 'algebra_amgm_sumasqdivbgeqsuma', 'algebra_apbmpcneq0_aeq0anbeq0anceq0', 'algebra_apbon2pownleqapownpbpowon2', 'algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3', 'algebra_bleqa_apbon2msqrtableqambsqon8b', 'algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778', 'algebra_ineq_nto1onlt2m1on', 'algebra_others_exirrpowirrrat', 'algebra_sqineq_unitcircatbpabsamblt1', 'algebra_sqineq_unitcircatbpamblt1', 'algebra_sum1onsqrt2to1onsqrt10000lt198', 'amc12_2000_p1', 'amc12_2000_p12', 'amc12_2000_p20', 'amc12_2000_p6', 'amc12_2001_p21', 'amc12_2001_p5', 'amc12a_2002_p13', 'amc12a_2003_p23', 'amc12a_2003_p5', 'amc12a_2008_p25', 'amc12a_2009_p6', 'amc12a_2009_p7', 'amc12a_2019_p12', 'amc12a_2020_p10', 'amc12a_2020_p15', 'amc12a_2020_p25', 'amc12a_2020_p4', 'amc12a_2020_p7', 'amc12a_2020_p9', 'amc12a_2021_p12', 'amc12a_2021_p14', 'amc12a_2021_p18', 'amc12a_2021_p19', 'amc12a_2021_p22', 'amc12a_2021_p25', 'amc12a_2021_p3', 'amc12a_2021_p8', 'amc12b_2002_p4', 'amc12b_2002_p7', 'amc12b_2020_p13', 'amc12b_2020_p21', 'amc12b_2020_p22', 'amc12b_2021_p1', 'amc12b_2021_p13', 'amc12b_2021_p18', 'amc12b_2021_p3', 'amc12b_2021_p4', 'amc12b_2021_p9', 'imo_1959_p1', 'imo_1960_p2', 'imo_1962_p2', 'imo_1963_p5', 'imo_1964_p2', 'imo_1965_p2', 'imo_1968_p5_1', 'imo_1969_p2', 'imo_1974_p3', 'imo_1977_p6', 'imo_1981_p6', 'imo_1982_p1', 'imo_1983_p6', 'imo_1984_p6', 'imo_1985_p6', 'imo_1992_p1', 'imo_1997_p5', 'imo_2001_p6', 'imo_2019_p1', 'imosl_2007_algebra_p6', 'induction_11div10tonmn1ton', 'induction_12dvd4expnp1p20', 'induction_1pxpownlt1pnx', 'induction_nfactltnexpnm1ngt3', 'induction_pord1p1on2powklt5on2', 'induction_pprime_pdvdapowpma', 'induction_prod1p1onk3le3m1onn', 'induction_sumkexp3eqsumksq'] +2026-01-11 01:39:43,077 - __main__ - INFO - Executing 243 theorems in parallel using 4 workers +2026-01-11 01:39:43,123 - __main__ - INFO - Attempting to prove lemma: aime_1983_p2 +2026-01-11 01:39:43,124 - __main__ - INFO - Attempt 2 for proving lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:43,124 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p2 (theorem_idx=0) with timeout: 600 seconds +2026-01-11 01:39:43,128 - __main__ - INFO - Attempting to prove lemma: aime_1989_p8 +2026-01-11 01:39:43,129 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,131 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_at2malt1 +2026-01-11 01:39:43,132 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,136 - __main__ - INFO - Attempting to prove lemma: amc12a_2013_p4 +2026-01-11 01:39:43,136 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p6 +2026-01-11 01:39:43,137 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,137 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,139 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p9 +2026-01-11 01:39:43,139 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,143 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p19 +2026-01-11 01:39:43,143 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,146 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p2 +2026-01-11 01:39:43,146 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,148 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p2 +2026-01-11 01:39:43,148 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,150 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p6 +2026-01-11 01:39:43,150 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,152 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_125 +2026-01-11 01:39:43,152 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,154 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_129 +2026-01-11 01:39:43,154 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,155 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_137 +2026-01-11 01:39:43,156 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,157 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_139 +2026-01-11 01:39:43,157 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,159 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_141 +2026-01-11 01:39:43,159 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:43,159 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_141 (theorem_idx=14) with timeout: 600 seconds +2026-01-11 01:39:43,160 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_142 +2026-01-11 01:39:43,160 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,162 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_143 +2026-01-11 01:39:43,162 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,164 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_148 +2026-01-11 01:39:43,164 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,166 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_158 +2026-01-11 01:39:43,166 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:43,166 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_158 (theorem_idx=18) with timeout: 600 seconds +2026-01-11 01:39:43,167 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_160 +2026-01-11 01:39:43,167 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,170 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_171 +2026-01-11 01:39:43,170 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,172 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_176 +2026-01-11 01:39:43,172 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,175 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_24 +2026-01-11 01:39:43,175 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:39:43,177 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_246 +2026-01-11 01:39:43,178 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:43,178 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_246 (theorem_idx=23) with timeout: 600 seconds +2026-01-11 01:39:58,979 - __main__ - INFO - Prover for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:39:58,979 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 9.324727535247803 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 1, 'total_queries': 18} + + + +2026-01-11 01:39:58,980 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_263 +2026-01-11 01:39:58,980 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:39:58,980 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_263 (theorem_idx=24) with timeout: 600 seconds +2026-01-11 01:40:25,564 - __main__ - INFO - Prover for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:40:25,564 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 14.070523977279663 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 1, 'total_queries': 10} + + + +2026-01-11 01:40:25,566 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_270 +2026-01-11 01:40:25,566 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:40:25,566 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_270 (theorem_idx=25) with timeout: 600 seconds +2026-01-11 01:41:02,144 - __main__ - INFO - Prover for lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:41:02,144 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 15.065742015838623 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 1, 'total_queries': 60} + + + +2026-01-11 01:41:02,146 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_296 +2026-01-11 01:41:02,146 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:02,149 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_302 +2026-01-11 01:41:02,149 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:02,151 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_304 +2026-01-11 01:41:02,152 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:02,154 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_314 +2026-01-11 01:41:02,154 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:02,157 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_329 +2026-01-11 01:41:02,157 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:02,160 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_33 +2026-01-11 01:41:02,160 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:41:02,160 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_33 (theorem_idx=31) with timeout: 600 seconds +2026-01-11 01:41:17,946 - __main__ - INFO - Prover for lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:41:17,946 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 69.57757878303528 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 1, 'total_queries': 27} + + + +2026-01-11 01:41:17,948 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_346 +2026-01-11 01:41:17,948 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,951 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_354 +2026-01-11 01:41:17,951 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,954 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_359 +2026-01-11 01:41:17,954 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,957 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_388 +2026-01-11 01:41:17,957 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,959 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_400 +2026-01-11 01:41:17,959 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,962 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_412 +2026-01-11 01:41:17,962 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,964 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_419 +2026-01-11 01:41:17,964 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,966 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_432 +2026-01-11 01:41:17,966 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,968 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_44 +2026-01-11 01:41:17,968 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:17,970 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_440 +2026-01-11 01:41:17,970 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:41:17,970 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_440 (theorem_idx=41) with timeout: 600 seconds +2026-01-11 01:41:50,515 - __main__ - INFO - Prover for lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:41:50,515 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_246 + (a b : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = a * x^4 - b * x^2 + x + 5) + (h₂ : f (-3) = 2) : + f 3 = 8 := + +by +have h' : 81 * a - 9 * b = 0 := by + have h₀' := h₂ + simp [h₀] at h₀' + linarith +simp [h₀, h'] +norm_num [h'] +simp [h', mul_comm, mul_left_comm, mul_assoc, add_comm, add_left_comm, add_assoc] at * +simp [h'] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_246 + (a b : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = a * x^4 - b * x^2 + x + 5) + (h₂ : f (-3) = 2) : + f 3 = 8 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 37 +SearchTimeInSecs: 101.04377579689026 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 1, 'total_queries': 44} + + + +2026-01-11 01:41:50,516 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_441 +2026-01-11 01:41:50,517 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:50,520 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_478 +2026-01-11 01:41:50,520 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:50,523 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_513 +2026-01-11 01:41:50,523 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:50,525 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_76 +2026-01-11 01:41:50,525 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:41:50,528 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_80 +2026-01-11 01:41:50,528 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:41:50,528 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_80 (theorem_idx=46) with timeout: 600 seconds +2026-01-11 01:42:11,466 - __main__ - INFO - Prover for lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:42:11,466 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_33 + (x y z : ℝ) + (h₀ : x ≠ 0) + (h₁ : 2 * x = 5 * y) + (h₂ : 7 * y = 10 * z) : + z / x = 7 / 25 := + +by +-- Rewrite the equalities into division form and simplify +have hy : y = 2 * x / 5 := by + field_simp [h₁] +have hz : z = 7 * y / 10 := by + field_simp [h₂] +simp [hy, hz, h₀] +field_simp [h₀] +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_33 + (x y z : ℝ) + (h₀ : x ≠ 0) + (h₁ : 2 * x = 5 * y) + (h₂ : 7 * y = 10 * z) : + z / x = 7 / 25 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 56.66706347465515 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 1, 'total_queries': 47} + + + +2026-01-11 01:42:11,468 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_12 +2026-01-11 01:42:11,468 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:11,471 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_127 +2026-01-11 01:42:11,471 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:11,473 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_135 +2026-01-11 01:42:11,473 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:11,476 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_150 +2026-01-11 01:42:11,476 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:42:11,476 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_150 (theorem_idx=50) with timeout: 600 seconds +2026-01-11 01:42:22,707 - __main__ - INFO - Prover for lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:42:22,708 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 46.720688343048096 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 1, 'total_queries': 39} + + + +2026-01-11 01:42:22,710 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_175 +2026-01-11 01:42:22,710 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,712 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_185 +2026-01-11 01:42:22,712 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,715 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_207 +2026-01-11 01:42:22,715 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,718 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_212 +2026-01-11 01:42:22,718 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,721 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_229 +2026-01-11 01:42:22,721 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,723 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_235 +2026-01-11 01:42:22,723 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,725 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_237 +2026-01-11 01:42:22,725 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,727 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_239 +2026-01-11 01:42:22,727 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:22,729 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_247 +2026-01-11 01:42:22,729 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:42:22,729 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_247 (theorem_idx=59) with timeout: 600 seconds +2026-01-11 01:42:30,364 - __main__ - INFO - Prover for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:42:30,364 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 28.530556678771973 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 12} + + + +2026-01-11 01:42:30,366 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_254 +2026-01-11 01:42:30,366 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,369 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_299 +2026-01-11 01:42:30,369 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,372 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_3 +2026-01-11 01:42:30,372 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,375 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_341 +2026-01-11 01:42:30,375 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,378 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_342 +2026-01-11 01:42:30,378 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,380 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_343 +2026-01-11 01:42:30,380 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,382 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_345 +2026-01-11 01:42:30,382 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,384 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_517 +2026-01-11 01:42:30,385 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,387 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_551 +2026-01-11 01:42:30,387 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,389 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_66 +2026-01-11 01:42:30,389 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,391 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_728 +2026-01-11 01:42:30,391 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,392 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_769 +2026-01-11 01:42:30,392 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,394 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_85 +2026-01-11 01:42:30,394 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:42:30,395 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_107 +2026-01-11 01:42:30,395 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:42:30,395 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_107 (theorem_idx=73) with timeout: 600 seconds +2026-01-11 01:43:04,447 - __main__ - INFO - Prover for lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:43:04,447 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 22.055283069610596 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 1, 'total_queries': 19} + + + +2026-01-11 01:43:04,448 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_113 +2026-01-11 01:43:04,449 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:43:04,449 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_113 (theorem_idx=74) with timeout: 600 seconds +2026-01-11 01:43:15,065 - __main__ - INFO - Prover for lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:43:15,065 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 40.324326038360596 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 1, 'total_queries': 29} + + + +2026-01-11 01:43:15,067 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_114 +2026-01-11 01:43:15,067 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:43:15,067 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_114 (theorem_idx=75) with timeout: 600 seconds +2026-01-11 01:43:58,187 - __main__ - INFO - Prover for lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:43:58,187 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_113 + (x : ℝ) : + x^2 - 14 * x + 3 ≥ 7^2 - 14 * 7 + 3 := + +by +-- Rewrite the goal as a completed square and use non‑negativity +calc + x ^ 2 - 14 * x + 3 + = (x - 7)^2 - 46 := by ring + _ ≥ -46 := by + -- `(x - 7)^2 - 46 ≥ -46` is equivalent to `0 ≤ (x - 7)^2` + have h : 0 ≤ (x - 7)^2 := pow_two_nonneg (x - 7) + simpa [sub_eq, add_comm, add_left_comm, add_assoc] using h + _ = 7 ^ 2 - 14 * 7 + 3 := by ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_113 + (x : ℝ) : + x^2 - 14 * x + 3 ≥ 7^2 - 14 * 7 + 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 27.55092740058899 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 1, 'total_queries': 43} + + + +2026-01-11 01:43:58,189 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_153 +2026-01-11 01:43:58,189 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:43:58,192 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_156 +2026-01-11 01:43:58,192 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:43:58,192 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_156 (theorem_idx=77) with timeout: 600 seconds +2026-01-11 01:45:14,019 - __main__ - INFO - Prover for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:45:14,019 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 304.19815587997437 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 54, 'attempt_idx': 1, 'total_queries': 83} + + + +2026-01-11 01:45:14,021 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_17 +2026-01-11 01:45:14,021 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:45:14,021 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_17 (theorem_idx=78) with timeout: 600 seconds +2026-01-11 01:46:50,134 - __main__ - INFO - Prover for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:46:50,134 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 71 +SearchTimeInSecs: 196.29301285743713 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 60, 'attempt_idx': 1, 'total_queries': 123} + + + +2026-01-11 01:46:50,136 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_170 +2026-01-11 01:46:50,136 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:46:50,137 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_170 (theorem_idx=79) with timeout: 600 seconds +2026-01-11 01:47:28,741 - __main__ - INFO - Prover for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:47:28,741 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 118.70282769203186 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 55} + + + +2026-01-11 01:47:28,743 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_184 +2026-01-11 01:47:28,743 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:47:28,743 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_184 (theorem_idx=80) with timeout: 600 seconds +2026-01-11 01:47:31,962 - __main__ - INFO - Prover for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:47:31,962 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 294.8728380203247 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 23, 'attempt_idx': 1, 'total_queries': 38} + + + +2026-01-11 01:47:31,964 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_188 +2026-01-11 01:47:31,964 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:47:31,967 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_196 +2026-01-11 01:47:31,967 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:47:31,967 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_196 (theorem_idx=82) with timeout: 600 seconds +2026-01-11 01:49:24,500 - __main__ - INFO - Prover for lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:49:24,500 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 92.56320643424988 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 1, 'total_queries': 22} + + + +2026-01-11 01:49:24,503 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_208 +2026-01-11 01:49:24,503 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:49:24,503 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_208 (theorem_idx=83) with timeout: 600 seconds +2026-01-11 01:50:22,695 - __main__ - INFO - Prover for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:50:22,695 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 49.164029121398926 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 25} + + + +2026-01-11 01:50:22,697 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_209 +2026-01-11 01:50:22,697 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:50:22,700 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_215 +2026-01-11 01:50:22,700 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:50:22,700 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_215 (theorem_idx=85) with timeout: 600 seconds +2026-01-11 01:50:27,040 - __main__ - INFO - Prover for lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:50:27,040 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_170 + (S : Finset ℤ) + (h₀ : ∀ (n : ℤ), n ∈ S ↔ abs (n - 2) ≤ 5 + 6 / 10) : + S.card = 11 := + +by +norm_num +have hmem : ∀ n : ℤ, n ∈ S ↔ |n - 2| ≤ (5 : ℤ) := by + intro n + simpa using h₀ n +-- We prove that `S` is the integer interval `[-3,7]` +have hS : S = Finset.Icc (-3 : ℤ) 7 := by + ext n + constructor + · intro hn + -- Use the characterization `hmem` + have hle : |n - 2| ≤ (5 : ℤ) := (hmem n).mp hn + -- Convert the absolute value inequality to bounds on `n` + rcases abs_le.mp hle with ⟨hneg, hpos⟩ + -- From `n - 2 ≤ 5` we get `n ≤ 7` + have hnle : n ≤ 7 := by linarith + -- From `-(n - 2) ≤ 5` we get `-3 ≤ n` + have hnl : -3 ≤ n := by linarith + exact (Finset.mem_Icc).mpr ⟨hnl, hnle⟩ + · intro hn + -- Convert the bounds back to the absolute value inequality + have hbound : -3 ≤ n ∧ n ≤ 7 := (Finset.mem_Icc).mp hn + rcases hbound with ⟨hneg, hpos⟩ + have hpos' : n - 2 ≤ 5 := by linarith + have hneg' : -5 ≤ n - 2 := by linarith + have hle : |n - 2| ≤ (5 : ℤ) := abs_le.mpr ⟨hneg', hpos'⟩ + exact (hmem n).mpr hle +-- Now use the cardinality of a finite interval +simpa [hS] using Finset.card_Icc (a:=(-3 : ℤ)) (b:=7) + + +ProofFile: None +LemmaName: theorem mathd_algebra_170 + (S : Finset ℤ) + (h₀ : ∀ (n : ℤ), n ∈ S ↔ abs (n - 2) ≤ 5 + 6 / 10) : + S.card = 11 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 197.14386749267578 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 1, 'total_queries': 49} + + + +2026-01-11 01:50:27,042 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_275 +2026-01-11 01:50:27,042 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:50:27,042 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_275 (theorem_idx=86) with timeout: 600 seconds +2026-01-11 01:51:00,122 - __main__ - INFO - Prover for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:51:00,123 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 28 +SearchTimeInSecs: 200.35814261436462 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 1, 'total_queries': 92} + + + +2026-01-11 01:51:00,126 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_276 +2026-01-11 01:51:00,126 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:51:00,126 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_276 (theorem_idx=87) with timeout: 600 seconds +2026-01-11 01:52:55,435 - __main__ - INFO - Prover for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:52:55,435 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 141.95227646827698 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 1, 'total_queries': 33} + + + +2026-01-11 01:52:55,437 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_288 +2026-01-11 01:52:55,437 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:52:55,437 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_288 (theorem_idx=88) with timeout: 600 seconds +2026-01-11 01:53:58,373 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 01:53:58,531 - __main__ - INFO - Failed to prove lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:53:58,531 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_156 + +2026-01-11 01:53:58,533 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_289 +2026-01-11 01:53:58,533 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:53:58,536 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_293 +2026-01-11 01:53:58,536 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:53:58,539 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_313 +2026-01-11 01:53:58,539 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:53:58,539 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_313 (theorem_idx=91) with timeout: 600 seconds +2026-01-11 01:55:11,497 - __main__ - INFO - Prover for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:55:11,498 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_288 + (x y : ℝ) + (n : NNReal) + (h₀ : x < 0 ∧ y < 0) + (h₁ : abs y = 6) + (h₂ : Real.sqrt ((x - 8)^2 + (y - 3)^2) = 15) + (h₃ : Real.sqrt (x^2 + y^2) = Real.sqrt n) : + n = 52 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_288 + (x y : ℝ) + (n : NNReal) + (h₀ : x < 0 ∧ y < 0) + (h₁ : abs y = 6) + (h₂ : Real.sqrt ((x - 8)^2 + (y - 3)^2) = 15) + (h₃ : Real.sqrt (x^2 + y^2) = Real.sqrt n) : + n = 52 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 112.47085666656494 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 27} + + + +2026-01-11 01:55:11,499 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_320 +2026-01-11 01:55:11,500 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:55:11,500 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_320 (theorem_idx=92) with timeout: 600 seconds +2026-01-11 01:55:11,916 - __main__ - INFO - Prover for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:55:11,916 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 44 +SearchTimeInSecs: 237.3851227760315 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 1, 'total_queries': 58} + + + +2026-01-11 01:55:11,918 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_332 +2026-01-11 01:55:11,918 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:55:11,918 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_332 (theorem_idx=93) with timeout: 600 seconds +2026-01-11 01:55:46,462 - __main__ - INFO - Prover for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:55:46,462 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 48 +SearchTimeInSecs: 306.4146647453308 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 48, 'attempt_idx': 1, 'total_queries': 76} + + + +2026-01-11 01:55:46,465 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_338 +2026-01-11 01:55:46,465 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:55:46,468 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_342 +2026-01-11 01:55:46,468 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:55:46,470 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_362 +2026-01-11 01:55:46,470 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:55:46,471 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_362 (theorem_idx=96) with timeout: 600 seconds +2026-01-11 01:56:02,369 - __main__ - INFO - Prover for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:56:02,369 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 106.88887882232666 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 23, 'attempt_idx': 1, 'total_queries': 75} + + + +2026-01-11 01:56:02,371 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_392 +2026-01-11 01:56:02,371 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:56:02,371 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_392 (theorem_idx=97) with timeout: 600 seconds +2026-01-11 01:56:57,611 - __main__ - INFO - Prover for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:56:57,611 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 86.78467965126038 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 1, 'total_queries': 38} + + + +2026-01-11 01:56:57,613 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_398 +2026-01-11 01:56:57,613 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:56:57,616 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_427 +2026-01-11 01:56:57,616 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:56:57,619 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_452 +2026-01-11 01:56:57,619 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:56:57,619 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_452 (theorem_idx=100) with timeout: 600 seconds +2026-01-11 01:57:32,118 - __main__ - INFO - Prover for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:57:32,118 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 77.54823708534241 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 1, 'total_queries': 38} + + + +2026-01-11 01:57:32,120 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_459 +2026-01-11 01:57:32,120 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 01:57:32,123 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_484 +2026-01-11 01:57:32,123 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:57:32,123 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_484 (theorem_idx=102) with timeout: 600 seconds +2026-01-11 01:58:01,218 - __main__ - INFO - Prover for lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:58:01,218 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_484 : + Real.log 27 / Real.log 3 = 3 := + +by + have hpos : (0 : ℝ) < 3 := by norm_num + have hlog : Real.log (3 ^ 3) = 3 * Real.log 3 := by + simpa using Real.log_pow 3 3 hpos + -- rewrite the goal using hlog + calc + Real.log 27 / Real.log 3 + = Real.log (3 ^ 3) / Real.log 3 := by + -- 27 = 3^3 + norm_num + _ = (3 * Real.log 3) / Real.log 3 := by + simpa [pow_three] using congrArg (fun x => x / Real.log 3) hlog + _ = 3 := by + -- divide by the same nonzero number + field_simp [hpos.ne', mul_comm] + + +ProofFile: None +LemmaName: theorem mathd_algebra_484 : + Real.log 27 / Real.log 3 = 3 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 6.522753000259399 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 21} + + + +2026-01-11 01:58:01,220 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_487 +2026-01-11 01:58:01,221 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:58:01,221 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_487 (theorem_idx=103) with timeout: 600 seconds +2026-01-11 01:59:38,652 - __main__ - INFO - Prover for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 01:59:38,652 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 212.72770285606384 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 1, 'total_queries': 103} + + + +2026-01-11 01:59:38,654 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_598 +2026-01-11 01:59:38,654 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 01:59:38,654 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_598 (theorem_idx=104) with timeout: 600 seconds +2026-01-11 02:00:09,864 - __main__ - INFO - Prover for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:00:09,865 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 118.11776685714722 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 8} + + + +2026-01-11 02:00:09,866 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_756 +2026-01-11 02:00:09,866 - __main__ - INFO - Attempt 2 for proving lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:00:09,867 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_756 (theorem_idx=105) with timeout: 600 seconds +2026-01-11 02:00:44,914 - __main__ - INFO - Prover for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:00:44,915 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 23.28092670440674 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 1, 'total_queries': 11} + + + +2026-01-11 02:00:44,916 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_100 +2026-01-11 02:00:44,916 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:00:44,917 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_100 (theorem_idx=106) with timeout: 600 seconds +2026-01-11 02:02:54,938 - __main__ - INFO - Prover for lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:02:54,938 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 182.2092583179474 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 1, 'total_queries': 42} + + + +2026-01-11 02:02:54,940 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_1124 +2026-01-11 02:02:54,940 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:02:54,940 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_1124 (theorem_idx=107) with timeout: 600 seconds +2026-01-11 02:03:20,317 - __main__ - INFO - Prover for lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:03:20,318 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 139.57292437553406 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 32, 'attempt_idx': 1, 'total_queries': 56} + + + +2026-01-11 02:03:20,320 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_222 +2026-01-11 02:03:20,320 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:03:20,320 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_222 (theorem_idx=108) with timeout: 600 seconds +2026-01-11 02:04:02,127 - __main__ - INFO - Prover for lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:04:02,127 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_222 + (b : ℕ) + (h₀ : Nat.lcm 120 b = 3720) + (h₁ : Nat.gcd 120 b = 8) : + b = 248 := + +by +-- Use the standard identity `lcm a b * gcd a b = a * b` +have hmul : Nat.lcm 120 b * Nat.gcd 120 b = 120 * b := by + simpa using Nat.lcm_gcd_mul 120 b +-- Rewrite the left hand side using the given equalities +have hcalc : 120 * b = 3720 * 8 := by + simpa [h₀, h₁] using hmul.symm +-- Simplify the right hand side numerically +have hcalc' : 120 * b = 29760 := by + simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using hcalc +-- Cancel the common factor `120` (which is nonzero) +have hb : b = 248 := by + apply Nat.mul_left_cancel (by decide : 0 < (120 : ℕ)) + -- rewrite `120 * b` to `120 * 248` using `hcalc'` + simpa [hcalc'] using (by rfl : 120 * b = 120 * b) +-- Conclude the goal +exact hb + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_222 + (b : ℕ) + (h₀ : Nat.lcm 120 b = 3720) + (h₁ : Nat.gcd 120 b = 8) : + b = 248 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 11.278450727462769 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 7} + + + +2026-01-11 02:04:02,129 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_227 +2026-01-11 02:04:02,129 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:04:02,129 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_227 (theorem_idx=109) with timeout: 600 seconds +2026-01-11 02:05:11,677 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:05:11,829 - __main__ - INFO - Failed to prove lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:05:11,830 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_320 + +2026-01-11 02:05:11,831 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_233 +2026-01-11 02:05:11,831 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:05:11,831 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_233 (theorem_idx=110) with timeout: 600 seconds +2026-01-11 02:06:31,707 - __main__ - INFO - Prover for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:06:31,708 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 64.56293630599976 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 1, 'total_queries': 39} + + + +2026-01-11 02:06:31,709 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_234 +2026-01-11 02:06:31,709 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:06:31,709 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_234 (theorem_idx=111) with timeout: 600 seconds +2026-01-11 02:06:46,802 - __main__ - INFO - Prover for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:06:46,802 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 155.00290083885193 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 1, 'total_queries': 21} + + + +2026-01-11 02:06:46,804 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_277 +2026-01-11 02:06:46,804 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:06:46,804 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_277 (theorem_idx=112) with timeout: 600 seconds +2026-01-11 02:06:57,730 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:06:57,881 - __main__ - INFO - Failed to prove lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:06:57,881 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_452 + +2026-01-11 02:06:57,883 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_293 +2026-01-11 02:06:57,883 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:06:57,883 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_293 (theorem_idx=113) with timeout: 600 seconds +2026-01-11 02:09:25,058 - __main__ - INFO - Prover for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:09:25,058 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 382.9550166130066 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 38, 'attempt_idx': 1, 'total_queries': 63} + + + +2026-01-11 02:09:25,060 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_296 +2026-01-11 02:09:25,060 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:09:25,060 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_296 (theorem_idx=114) with timeout: 600 seconds +2026-01-11 02:10:56,353 - __main__ - INFO - Prover for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:10:56,353 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 241.11672139167786 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 1, 'total_queries': 32} + + + +2026-01-11 02:10:56,355 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_314 +2026-01-11 02:10:56,355 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:10:56,355 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_314 (theorem_idx=115) with timeout: 600 seconds +2026-01-11 02:11:13,977 - __main__ - INFO - Prover for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:11:13,977 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 259.63991379737854 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 1, 'total_queries': 37} + + + +2026-01-11 02:11:13,978 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_320 +2026-01-11 02:11:13,979 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:11:13,979 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_320 (theorem_idx=116) with timeout: 600 seconds +2026-01-11 02:12:39,163 - __main__ - INFO - Prover for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:12:39,163 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 168.8838427066803 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 20} + + + +2026-01-11 02:12:39,165 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_321 +2026-01-11 02:12:39,165 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:12:39,165 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_321 (theorem_idx=117) with timeout: 600 seconds +2026-01-11 02:13:56,251 - __main__ - INFO - Prover for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:13:56,251 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_293 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 11∣20 * 100 + 10 * n + 7) : + n = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_293 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 11∣20 * 100 + 10 * n + 7) : + n = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 42 +SearchTimeInSecs: 406.9611349105835 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 42, 'attempt_idx': 1, 'total_queries': 86} + + + +2026-01-11 02:13:56,253 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_328 +2026-01-11 02:13:56,253 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:13:56,256 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_34 +2026-01-11 02:13:56,256 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:13:56,256 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_34 (theorem_idx=119) with timeout: 600 seconds +2026-01-11 02:14:03,458 - __main__ - INFO - Prover for lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:14:03,459 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_314 + (r n : ℕ) + (h₀ : r = 1342 % 13) + (h₁ : 0 < n) + (h₂ : 1342∣n) + (h₃ : n % 13 < r) : + 6710 ≤ n := + +by +obtain ⟨k, rfl⟩ := h₂ +-- First we prove that `k ≥ 5` by a case analysis on `k`. +have hk : 5 ≤ k := by + -- eliminate the impossible small values of `k` + cases k with + | zero => + -- `k = 0` contradicts `h₁ : 0 < 1342 * k` + simpa using h₁ + | succ k₁ => + -- now `k = k₁ + 1` + cases k₁ with + | zero => + -- `k = 1` gives `(1342 * 1) % 13 = 3`, not `< 3` + have : (1342 * 1) % 13 = 3 := by + norm_num + have : (1342 * 1) % 13 < 3 := by + simpa [h₀] using h₃ + exact absurd this (by decide) + | succ k₂ => + cases k₂ with + | zero => + -- `k = 2` gives `(1342 * 2) % 13 = 6`, not `< 3` + have : (1342 * 2) % 13 = 6 := by + norm_num + have : (1342 * 2) % 13 < 3 := by + simpa [h₀] using h₃ + exact absurd this (by decide) + | succ k₃ => + cases k₃ with + | zero => + -- `k = 3` gives `(1342 * 3) % 13 = 9`, not `< 3` + have : (1342 * 3) % 13 = 9 := by + norm_num + have : (1342 * 3) % 13 < 3 := by + simpa [h₀] using h₃ + exact absurd this (by decide) + | succ k₄ => + cases k₄ with + | zero => + -- `k = 4` gives `(1342 * 4) % 13 = 12`, not `< 3` + have : (1342 * 4) % 13 = 12 := by + norm_num + have : (1342 * 4) % 13 < 3 := by + simpa [h₀] using h₃ + exact absurd this (by decide) + | succ k₅ => + -- `k ≥ 5` in this branch + exact Nat.succ_le_succ (Nat.succ_le_succ (Nat.succ_le_succ (Nat.succ_le_succ (Nat.succ_le_succ (Nat.zero_le k₅))))) +-- Now we can finish the inequality using the bound on `k`. +calc + 6710 = 1342 * 5 := by norm_num + _ ≤ 1342 * k := Nat.mul_le_mul_left 1342 hk + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_314 + (r n : ℕ) + (h₀ : r = 1342 % 13) + (h₁ : 0 < n) + (h₂ : 1342∣n) + (h₃ : n % 13 < r) : + 6710 ≤ n := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 169.14254593849182 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 43} + + + +2026-01-11 02:14:03,461 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_353 +2026-01-11 02:14:03,461 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:14:03,461 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_353 (theorem_idx=120) with timeout: 600 seconds +2026-01-11 02:14:38,649 - __main__ - INFO - Prover for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:14:38,649 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 186.58165669441223 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 1, 'total_queries': 15} + + + +2026-01-11 02:14:38,651 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_427 +2026-01-11 02:14:38,651 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:14:38,651 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_427 (theorem_idx=121) with timeout: 600 seconds +2026-01-11 02:14:45,396 - __main__ - INFO - Prover for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:14:45,396 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 35.0022029876709 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 1, 'total_queries': 11} + + + +2026-01-11 02:14:45,398 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_430 +2026-01-11 02:14:45,398 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:14:45,398 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_430 (theorem_idx=122) with timeout: 600 seconds +2026-01-11 02:14:48,041 - __main__ - INFO - Prover for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:14:48,041 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 56 +SearchTimeInSecs: 115.1153666973114 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 1, 'total_queries': 89} + + + +2026-01-11 02:14:48,043 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_435 +2026-01-11 02:14:48,043 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:14:48,043 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_435 (theorem_idx=123) with timeout: 600 seconds +2026-01-11 02:16:02,545 - __main__ - INFO - Prover for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:16:02,545 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 60.45443367958069 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 1, 'total_queries': 6} + + + +2026-01-11 02:16:02,547 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_447 +2026-01-11 02:16:02,547 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:16:02,550 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_451 +2026-01-11 02:16:02,550 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:16:02,550 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_451 (theorem_idx=125) with timeout: 600 seconds +2026-01-11 02:16:05,901 - __main__ - INFO - Prover for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:16:05,902 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 72.10774111747742 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 24} + + + +2026-01-11 02:16:05,903 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_457 +2026-01-11 02:16:05,903 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:16:05,904 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_457 (theorem_idx=126) with timeout: 600 seconds +2026-01-11 02:16:47,097 - __main__ - INFO - Prover for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:16:47,097 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 27.94366216659546 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 24} + + + +2026-01-11 02:16:47,099 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_483 +2026-01-11 02:16:47,099 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:16:47,102 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_495 +2026-01-11 02:16:47,102 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:16:47,102 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_495 (theorem_idx=128) with timeout: 600 seconds +2026-01-11 02:17:34,657 - __main__ - INFO - Prover for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:17:34,657 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 67 +SearchTimeInSecs: 202.4569709300995 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 58, 'attempt_idx': 1, 'total_queries': 105} + + + +2026-01-11 02:17:34,659 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_5 +2026-01-11 02:17:34,659 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:17:34,659 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_5 (theorem_idx=129) with timeout: 600 seconds +2026-01-11 02:19:34,408 - __main__ - INFO - Prover for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:19:34,408 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 109.22068643569946 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 58} + + + +2026-01-11 02:19:34,410 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_521 +2026-01-11 02:19:34,410 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:19:34,410 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_521 (theorem_idx=130) with timeout: 600 seconds +2026-01-11 02:20:55,165 - __main__ - INFO - Prover for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:20:55,165 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 68 +SearchTimeInSecs: 283.75245118141174 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 70, 'attempt_idx': 1, 'total_queries': 104} + + + +2026-01-11 02:20:55,167 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_541 +2026-01-11 02:20:55,167 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:20:55,167 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_541 (theorem_idx=131) with timeout: 600 seconds +2026-01-11 02:21:57,979 - __main__ - INFO - Prover for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:21:57,980 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := + +by +have hsum : a = 1092 := by + norm_num [h₀] +simp [hsum] +norm_num +norm_num [divisors] +norm_num [divisors, Finset.mem_Ico, Finset.mem_range, Nat.Prime] +simp [Finset.sum_filter, Finset.mem_Ico, Nat.irreducible_iff_prime] +norm_num +classical +simp [Finset.sum_filter, Finset.mem_Ico, Nat.mem_divisors, Nat.irreducible_iff_prime] + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 118 +SearchTimeInSecs: 431.60743618011475 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 1, 'total_queries': 141} + + + +2026-01-11 02:21:57,981 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_552 +2026-01-11 02:21:57,982 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:21:57,982 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_552 (theorem_idx=132) with timeout: 600 seconds +2026-01-11 02:24:34,493 - __main__ - INFO - Prover for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:24:34,493 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 145.80781173706055 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 1, 'total_queries': 45} + + + +2026-01-11 02:24:34,495 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_559 +2026-01-11 02:24:34,495 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:24:34,498 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_582 +2026-01-11 02:24:34,498 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:24:34,506 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_618 +2026-01-11 02:24:34,506 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:24:34,506 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_618 (theorem_idx=135) with timeout: 600 seconds +2026-01-11 02:26:09,737 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:26:09,888 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:26:09,888 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: mathd_numbertheory_618 + +2026-01-11 02:26:09,890 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_711 +2026-01-11 02:26:09,890 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:26:09,890 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_711 (theorem_idx=136) with timeout: 600 seconds +2026-01-11 02:26:47,288 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:26:47,441 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:26:47,441 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_495 + +2026-01-11 02:26:47,443 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_764 +2026-01-11 02:26:47,443 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:26:47,443 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_764 (theorem_idx=137) with timeout: 600 seconds +2026-01-11 02:28:50,078 - __main__ - INFO - Prover for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:28:50,078 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 64 +SearchTimeInSecs: 450.4849877357483 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 60, 'attempt_idx': 1, 'total_queries': 60} + + + +2026-01-11 02:28:50,080 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_765 +2026-01-11 02:28:50,080 - __main__ - INFO - Attempt 2 for proving lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:28:50,080 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_765 (theorem_idx=138) with timeout: 600 seconds +2026-01-11 02:29:19,448 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:29:19,601 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:29:19,602 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: mathd_numbertheory_764 + +2026-01-11 02:29:19,603 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_99 +2026-01-11 02:29:19,603 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:29:19,607 - __main__ - INFO - Attempting to prove lemma: numbertheory_2pownm1prime_nprime +2026-01-11 02:29:19,607 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:29:19,607 - __main__ - INFO - Running the prover agent for lemma: numbertheory_2pownm1prime_nprime (theorem_idx=140) with timeout: 600 seconds +2026-01-11 02:29:34,595 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:29:34,748 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:29:34,748 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_521 + +2026-01-11 02:29:34,750 - __main__ - INFO - Attempting to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 +2026-01-11 02:29:34,750 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:29:34,750 - __main__ - INFO - Running the prover agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 (theorem_idx=141) with timeout: 600 seconds +2026-01-11 02:29:55,620 - __main__ - INFO - Prover for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:29:55,620 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 23.387073278427124 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 7} + + + +2026-01-11 02:29:55,622 - __main__ - INFO - Attempting to prove lemma: numbertheory_4x3m7y3neq2003 +2026-01-11 02:29:55,622 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:29:55,622 - __main__ - INFO - Running the prover agent for lemma: numbertheory_4x3m7y3neq2003 (theorem_idx=142) with timeout: 600 seconds +2026-01-11 02:35:24,621 - __main__ - INFO - Prover for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:35:24,622 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 44 +SearchTimeInSecs: 539.1816608905792 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 51, 'attempt_idx': 1, 'total_queries': 94} + + + +2026-01-11 02:35:24,623 - __main__ - INFO - Attempting to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 +2026-01-11 02:35:24,623 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:35:24,623 - __main__ - INFO - Running the prover agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 (theorem_idx=143) with timeout: 600 seconds +2026-01-11 02:37:05,769 - __main__ - INFO - Prover for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:37:05,769 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 48 +SearchTimeInSecs: 432.23352098464966 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 52, 'attempt_idx': 1, 'total_queries': 63} + + + +2026-01-11 02:37:05,771 - __main__ - INFO - Attempting to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 +2026-01-11 02:37:05,771 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:37:05,771 - __main__ - INFO - Running the prover agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 (theorem_idx=144) with timeout: 600 seconds +2026-01-11 02:38:50,252 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:38:50,405 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:38:50,405 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_765 + +2026-01-11 02:38:50,406 - __main__ - INFO - Attempting to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown +2026-01-11 02:38:50,407 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:38:50,407 - __main__ - INFO - Running the prover agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown (theorem_idx=145) with timeout: 600 seconds +2026-01-11 02:39:55,809 - __main__ - INFO - Prover Agent for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:39:55,965 - __main__ - INFO - Failed to prove lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:39:55,965 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_4x3m7y3neq2003 + +2026-01-11 02:39:55,967 - __main__ - INFO - Attempting to prove lemma: numbertheory_x5neqy2p4 +2026-01-11 02:39:55,967 - __main__ - INFO - Attempt 2 for proving lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:39:55,967 - __main__ - INFO - Running the prover agent for lemma: numbertheory_x5neqy2p4 (theorem_idx=146) with timeout: 600 seconds +2026-01-11 02:41:58,763 - __main__ - INFO - Prover for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:41:58,763 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 114.47480249404907 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 18} + + + +2026-01-11 02:41:58,765 - __main__ - INFO - Attempting to prove lemma: aime_1983_p1 +2026-01-11 02:41:58,765 - __main__ - INFO - Attempt 2 for proving lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:41:58,765 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p1 (theorem_idx=147) with timeout: 600 seconds +2026-01-11 02:43:56,760 - __main__ - INFO - Prover for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:43:56,760 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := + +by +-- First, rewrite the odd number `a` as `2 * k + 1` and the multiple of `4` `b` as `4 * m` +rcases h₀ with ⟨k, hk⟩ +rcases h₁ with ⟨m, hm⟩ + +-- Compute the remainder of `a ^ 2` modulo `8` +have h_a : (a ^ 2) % 8 = 1 := by + -- rewrite `a` using `hk` + have : a = 2 * k + 1 := hk + -- expand the square and simplify modulo `8` + simp [this, pow_two, mul_comm, mul_left_comm, mul_assoc] at * + norm_num + +-- Compute the remainder of `b ^ 2` modulo `8` +have h_b : (b ^ 2) % 8 = 0 := by + -- rewrite `b` using `hm` + have : b = 4 * m := hm + -- expand the square and simplify modulo `8` + simp [this, pow_two, mul_comm, mul_left_comm, mul_assoc] at * + norm_num + +-- Combine the two remainders +simp [mod_add_mod, h_a, h_b, add_comm, add_left_comm, add_assoc] at * +simp [hk, hm, pow_two, mul_comm, mul_left_comm, mul_assoc, mod_add_mod] at * +norm_num + + +ProofFile: None +LemmaName: theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 103 +SearchTimeInSecs: 489.49790263175964 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 1, 'total_queries': 135} + + + +2026-01-11 02:43:56,762 - __main__ - INFO - Attempting to prove lemma: aime_1983_p3 +2026-01-11 02:43:56,762 - __main__ - INFO - Attempt 2 for proving lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:43:56,762 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p3 (theorem_idx=148) with timeout: 600 seconds +2026-01-11 02:45:31,791 - __main__ - INFO - Prover for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:45:31,791 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 77.09266114234924 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 1, 'total_queries': 21} + + + +2026-01-11 02:45:31,793 - __main__ - INFO - Attempting to prove lemma: aime_1984_p1 +2026-01-11 02:45:31,793 - __main__ - INFO - Attempt 2 for proving lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:45:31,793 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p1 (theorem_idx=149) with timeout: 600 seconds +2026-01-11 02:47:05,919 - __main__ - INFO - Prover Agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:47:06,071 - __main__ - INFO - Failed to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:47:06,071 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 + +2026-01-11 02:47:06,073 - __main__ - INFO - Attempting to prove lemma: aime_1984_p7 +2026-01-11 02:47:06,073 - __main__ - INFO - Attempt 2 for proving lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:47:06,073 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p7 (theorem_idx=150) with timeout: 600 seconds +2026-01-11 02:47:53,031 - __main__ - INFO - Prover for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:47:53,031 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 37 +SearchTimeInSecs: 347.3501331806183 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 37, 'attempt_idx': 1, 'total_queries': 37} + + + +2026-01-11 02:47:53,032 - __main__ - INFO - Attempting to prove lemma: aime_1987_p5 +2026-01-11 02:47:53,033 - __main__ - INFO - Attempt 2 for proving lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:47:53,033 - __main__ - INFO - Running the prover agent for lemma: aime_1987_p5 (theorem_idx=151) with timeout: 600 seconds +2026-01-11 02:48:50,533 - __main__ - INFO - Prover Agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:48:50,692 - __main__ - INFO - Failed to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:48:50,692 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + +2026-01-11 02:48:50,694 - __main__ - INFO - Attempting to prove lemma: aime_1988_p8 +2026-01-11 02:48:50,694 - __main__ - INFO - Attempt 2 for proving lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:48:50,694 - __main__ - INFO - Running the prover agent for lemma: aime_1988_p8 (theorem_idx=152) with timeout: 600 seconds +2026-01-11 02:51:47,693 - __main__ - INFO - Prover for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:51:47,694 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 33 +SearchTimeInSecs: 262.37610912323 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 1, 'total_queries': 39} + + + +2026-01-11 02:51:47,695 - __main__ - INFO - Attempting to prove lemma: aime_1990_p15 +2026-01-11 02:51:47,695 - __main__ - INFO - Attempt 2 for proving lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:51:47,695 - __main__ - INFO - Running the prover agent for lemma: aime_1990_p15 (theorem_idx=153) with timeout: 600 seconds +2026-01-11 02:53:20,533 - __main__ - INFO - Prover for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:53:20,533 - __main__ - INFO - Dumping proof search result: +theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 317.246054649353 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 1, 'total_queries': 39} + + + +2026-01-11 02:53:20,535 - __main__ - INFO - Attempting to prove lemma: aime_1990_p4 +2026-01-11 02:53:20,535 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 02:53:20,538 - __main__ - INFO - Attempting to prove lemma: aime_1991_p9 +2026-01-11 02:53:20,538 - __main__ - INFO - Attempt 2 for proving lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:53:20,538 - __main__ - INFO - Running the prover agent for lemma: aime_1991_p9 (theorem_idx=155) with timeout: 600 seconds +2026-01-11 02:55:31,975 - __main__ - INFO - Prover Agent for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 02:55:32,127 - __main__ - INFO - Failed to prove lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:55:32,127 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1984_p1 + +2026-01-11 02:55:32,129 - __main__ - INFO - Attempting to prove lemma: aime_1994_p3 +2026-01-11 02:55:32,129 - __main__ - INFO - Attempt 2 for proving lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:55:32,129 - __main__ - INFO - Running the prover agent for lemma: aime_1994_p3 (theorem_idx=156) with timeout: 600 seconds +2026-01-11 02:56:16,141 - __main__ - INFO - Prover for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:56:16,141 - __main__ - INFO - Dumping proof search result: +theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 427.47270154953003 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 1, 'total_queries': 60} + + + +2026-01-11 02:56:16,143 - __main__ - INFO - Attempting to prove lemma: aime_1995_p7 +2026-01-11 02:56:16,143 - __main__ - INFO - Attempt 2 for proving lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:56:16,143 - __main__ - INFO - Running the prover agent for lemma: aime_1995_p7 (theorem_idx=157) with timeout: 600 seconds +2026-01-11 02:58:00,063 - __main__ - INFO - Prover for lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:58:00,064 - __main__ - INFO - Dumping proof search result: +theorem aime_1990_p15 + (a b x y : ℝ) + (h₀ : a * x + b * y = 3) + (h₁ : a * x^2 + b * y^2 = 7) + (h₂ : a * x^3 + b * y^3 = 16) + (h₃ : a * x^4 + b * y^4 = 42) : + a * x^5 + b * y^5 = 20 := + +by +have hE1 : (x + y) * 3 - (x * y) * (a + b) = 7 := by + have : a * x ^ 2 + b * y ^ 2 = (x + y) * (a * x + b * y) - (x * y) * (a + b) := by ring + simpa [h₀, h₁] using this.symm +-- Rewrite the recurrence using the known weighted sums to obtain a linear equation +have hA : (x + y) * 7 - (x * y) * 3 = 16 := by + -- start from the algebraic identity + have h : a * x ^ 3 + b * y ^ 3 = (x + y) * (a * x ^ 2 + b * y ^ 2) - (x * y) * (a * x + b * y) := by + ring + -- take the symmetric version and substitute the known values + have h' := h.symm + simpa [h₀, h₁, h₂] using h' +-- derive the two linear equations for (x + y) and (x * y) +have hxy1 : 7 * (x + y) - 3 * (x * y) = 16 := by + simpa [mul_comm, mul_left_comm, mul_assoc] using hA +have hxy2 : 16 * (x + y) - 7 * (x * y) = 42 := by + -- use the recurrence for the fourth power + have hrec4 : a * x ^ 4 + b * y ^ 4 = + (x + y) * (a * x ^ 3 + b * y ^ 3) - (x * y) * (a * x ^ 2 + b * y ^ 2) := by ring + have h' := hrec4.symm + simpa [h₀, h₁, h₂, h₃, mul_comm, mul_left_comm, mul_assoc] using h' +-- Solve the linear system for S = x + y and P = x * y +have hS : x + y = -14 := by + linear_combination 7 * hxy1 - 3 * hxy2 +have hP : x * y = -38 := by + linear_combination 16 * hxy1 - 7 * hxy2 +-- Use the recurrence for the fifth power +calc + a * x ^ 5 + b * y ^ 5 + = (x + y) * (a * x ^ 4 + b * y ^ 4) - (x * y) * (a * x ^ 3 + b * y ^ 3) := by ring + _ = (x + y) * 42 - (x * y) * 16 := by + simp [h₃, h₂] + _ = (-14) * 42 - (-38) * 16 := by + simp [hS, hP] + _ = 20 := by norm_num + + +ProofFile: None +LemmaName: theorem aime_1990_p15 + (a b x y : ℝ) + (h₀ : a * x + b * y = 3) + (h₁ : a * x^2 + b * y^2 = 7) + (h₂ : a * x^3 + b * y^3 = 16) + (h₃ : a * x^4 + b * y^4 = 42) : + a * x^5 + b * y^5 = 20 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 342.6319329738617 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 1, 'total_queries': 29} + + + +2026-01-11 02:58:00,065 - __main__ - INFO - Attempting to prove lemma: aime_1997_p9 +2026-01-11 02:58:00,065 - __main__ - INFO - Attempt 2 for proving lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:58:00,066 - __main__ - INFO - Running the prover agent for lemma: aime_1997_p9 (theorem_idx=158) with timeout: 600 seconds +2026-01-11 02:59:19,560 - __main__ - INFO - Prover for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 02:59:19,560 - __main__ - INFO - Dumping proof search result: +theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 216.4428849220276 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 1, 'total_queries': 87} + + + +2026-01-11 02:59:19,562 - __main__ - INFO - Attempting to prove lemma: aime_1999_p11 +2026-01-11 02:59:19,562 - __main__ - INFO - Attempt 2 for proving lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 02:59:19,562 - __main__ - INFO - Running the prover agent for lemma: aime_1999_p11 (theorem_idx=159) with timeout: 600 seconds +2026-01-11 03:02:23,493 - __main__ - INFO - Prover for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:02:23,494 - __main__ - INFO - Dumping proof search result: +theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 28 +SearchTimeInSecs: 341.6916229724884 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 1, 'total_queries': 32} + + + +2026-01-11 03:02:23,495 - __main__ - INFO - Attempting to prove lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 +2026-01-11 03:02:23,496 - __main__ - INFO - Attempt 2 for proving lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:02:23,496 - __main__ - INFO - Running the prover agent for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 (theorem_idx=160) with timeout: 600 seconds +2026-01-11 03:03:20,663 - __main__ - INFO - Prover Agent for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:03:20,825 - __main__ - INFO - Failed to prove lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:03:20,826 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1991_p9 + +2026-01-11 03:03:20,827 - __main__ - INFO - Attempting to prove lemma: algebra_9onxpypzleqsum2onxpy +2026-01-11 03:03:20,828 - __main__ - INFO - Attempt 2 for proving lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:03:20,828 - __main__ - INFO - Running the prover agent for lemma: algebra_9onxpypzleqsum2onxpy (theorem_idx=161) with timeout: 600 seconds +2026-01-11 03:03:39,669 - __main__ - INFO - Prover for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:03:39,669 - __main__ - INFO - Dumping proof search result: +theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 65.17280602455139 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 18} + + + +2026-01-11 03:03:39,671 - __main__ - INFO - Attempting to prove lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 +2026-01-11 03:03:39,671 - __main__ - INFO - Attempt 2 for proving lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:03:39,671 - __main__ - INFO - Running the prover agent for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 (theorem_idx=162) with timeout: 600 seconds +2026-01-11 03:04:35,083 - __main__ - INFO - Prover for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:04:35,083 - __main__ - INFO - Dumping proof search result: +theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 43.74424195289612 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 61} + + + +2026-01-11 03:04:35,085 - __main__ - INFO - Attempting to prove lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa +2026-01-11 03:04:35,085 - __main__ - INFO - Attempt 2 for proving lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:04:35,086 - __main__ - INFO - Running the prover agent for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa (theorem_idx=163) with timeout: 600 seconds +2026-01-11 03:05:13,576 - __main__ - INFO - Prover for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:05:13,576 - __main__ - INFO - Dumping proof search result: +theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 97.20622634887695 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 15} + + + +2026-01-11 03:05:13,578 - __main__ - INFO - Attempting to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 +2026-01-11 03:05:13,578 - __main__ - INFO - Attempt 2 for proving lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:05:13,578 - __main__ - INFO - Running the prover agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 (theorem_idx=164) with timeout: 600 seconds +2026-01-11 03:07:42,671 - __main__ - INFO - Prover for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:07:42,671 - __main__ - INFO - Dumping proof search result: +theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 172.10295724868774 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 37} + + + +2026-01-11 03:07:42,673 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 +2026-01-11 03:07:42,673 - __main__ - INFO - Attempt 2 for proving lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:07:42,673 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 (theorem_idx=165) with timeout: 600 seconds +2026-01-11 03:08:00,143 - __main__ - INFO - Prover Agent for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:08:00,299 - __main__ - INFO - Failed to prove lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:08:00,299 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1997_p9 + +2026-01-11 03:08:00,301 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sumasqdivbgeqsuma +2026-01-11 03:08:00,301 - __main__ - INFO - Attempt 2 for proving lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:08:00,301 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sumasqdivbgeqsuma (theorem_idx=166) with timeout: 600 seconds +2026-01-11 03:09:19,732 - __main__ - INFO - Prover Agent for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:09:19,901 - __main__ - INFO - Failed to prove lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:09:19,902 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1999_p11 + +2026-01-11 03:09:19,904 - __main__ - INFO - Attempting to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 +2026-01-11 03:09:19,904 - __main__ - INFO - Attempt 2 for proving lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:09:19,904 - __main__ - INFO - Running the prover agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 (theorem_idx=167) with timeout: 600 seconds +2026-01-11 03:09:27,874 - __main__ - INFO - Prover for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:09:27,874 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 84.58534336090088 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 1, 'total_queries': 11} + + + +2026-01-11 03:09:27,876 - __main__ - INFO - Attempting to prove lemma: algebra_apbon2pownleqapownpbpowon2 +2026-01-11 03:09:27,876 - __main__ - INFO - Attempt 2 for proving lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:09:27,876 - __main__ - INFO - Running the prover agent for lemma: algebra_apbon2pownleqapownpbpowon2 (theorem_idx=168) with timeout: 600 seconds +2026-01-11 03:13:18,690 - __main__ - INFO - Prover for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:13:18,690 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 209.7784173488617 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 1, 'total_queries': 53} + + + +2026-01-11 03:13:18,692 - __main__ - INFO - Attempting to prove lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 +2026-01-11 03:13:18,692 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 03:13:18,695 - __main__ - INFO - Attempting to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b +2026-01-11 03:13:18,695 - __main__ - INFO - Attempt 2 for proving lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:13:18,695 - __main__ - INFO - Running the prover agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b (theorem_idx=170) with timeout: 600 seconds +2026-01-11 03:15:13,765 - __main__ - INFO - Prover Agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:15:13,910 - __main__ - INFO - Failed to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:15:13,910 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + +2026-01-11 03:15:13,911 - __main__ - INFO - Attempting to prove lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 +2026-01-11 03:15:13,911 - __main__ - INFO - Attempt 2 for proving lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:15:13,911 - __main__ - INFO - Running the prover agent for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 (theorem_idx=171) with timeout: 600 seconds +2026-01-11 03:15:43,663 - __main__ - INFO - Prover for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:15:43,663 - __main__ - INFO - Dumping proof search result: +theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 130.68164801597595 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 1, 'total_queries': 26} + + + +2026-01-11 03:15:43,665 - __main__ - INFO - Attempting to prove lemma: algebra_ineq_nto1onlt2m1on +2026-01-11 03:15:43,665 - __main__ - INFO - Attempt 2 for proving lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:15:43,665 - __main__ - INFO - Running the prover agent for lemma: algebra_ineq_nto1onlt2m1on (theorem_idx=172) with timeout: 600 seconds +2026-01-11 03:18:00,476 - __main__ - INFO - Prover Agent for lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:18:00,633 - __main__ - INFO - Failed to prove lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:18:00,634 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_amgm_sumasqdivbgeqsuma + +2026-01-11 03:18:00,635 - __main__ - INFO - Attempting to prove lemma: algebra_others_exirrpowirrrat +2026-01-11 03:18:00,635 - __main__ - INFO - Attempt 2 for proving lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:18:00,636 - __main__ - INFO - Running the prover agent for lemma: algebra_others_exirrpowirrrat (theorem_idx=173) with timeout: 600 seconds +2026-01-11 03:19:20,099 - __main__ - INFO - Prover Agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:19:20,214 - __main__ - INFO - Failed to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:19:20,214 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 + +2026-01-11 03:19:20,216 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpabsamblt1 +2026-01-11 03:19:20,216 - __main__ - INFO - Attempt 2 for proving lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:19:20,216 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpabsamblt1 (theorem_idx=174) with timeout: 600 seconds +2026-01-11 03:20:15,638 - __main__ - INFO - Prover for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:20:15,638 - __main__ - INFO - Dumping proof search result: +theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 120.76455283164978 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 1, 'total_queries': 64} + + + +2026-01-11 03:20:15,640 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpamblt1 +2026-01-11 03:20:15,640 - __main__ - INFO - Attempt 2 for proving lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:20:15,640 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpamblt1 (theorem_idx=175) with timeout: 600 seconds +2026-01-11 03:20:28,248 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:20:28,249 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 60.122928619384766 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 1, 'total_queries': 12} + + + +2026-01-11 03:20:28,252 - __main__ - INFO - Attempting to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 +2026-01-11 03:20:28,252 - __main__ - INFO - Attempt 2 for proving lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:20:28,252 - __main__ - INFO - Running the prover agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 (theorem_idx=176) with timeout: 600 seconds +2026-01-11 03:20:44,323 - __main__ - INFO - Prover Agent for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:20:44,478 - __main__ - INFO - Failed to prove lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:20:44,478 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: algebra_ineq_nto1onlt2m1on + +2026-01-11 03:20:44,480 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p1 +2026-01-11 03:20:44,480 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:20:44,480 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p1 (theorem_idx=177) with timeout: 600 seconds +2026-01-11 03:20:51,791 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:20:51,791 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + (a - b) ≤ 1 := + +by +have h_sq : (a - b) ^ 2 ≥ (0 : ℝ) := by + nlinarith +have h_ab : a * b ≤ (1 : ℝ) / 2 := by + nlinarith [h₀, h_sq] +nlinarith [h₀, h_ab] + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + (a - b) ≤ 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 13.779382467269897 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 17} + + + +2026-01-11 03:20:51,793 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p12 +2026-01-11 03:20:51,793 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:20:51,793 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p12 (theorem_idx=178) with timeout: 600 seconds +2026-01-11 03:21:15,869 - __main__ - INFO - Prover for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:21:15,869 - __main__ - INFO - Dumping proof search result: +theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 48 +SearchTimeInSecs: 342.780855178833 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 46, 'attempt_idx': 1, 'total_queries': 86} + + + +2026-01-11 03:21:15,871 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p20 +2026-01-11 03:21:15,871 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:21:15,871 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p20 (theorem_idx=179) with timeout: 600 seconds +2026-01-11 03:22:16,855 - __main__ - INFO - Prover for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:22:16,855 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 75.22548031806946 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 1, 'total_queries': 23} + + + +2026-01-11 03:22:16,857 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p6 +2026-01-11 03:22:16,857 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:22:16,857 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p6 (theorem_idx=180) with timeout: 600 seconds +2026-01-11 03:24:20,091 - __main__ - INFO - Prover for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:24:20,091 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 40 +SearchTimeInSecs: 197.0830578804016 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 1, 'total_queries': 80} + + + +2026-01-11 03:24:20,093 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p21 +2026-01-11 03:24:20,093 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:24:20,094 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p21 (theorem_idx=181) with timeout: 600 seconds +2026-01-11 03:24:56,870 - __main__ - INFO - Prover Agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:24:57,026 - __main__ - INFO - Failed to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:24:57,026 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 + +2026-01-11 03:24:57,028 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p5 +2026-01-11 03:24:57,028 - __main__ - INFO - Attempt 2 for proving lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:24:57,028 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p5 (theorem_idx=182) with timeout: 600 seconds +2026-01-11 03:25:33,983 - __main__ - INFO - Prover for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:25:33,983 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 29.9068922996521 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 1, 'total_queries': 9} + + + +2026-01-11 03:25:33,985 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p13 +2026-01-11 03:25:33,985 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:25:33,985 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p13 (theorem_idx=183) with timeout: 600 seconds +2026-01-11 03:27:20,449 - __main__ - INFO - Prover for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:27:20,449 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 161.91223978996277 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 33, 'attempt_idx': 1, 'total_queries': 57} + + + +2026-01-11 03:27:20,451 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p23 +2026-01-11 03:27:20,451 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:27:20,451 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p23 (theorem_idx=184) with timeout: 600 seconds +2026-01-11 03:29:37,442 - __main__ - INFO - Prover for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:29:37,442 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 120.54215121269226 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 17} + + + +2026-01-11 03:29:37,443 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p5 +2026-01-11 03:29:37,444 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 03:29:37,447 - __main__ - INFO - Attempting to prove lemma: amc12a_2008_p25 +2026-01-11 03:29:37,447 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:29:37,447 - __main__ - INFO - Running the prover agent for lemma: amc12a_2008_p25 (theorem_idx=186) with timeout: 600 seconds +2026-01-11 03:31:15,979 - __main__ - INFO - Prover Agent for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:31:16,136 - __main__ - INFO - Failed to prove lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:31:16,136 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12_2000_p20 + +2026-01-11 03:31:16,138 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p6 +2026-01-11 03:31:16,138 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:31:16,138 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p6 (theorem_idx=187) with timeout: 600 seconds +2026-01-11 03:32:17,006 - __main__ - INFO - Prover Agent for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:32:17,163 - __main__ - INFO - Failed to prove lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:32:17,163 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12_2000_p6 + +2026-01-11 03:32:17,165 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p7 +2026-01-11 03:32:17,165 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:32:17,165 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p7 (theorem_idx=188) with timeout: 600 seconds +2026-01-11 03:32:25,946 - __main__ - INFO - Prover for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:32:25,946 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 44.561219215393066 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 1, 'total_queries': 103} + + + +2026-01-11 03:32:25,948 - __main__ - INFO - Attempting to prove lemma: amc12a_2019_p12 +2026-01-11 03:32:25,948 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:32:25,948 - __main__ - INFO - Running the prover agent for lemma: amc12a_2019_p12 (theorem_idx=189) with timeout: 600 seconds +2026-01-11 03:35:34,173 - __main__ - INFO - Prover Agent for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:35:34,328 - __main__ - INFO - Failed to prove lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:35:34,329 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2002_p13 + +2026-01-11 03:35:34,331 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p10 +2026-01-11 03:35:34,331 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:35:34,331 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p10 (theorem_idx=190) with timeout: 600 seconds +2026-01-11 03:39:37,628 - __main__ - INFO - Prover Agent for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:39:37,785 - __main__ - INFO - Failed to prove lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:39:37,785 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2008_p25 + +2026-01-11 03:39:37,787 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p15 +2026-01-11 03:39:37,787 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:39:37,787 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p15 (theorem_idx=191) with timeout: 600 seconds +2026-01-11 03:42:17,354 - __main__ - INFO - Prover Agent for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:42:17,510 - __main__ - INFO - Failed to prove lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:42:17,510 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2009_p7 + +2026-01-11 03:42:17,512 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p25 +2026-01-11 03:42:17,512 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:42:17,512 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p25 (theorem_idx=192) with timeout: 600 seconds +2026-01-11 03:42:26,046 - __main__ - INFO - Prover Agent for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:42:26,200 - __main__ - INFO - Failed to prove lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:42:26,200 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2019_p12 + +2026-01-11 03:42:26,202 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p4 +2026-01-11 03:42:26,202 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:42:26,202 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p4 (theorem_idx=193) with timeout: 600 seconds +2026-01-11 03:43:28,431 - __main__ - INFO - Prover for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:43:28,431 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 45.565048933029175 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 1, 'total_queries': 22} + + + +2026-01-11 03:43:28,433 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p7 +2026-01-11 03:43:28,434 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:43:28,434 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p7 (theorem_idx=194) with timeout: 600 seconds +2026-01-11 03:44:04,653 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:44:04,811 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:44:04,811 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2020_p4 + +2026-01-11 03:44:04,813 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p9 +2026-01-11 03:44:04,813 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:44:04,813 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p9 (theorem_idx=195) with timeout: 600 seconds +2026-01-11 03:45:34,465 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:45:34,619 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:45:34,619 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p10 + +2026-01-11 03:45:34,621 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p12 +2026-01-11 03:45:34,621 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:45:34,621 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p12 (theorem_idx=196) with timeout: 600 seconds +2026-01-11 03:45:42,271 - __main__ - INFO - Prover for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:45:42,272 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 121.28840065002441 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 1, 'total_queries': 26} + + + +2026-01-11 03:45:42,273 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p14 +2026-01-11 03:45:42,274 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:45:42,274 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p14 (theorem_idx=197) with timeout: 600 seconds +2026-01-11 03:46:35,977 - __main__ - INFO - Prover for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:46:35,977 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 132.98494386672974 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 1, 'total_queries': 28} + + + +2026-01-11 03:46:35,979 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p18 +2026-01-11 03:46:35,979 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:46:35,979 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p18 (theorem_idx=198) with timeout: 600 seconds +2026-01-11 03:48:01,861 - __main__ - INFO - Prover for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:48:01,862 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 69.47231340408325 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 1, 'total_queries': 5} + + + +2026-01-11 03:48:01,863 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p19 +2026-01-11 03:48:01,864 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:48:01,864 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p19 (theorem_idx=199) with timeout: 600 seconds +2026-01-11 03:48:38,654 - __main__ - INFO - Prover for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:48:38,654 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 18.7670795917511 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 2} + + + +2026-01-11 03:48:38,656 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p22 +2026-01-11 03:48:38,656 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:48:38,656 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p22 (theorem_idx=200) with timeout: 600 seconds +2026-01-11 03:49:37,973 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:49:38,130 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:49:38,130 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p15 + +2026-01-11 03:49:38,132 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p25 +2026-01-11 03:49:38,132 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:49:38,132 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p25 (theorem_idx=201) with timeout: 600 seconds +2026-01-11 03:50:19,274 - __main__ - INFO - Prover for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:50:19,274 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 263.4129128456116 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 1, 'total_queries': 26} + + + +2026-01-11 03:50:19,279 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p3 +2026-01-11 03:50:19,279 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 03:50:19,283 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p8 +2026-01-11 03:50:19,283 - __main__ - INFO - Attempt 2 for proving lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:50:19,283 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p8 (theorem_idx=203) with timeout: 600 seconds +2026-01-11 03:50:51,360 - __main__ - INFO - Prover for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:50:51,360 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 47.92670392990112 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 1, 'total_queries': 17} + + + +2026-01-11 03:50:51,362 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p4 +2026-01-11 03:50:51,362 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:50:51,362 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p4 (theorem_idx=204) with timeout: 600 seconds +2026-01-11 03:55:34,769 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:55:34,933 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:55:34,933 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p12 + +2026-01-11 03:55:34,935 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p7 +2026-01-11 03:55:34,935 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:55:34,935 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p7 (theorem_idx=205) with timeout: 600 seconds +2026-01-11 03:56:24,020 - __main__ - INFO - Prover for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:56:24,021 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 318.14501309394836 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 1, 'total_queries': 40} + + + +2026-01-11 03:56:24,022 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p13 +2026-01-11 03:56:24,022 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:56:24,022 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p13 (theorem_idx=206) with timeout: 600 seconds +2026-01-11 03:58:19,641 - __main__ - INFO - Prover for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:58:19,641 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 93.83242774009705 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 44} + + + +2026-01-11 03:58:19,643 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p21 +2026-01-11 03:58:19,643 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:58:19,643 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p21 (theorem_idx=207) with timeout: 600 seconds +2026-01-11 03:58:38,825 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 03:58:39,009 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:58:39,009 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p22 + +2026-01-11 03:58:39,011 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p22 +2026-01-11 03:58:39,012 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:58:39,012 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p22 (theorem_idx=208) with timeout: 600 seconds +2026-01-11 03:59:38,843 - __main__ - INFO - Prover for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:59:38,843 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 68.49664521217346 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 1, 'total_queries': 14} + + + +2026-01-11 03:59:38,845 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p1 +2026-01-11 03:59:38,845 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:59:38,845 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p1 (theorem_idx=209) with timeout: 600 seconds +2026-01-11 03:59:41,377 - __main__ - INFO - Prover for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 03:59:41,377 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 43.951738357543945 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 11} + + + +2026-01-11 03:59:41,379 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p13 +2026-01-11 03:59:41,379 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 03:59:41,379 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p13 (theorem_idx=210) with timeout: 600 seconds +2026-01-11 04:00:19,437 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:00:19,591 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:00:19,592 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p8 + +2026-01-11 04:00:19,594 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p18 +2026-01-11 04:00:19,594 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:00:19,594 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p18 (theorem_idx=211) with timeout: 600 seconds +2026-01-11 04:00:26,294 - __main__ - INFO - Prover for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:00:26,294 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 20.865824222564697 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 1, 'total_queries': 9} + + + +2026-01-11 04:00:26,296 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p3 +2026-01-11 04:00:26,296 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:00:26,296 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p3 (theorem_idx=212) with timeout: 600 seconds +2026-01-11 04:03:20,767 - __main__ - INFO - Prover for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:03:20,767 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 201.51716661453247 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 1, 'total_queries': 43} + + + +2026-01-11 04:03:20,769 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p4 +2026-01-11 04:03:20,769 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:03:20,769 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p4 (theorem_idx=213) with timeout: 600 seconds +2026-01-11 04:05:35,029 - __main__ - INFO - Prover Agent for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:05:35,183 - __main__ - INFO - Failed to prove lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:05:35,183 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12b_2002_p7 + +2026-01-11 04:05:35,185 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p9 +2026-01-11 04:05:35,185 - __main__ - INFO - Attempt 2 for proving lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:05:35,185 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p9 (theorem_idx=214) with timeout: 600 seconds +2026-01-11 04:06:48,094 - __main__ - INFO - Prover for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:06:48,094 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 37 +SearchTimeInSecs: 193.77722764015198 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 37, 'attempt_idx': 1, 'total_queries': 55} + + + +2026-01-11 04:06:48,096 - __main__ - INFO - Attempting to prove lemma: imo_1959_p1 +2026-01-11 04:06:48,096 - __main__ - INFO - Attempt 2 for proving lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:06:48,096 - __main__ - INFO - Running the prover agent for lemma: imo_1959_p1 (theorem_idx=215) with timeout: 600 seconds +2026-01-11 04:08:44,179 - __main__ - INFO - Prover for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:08:44,180 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 488.39348220825195 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 52, 'attempt_idx': 1, 'total_queries': 152} + + + +2026-01-11 04:08:44,181 - __main__ - INFO - Attempting to prove lemma: imo_1960_p2 +2026-01-11 04:08:44,181 - __main__ - INFO - Attempt 2 for proving lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:08:44,181 - __main__ - INFO - Running the prover agent for lemma: imo_1960_p2 (theorem_idx=216) with timeout: 600 seconds +2026-01-11 04:09:28,371 - __main__ - INFO - Prover for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:09:28,372 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 104 +SearchTimeInSecs: 534.3858830928802 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 95, 'attempt_idx': 1, 'total_queries': 110} + + + +2026-01-11 04:09:28,374 - __main__ - INFO - Attempting to prove lemma: imo_1962_p2 +2026-01-11 04:09:28,374 - __main__ - INFO - Attempt 2 for proving lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:09:28,374 - __main__ - INFO - Running the prover agent for lemma: imo_1962_p2 (theorem_idx=217) with timeout: 600 seconds +2026-01-11 04:09:32,647 - __main__ - INFO - Prover for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:09:32,647 - __main__ - INFO - Dumping proof search result: +theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 154.83434867858887 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 1, 'total_queries': 34} + + + +2026-01-11 04:09:32,649 - __main__ - INFO - Attempting to prove lemma: imo_1963_p5 +2026-01-11 04:09:32,649 - __main__ - INFO - Attempt 2 for proving lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:09:32,649 - __main__ - INFO - Running the prover agent for lemma: imo_1963_p5 (theorem_idx=218) with timeout: 600 seconds +2026-01-11 04:10:16,181 - __main__ - INFO - Prover for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:10:16,181 - __main__ - INFO - Dumping proof search result: +theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 35.46665096282959 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 17} + + + +2026-01-11 04:10:16,183 - __main__ - INFO - Attempting to prove lemma: imo_1964_p2 +2026-01-11 04:10:16,183 - __main__ - INFO - Attempt 2 for proving lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:10:16,183 - __main__ - INFO - Running the prover agent for lemma: imo_1964_p2 (theorem_idx=219) with timeout: 600 seconds +2026-01-11 04:10:55,497 - __main__ - INFO - Prover for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:10:55,497 - __main__ - INFO - Dumping proof search result: +theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := + +by + + + +ProofFile: None +LemmaName: theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 19.00426983833313 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 1, 'total_queries': 23} + + + +2026-01-11 04:10:55,499 - __main__ - INFO - Attempting to prove lemma: imo_1965_p2 +2026-01-11 04:10:55,499 - __main__ - INFO - Attempt 2 for proving lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:10:55,500 - __main__ - INFO - Running the prover agent for lemma: imo_1965_p2 (theorem_idx=220) with timeout: 600 seconds +2026-01-11 04:12:33,133 - __main__ - INFO - Prover for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:12:33,133 - __main__ - INFO - Dumping proof search result: +theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 221.05434560775757 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 1, 'total_queries': 33} + + + +2026-01-11 04:12:33,135 - __main__ - INFO - Attempting to prove lemma: imo_1968_p5_1 +2026-01-11 04:12:33,135 - __main__ - INFO - Attempt 2 for proving lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:12:33,135 - __main__ - INFO - Running the prover agent for lemma: imo_1968_p5_1 (theorem_idx=221) with timeout: 600 seconds +2026-01-11 04:13:54,437 - __main__ - INFO - Prover for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:13:54,437 - __main__ - INFO - Dumping proof search result: +theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 153.56011867523193 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 1, 'total_queries': 20} + + + +2026-01-11 04:13:54,439 - __main__ - INFO - Attempting to prove lemma: imo_1969_p2 +2026-01-11 04:13:54,439 - __main__ - INFO - Attempt 2 for proving lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:13:54,439 - __main__ - INFO - Running the prover agent for lemma: imo_1969_p2 (theorem_idx=222) with timeout: 600 seconds +2026-01-11 04:14:02,423 - __main__ - INFO - Prover for lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:14:02,424 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := + +by +norm_num +set L5 := Real.log 5 / Real.log 2 with hL5 +-- Introduce the non‑zero hypotheses needed for `Real.log_mul` +have h5ne : (5 : ℝ) ≠ 0 := by exact ne_of_gt (by norm_num) +have h16ne : (16 : ℝ) ≠ 0 := by exact ne_of_gt (by norm_num) +have h32ne : (32 : ℝ) ≠ 0 := by exact ne_of_gt (by norm_num) +have h4ne : (4 : ℝ) ≠ 0 := by exact ne_of_gt (by norm_num) +have h8ne : (8 : ℝ) ≠ 0 := by exact ne_of_gt (by norm_num) + + +ProofFile: None +LemmaName: theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 110 +SearchTimeInSecs: 495.88635325431824 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 1, 'total_queries': 141} + + + +2026-01-11 04:14:02,425 - __main__ - INFO - Attempting to prove lemma: imo_1974_p3 +2026-01-11 04:14:02,425 - __main__ - INFO - Attempt 2 for proving lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:14:02,426 - __main__ - INFO - Running the prover agent for lemma: imo_1974_p3 (theorem_idx=223) with timeout: 600 seconds +2026-01-11 04:15:04,222 - __main__ - INFO - Prover for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:15:04,222 - __main__ - INFO - Dumping proof search result: +theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := + +by + + + +ProofFile: None +LemmaName: theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 62.698484659194946 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 18} + + + +2026-01-11 04:15:04,225 - __main__ - INFO - Attempting to prove lemma: imo_1977_p6 +2026-01-11 04:15:04,225 - __main__ - INFO - Attempt 2 for proving lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:15:04,225 - __main__ - INFO - Running the prover agent for lemma: imo_1977_p6 (theorem_idx=224) with timeout: 600 seconds +2026-01-11 04:15:44,050 - __main__ - INFO - Prover for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:15:44,050 - __main__ - INFO - Dumping proof search result: +theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 361.35489225387573 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 30, 'attempt_idx': 1, 'total_queries': 41} + + + +2026-01-11 04:15:44,052 - __main__ - INFO - Attempting to prove lemma: imo_1981_p6 +2026-01-11 04:15:44,052 - __main__ - INFO - Attempt 2 for proving lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:15:44,052 - __main__ - INFO - Running the prover agent for lemma: imo_1981_p6 (theorem_idx=225) with timeout: 600 seconds +2026-01-11 04:15:55,528 - __main__ - INFO - Prover Agent for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:15:55,682 - __main__ - INFO - Failed to prove lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:15:55,682 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: imo_1974_p3 + +2026-01-11 04:15:55,684 - __main__ - INFO - Attempting to prove lemma: imo_1982_p1 +2026-01-11 04:15:55,684 - __main__ - INFO - Attempt 2 for proving lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:15:55,684 - __main__ - INFO - Running the prover agent for lemma: imo_1982_p1 (theorem_idx=226) with timeout: 600 seconds +2026-01-11 04:16:57,745 - __main__ - INFO - Prover Agent for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:16:57,901 - __main__ - INFO - Failed to prove lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:16:57,901 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: imo_1981_p6 + +2026-01-11 04:16:57,903 - __main__ - INFO - Attempting to prove lemma: imo_1983_p6 +2026-01-11 04:16:57,903 - __main__ - INFO - Attempt 2 for proving lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:16:57,903 - __main__ - INFO - Running the prover agent for lemma: imo_1983_p6 (theorem_idx=227) with timeout: 600 seconds +2026-01-11 04:18:20,782 - __main__ - INFO - Prover for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:18:20,782 - __main__ - INFO - Dumping proof search result: +theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := + +by + + + +ProofFile: None +LemmaName: theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 31 +SearchTimeInSecs: 325.9814555644989 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 1, 'total_queries': 29} + + + +2026-01-11 04:18:20,786 - __main__ - INFO - Attempting to prove lemma: imo_1984_p6 +2026-01-11 04:18:20,786 - __main__ - INFO - Attempt 2 for proving lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:18:20,786 - __main__ - INFO - Running the prover agent for lemma: imo_1984_p6 (theorem_idx=228) with timeout: 600 seconds +2026-01-11 04:18:24,853 - __main__ - INFO - Prover for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:18:24,853 - __main__ - INFO - Dumping proof search result: +theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 79.19929218292236 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 1, 'total_queries': 15} + + + +2026-01-11 04:18:24,855 - __main__ - INFO - Attempting to prove lemma: imo_1985_p6 +2026-01-11 04:18:24,855 - __main__ - INFO - Attempt 2 for proving lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:18:24,855 - __main__ - INFO - Running the prover agent for lemma: imo_1985_p6 (theorem_idx=229) with timeout: 600 seconds +2026-01-11 04:19:27,242 - __main__ - INFO - Prover for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:19:27,242 - __main__ - INFO - Dumping proof search result: +theorem imo_1985_p6 + (f : ℕ → NNReal → ℝ) + (h₀ : ∀ x, f 1 x = x) + (h₁ : ∀ x n, f (n + 1) x = f n x * (f n x + 1 / n)) : + ∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := + +by +apply? + + +ProofFile: None +LemmaName: theorem imo_1985_p6 + (f : ℕ → NNReal → ℝ) + (h₀ : ∀ x, f 1 x = x) + (h₁ : ∀ x n, f (n + 1) x = f n x * (f n x + 1 / n)) : + ∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 31.221400022506714 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 1, 'total_queries': 5} + + + +2026-01-11 04:19:27,244 - __main__ - INFO - Attempting to prove lemma: imo_1992_p1 +2026-01-11 04:19:27,244 - __main__ - INFO - Attempt 2 for proving lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:19:27,244 - __main__ - INFO - Running the prover agent for lemma: imo_1992_p1 (theorem_idx=230) with timeout: 600 seconds +2026-01-11 04:20:01,836 - __main__ - INFO - Prover for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:20:01,836 - __main__ - INFO - Dumping proof search result: +theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 24.0419819355011 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 1, 'total_queries': 15} + + + +2026-01-11 04:20:01,838 - __main__ - INFO - Attempting to prove lemma: imo_1997_p5 +2026-01-11 04:20:01,838 - __main__ - INFO - Attempt 2 for proving lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:20:01,838 - __main__ - INFO - Running the prover agent for lemma: imo_1997_p5 (theorem_idx=231) with timeout: 600 seconds +2026-01-11 04:23:00,205 - __main__ - INFO - Prover for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:23:00,205 - __main__ - INFO - Dumping proof search result: +theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 264.70497155189514 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 1, 'total_queries': 17} + + + +2026-01-11 04:23:00,207 - __main__ - INFO - Attempting to prove lemma: imo_2001_p6 +2026-01-11 04:23:00,207 - __main__ - INFO - Attempt 2 for proving lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:23:00,207 - __main__ - INFO - Running the prover agent for lemma: imo_2001_p6 (theorem_idx=232) with timeout: 600 seconds +2026-01-11 04:25:04,364 - __main__ - INFO - Prover Agent for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:25:04,519 - __main__ - INFO - Failed to prove lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:25:04,519 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1977_p6 + +2026-01-11 04:25:04,521 - __main__ - INFO - Attempting to prove lemma: imo_2019_p1 +2026-01-11 04:25:04,521 - __main__ - INFO - Attempt 2 for proving lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:25:04,521 - __main__ - INFO - Running the prover agent for lemma: imo_2019_p1 (theorem_idx=233) with timeout: 600 seconds +2026-01-11 04:25:11,852 - __main__ - INFO - Prover for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:25:11,852 - __main__ - INFO - Dumping proof search result: +theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 116.09119963645935 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 16} + + + +2026-01-11 04:25:11,854 - __main__ - INFO - Attempting to prove lemma: imosl_2007_algebra_p6 +2026-01-11 04:25:11,854 - __main__ - INFO - Attempt 2 for proving lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:25:11,854 - __main__ - INFO - Running the prover agent for lemma: imosl_2007_algebra_p6 (theorem_idx=234) with timeout: 600 seconds +2026-01-11 04:25:55,875 - __main__ - INFO - Prover Agent for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:25:56,011 - __main__ - INFO - Failed to prove lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:25:56,011 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1982_p1 + +2026-01-11 04:25:56,013 - __main__ - INFO - Attempting to prove lemma: induction_11div10tonmn1ton +2026-01-11 04:25:56,013 - __main__ - INFO - Attempt 2 for proving lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:25:56,013 - __main__ - INFO - Running the prover agent for lemma: induction_11div10tonmn1ton (theorem_idx=235) with timeout: 600 seconds +2026-01-11 04:28:04,622 - __main__ - INFO - Prover for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:28:04,622 - __main__ - INFO - Dumping proof search result: +theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 148.64550161361694 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 1, 'total_queries': 38} + + + +2026-01-11 04:28:04,624 - __main__ - INFO - Attempting to prove lemma: induction_12dvd4expnp1p20 +2026-01-11 04:28:04,624 - __main__ - INFO - Skipping the attempt for proving lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:28:04,627 - __main__ - INFO - Attempting to prove lemma: induction_1pxpownlt1pnx +2026-01-11 04:28:04,627 - __main__ - INFO - Attempt 2 for proving lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:28:04,627 - __main__ - INFO - Running the prover agent for lemma: induction_1pxpownlt1pnx (theorem_idx=237) with timeout: 600 seconds +2026-01-11 04:28:44,761 - __main__ - INFO - Prover for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:28:44,761 - __main__ - INFO - Dumping proof search result: +theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := + +by + + + +ProofFile: None +LemmaName: theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 149.85522174835205 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 27, 'attempt_idx': 1, 'total_queries': 44} + + + +2026-01-11 04:28:44,763 - __main__ - INFO - Attempting to prove lemma: induction_nfactltnexpnm1ngt3 +2026-01-11 04:28:44,763 - __main__ - INFO - Attempt 2 for proving lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:28:44,763 - __main__ - INFO - Running the prover agent for lemma: induction_nfactltnexpnm1ngt3 (theorem_idx=238) with timeout: 600 seconds +2026-01-11 04:29:36,934 - __main__ - INFO - Prover for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:29:36,934 - __main__ - INFO - Dumping proof search result: +theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := + +by + + + +ProofFile: None +LemmaName: theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 74.3596305847168 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 1, 'total_queries': 15} + + + +2026-01-11 04:29:36,936 - __main__ - INFO - Attempting to prove lemma: induction_pord1p1on2powklt5on2 +2026-01-11 04:29:36,936 - __main__ - INFO - Attempt 2 for proving lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:29:36,936 - __main__ - INFO - Running the prover agent for lemma: induction_pord1p1on2powklt5on2 (theorem_idx=239) with timeout: 600 seconds +2026-01-11 04:30:01,337 - __main__ - INFO - Prover for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:30:01,337 - __main__ - INFO - Dumping proof search result: +theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := + +by + + + +ProofFile: None +LemmaName: theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 67.84966969490051 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 1, 'total_queries': 9} + + + +2026-01-11 04:30:01,339 - __main__ - INFO - Attempting to prove lemma: induction_pprime_pdvdapowpma +2026-01-11 04:30:01,339 - __main__ - INFO - Attempt 2 for proving lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:30:01,339 - __main__ - INFO - Running the prover agent for lemma: induction_pprime_pdvdapowpma (theorem_idx=240) with timeout: 600 seconds +2026-01-11 04:30:02,028 - __main__ - INFO - Prover Agent for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:30:02,189 - __main__ - INFO - Failed to prove lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:30:02,189 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1997_p5 + +2026-01-11 04:30:02,191 - __main__ - INFO - Attempting to prove lemma: induction_prod1p1onk3le3m1onn +2026-01-11 04:30:02,191 - __main__ - INFO - Attempt 2 for proving lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:30:02,191 - __main__ - INFO - Running the prover agent for lemma: induction_prod1p1onk3le3m1onn (theorem_idx=241) with timeout: 600 seconds +2026-01-11 04:30:30,975 - __main__ - INFO - Prover for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:30:30,976 - __main__ - INFO - Dumping proof search result: +theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := + +by + + + +ProofFile: None +LemmaName: theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 12.446749210357666 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 1, 'total_queries': 6} + + + +2026-01-11 04:30:30,977 - __main__ - INFO - Attempting to prove lemma: induction_sumkexp3eqsumksq +2026-01-11 04:30:30,978 - __main__ - INFO - Attempt 2 for proving lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:30:30,978 - __main__ - INFO - Running the prover agent for lemma: induction_sumkexp3eqsumksq (theorem_idx=242) with timeout: 600 seconds +2026-01-11 04:31:49,463 - __main__ - INFO - Prover for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:31:49,463 - __main__ - INFO - Dumping proof search result: +theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 120.470787525177 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 1, 'total_queries': 34} + + + +2026-01-11 04:32:54,789 - __main__ - INFO - Prover for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:32:54,789 - __main__ - INFO - Dumping proof search result: +theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 130.01475954055786 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 1, 'total_queries': 34} + + + +2026-01-11 04:35:04,706 - __main__ - INFO - Prover Agent for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:35:04,862 - __main__ - INFO - Failed to prove lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:35:04,862 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_2019_p1 + +2026-01-11 04:39:23,917 - __main__ - INFO - Prover for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:39:23,917 - __main__ - INFO - Dumping proof search result: +theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := + +by +induction' n with n ih +simp +by_cases hpos : 0 < n +-- Step 1: express the product up to `n+1` as the product up to `n` times the last factor +have hprod : + ∏ k ∈ Finset.Icc 1 (n + 1), (1 + 1 / (k : ℝ) ^ 3) = + (∏ k ∈ Finset.Icc 1 n, (1 + 1 / (k : ℝ) ^ 3)) * + (1 + 1 / ((n + 1 : ℝ) ^ 3)) := by + simpa [Finset.prod_Icc_succ_top] +have hle : ∏ k ∈ Finset.Icc 1 n, (1 + 1 / (k : ℝ) ^ 3) ≤ 3 - 1 / (n : ℝ) := by + exact ih hpos +have hmul : + (∏ k ∈ Finset.Icc 1 n, (1 + 1 / (k : ℝ) ^ 3)) * + (1 + 1 / ((n + 1 : ℝ) ^ 3)) ≤ + (3 - 1 / (n : ℝ)) * (1 + 1 / ((n + 1 : ℝ) ^ 3)) := by + -- the last factor is positive + have hpos_factor : (0 : ℝ) ≤ 1 + 1 / ((n + 1 : ℝ) ^ 3) := by + have hpos' : (0 : ℝ) < (n + 1 : ℝ) := by positivity + have : 0 < 1 / ((n + 1 : ℝ) ^ 3) := by + exact div_pos (by norm_num) (by positivity) + linarith + exact mul_le_mul_of_nonneg_right hle hpos_factor + + +ProofFile: None +LemmaName: theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 102 +SearchTimeInSecs: 548.3815395832062 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 1, 'total_queries': 155} + + + +2026-01-11 04:39:23,952 - __main__ - INFO - Reloaded checkpoint info for attempt 3 +2026-01-11 04:39:24,036 - __main__ - INFO - Reloaded proof results for attempt 3 +2026-01-11 04:39:24,037 - __main__ - INFO - Getting all lemmas in file: data/test/miniF2F-lean4/MiniF2F/Test.lean with timeout: 3000 seconds +2026-01-11 04:39:24,095 - __main__ - INFO - Discovered 244 lemmas +2026-01-11 04:39:24,095 - __main__ - INFO - Lemma names: ['mathd_algebra_478', 'numbertheory_4x3m7y3neq2003', 'aime_1983_p1', 'amc12_2001_p5', 'mathd_algebra_141', 'mathd_numbertheory_3', 'imo_1969_p2', 'mathd_algebra_44', 'mathd_algebra_209', 'mathd_numbertheory_1124'] ... ['aime_1989_p8', 'mathd_numbertheory_296', 'mathd_algebra_142', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'mathd_algebra_400', 'aime_1995_p7', 'mathd_numbertheory_185', 'mathd_algebra_441', 'mathd_numbertheory_582', 'mathd_algebra_338'] +2026-01-11 04:39:24,124 - __main__ - INFO - Discovered 243 lemmas to prove in data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:39:24,125 - __main__ - INFO - Lemmas to prove in file data/test/miniF2F-lean4/MiniF2F/Test.lean: +['aime_1983_p2', 'aime_1989_p8', 'algebra_sqineq_at2malt1', 'amc12a_2002_p6', 'amc12a_2013_p4', 'amc12a_2021_p9', 'amc12b_2002_p19', 'amc12b_2002_p2', 'amc12b_2020_p2', 'amc12b_2020_p6', 'mathd_algebra_125', 'mathd_algebra_129', 'mathd_algebra_137', 'mathd_algebra_139', 'mathd_algebra_141', 'mathd_algebra_142', 'mathd_algebra_143', 'mathd_algebra_148', 'mathd_algebra_158', 'mathd_algebra_160', 'mathd_algebra_171', 'mathd_algebra_176', 'mathd_algebra_24', 'mathd_algebra_246', 'mathd_algebra_263', 'mathd_algebra_270', 'mathd_algebra_296', 'mathd_algebra_302', 'mathd_algebra_304', 'mathd_algebra_314', 'mathd_algebra_329', 'mathd_algebra_33', 'mathd_algebra_346', 'mathd_algebra_354', 'mathd_algebra_359', 'mathd_algebra_388', 'mathd_algebra_400', 'mathd_algebra_412', 'mathd_algebra_419', 'mathd_algebra_432', 'mathd_algebra_44', 'mathd_algebra_440', 'mathd_algebra_441', 'mathd_algebra_478', 'mathd_algebra_513', 'mathd_algebra_76', 'mathd_algebra_80', 'mathd_numbertheory_12', 'mathd_numbertheory_127', 'mathd_numbertheory_135', 'mathd_numbertheory_150', 'mathd_numbertheory_175', 'mathd_numbertheory_185', 'mathd_numbertheory_207', 'mathd_numbertheory_212', 'mathd_numbertheory_229', 'mathd_numbertheory_235', 'mathd_numbertheory_237', 'mathd_numbertheory_239', 'mathd_numbertheory_247', 'mathd_numbertheory_254', 'mathd_numbertheory_299', 'mathd_numbertheory_3', 'mathd_numbertheory_341', 'mathd_numbertheory_342', 'mathd_numbertheory_343', 'mathd_numbertheory_345', 'mathd_numbertheory_517', 'mathd_numbertheory_551', 'mathd_numbertheory_66', 'mathd_numbertheory_728', 'mathd_numbertheory_769', 'mathd_numbertheory_85', 'mathd_algebra_107', 'mathd_algebra_113', 'mathd_algebra_114', 'mathd_algebra_153', 'mathd_algebra_156', 'mathd_algebra_17', 'mathd_algebra_170', 'mathd_algebra_184', 'mathd_algebra_188', 'mathd_algebra_196', 'mathd_algebra_208', 'mathd_algebra_209', 'mathd_algebra_215', 'mathd_algebra_275', 'mathd_algebra_276', 'mathd_algebra_288', 'mathd_algebra_289', 'mathd_algebra_293', 'mathd_algebra_313', 'mathd_algebra_320', 'mathd_algebra_332', 'mathd_algebra_338', 'mathd_algebra_342', 'mathd_algebra_362', 'mathd_algebra_392', 'mathd_algebra_398', 'mathd_algebra_427', 'mathd_algebra_452', 'mathd_algebra_459', 'mathd_algebra_484', 'mathd_algebra_487', 'mathd_algebra_598', 'mathd_algebra_756', 'mathd_numbertheory_100', 'mathd_numbertheory_1124', 'mathd_numbertheory_222', 'mathd_numbertheory_227', 'mathd_numbertheory_233', 'mathd_numbertheory_234', 'mathd_numbertheory_277', 'mathd_numbertheory_293', 'mathd_numbertheory_296', 'mathd_numbertheory_314', 'mathd_numbertheory_320', 'mathd_numbertheory_321', 'mathd_numbertheory_328', 'mathd_numbertheory_34', 'mathd_numbertheory_353', 'mathd_numbertheory_427', 'mathd_numbertheory_430', 'mathd_numbertheory_435', 'mathd_numbertheory_447', 'mathd_numbertheory_451', 'mathd_numbertheory_457', 'mathd_numbertheory_483', 'mathd_numbertheory_495', 'mathd_numbertheory_5', 'mathd_numbertheory_521', 'mathd_numbertheory_541', 'mathd_numbertheory_552', 'mathd_numbertheory_559', 'mathd_numbertheory_582', 'mathd_numbertheory_618', 'mathd_numbertheory_711', 'mathd_numbertheory_764', 'mathd_numbertheory_765', 'mathd_numbertheory_99', 'numbertheory_2pownm1prime_nprime', 'numbertheory_3pow2pownm1mod2pownp3eq2pownp2', 'numbertheory_4x3m7y3neq2003', 'numbertheory_aoddbdiv4asqpbsqmod8eq1', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown', 'numbertheory_x5neqy2p4', 'aime_1983_p1', 'aime_1983_p3', 'aime_1984_p1', 'aime_1984_p7', 'aime_1987_p5', 'aime_1988_p8', 'aime_1990_p15', 'aime_1990_p4', 'aime_1991_p9', 'aime_1994_p3', 'aime_1995_p7', 'aime_1997_p9', 'aime_1999_p11', 'algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7', 'algebra_9onxpypzleqsum2onxpy', 'algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2', 'algebra_absapbon1pabsapbleqsumabsaon1pabsa', 'algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1', 'algebra_amgm_sum1toneqn_prod1tonleq1', 'algebra_amgm_sumasqdivbgeqsuma', 'algebra_apbmpcneq0_aeq0anbeq0anceq0', 'algebra_apbon2pownleqapownpbpowon2', 'algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3', 'algebra_bleqa_apbon2msqrtableqambsqon8b', 'algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778', 'algebra_ineq_nto1onlt2m1on', 'algebra_others_exirrpowirrrat', 'algebra_sqineq_unitcircatbpabsamblt1', 'algebra_sqineq_unitcircatbpamblt1', 'algebra_sum1onsqrt2to1onsqrt10000lt198', 'amc12_2000_p1', 'amc12_2000_p12', 'amc12_2000_p20', 'amc12_2000_p6', 'amc12_2001_p21', 'amc12_2001_p5', 'amc12a_2002_p13', 'amc12a_2003_p23', 'amc12a_2003_p5', 'amc12a_2008_p25', 'amc12a_2009_p6', 'amc12a_2009_p7', 'amc12a_2019_p12', 'amc12a_2020_p10', 'amc12a_2020_p15', 'amc12a_2020_p25', 'amc12a_2020_p4', 'amc12a_2020_p7', 'amc12a_2020_p9', 'amc12a_2021_p12', 'amc12a_2021_p14', 'amc12a_2021_p18', 'amc12a_2021_p19', 'amc12a_2021_p22', 'amc12a_2021_p25', 'amc12a_2021_p3', 'amc12a_2021_p8', 'amc12b_2002_p4', 'amc12b_2002_p7', 'amc12b_2020_p13', 'amc12b_2020_p21', 'amc12b_2020_p22', 'amc12b_2021_p1', 'amc12b_2021_p13', 'amc12b_2021_p18', 'amc12b_2021_p3', 'amc12b_2021_p4', 'amc12b_2021_p9', 'imo_1959_p1', 'imo_1960_p2', 'imo_1962_p2', 'imo_1963_p5', 'imo_1964_p2', 'imo_1965_p2', 'imo_1968_p5_1', 'imo_1969_p2', 'imo_1974_p3', 'imo_1977_p6', 'imo_1981_p6', 'imo_1982_p1', 'imo_1983_p6', 'imo_1984_p6', 'imo_1985_p6', 'imo_1992_p1', 'imo_1997_p5', 'imo_2001_p6', 'imo_2019_p1', 'imosl_2007_algebra_p6', 'induction_11div10tonmn1ton', 'induction_12dvd4expnp1p20', 'induction_1pxpownlt1pnx', 'induction_nfactltnexpnm1ngt3', 'induction_pord1p1on2powklt5on2', 'induction_pprime_pdvdapowpma', 'induction_prod1p1onk3le3m1onn', 'induction_sumkexp3eqsumksq'] +2026-01-11 04:39:24,125 - __main__ - INFO - Executing 243 theorems in parallel using 4 workers +2026-01-11 04:39:24,174 - __main__ - INFO - Attempting to prove lemma: aime_1983_p2 +2026-01-11 04:39:24,175 - __main__ - INFO - Attempt 3 for proving lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:39:24,175 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p2 (theorem_idx=0) with timeout: 600 seconds +2026-01-11 04:39:24,180 - __main__ - INFO - Attempting to prove lemma: aime_1989_p8 +2026-01-11 04:39:24,180 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,182 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_at2malt1 +2026-01-11 04:39:24,183 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,185 - __main__ - INFO - Attempting to prove lemma: amc12a_2013_p4 +2026-01-11 04:39:24,185 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,186 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p6 +2026-01-11 04:39:24,186 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,188 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p9 +2026-01-11 04:39:24,188 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,191 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p19 +2026-01-11 04:39:24,191 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,194 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p2 +2026-01-11 04:39:24,194 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,195 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p2 +2026-01-11 04:39:24,195 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,197 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p6 +2026-01-11 04:39:24,197 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,199 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_125 +2026-01-11 04:39:24,199 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,200 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_129 +2026-01-11 04:39:24,200 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,202 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_137 +2026-01-11 04:39:24,202 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,203 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_139 +2026-01-11 04:39:24,204 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,205 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_141 +2026-01-11 04:39:24,205 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:39:24,205 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_141 (theorem_idx=14) with timeout: 600 seconds +2026-01-11 04:39:24,206 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_142 +2026-01-11 04:39:24,206 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,208 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_143 +2026-01-11 04:39:24,208 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,209 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_148 +2026-01-11 04:39:24,209 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,212 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_158 +2026-01-11 04:39:24,212 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:39:24,212 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_158 (theorem_idx=18) with timeout: 600 seconds +2026-01-11 04:39:24,212 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_160 +2026-01-11 04:39:24,213 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,215 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_171 +2026-01-11 04:39:24,216 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,218 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_176 +2026-01-11 04:39:24,218 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,220 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_24 +2026-01-11 04:39:24,220 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,222 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_246 +2026-01-11 04:39:24,222 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:39:24,225 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_263 +2026-01-11 04:39:24,225 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:39:24,225 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_263 (theorem_idx=24) with timeout: 600 seconds +2026-01-11 04:40:05,280 - __main__ - INFO - Prover for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:40:05,281 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 34.02934145927429 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 15} + + + +2026-01-11 04:40:05,283 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_270 +2026-01-11 04:40:05,283 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:40:05,283 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_270 (theorem_idx=25) with timeout: 600 seconds +2026-01-11 04:40:16,711 - __main__ - INFO - Prover for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:40:16,711 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 39.34453010559082 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 17} + + + +2026-01-11 04:40:16,714 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_296 +2026-01-11 04:40:16,714 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,716 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_302 +2026-01-11 04:40:16,716 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,719 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_304 +2026-01-11 04:40:16,719 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,722 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_314 +2026-01-11 04:40:16,722 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,725 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_329 +2026-01-11 04:40:16,725 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,728 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_33 +2026-01-11 04:40:16,728 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,730 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_346 +2026-01-11 04:40:16,731 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,733 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_354 +2026-01-11 04:40:16,733 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,735 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_359 +2026-01-11 04:40:16,735 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,737 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_388 +2026-01-11 04:40:16,737 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,739 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_400 +2026-01-11 04:40:16,739 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,741 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_412 +2026-01-11 04:40:16,741 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,743 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_419 +2026-01-11 04:40:16,743 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,744 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_432 +2026-01-11 04:40:16,744 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,746 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_44 +2026-01-11 04:40:16,746 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:16,748 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_440 +2026-01-11 04:40:16,748 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:40:16,748 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_440 (theorem_idx=41) with timeout: 600 seconds +2026-01-11 04:40:54,998 - __main__ - INFO - Prover for lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:40:54,998 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := + +by +-- Express f 1 in terms of the definition +have h1 : f 1 = 1 / (1 + 2) := h₀ 1 (by norm_num) +-- Show that f 1 is not -2 so we can apply h₀ to x = f 1 +have hne : f 1 ≠ -2 := by + have : (1 : ℝ) / (1 + 2) ≠ -2 := by norm_num + simpa [h1] using this +-- Apply the definition to f (f 1) +have h2 : f (f 1) = 1 / (f 1 + 2) := h₀ (f 1) hne +-- Simplify the goal using the two equalities +simp [h1, h2] +field_simp +simp +have h3 : f ((1 + 2)⁻¹) = 1 / ((1 + 2)⁻¹ + 2) := by + simpa [h1] using h2 +simp [h3] +field_simp +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_270 + (f : ℝ → ℝ) + (h₀ : ∀ x, x ≠ -2 -> f x = 1 / (x + 2)) : + f (f 1) = 3/7 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 23.38656210899353 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 10} + + + +2026-01-11 04:40:55,000 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_441 +2026-01-11 04:40:55,000 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:55,003 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_478 +2026-01-11 04:40:55,003 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:55,006 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_513 +2026-01-11 04:40:55,006 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:55,009 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_76 +2026-01-11 04:40:55,009 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:40:55,011 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_80 +2026-01-11 04:40:55,011 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:40:55,011 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_80 (theorem_idx=46) with timeout: 600 seconds +2026-01-11 04:41:21,868 - __main__ - INFO - Prover for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:41:21,868 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 14.740355730056763 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 12} + + + +2026-01-11 04:41:21,870 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_12 +2026-01-11 04:41:21,870 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:21,873 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_127 +2026-01-11 04:41:21,873 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:21,876 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_135 +2026-01-11 04:41:21,876 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:21,879 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_150 +2026-01-11 04:41:21,879 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:41:21,879 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_150 (theorem_idx=50) with timeout: 600 seconds +2026-01-11 04:41:29,648 - __main__ - INFO - Prover for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:41:29,648 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 100.38325023651123 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 2, 'total_queries': 75} + + + +2026-01-11 04:41:29,650 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_175 +2026-01-11 04:41:29,650 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,653 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_185 +2026-01-11 04:41:29,653 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,656 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_207 +2026-01-11 04:41:29,656 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,659 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_212 +2026-01-11 04:41:29,659 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,661 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_229 +2026-01-11 04:41:29,661 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,664 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_235 +2026-01-11 04:41:29,664 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,666 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_237 +2026-01-11 04:41:29,666 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,669 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_239 +2026-01-11 04:41:29,669 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:41:29,671 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_247 +2026-01-11 04:41:29,671 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:41:29,671 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_247 (theorem_idx=59) with timeout: 600 seconds +2026-01-11 04:43:58,000 - __main__ - INFO - Prover for lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:43:58,000 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := + +by +field_simp at h₀; linarith [h₀] + + +ProofFile: None +LemmaName: theorem mathd_algebra_440 + (x : ℝ) + (h₀ : 3 / 2 / 3 = x / 10) : + x = 5 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 66 +SearchTimeInSecs: 194.82344007492065 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 57, 'attempt_idx': 2, 'total_queries': 70} + + + +2026-01-11 04:43:58,002 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_254 +2026-01-11 04:43:58,002 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,005 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_299 +2026-01-11 04:43:58,005 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,008 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_3 +2026-01-11 04:43:58,008 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,011 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_341 +2026-01-11 04:43:58,011 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,014 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_342 +2026-01-11 04:43:58,014 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,017 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_343 +2026-01-11 04:43:58,017 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,019 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_345 +2026-01-11 04:43:58,019 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,021 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_517 +2026-01-11 04:43:58,021 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,023 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_551 +2026-01-11 04:43:58,023 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,025 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_66 +2026-01-11 04:43:58,025 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,027 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_728 +2026-01-11 04:43:58,027 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,029 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_769 +2026-01-11 04:43:58,029 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,031 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_85 +2026-01-11 04:43:58,031 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:43:58,032 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_107 +2026-01-11 04:43:58,032 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:43:58,032 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_107 (theorem_idx=73) with timeout: 600 seconds +2026-01-11 04:44:33,185 - __main__ - INFO - Prover for lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:44:33,185 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := + +by +calc + (x + 4) ^ 2 + (y - 3) ^ 2 + = x ^ 2 + 8 * x + y ^ 2 - 6 * y + 25 := by ring + _ = 0 + 25 := by simpa [h₀] + _ = 25 := by norm_num + _ = 5 ^ 2 := by norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_107 + (x y : ℝ) + (h₀ : x^2 + 8 * x + y^2 - 6 * y = 0) : + (x + 4)^2 + (y-3)^2 = 5^2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 17.043540239334106 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 10} + + + +2026-01-11 04:44:33,187 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_113 +2026-01-11 04:44:33,187 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:44:33,191 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_114 +2026-01-11 04:44:33,191 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:44:33,191 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_114 (theorem_idx=75) with timeout: 600 seconds +2026-01-11 04:45:18,107 - __main__ - INFO - Prover for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:45:18,107 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 210.95460295677185 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 2, 'total_queries': 41} + + + +2026-01-11 04:45:18,110 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_153 +2026-01-11 04:45:18,110 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:45:18,113 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_156 +2026-01-11 04:45:18,113 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:45:18,113 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_156 (theorem_idx=77) with timeout: 600 seconds +2026-01-11 04:49:03,678 - __main__ - INFO - Prover for lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:49:03,678 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := + +by +-- Convert the hypothesis into a modular congruence +have h1 : (3 * n) ≡ 2 [MOD 11] := by + simpa [Nat.ModEq] using h₀ +-- Multiply both sides by the inverse of 3 modulo 11 (which is 4) +have h2 : (12 * n) ≡ 8 [MOD 11] := by + simpa [Nat.mul_comm, Nat.mul_left_comm, Nat.mul_assoc] using + (Nat.ModEq.mul_left 4 h1) +-- Turn the ModEq into an equality of remainders and simplify +have h3 : n % 11 = 8 := by + -- `h2` is an equality of remainders + have h2' : (12 * n) % 11 = 8 % 11 := by + simpa using h2 + -- Since 12 ≡ 1 (mod 11), the left side reduces to `n % 11` + simpa [Nat.mul_mod, Nat.mod_mul_left_mod] using h2' +exact h3 + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_247 + (n : ℕ) + (h₀ : (3 * n) % 11 = 2) : + n % 11 = 8 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 65 +SearchTimeInSecs: 436.68887734413147 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 64, 'attempt_idx': 2, 'total_queries': 68} + + + +2026-01-11 04:49:03,680 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_17 +2026-01-11 04:49:03,680 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:49:03,680 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_17 (theorem_idx=78) with timeout: 600 seconds +2026-01-11 04:49:16,003 - __main__ - INFO - Prover for lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:49:16,004 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := + +by + -- Compute the second finite sum as an integer +have hsum2 : (∑ k in Finset.range 5, (a + 2 * k) : ℤ) = 5 * (a : ℤ) + 20 := by norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 110 +SearchTimeInSecs: 567.8091804981232 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 2, 'total_queries': 111} + + + +2026-01-11 04:49:16,006 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_170 +2026-01-11 04:49:16,006 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:49:16,009 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_184 +2026-01-11 04:49:16,009 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:49:16,009 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_184 (theorem_idx=80) with timeout: 600 seconds +2026-01-11 04:50:02,596 - __main__ - INFO - Prover for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:50:02,596 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_17 + (a : ℝ) + (h₀ : Real.sqrt (4 + Real.sqrt (16 + 16 * a)) + Real.sqrt (1 + Real.sqrt (1 + a)) = 6) : + a = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 43.4576780796051 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 2, 'total_queries': 14} + + + +2026-01-11 04:50:02,598 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_188 +2026-01-11 04:50:02,598 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:50:02,601 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_196 +2026-01-11 04:50:02,601 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:50:02,601 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_196 (theorem_idx=82) with timeout: 600 seconds +2026-01-11 04:50:29,639 - __main__ - INFO - Prover for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:50:29,639 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 63.38524675369263 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 2, 'total_queries': 37} + + + +2026-01-11 04:50:29,641 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_208 +2026-01-11 04:50:29,641 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:50:29,641 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_208 (theorem_idx=83) with timeout: 600 seconds +2026-01-11 04:50:30,924 - __main__ - INFO - Prover for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:50:30,924 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := + +by +simp [h₀] at * +norm_num +have h1 : (64 : ℝ) ^ (1 / 3) = 4 := by norm_num +simp [h1] at * +norm_num +have h1 : (64 : ℝ) ^ (1 / 3) = 4 := by norm_num +simp [h1] at * +norm_num +simp [h1] +cases h₀ + + +ProofFile: None +LemmaName: theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 121 +SearchTimeInSecs: 339.14033603668213 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 2, 'total_queries': 160} + + + +2026-01-11 04:50:30,926 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_209 +2026-01-11 04:50:30,926 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:50:30,929 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_215 +2026-01-11 04:50:30,929 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:50:30,929 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_215 (theorem_idx=85) with timeout: 600 seconds +2026-01-11 04:51:21,510 - __main__ - INFO - Prover for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:51:21,510 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 43.007166385650635 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 2, 'total_queries': 20} + + + +2026-01-11 04:51:21,514 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_275 +2026-01-11 04:51:21,514 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:51:21,514 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_275 (theorem_idx=86) with timeout: 600 seconds +2026-01-11 04:51:26,628 - __main__ - INFO - Prover for lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:51:26,628 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := + +by +-- First, identify the concrete elements of `S` using the given characterization +have hS : S = ({-1, 5} : Finset ℝ) := by + ext x + constructor + · intro hx + have hx' : |2 - x| = (3 : ℝ) := (h₀ x).1 hx + have : 2 - x = 3 ∨ 2 - x = -3 := by + simpa [abs_eq] using hx' + rcases this with h | h + · have : x = -1 := by linarith + simpa [Finset.mem_insert, Finset.mem_singleton, this] + · have : x = 5 := by linarith + simpa [Finset.mem_insert, Finset.mem_singleton, this] + · intro hx + have hx' : x = -1 ∨ x = 5 := by + simpa [Finset.mem_insert, Finset.mem_singleton] using hx + rcases hx' with h | h + · subst h + have : |2 - (-1)| = (3 : ℝ) := by norm_num + exact (h₀ _).2 this + · subst h + have : |2 - (5 : ℝ)| = (3 : ℝ) := by norm_num + exact (h₀ _).2 this +-- Compute the sum using the explicit description of `S` +simp [hS, Finset.sum_insert, Finset.sum_singleton, Finset.mem_insert, Finset.mem_singleton] +norm_num + + +ProofFile: None +LemmaName: theorem mathd_algebra_196 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ abs (2 - x) = 3) : + ∑ k ∈ S, k = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 54.979313135147095 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 2, 'total_queries': 30} + + + +2026-01-11 04:51:26,631 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_276 +2026-01-11 04:51:26,631 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:51:26,631 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_276 (theorem_idx=87) with timeout: 600 seconds +2026-01-11 04:51:27,360 - __main__ - INFO - Prover for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:51:27,360 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 45.36877226829529 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 25} + + + +2026-01-11 04:51:27,362 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_288 +2026-01-11 04:51:27,362 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:51:27,363 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_288 (theorem_idx=88) with timeout: 600 seconds +2026-01-11 04:53:02,253 - __main__ - INFO - Prover for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:53:02,253 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 88.34760570526123 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 60} + + + +2026-01-11 04:53:02,258 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_289 +2026-01-11 04:53:02,258 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:53:02,262 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_293 +2026-01-11 04:53:02,262 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:53:02,267 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_313 +2026-01-11 04:53:02,267 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:53:02,267 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_313 (theorem_idx=91) with timeout: 600 seconds +2026-01-11 04:55:18,290 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 04:55:18,519 - __main__ - INFO - Failed to prove lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:55:18,520 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_156 + +2026-01-11 04:55:18,522 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_320 +2026-01-11 04:55:18,522 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:55:18,522 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_320 (theorem_idx=92) with timeout: 600 seconds +2026-01-11 04:55:28,483 - __main__ - INFO - Prover for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:55:28,483 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 227.74739027023315 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 2, 'total_queries': 68} + + + +2026-01-11 04:55:28,485 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_332 +2026-01-11 04:55:28,485 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:55:28,485 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_332 (theorem_idx=93) with timeout: 600 seconds +2026-01-11 04:57:19,277 - __main__ - INFO - Prover for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:57:19,277 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 92.9657392501831 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 2, 'total_queries': 23} + + + +2026-01-11 04:57:19,279 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_338 +2026-01-11 04:57:19,279 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:57:19,282 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_342 +2026-01-11 04:57:19,282 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:57:19,285 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_362 +2026-01-11 04:57:19,285 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:57:19,285 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_362 (theorem_idx=96) with timeout: 600 seconds +2026-01-11 04:58:42,312 - __main__ - INFO - Prover for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:58:42,312 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 113 +SearchTimeInSecs: 324.1302399635315 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 93, 'attempt_idx': 2, 'total_queries': 116} + + + +2026-01-11 04:58:42,314 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_392 +2026-01-11 04:58:42,314 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:58:42,314 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_392 (theorem_idx=97) with timeout: 600 seconds +2026-01-11 04:58:46,678 - __main__ - INFO - Prover for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 04:58:46,678 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 199.84609007835388 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 2, 'total_queries': 17} + + + +2026-01-11 04:58:46,680 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_398 +2026-01-11 04:58:46,680 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:58:46,683 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_427 +2026-01-11 04:58:46,683 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 04:58:46,686 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_452 +2026-01-11 04:58:46,686 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 04:58:46,686 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_452 (theorem_idx=100) with timeout: 600 seconds +2026-01-11 05:01:27,548 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:01:27,711 - __main__ - INFO - Failed to prove lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:01:27,711 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_288 + +2026-01-11 05:01:27,713 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_459 +2026-01-11 05:01:27,713 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:01:27,715 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_484 +2026-01-11 05:01:27,715 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:01:27,717 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_487 +2026-01-11 05:01:27,718 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:01:27,718 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_487 (theorem_idx=103) with timeout: 600 seconds +2026-01-11 05:03:20,462 - __main__ - INFO - Prover for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:03:20,462 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 102.7048978805542 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 2, 'total_queries': 15} + + + +2026-01-11 05:03:20,464 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_598 +2026-01-11 05:03:20,464 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:03:20,464 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_598 (theorem_idx=104) with timeout: 600 seconds +2026-01-11 05:05:59,728 - __main__ - INFO - Prover for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:05:59,728 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 65 +SearchTimeInSecs: 425.7493669986725 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 63, 'attempt_idx': 2, 'total_queries': 76} + + + +2026-01-11 05:05:59,730 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_756 +2026-01-11 05:05:59,730 - __main__ - INFO - Attempt 3 for proving lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:05:59,730 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_756 (theorem_idx=105) with timeout: 600 seconds +2026-01-11 05:06:30,270 - __main__ - INFO - Prover for lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:06:30,270 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := + +by +have ha : a = Real.log 5 / Real.log 4 := by + have h : Real.log (4 ^ a) = Real.log 5 := by + simpa using congrArg Real.log h₁ + have h' : a * Real.log 4 = Real.log 5 := by + simpa [Real.log_rpow] using h + field_simp [h'] +-- Derive the logarithmic expressions for b, c, and d +have hb : b = Real.log 6 / Real.log 5 := by + have h : Real.log (5 ^ b) = Real.log 6 := by + simpa using congrArg Real.log h₂ + have h' : b * Real.log 5 = Real.log 6 := by + simpa [Real.log_rpow] using h + field_simp [h'] +have hc : c = Real.log 7 / Real.log 6 := by + have h : Real.log (6 ^ c) = Real.log 7 := by + simpa using congrArg Real.log h₃ + have h' : c * Real.log 6 = Real.log 7 := by + simpa [Real.log_rpow] using h + field_simp [h'] +have hd : d = Real.log 8 / Real.log 7 := by + have h : Real.log (7 ^ d) = Real.log 8 := by + simpa using congrArg Real.log h₄ + have h' : d * Real.log 7 = Real.log 8 := by + simpa [Real.log_rpow] using h + field_simp [h'] +-- Use the four equalities to simplify the product +field_simp [ha, hb, hc, hd] +ring +have h4 : Real.log (2 ^ 2) = 2 * Real.log 2 := by + simpa using Real.log_rpow (2 : ℝ) 2 +have h8 : Real.log (2 ^ 3) = 3 * Real.log 2 := by + simpa using Real.log_rpow (2 : ℝ) 3 +have h4' : Real.log 4 = 2 * Real.log 2 := by + have : (4 : ℝ) = 2 ^ 2 := by norm_num + simpa [this] using h4 +have h8' : Real.log 8 = 3 * Real.log 2 := by + have : (8 : ℝ) = 2 ^ 3 := by norm_num + simpa [this] using h8 +simp [h4', h8'] +ring + + +ProofFile: None +LemmaName: theorem mathd_algebra_598 + (a b c d : ℝ) + (h₁ : ((4:ℝ)^a) = 5) + (h₂ : ((5:ℝ)^b) = 6) + (h₃ : ((6:ℝ)^c) = 7) + (h₄ : ((7:ℝ)^d) = 8) : + a * b * c * d = 3 / 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 169.1121485233307 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 2, 'total_queries': 41} + + + +2026-01-11 05:06:30,272 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_100 +2026-01-11 05:06:30,272 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:06:30,272 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_100 (theorem_idx=106) with timeout: 600 seconds +2026-01-11 05:07:08,095 - __main__ - INFO - Prover for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:07:08,095 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 56.02709078788757 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 2, 'total_queries': 14} + + + +2026-01-11 05:07:08,097 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_1124 +2026-01-11 05:07:08,097 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:07:08,097 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_1124 (theorem_idx=107) with timeout: 600 seconds +2026-01-11 05:07:19,464 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:07:19,630 - __main__ - INFO - Failed to prove lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:07:19,630 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_362 + +2026-01-11 05:07:19,632 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_222 +2026-01-11 05:07:19,632 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:07:19,635 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_227 +2026-01-11 05:07:19,635 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:07:19,635 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_227 (theorem_idx=109) with timeout: 600 seconds +2026-01-11 05:08:35,730 - __main__ - INFO - Prover for lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:08:35,730 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 110.31636762619019 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 2, 'total_queries': 51} + + + +2026-01-11 05:08:35,732 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_233 +2026-01-11 05:08:35,732 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:08:35,732 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_233 (theorem_idx=110) with timeout: 600 seconds +2026-01-11 05:08:46,863 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:08:47,028 - __main__ - INFO - Failed to prove lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:08:47,029 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_452 + +2026-01-11 05:08:47,033 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_234 +2026-01-11 05:08:47,034 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:08:47,034 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_234 (theorem_idx=111) with timeout: 600 seconds +2026-01-11 05:09:27,413 - __main__ - INFO - Prover for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:09:27,413 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 38.059956312179565 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 2, 'total_queries': 34} + + + +2026-01-11 05:09:27,415 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_277 +2026-01-11 05:09:27,415 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:09:27,415 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_277 (theorem_idx=112) with timeout: 600 seconds +2026-01-11 05:17:08,238 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:17:08,400 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:17:08,400 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_1124 + +2026-01-11 05:17:08,402 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_293 +2026-01-11 05:17:08,402 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:17:08,403 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_293 (theorem_idx=113) with timeout: 600 seconds +2026-01-11 05:17:19,784 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:17:19,949 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:17:19,949 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_227 + +2026-01-11 05:17:19,951 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_296 +2026-01-11 05:17:19,951 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:17:19,951 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_296 (theorem_idx=114) with timeout: 600 seconds +2026-01-11 05:17:48,485 - __main__ - INFO - Prover for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:17:48,485 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 94 +SearchTimeInSecs: 519.6565146446228 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 88, 'attempt_idx': 2, 'total_queries': 110} + + + +2026-01-11 05:17:48,487 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_314 +2026-01-11 05:17:48,487 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:17:48,490 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_320 +2026-01-11 05:17:48,490 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:17:48,490 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_320 (theorem_idx=116) with timeout: 600 seconds +2026-01-11 05:19:27,576 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:19:27,742 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:19:27,743 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_277 + +2026-01-11 05:19:27,745 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_321 +2026-01-11 05:19:27,745 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:19:27,745 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_321 (theorem_idx=117) with timeout: 600 seconds +2026-01-11 05:22:13,484 - __main__ - INFO - Prover for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:22:13,484 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 151.23786640167236 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 2, 'total_queries': 85} + + + +2026-01-11 05:22:13,486 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_328 +2026-01-11 05:22:13,486 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:22:13,489 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_34 +2026-01-11 05:22:13,490 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:22:13,490 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_34 (theorem_idx=119) with timeout: 600 seconds +2026-01-11 05:22:17,458 - __main__ - INFO - Prover for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:22:17,458 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 251.95387840270996 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 30, 'attempt_idx': 2, 'total_queries': 45} + + + +2026-01-11 05:22:17,460 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_353 +2026-01-11 05:22:17,460 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:22:17,460 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_353 (theorem_idx=120) with timeout: 600 seconds +2026-01-11 05:24:56,001 - __main__ - INFO - Prover for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:24:56,001 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 149.28684329986572 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 2, 'total_queries': 18} + + + +2026-01-11 05:24:56,004 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_427 +2026-01-11 05:24:56,004 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:24:56,004 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_427 (theorem_idx=121) with timeout: 600 seconds +2026-01-11 05:25:19,706 - __main__ - INFO - Prover for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:25:19,706 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 173.41095733642578 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 42, 'attempt_idx': 2, 'total_queries': 100} + + + +2026-01-11 05:25:19,708 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_430 +2026-01-11 05:25:19,708 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:25:19,708 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_430 (theorem_idx=122) with timeout: 600 seconds +2026-01-11 05:26:57,370 - __main__ - INFO - Prover for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:26:57,370 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 89.50961351394653 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 22} + + + +2026-01-11 05:26:57,372 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_435 +2026-01-11 05:26:57,372 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:26:57,372 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_435 (theorem_idx=123) with timeout: 600 seconds +2026-01-11 05:27:08,581 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:27:08,710 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:27:08,710 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_293 + +2026-01-11 05:27:08,712 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_447 +2026-01-11 05:27:08,712 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:27:08,715 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_451 +2026-01-11 05:27:08,715 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:27:08,715 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_451 (theorem_idx=125) with timeout: 600 seconds +2026-01-11 05:27:20,037 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:27:20,208 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:27:20,208 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_296 + +2026-01-11 05:27:20,211 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_457 +2026-01-11 05:27:20,211 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:27:20,211 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_457 (theorem_idx=126) with timeout: 600 seconds +2026-01-11 05:27:47,170 - __main__ - INFO - Prover for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:27:47,170 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 42 +SearchTimeInSecs: 163.35295915603638 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 39, 'attempt_idx': 2, 'total_queries': 139} + + + +2026-01-11 05:27:47,172 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_483 +2026-01-11 05:27:47,172 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:27:47,175 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_495 +2026-01-11 05:27:47,175 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:27:47,175 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_495 (theorem_idx=128) with timeout: 600 seconds +2026-01-11 05:30:47,846 - __main__ - INFO - Prover for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:30:47,847 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 195.12593340873718 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 48, 'attempt_idx': 2, 'total_queries': 56} + + + +2026-01-11 05:30:47,849 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_5 +2026-01-11 05:30:47,849 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:30:47,849 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_5 (theorem_idx=129) with timeout: 600 seconds +2026-01-11 05:33:23,008 - __main__ - INFO - Prover for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:33:23,008 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 64 +SearchTimeInSecs: 364.83179783821106 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 58, 'attempt_idx': 2, 'total_queries': 128} + + + +2026-01-11 05:33:23,010 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_521 +2026-01-11 05:33:23,010 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:33:23,010 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_521 (theorem_idx=130) with timeout: 600 seconds +2026-01-11 05:33:58,893 - __main__ - INFO - Prover for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:33:58,893 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 179.86379861831665 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 22} + + + +2026-01-11 05:33:58,895 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_541 +2026-01-11 05:33:58,895 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:33:58,895 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_541 (theorem_idx=131) with timeout: 600 seconds +2026-01-11 05:34:42,995 - __main__ - INFO - Prover for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:34:42,995 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 41 +SearchTimeInSecs: 451.7189311981201 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 2, 'total_queries': 50} + + + +2026-01-11 05:34:42,998 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_552 +2026-01-11 05:34:42,998 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:34:42,998 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_552 (theorem_idx=132) with timeout: 600 seconds +2026-01-11 05:37:05,348 - __main__ - INFO - Prover for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:37:05,349 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 163.22230291366577 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 2, 'total_queries': 79} + + + +2026-01-11 05:37:05,351 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_559 +2026-01-11 05:37:05,351 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:37:05,354 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_582 +2026-01-11 05:37:05,354 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:37:05,361 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_618 +2026-01-11 05:37:05,361 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:37:05,362 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_618 (theorem_idx=135) with timeout: 600 seconds +2026-01-11 05:37:42,294 - __main__ - INFO - Prover for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:37:42,295 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 168.4158718585968 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 2, 'total_queries': 27} + + + +2026-01-11 05:37:42,297 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_711 +2026-01-11 05:37:42,297 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:37:42,297 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_711 (theorem_idx=136) with timeout: 600 seconds +2026-01-11 05:37:47,269 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:37:47,433 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:37:47,433 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_495 + +2026-01-11 05:37:47,435 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_764 +2026-01-11 05:37:47,436 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:37:47,436 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_764 (theorem_idx=137) with timeout: 600 seconds +2026-01-11 05:38:42,013 - __main__ - INFO - Prover for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:38:42,013 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 40.11486005783081 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 4} + + + +2026-01-11 05:38:42,015 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_765 +2026-01-11 05:38:42,015 - __main__ - INFO - Attempt 3 for proving lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:38:42,015 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_765 (theorem_idx=138) with timeout: 600 seconds +2026-01-11 05:41:48,470 - __main__ - INFO - Prover for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:41:48,470 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 268.8919141292572 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 2, 'total_queries': 28} + + + +2026-01-11 05:41:48,472 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_99 +2026-01-11 05:41:48,472 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:41:48,475 - __main__ - INFO - Attempting to prove lemma: numbertheory_2pownm1prime_nprime +2026-01-11 05:41:48,475 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:41:48,475 - __main__ - INFO - Running the prover agent for lemma: numbertheory_2pownm1prime_nprime (theorem_idx=140) with timeout: 600 seconds +2026-01-11 05:41:55,988 - __main__ - INFO - Prover for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:41:55,988 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 183.92014050483704 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 2, 'total_queries': 17} + + + +2026-01-11 05:41:55,991 - __main__ - INFO - Attempting to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 +2026-01-11 05:41:55,991 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:41:55,991 - __main__ - INFO - Running the prover agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 (theorem_idx=141) with timeout: 600 seconds +2026-01-11 05:42:17,040 - __main__ - INFO - Prover for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:42:17,041 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 16.209883451461792 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 2, 'total_queries': 5} + + + +2026-01-11 05:42:17,043 - __main__ - INFO - Attempting to prove lemma: numbertheory_4x3m7y3neq2003 +2026-01-11 05:42:17,043 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:42:17,043 - __main__ - INFO - Running the prover agent for lemma: numbertheory_4x3m7y3neq2003 (theorem_idx=142) with timeout: 600 seconds +2026-01-11 05:43:23,190 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:43:23,354 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:43:23,354 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_521 + +2026-01-11 05:43:23,356 - __main__ - INFO - Attempting to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 +2026-01-11 05:43:23,356 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:43:23,356 - __main__ - INFO - Running the prover agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 (theorem_idx=143) with timeout: 600 seconds +2026-01-11 05:47:42,477 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:47:42,639 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:47:42,639 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_711 + +2026-01-11 05:47:42,641 - __main__ - INFO - Attempting to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 +2026-01-11 05:47:42,641 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:47:42,641 - __main__ - INFO - Running the prover agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 (theorem_idx=144) with timeout: 600 seconds +2026-01-11 05:48:48,413 - __main__ - INFO - Prover for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:48:48,413 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_exk2powkeqapb2mulbpa2_aeq1 + (a b : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : ∃ k > 0, 2^k = (a + b^2) * (b + a^2)) : + a = 1 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_exk2powkeqapb2mulbpa2_aeq1 + (a b : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : ∃ k > 0, 2^k = (a + b^2) * (b + a^2)) : + a = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 40.84894037246704 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 6} + + + +2026-01-11 05:48:48,415 - __main__ - INFO - Attempting to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown +2026-01-11 05:48:48,415 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:48:48,415 - __main__ - INFO - Running the prover agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown (theorem_idx=145) with timeout: 600 seconds +2026-01-11 05:51:56,177 - __main__ - INFO - Prover Agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:51:56,339 - __main__ - INFO - Failed to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:51:56,339 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + +2026-01-11 05:51:56,341 - __main__ - INFO - Attempting to prove lemma: numbertheory_x5neqy2p4 +2026-01-11 05:51:56,341 - __main__ - INFO - Attempt 3 for proving lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:51:56,341 - __main__ - INFO - Running the prover agent for lemma: numbertheory_x5neqy2p4 (theorem_idx=146) with timeout: 600 seconds +2026-01-11 05:52:17,118 - __main__ - INFO - Prover Agent for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:52:17,281 - __main__ - INFO - Failed to prove lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:52:17,281 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_4x3m7y3neq2003 + +2026-01-11 05:52:17,283 - __main__ - INFO - Attempting to prove lemma: aime_1983_p1 +2026-01-11 05:52:17,283 - __main__ - INFO - Attempt 3 for proving lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:52:17,283 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p1 (theorem_idx=147) with timeout: 600 seconds +2026-01-11 05:53:01,117 - __main__ - INFO - Prover for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:53:01,118 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 242.68990564346313 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 2, 'total_queries': 26} + + + +2026-01-11 05:53:01,120 - __main__ - INFO - Attempting to prove lemma: aime_1983_p3 +2026-01-11 05:53:01,120 - __main__ - INFO - Attempt 3 for proving lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:53:01,120 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p3 (theorem_idx=148) with timeout: 600 seconds +2026-01-11 05:53:23,533 - __main__ - INFO - Prover Agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 05:53:23,694 - __main__ - INFO - Failed to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:53:23,694 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 + +2026-01-11 05:53:23,697 - __main__ - INFO - Attempting to prove lemma: aime_1984_p1 +2026-01-11 05:53:23,697 - __main__ - INFO - Attempt 3 for proving lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:53:23,697 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p1 (theorem_idx=149) with timeout: 600 seconds +2026-01-11 05:55:12,239 - __main__ - INFO - Prover for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:55:12,239 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 168.08360171318054 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 2, 'total_queries': 58} + + + +2026-01-11 05:55:12,241 - __main__ - INFO - Attempting to prove lemma: aime_1984_p7 +2026-01-11 05:55:12,241 - __main__ - INFO - Attempt 3 for proving lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:55:12,241 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p7 (theorem_idx=150) with timeout: 600 seconds +2026-01-11 05:57:49,983 - __main__ - INFO - Prover for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:57:49,983 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 137.78465366363525 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 34} + + + +2026-01-11 05:57:49,985 - __main__ - INFO - Attempting to prove lemma: aime_1987_p5 +2026-01-11 05:57:49,985 - __main__ - INFO - Attempt 3 for proving lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:57:49,985 - __main__ - INFO - Running the prover agent for lemma: aime_1987_p5 (theorem_idx=151) with timeout: 600 seconds +2026-01-11 05:59:28,060 - __main__ - INFO - Prover for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:59:28,060 - __main__ - INFO - Dumping proof search result: +theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 87.83529543876648 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 2, 'total_queries': 22} + + + +2026-01-11 05:59:28,062 - __main__ - INFO - Attempting to prove lemma: aime_1988_p8 +2026-01-11 05:59:28,062 - __main__ - INFO - Attempt 3 for proving lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:59:28,062 - __main__ - INFO - Running the prover agent for lemma: aime_1988_p8 (theorem_idx=152) with timeout: 600 seconds +2026-01-11 05:59:51,320 - __main__ - INFO - Prover for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:59:51,320 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 47 +SearchTimeInSecs: 389.341388463974 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 2, 'total_queries': 51} + + + +2026-01-11 05:59:51,322 - __main__ - INFO - Attempting to prove lemma: aime_1990_p15 +2026-01-11 05:59:51,322 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:59:51,325 - __main__ - INFO - Attempting to prove lemma: aime_1990_p4 +2026-01-11 05:59:51,325 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 05:59:51,328 - __main__ - INFO - Attempting to prove lemma: aime_1991_p9 +2026-01-11 05:59:51,328 - __main__ - INFO - Attempt 3 for proving lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:59:51,328 - __main__ - INFO - Running the prover agent for lemma: aime_1991_p9 (theorem_idx=155) with timeout: 600 seconds +2026-01-11 05:59:54,532 - __main__ - INFO - Prover for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 05:59:54,532 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 58 +SearchTimeInSecs: 469.7427890300751 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 50, 'attempt_idx': 2, 'total_queries': 58} + + + +2026-01-11 05:59:54,534 - __main__ - INFO - Attempting to prove lemma: aime_1994_p3 +2026-01-11 05:59:54,534 - __main__ - INFO - Attempt 3 for proving lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 05:59:54,534 - __main__ - INFO - Running the prover agent for lemma: aime_1994_p3 (theorem_idx=156) with timeout: 600 seconds +2026-01-11 06:02:31,955 - __main__ - INFO - Prover for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:02:31,955 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 93 +SearchTimeInSecs: 532.6529982089996 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 89, 'attempt_idx': 2, 'total_queries': 89} + + + +2026-01-11 06:02:31,957 - __main__ - INFO - Attempting to prove lemma: aime_1995_p7 +2026-01-11 06:02:31,957 - __main__ - INFO - Attempt 3 for proving lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:02:31,957 - __main__ - INFO - Running the prover agent for lemma: aime_1995_p7 (theorem_idx=157) with timeout: 600 seconds +2026-01-11 06:03:58,998 - __main__ - INFO - Prover Agent for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:03:59,161 - __main__ - INFO - Failed to prove lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:03:59,161 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: aime_1994_p3 + +2026-01-11 06:03:59,163 - __main__ - INFO - Attempting to prove lemma: aime_1997_p9 +2026-01-11 06:03:59,163 - __main__ - INFO - Attempt 3 for proving lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:03:59,163 - __main__ - INFO - Running the prover agent for lemma: aime_1997_p9 (theorem_idx=158) with timeout: 600 seconds +2026-01-11 06:04:47,786 - __main__ - INFO - Prover for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:04:47,786 - __main__ - INFO - Dumping proof search result: +theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 109.12984585762024 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 29} + + + +2026-01-11 06:04:47,788 - __main__ - INFO - Attempting to prove lemma: aime_1999_p11 +2026-01-11 06:04:47,788 - __main__ - INFO - Attempt 3 for proving lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:04:47,788 - __main__ - INFO - Running the prover agent for lemma: aime_1999_p11 (theorem_idx=159) with timeout: 600 seconds +2026-01-11 06:05:08,844 - __main__ - INFO - Prover for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:05:08,844 - __main__ - INFO - Dumping proof search result: +theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1988_p8 + (f : ℕ → ℕ → ℝ) + (h₀ : ∀ x, 0 < x → f x x = x) + (h₁ : ∀ x y, (0 < x ∧ 0 < y) → f x y = f y x) + (h₂ : ∀ x y, (0 < x ∧ 0 < y) → (↑x + ↑y) * f x y = y * (f x (x + y))) : + f 14 52 = 364 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 321.8274049758911 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 2, 'total_queries': 47} + + + +2026-01-11 06:05:08,846 - __main__ - INFO - Attempting to prove lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 +2026-01-11 06:05:08,846 - __main__ - INFO - Attempt 3 for proving lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:05:08,846 - __main__ - INFO - Running the prover agent for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 (theorem_idx=160) with timeout: 600 seconds +2026-01-11 06:08:14,875 - __main__ - INFO - Prover Agent for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:08:15,037 - __main__ - INFO - Failed to prove lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:08:15,038 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: aime_1999_p11 + +2026-01-11 06:08:15,040 - __main__ - INFO - Attempting to prove lemma: algebra_9onxpypzleqsum2onxpy +2026-01-11 06:08:15,040 - __main__ - INFO - Attempt 3 for proving lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:08:15,040 - __main__ - INFO - Running the prover agent for lemma: algebra_9onxpypzleqsum2onxpy (theorem_idx=161) with timeout: 600 seconds +2026-01-11 06:09:51,501 - __main__ - INFO - Prover Agent for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:09:51,664 - __main__ - INFO - Failed to prove lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:09:51,664 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1991_p9 + +2026-01-11 06:09:51,668 - __main__ - INFO - Attempting to prove lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 +2026-01-11 06:09:51,669 - __main__ - INFO - Attempt 3 for proving lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:09:51,669 - __main__ - INFO - Running the prover agent for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 (theorem_idx=162) with timeout: 600 seconds +2026-01-11 06:10:31,304 - __main__ - INFO - Prover for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:10:31,304 - __main__ - INFO - Dumping proof search result: +theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 122.24821138381958 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 22} + + + +2026-01-11 06:10:31,306 - __main__ - INFO - Attempting to prove lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa +2026-01-11 06:10:31,306 - __main__ - INFO - Attempt 3 for proving lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:10:31,306 - __main__ - INFO - Running the prover agent for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa (theorem_idx=163) with timeout: 600 seconds +2026-01-11 06:11:50,018 - __main__ - INFO - Prover for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:11:50,018 - __main__ - INFO - Dumping proof search result: +theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 106.07153725624084 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 2, 'total_queries': 21} + + + +2026-01-11 06:11:50,020 - __main__ - INFO - Attempting to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 +2026-01-11 06:11:50,020 - __main__ - INFO - Attempt 3 for proving lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:11:50,020 - __main__ - INFO - Running the prover agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 (theorem_idx=164) with timeout: 600 seconds +2026-01-11 06:13:11,105 - __main__ - INFO - Prover for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:13:11,105 - __main__ - INFO - Dumping proof search result: +theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 101 +SearchTimeInSecs: 471.02767038345337 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 95, 'attempt_idx': 2, 'total_queries': 104} + + + +2026-01-11 06:13:11,107 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 +2026-01-11 06:13:11,107 - __main__ - INFO - Attempt 3 for proving lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:13:11,107 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 (theorem_idx=165) with timeout: 600 seconds +2026-01-11 06:13:23,575 - __main__ - INFO - Prover for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:13:23,575 - __main__ - INFO - Dumping proof search result: +theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 158.67150688171387 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 2, 'total_queries': 28} + + + +2026-01-11 06:13:23,577 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sumasqdivbgeqsuma +2026-01-11 06:13:23,577 - __main__ - INFO - Attempt 3 for proving lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:13:23,577 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sumasqdivbgeqsuma (theorem_idx=166) with timeout: 600 seconds +2026-01-11 06:13:59,352 - __main__ - INFO - Prover Agent for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:13:59,515 - __main__ - INFO - Failed to prove lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:13:59,515 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1997_p9 + +2026-01-11 06:13:59,517 - __main__ - INFO - Attempting to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 +2026-01-11 06:13:59,517 - __main__ - INFO - Attempt 3 for proving lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:13:59,517 - __main__ - INFO - Running the prover agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 (theorem_idx=167) with timeout: 600 seconds +2026-01-11 06:14:44,190 - __main__ - INFO - Prover for lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:14:44,191 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sumasqdivbgeqsuma + (a b c d : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) : + a^2 / b + b^2 / c + c^2 / d + d^2 / a ≥ a + b + c + d := + +by +-- Prove each pairwise AM–GM inequality +have h_ab : a ^ 2 / b + b ≥ 2 * a := by + have hbpos : 0 < b := (h₀).2.1 + have h_eq : a ^ 2 / b + b - 2 * a = (a - b) ^ 2 / b := by + field_simp [pow_two] ; ring + have h_nonneg : 0 ≤ (a - b) ^ 2 / b := by + have h_num : 0 ≤ (a - b) ^ 2 := by exact pow_two_nonneg _ + exact div_nonneg h_num (le_of_lt hbpos) + have : a ^ 2 / b + b - 2 * a ≥ 0 := by + simpa [h_eq] using h_nonneg + linarith +have h_bc : b ^ 2 / c + c ≥ 2 * b := by + have hcpos : 0 < c := (h₀).2.2.1 + have h_eq : b ^ 2 / c + c - 2 * b = (b - c) ^ 2 / c := by + field_simp [pow_two] ; ring + have h_nonneg : 0 ≤ (b - c) ^ 2 / c := by + have h_num : 0 ≤ (b - c) ^ 2 := by exact pow_two_nonneg _ + exact div_nonneg h_num (le_of_lt hcpos) + have : b ^ 2 / c + c - 2 * b ≥ 0 := by + simpa [h_eq] using h_nonneg + linarith +have h_cd : c ^ 2 / d + d ≥ 2 * c := by + have hdpos : 0 < d := (h₀).2.2.2 + have h_eq : c ^ 2 / d + d - 2 * c = (c - d) ^ 2 / d := by + field_simp [pow_two] ; ring + have h_nonneg : 0 ≤ (c - d) ^ 2 / d := by + have h_num : 0 ≤ (c - d) ^ 2 := by exact pow_two_nonneg _ + exact div_nonneg h_num (le_of_lt hdpos) + have : c ^ 2 / d + d - 2 * c ≥ 0 := by + simpa [h_eq] using h_nonneg + linarith +have h_da : d ^ 2 / a + a ≥ 2 * d := by + have hapos : 0 < a := (h₀).1 + have h_eq : d ^ 2 / a + a - 2 * d = (d - a) ^ 2 / a := by + field_simp [pow_two] ; ring + have h_nonneg : 0 ≤ (d - a) ^ 2 / a := by + have h_num : 0 ≤ (d - a) ^ 2 := by exact pow_two_nonneg _ + exact div_nonneg h_num (le_of_lt hapos) + have : d ^ 2 / a + a - 2 * d ≥ 0 := by + simpa [h_eq] using h_nonneg + linarith + +-- Sum all four inequalities +have h_sum : a ^ 2 / b + b + b ^ 2 / c + c + c ^ 2 / d + d + d ^ 2 / a + a ≥ + 2 * a + 2 * b + 2 * c + 2 * d := by + have := add_le_add h_ab h_bc + have := add_le_add this h_cd + have := add_le_add this h_da + simpa [two_mul, add_comm, add_left_comm, add_assoc] using this + +-- Rearrange the inequality to the desired form +linarith + + +ProofFile: None +LemmaName: theorem algebra_amgm_sumasqdivbgeqsuma + (a b c d : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) : + a^2 / b + b^2 / c + c^2 / d + d^2 / a ≥ a + b + c + d := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 50.67834115028381 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 2, 'total_queries': 3} + + + +2026-01-11 06:14:44,192 - __main__ - INFO - Attempting to prove lemma: algebra_apbon2pownleqapownpbpowon2 +2026-01-11 06:14:44,193 - __main__ - INFO - Attempt 3 for proving lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:14:44,193 - __main__ - INFO - Running the prover agent for lemma: algebra_apbon2pownleqapownpbpowon2 (theorem_idx=168) with timeout: 600 seconds +2026-01-11 06:15:43,496 - __main__ - INFO - Prover for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:15:43,496 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 134.09623527526855 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 2, 'total_queries': 29} + + + +2026-01-11 06:15:43,498 - __main__ - INFO - Attempting to prove lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 +2026-01-11 06:15:43,498 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 06:15:43,501 - __main__ - INFO - Attempting to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b +2026-01-11 06:15:43,501 - __main__ - INFO - Attempt 3 for proving lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:15:43,501 - __main__ - INFO - Running the prover agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b (theorem_idx=170) with timeout: 600 seconds +2026-01-11 06:16:17,125 - __main__ - INFO - Prover for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:16:17,125 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 71.32959151268005 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 2, 'total_queries': 42} + + + +2026-01-11 06:16:17,127 - __main__ - INFO - Attempting to prove lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 +2026-01-11 06:16:17,127 - __main__ - INFO - Attempt 3 for proving lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:16:17,127 - __main__ - INFO - Running the prover agent for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 (theorem_idx=171) with timeout: 600 seconds +2026-01-11 06:16:43,258 - __main__ - INFO - Prover for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:16:43,258 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 154.12468028068542 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 12} + + + +2026-01-11 06:16:43,260 - __main__ - INFO - Attempting to prove lemma: algebra_ineq_nto1onlt2m1on +2026-01-11 06:16:43,260 - __main__ - INFO - Attempt 3 for proving lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:16:43,260 - __main__ - INFO - Running the prover agent for lemma: algebra_ineq_nto1onlt2m1on (theorem_idx=172) with timeout: 600 seconds +2026-01-11 06:21:50,169 - __main__ - INFO - Prover Agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:21:50,335 - __main__ - INFO - Failed to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:21:50,335 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + +2026-01-11 06:21:50,337 - __main__ - INFO - Attempting to prove lemma: algebra_others_exirrpowirrrat +2026-01-11 06:21:50,337 - __main__ - INFO - Attempt 3 for proving lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:21:50,337 - __main__ - INFO - Running the prover agent for lemma: algebra_others_exirrpowirrrat (theorem_idx=173) with timeout: 600 seconds +2026-01-11 06:23:46,592 - __main__ - INFO - Prover for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:23:46,592 - __main__ - INFO - Dumping proof search result: +theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 33 +SearchTimeInSecs: 430.9533452987671 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 37, 'attempt_idx': 2, 'total_queries': 83} + + + +2026-01-11 06:23:46,594 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpabsamblt1 +2026-01-11 06:23:46,595 - __main__ - INFO - Attempt 3 for proving lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:23:46,595 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpabsamblt1 (theorem_idx=174) with timeout: 600 seconds +2026-01-11 06:24:24,109 - __main__ - INFO - Prover for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:24:24,109 - __main__ - INFO - Dumping proof search result: +theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := + +by + + + +ProofFile: None +LemmaName: theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 443.88540625572205 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 50, 'attempt_idx': 2, 'total_queries': 50} + + + +2026-01-11 06:24:24,111 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpamblt1 +2026-01-11 06:24:24,111 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 06:24:24,114 - __main__ - INFO - Attempting to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 +2026-01-11 06:24:24,114 - __main__ - INFO - Attempt 3 for proving lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:24:24,114 - __main__ - INFO - Running the prover agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 (theorem_idx=176) with timeout: 600 seconds +2026-01-11 06:25:43,589 - __main__ - INFO - Prover Agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:25:43,757 - __main__ - INFO - Failed to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:25:43,757 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b + +2026-01-11 06:25:43,759 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p1 +2026-01-11 06:25:43,759 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:25:43,759 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p1 (theorem_idx=177) with timeout: 600 seconds +2026-01-11 06:25:59,168 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:25:59,168 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 124.96107816696167 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 2, 'total_queries': 20} + + + +2026-01-11 06:25:59,170 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p12 +2026-01-11 06:25:59,170 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:25:59,170 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p12 (theorem_idx=178) with timeout: 600 seconds +2026-01-11 06:26:42,487 - __main__ - INFO - Prover for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:26:42,487 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 42.531750440597534 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 15} + + + +2026-01-11 06:26:42,489 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p20 +2026-01-11 06:26:42,489 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:26:42,489 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p20 (theorem_idx=179) with timeout: 600 seconds +2026-01-11 06:29:42,556 - __main__ - INFO - Prover for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:29:42,556 - __main__ - INFO - Dumping proof search result: +theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 59 +SearchTimeInSecs: 456.6015245914459 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 59, 'attempt_idx': 2, 'total_queries': 71} + + + +2026-01-11 06:29:42,558 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p6 +2026-01-11 06:29:42,558 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:29:42,558 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p6 (theorem_idx=180) with timeout: 600 seconds +2026-01-11 06:29:53,918 - __main__ - INFO - Prover for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:29:53,919 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 222.20543265342712 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 2, 'total_queries': 62} + + + +2026-01-11 06:29:53,921 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p21 +2026-01-11 06:29:53,921 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:29:53,921 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p21 (theorem_idx=181) with timeout: 600 seconds +2026-01-11 06:30:56,416 - __main__ - INFO - Prover for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:30:56,416 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 229.97061824798584 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 2, 'total_queries': 21} + + + +2026-01-11 06:30:56,418 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p5 +2026-01-11 06:30:56,418 - __main__ - INFO - Attempt 3 for proving lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:30:56,418 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p5 (theorem_idx=182) with timeout: 600 seconds +2026-01-11 06:31:40,930 - __main__ - INFO - Prover for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:31:40,930 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 86.84052634239197 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 2, 'total_queries': 43} + + + +2026-01-11 06:31:40,932 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p13 +2026-01-11 06:31:40,932 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:31:40,932 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p13 (theorem_idx=183) with timeout: 600 seconds +2026-01-11 06:33:35,969 - __main__ - INFO - Prover for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:33:35,969 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 152.61392998695374 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 2, 'total_queries': 19} + + + +2026-01-11 06:33:35,971 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p23 +2026-01-11 06:33:35,971 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:33:35,971 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p23 (theorem_idx=184) with timeout: 600 seconds +2026-01-11 06:34:24,279 - __main__ - INFO - Prover Agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:34:24,444 - __main__ - INFO - Failed to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:34:24,444 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 + +2026-01-11 06:34:24,446 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p5 +2026-01-11 06:34:24,446 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 06:34:24,449 - __main__ - INFO - Attempting to prove lemma: amc12a_2008_p25 +2026-01-11 06:34:24,449 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:34:24,449 - __main__ - INFO - Running the prover agent for lemma: amc12a_2008_p25 (theorem_idx=186) with timeout: 600 seconds +2026-01-11 06:35:12,028 - __main__ - INFO - Prover for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:35:12,028 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 79.19535279273987 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 2, 'total_queries': 19} + + + +2026-01-11 06:35:12,030 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p6 +2026-01-11 06:35:12,030 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:35:12,030 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p6 (theorem_idx=187) with timeout: 600 seconds +2026-01-11 06:38:58,127 - __main__ - INFO - Prover for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:38:58,127 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 42 +SearchTimeInSecs: 202.96260952949524 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 2, 'total_queries': 52} + + + +2026-01-11 06:38:58,129 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p7 +2026-01-11 06:38:58,129 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:38:58,129 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p7 (theorem_idx=188) with timeout: 600 seconds +2026-01-11 06:39:11,162 - __main__ - INFO - Prover for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:39:11,162 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2008_p25 + (a b : ℕ → ℝ) + (h₀ : ∀ n, a (n + 1) = Real.sqrt 3 * a n - b n) + (h₁ : ∀ n, b (n + 1) = Real.sqrt 3 * b n + a n) + (h₂ : a 100 = 2) + (h₃ : b 100 = 4) : + a 1 + b 1 = 1 / (2^98) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2008_p25 + (a b : ℕ → ℝ) + (h₀ : ∀ n, a (n + 1) = Real.sqrt 3 * a n - b n) + (h₁ : ∀ n, b (n + 1) = Real.sqrt 3 * b n + a n) + (h₂ : a 100 = 2) + (h₃ : b 100 = 4) : + a 1 + b 1 = 1 / (2^98) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 264.49585700035095 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 2, 'total_queries': 16} + + + +2026-01-11 06:39:11,164 - __main__ - INFO - Attempting to prove lemma: amc12a_2019_p12 +2026-01-11 06:39:11,165 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:39:11,165 - __main__ - INFO - Running the prover agent for lemma: amc12a_2019_p12 (theorem_idx=189) with timeout: 600 seconds +2026-01-11 06:39:42,671 - __main__ - INFO - Prover Agent for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:39:42,834 - __main__ - INFO - Failed to prove lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:39:42,834 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12_2000_p6 + +2026-01-11 06:39:42,837 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p10 +2026-01-11 06:39:42,837 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:39:42,837 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p10 (theorem_idx=190) with timeout: 600 seconds +2026-01-11 06:41:41,118 - __main__ - INFO - Prover Agent for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:41:41,284 - __main__ - INFO - Failed to prove lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:41:41,284 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2002_p13 + +2026-01-11 06:41:41,286 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p15 +2026-01-11 06:41:41,286 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:41:41,286 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p15 (theorem_idx=191) with timeout: 600 seconds +2026-01-11 06:41:41,794 - __main__ - INFO - Prover for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:41:41,794 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p7 + (x : ℝ) + (n : ℕ) + (a : ℕ → ℝ) + (h₁ : ∀ m, a (m + 1) - a m = a (m + 2) - a (m + 1)) + (h₂ : a 1 = 2 * x - 3) + (h₃ : a 2 = 5 * x - 11) + (h₄ : a 3 = 3 * x + 1) + (h₅ : a n = 2009) : + n = 502 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2009_p7 + (x : ℝ) + (n : ℕ) + (a : ℕ → ℝ) + (h₁ : ∀ m, a (m + 1) - a m = a (m + 2) - a (m + 1)) + (h₂ : a 1 = 2 * x - 3) + (h₃ : a 2 = 5 * x - 11) + (h₄ : a 3 = 3 * x + 1) + (h₅ : a n = 2009) : + n = 502 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 143.3876552581787 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 2, 'total_queries': 16} + + + +2026-01-11 06:41:41,797 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p25 +2026-01-11 06:41:41,797 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:41:41,797 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p25 (theorem_idx=192) with timeout: 600 seconds +2026-01-11 06:43:52,645 - __main__ - INFO - Prover for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:43:52,645 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 104.30955362319946 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 2, 'total_queries': 18} + + + +2026-01-11 06:43:52,647 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p4 +2026-01-11 06:43:52,647 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:43:52,647 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p4 (theorem_idx=193) with timeout: 600 seconds +2026-01-11 06:45:20,868 - __main__ - INFO - Prover for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:45:20,868 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p10 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Real.logb 2 (Real.logb 16 n) = Real.logb 4 (Real.logb 4 n)) : + (Nat.digits 10 n).sum = 13 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p10 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Real.logb 2 (Real.logb 16 n) = Real.logb 4 (Real.logb 4 n)) : + (Nat.digits 10 n).sum = 13 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 33 +SearchTimeInSecs: 330.3094308376312 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 34, 'attempt_idx': 2, 'total_queries': 34} + + + +2026-01-11 06:45:20,870 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p7 +2026-01-11 06:45:20,870 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:45:20,870 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p7 (theorem_idx=194) with timeout: 600 seconds +2026-01-11 06:47:48,589 - __main__ - INFO - Prover for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:47:48,589 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 134.37694883346558 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 2, 'total_queries': 34} + + + +2026-01-11 06:47:48,591 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p9 +2026-01-11 06:47:48,591 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:47:48,591 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p9 (theorem_idx=195) with timeout: 600 seconds +2026-01-11 06:49:11,317 - __main__ - INFO - Prover Agent for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:49:11,506 - __main__ - INFO - Failed to prove lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:49:11,506 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2019_p12 + +2026-01-11 06:49:11,508 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p12 +2026-01-11 06:49:11,508 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:49:11,508 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p12 (theorem_idx=196) with timeout: 600 seconds +2026-01-11 06:49:28,835 - __main__ - INFO - Prover for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:49:28,836 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := + +by +classical +simp [h₀, Finset.card_filter] at * +norm_num +apply? + + +ProofFile: None +LemmaName: theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 308.69185066223145 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 37, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 2, 'total_queries': 37} + + + +2026-01-11 06:49:28,838 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p14 +2026-01-11 06:49:28,838 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:49:28,838 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p14 (theorem_idx=197) with timeout: 600 seconds +2026-01-11 06:51:39,939 - __main__ - INFO - Prover for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:51:39,939 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 213.967631816864 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 2, 'total_queries': 28} + + + +2026-01-11 06:51:39,941 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p18 +2026-01-11 06:51:39,941 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:51:39,941 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p18 (theorem_idx=198) with timeout: 600 seconds +2026-01-11 06:51:41,475 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 06:51:41,641 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:51:41,641 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p15 + +2026-01-11 06:51:41,643 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p19 +2026-01-11 06:51:41,643 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:51:41,643 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p19 (theorem_idx=199) with timeout: 600 seconds +2026-01-11 06:54:01,555 - __main__ - INFO - Prover for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:54:01,555 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 121.53080248832703 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 2, 'total_queries': 15} + + + +2026-01-11 06:54:01,557 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p22 +2026-01-11 06:54:01,557 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:54:01,557 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p22 (theorem_idx=200) with timeout: 600 seconds +2026-01-11 06:55:57,711 - __main__ - INFO - Prover for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:55:57,711 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 31 +SearchTimeInSecs: 373.8540070056915 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 2, 'total_queries': 55} + + + +2026-01-11 06:55:57,713 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p25 +2026-01-11 06:55:57,713 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:55:57,714 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p25 (theorem_idx=201) with timeout: 600 seconds +2026-01-11 06:57:35,409 - __main__ - INFO - Prover for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:57:35,409 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 73.15875244140625 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 19} + + + +2026-01-11 06:57:35,411 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p3 +2026-01-11 06:57:35,411 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 06:57:35,414 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p8 +2026-01-11 06:57:35,414 - __main__ - INFO - Attempt 3 for proving lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:57:35,414 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p8 (theorem_idx=203) with timeout: 600 seconds +2026-01-11 06:58:15,026 - __main__ - INFO - Prover for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 06:58:15,026 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 52 +SearchTimeInSecs: 520.468861579895 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 46, 'attempt_idx': 2, 'total_queries': 46} + + + +2026-01-11 06:58:15,028 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p4 +2026-01-11 06:58:15,028 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 06:58:15,028 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p4 (theorem_idx=204) with timeout: 600 seconds +2026-01-11 07:01:11,298 - __main__ - INFO - Prover for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:01:11,298 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := + +by +have h1eq : f (1 : ℚ) = 0 := by + -- Apply the multiplicative property with x = 1 and y = 1 + have h := h₀ (1 : ℚ) (by norm_num) (1 : ℚ) (by norm_num) + -- h : f (1 * 1) = f 1 + f 1 + -- Simplify the left hand side + have h' : f (1 : ℚ) = f (1 : ℚ) + f (1 : ℚ) := by + simpa using h + -- Rearrange to solve for f 1 + linarith + -- First prove the values of `f` at the primes `5` and `11` +have h5 : f (5 : ℚ) = (5 : ℝ) := by + exact h₁ 5 (by decide) +have h11 : f (11 : ℚ) = (11 : ℝ) := by + exact h₁ 11 (by decide) + + +ProofFile: None +LemmaName: theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 104 +SearchTimeInSecs: 556.5469830036163 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 2, 'total_queries': 105} + + + +2026-01-11 07:01:11,300 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p7 +2026-01-11 07:01:11,300 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:01:11,300 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p7 (theorem_idx=205) with timeout: 600 seconds +2026-01-11 07:01:18,579 - __main__ - INFO - Prover for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:01:18,579 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 206.50738096237183 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 2, 'total_queries': 14} + + + +2026-01-11 07:01:18,581 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p13 +2026-01-11 07:01:18,581 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:01:18,581 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p13 (theorem_idx=206) with timeout: 600 seconds +2026-01-11 07:03:20,583 - __main__ - INFO - Prover for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:03:20,583 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p7 + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : b = a + 1) + (h₂ : c = b + 1) + (h₃ : a * b * c = 8 * (a + b + c)) : + a^2 + (b^2 + c^2) = 77 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p7 + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : b = a + 1) + (h₂ : c = b + 1) + (h₃ : a * b * c = 8 * (a + b + c)) : + a^2 + (b^2 + c^2) = 77 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 116.80040168762207 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 2, 'total_queries': 10} + + + +2026-01-11 07:03:20,585 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p21 +2026-01-11 07:03:20,585 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:03:20,585 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p21 (theorem_idx=207) with timeout: 600 seconds +2026-01-11 07:03:38,323 - __main__ - INFO - Prover for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:03:38,324 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 116.27505135536194 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 2, 'total_queries': 26} + + + +2026-01-11 07:03:38,326 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p22 +2026-01-11 07:03:38,326 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:03:38,326 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p22 (theorem_idx=208) with timeout: 600 seconds +2026-01-11 07:04:01,709 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:04:01,874 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:04:01,874 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p22 + +2026-01-11 07:04:01,876 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p1 +2026-01-11 07:04:01,876 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:04:01,876 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p1 (theorem_idx=209) with timeout: 600 seconds +2026-01-11 07:04:18,790 - __main__ - INFO - Prover for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:04:18,790 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 47.44728493690491 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 2, 'total_queries': 8} + + + +2026-01-11 07:04:18,792 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p13 +2026-01-11 07:04:18,792 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:04:18,792 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p13 (theorem_idx=210) with timeout: 600 seconds +2026-01-11 07:06:00,807 - __main__ - INFO - Prover for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:06:00,807 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 122.78022289276123 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 2, 'total_queries': 26} + + + +2026-01-11 07:06:00,809 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p18 +2026-01-11 07:06:00,809 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:06:00,809 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p18 (theorem_idx=211) with timeout: 600 seconds +2026-01-11 07:07:52,750 - __main__ - INFO - Prover for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:07:52,750 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 93.4945957660675 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 2, 'total_queries': 71} + + + +2026-01-11 07:07:52,753 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p3 +2026-01-11 07:07:52,753 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:07:52,753 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p3 (theorem_idx=212) with timeout: 600 seconds +2026-01-11 07:08:12,941 - __main__ - INFO - Prover for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:08:12,942 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 581.1327469348907 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 52, 'attempt_idx': 2, 'total_queries': 78} + + + +2026-01-11 07:08:12,945 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p4 +2026-01-11 07:08:12,945 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:08:12,945 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p4 (theorem_idx=213) with timeout: 600 seconds +2026-01-11 07:08:18,532 - __main__ - INFO - Prover Agent for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:08:18,697 - __main__ - INFO - Failed to prove lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:08:18,697 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12b_2021_p13 + +2026-01-11 07:08:18,700 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p9 +2026-01-11 07:08:18,700 - __main__ - INFO - Attempt 3 for proving lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:08:18,700 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p9 (theorem_idx=214) with timeout: 600 seconds +2026-01-11 07:08:19,877 - __main__ - INFO - Prover for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:08:19,877 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 234.30639910697937 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 2, 'total_queries': 50} + + + +2026-01-11 07:08:19,879 - __main__ - INFO - Attempting to prove lemma: imo_1959_p1 +2026-01-11 07:08:19,879 - __main__ - INFO - Attempt 3 for proving lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:08:19,879 - __main__ - INFO - Running the prover agent for lemma: imo_1959_p1 (theorem_idx=215) with timeout: 600 seconds +2026-01-11 07:09:01,278 - __main__ - INFO - Prover for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:09:01,278 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 60.62347483634949 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 2, 'total_queries': 102} + + + +2026-01-11 07:09:01,280 - __main__ - INFO - Attempting to prove lemma: imo_1960_p2 +2026-01-11 07:09:01,280 - __main__ - INFO - Attempt 3 for proving lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:09:01,280 - __main__ - INFO - Running the prover agent for lemma: imo_1960_p2 (theorem_idx=216) with timeout: 600 seconds +2026-01-11 07:09:09,994 - __main__ - INFO - Prover for lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:09:09,994 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := + +by +have h80 : Real.log 80 = 4 * Real.log 2 + Real.log 5 := by + have : (80 : ℝ) = 2 ^ 4 * 5 := by norm_num + simpa [Real.log_mul, Real.log_pow, this] +have h40 : Real.log 40 = 3 * Real.log 2 + Real.log 5 := by + have : (40 : ℝ) = 2 ^ 3 * 5 := by norm_num + simpa [Real.log_mul, Real.log_pow, this] +have h160 : Real.log 160 = 5 * Real.log 2 + Real.log 5 := by + have : (160 : ℝ) = 2 ^ 5 * 5 := by norm_num + simpa [Real.log_mul, Real.log_pow, this] +have h20 : Real.log 20 = 2 * Real.log 2 + Real.log 5 := by + have : (20 : ℝ) = 2 ^ 2 * 5 := by norm_num + simpa [Real.log_mul, Real.log_pow, this] +field_simp [h80, h40, h160, h20] +ring + + +ProofFile: None +LemmaName: theorem amc12b_2021_p9 : + (Real.log 80 / Real.log 2) / (Real.log 2 / Real.log 40) - (Real.log 160 / Real.log 2) / (Real.log 2 / Real.log 20) = 2 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 33.744298219680786 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 2, 'total_queries': 107} + + + +2026-01-11 07:09:09,996 - __main__ - INFO - Attempting to prove lemma: imo_1962_p2 +2026-01-11 07:09:09,996 - __main__ - INFO - Attempt 3 for proving lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:09:09,996 - __main__ - INFO - Running the prover agent for lemma: imo_1962_p2 (theorem_idx=217) with timeout: 600 seconds +2026-01-11 07:10:37,480 - __main__ - INFO - Prover for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:10:37,481 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 130.5692162513733 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 2, 'total_queries': 58} + + + +2026-01-11 07:10:37,483 - __main__ - INFO - Attempting to prove lemma: imo_1963_p5 +2026-01-11 07:10:37,483 - __main__ - INFO - Attempt 3 for proving lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:10:37,483 - __main__ - INFO - Running the prover agent for lemma: imo_1963_p5 (theorem_idx=218) with timeout: 600 seconds +2026-01-11 07:14:03,388 - __main__ - INFO - Prover for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:14:03,389 - __main__ - INFO - Dumping proof search result: +theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 197.56293892860413 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 2, 'total_queries': 44} + + + +2026-01-11 07:14:03,391 - __main__ - INFO - Attempting to prove lemma: imo_1964_p2 +2026-01-11 07:14:03,391 - __main__ - INFO - Attempt 3 for proving lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:14:03,391 - __main__ - INFO - Running the prover agent for lemma: imo_1964_p2 (theorem_idx=219) with timeout: 600 seconds +2026-01-11 07:16:55,122 - __main__ - INFO - Prover for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:16:55,122 - __main__ - INFO - Dumping proof search result: +theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := + +by + + + +ProofFile: None +LemmaName: theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 150.1330964565277 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 2, 'total_queries': 22} + + + +2026-01-11 07:16:55,124 - __main__ - INFO - Attempting to prove lemma: imo_1965_p2 +2026-01-11 07:16:55,124 - __main__ - INFO - Attempt 3 for proving lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:16:55,124 - __main__ - INFO - Running the prover agent for lemma: imo_1965_p2 (theorem_idx=220) with timeout: 600 seconds +2026-01-11 07:17:19,188 - __main__ - INFO - Prover for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:17:19,188 - __main__ - INFO - Dumping proof search result: +theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 72 +SearchTimeInSecs: 528.9654955863953 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 68, 'attempt_idx': 2, 'total_queries': 86} + + + +2026-01-11 07:17:19,190 - __main__ - INFO - Attempting to prove lemma: imo_1968_p5_1 +2026-01-11 07:17:19,190 - __main__ - INFO - Attempt 3 for proving lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:17:19,190 - __main__ - INFO - Running the prover agent for lemma: imo_1968_p5_1 (theorem_idx=221) with timeout: 600 seconds +2026-01-11 07:17:56,384 - __main__ - INFO - Prover for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:17:56,385 - __main__ - INFO - Dumping proof search result: +theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 37.45816922187805 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 18} + + + +2026-01-11 07:17:56,387 - __main__ - INFO - Attempting to prove lemma: imo_1969_p2 +2026-01-11 07:17:56,387 - __main__ - INFO - Attempt 3 for proving lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:17:56,387 - __main__ - INFO - Running the prover agent for lemma: imo_1969_p2 (theorem_idx=222) with timeout: 600 seconds +2026-01-11 07:18:17,468 - __main__ - INFO - Prover for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:18:17,469 - __main__ - INFO - Dumping proof search result: +theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := + +by + + + +ProofFile: None +LemmaName: theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 13.564289808273315 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 2, 'total_queries': 11} + + + +2026-01-11 07:18:17,471 - __main__ - INFO - Attempting to prove lemma: imo_1974_p3 +2026-01-11 07:18:17,471 - __main__ - INFO - Attempt 3 for proving lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:18:17,471 - __main__ - INFO - Running the prover agent for lemma: imo_1974_p3 (theorem_idx=223) with timeout: 600 seconds +2026-01-11 07:18:54,021 - __main__ - INFO - Prover for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:18:54,021 - __main__ - INFO - Dumping proof search result: +theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := + +by + + + +ProofFile: None +LemmaName: theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 69.87139368057251 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 2, 'total_queries': 37} + + + +2026-01-11 07:18:54,023 - __main__ - INFO - Attempting to prove lemma: imo_1977_p6 +2026-01-11 07:18:54,023 - __main__ - INFO - Attempt 3 for proving lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:18:54,023 - __main__ - INFO - Running the prover agent for lemma: imo_1977_p6 (theorem_idx=224) with timeout: 600 seconds +2026-01-11 07:19:01,456 - __main__ - INFO - Prover Agent for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:19:01,620 - __main__ - INFO - Failed to prove lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:19:01,620 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1960_p2 + +2026-01-11 07:19:01,622 - __main__ - INFO - Attempting to prove lemma: imo_1981_p6 +2026-01-11 07:19:01,623 - __main__ - INFO - Attempt 3 for proving lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:19:01,623 - __main__ - INFO - Running the prover agent for lemma: imo_1981_p6 (theorem_idx=225) with timeout: 600 seconds +2026-01-11 07:19:10,080 - __main__ - INFO - Prover Agent for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:19:10,294 - __main__ - INFO - Failed to prove lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:19:10,295 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1962_p2 + +2026-01-11 07:19:10,504 - __main__ - INFO - Attempting to prove lemma: imo_1982_p1 +2026-01-11 07:19:10,504 - __main__ - INFO - Attempt 3 for proving lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:19:10,504 - __main__ - INFO - Running the prover agent for lemma: imo_1982_p1 (theorem_idx=226) with timeout: 600 seconds +2026-01-11 07:22:26,130 - __main__ - INFO - Prover for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:22:26,130 - __main__ - INFO - Dumping proof search result: +theorem imo_1982_p1 + (f : ℕ → ℕ) + (h₀ : ∀ m n, (0 < m ∧ 0 < n) → f (m + n) - f m - f n = 0 ∨ f (m + n) - f m - f n = 1) + (h₁ : f 2 = 0) + (h₂ : 0 < f 3) + (h₃ : f 9999 = 3333) : + f 1982 = 660 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1982_p1 + (f : ℕ → ℕ) + (h₀ : ∀ m n, (0 < m ∧ 0 < n) → f (m + n) - f m - f n = 0 ∨ f (m + n) - f m - f n = 1) + (h₁ : f 2 = 0) + (h₂ : 0 < f 3) + (h₃ : f 9999 = 3333) : + f 1982 = 660 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 185.28010439872742 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 2, 'total_queries': 15} + + + +2026-01-11 07:22:26,132 - __main__ - INFO - Attempting to prove lemma: imo_1983_p6 +2026-01-11 07:22:26,132 - __main__ - INFO - Attempt 3 for proving lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:22:26,132 - __main__ - INFO - Running the prover agent for lemma: imo_1983_p6 (theorem_idx=227) with timeout: 600 seconds +2026-01-11 07:22:30,928 - __main__ - INFO - Prover for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:22:30,928 - __main__ - INFO - Dumping proof search result: +theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 229.26089644432068 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 31, 'attempt_idx': 2, 'total_queries': 31} + + + +2026-01-11 07:22:30,930 - __main__ - INFO - Attempting to prove lemma: imo_1984_p6 +2026-01-11 07:22:30,930 - __main__ - INFO - Attempt 3 for proving lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:22:30,930 - __main__ - INFO - Running the prover agent for lemma: imo_1984_p6 (theorem_idx=228) with timeout: 600 seconds +2026-01-11 07:23:19,222 - __main__ - INFO - Prover for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:23:19,222 - __main__ - INFO - Dumping proof search result: +theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 45.7947142124176 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 2, 'total_queries': 19} + + + +2026-01-11 07:23:19,224 - __main__ - INFO - Attempting to prove lemma: imo_1985_p6 +2026-01-11 07:23:19,224 - __main__ - INFO - Attempt 3 for proving lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:23:19,224 - __main__ - INFO - Running the prover agent for lemma: imo_1985_p6 (theorem_idx=229) with timeout: 600 seconds +2026-01-11 07:25:06,503 - __main__ - INFO - Prover for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:25:06,503 - __main__ - INFO - Dumping proof search result: +theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 62 +SearchTimeInSecs: 351.1977524757385 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 54, 'attempt_idx': 2, 'total_queries': 54} + + + +2026-01-11 07:25:06,505 - __main__ - INFO - Attempting to prove lemma: imo_1992_p1 +2026-01-11 07:25:06,505 - __main__ - INFO - Attempt 3 for proving lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:25:06,505 - __main__ - INFO - Running the prover agent for lemma: imo_1992_p1 (theorem_idx=230) with timeout: 600 seconds +2026-01-11 07:25:16,232 - __main__ - INFO - Prover for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:25:16,232 - __main__ - INFO - Dumping proof search result: +theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 150.22306895256042 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 23} + + + +2026-01-11 07:25:16,234 - __main__ - INFO - Attempting to prove lemma: imo_1997_p5 +2026-01-11 07:25:16,234 - __main__ - INFO - Attempt 3 for proving lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:25:16,234 - __main__ - INFO - Running the prover agent for lemma: imo_1997_p5 (theorem_idx=231) with timeout: 600 seconds +2026-01-11 07:25:42,524 - __main__ - INFO - Prover for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:25:42,524 - __main__ - INFO - Dumping proof search result: +theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 17.45013928413391 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 2, 'total_queries': 4} + + + +2026-01-11 07:25:42,526 - __main__ - INFO - Attempting to prove lemma: imo_2001_p6 +2026-01-11 07:25:42,526 - __main__ - INFO - Attempt 3 for proving lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:25:42,526 - __main__ - INFO - Running the prover agent for lemma: imo_2001_p6 (theorem_idx=232) with timeout: 600 seconds +2026-01-11 07:25:52,834 - __main__ - INFO - Prover for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:25:52,835 - __main__ - INFO - Dumping proof search result: +theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 36.151089906692505 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 2, 'total_queries': 9} + + + +2026-01-11 07:25:52,837 - __main__ - INFO - Attempting to prove lemma: imo_2019_p1 +2026-01-11 07:25:52,837 - __main__ - INFO - Attempt 3 for proving lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:25:52,837 - __main__ - INFO - Running the prover agent for lemma: imo_2019_p1 (theorem_idx=233) with timeout: 600 seconds +2026-01-11 07:28:54,207 - __main__ - INFO - Prover Agent for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:28:54,368 - __main__ - INFO - Failed to prove lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:28:54,368 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1977_p6 + +2026-01-11 07:28:54,370 - __main__ - INFO - Attempting to prove lemma: imosl_2007_algebra_p6 +2026-01-11 07:28:54,370 - __main__ - INFO - Attempt 3 for proving lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:28:54,370 - __main__ - INFO - Running the prover agent for lemma: imosl_2007_algebra_p6 (theorem_idx=234) with timeout: 600 seconds +2026-01-11 07:30:53,622 - __main__ - INFO - Prover for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:30:53,622 - __main__ - INFO - Dumping proof search result: +theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 92.24094653129578 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 2, 'total_queries': 40} + + + +2026-01-11 07:30:53,624 - __main__ - INFO - Attempting to prove lemma: induction_11div10tonmn1ton +2026-01-11 07:30:53,624 - __main__ - INFO - Attempt 3 for proving lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:30:53,624 - __main__ - INFO - Running the prover agent for lemma: induction_11div10tonmn1ton (theorem_idx=235) with timeout: 600 seconds +2026-01-11 07:31:37,849 - __main__ - INFO - Prover for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:31:37,849 - __main__ - INFO - Dumping proof search result: +theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := + +by + + + +ProofFile: None +LemmaName: theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 24.960963010787964 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 2, 'total_queries': 33} + + + +2026-01-11 07:31:37,851 - __main__ - INFO - Attempting to prove lemma: induction_12dvd4expnp1p20 +2026-01-11 07:31:37,851 - __main__ - INFO - Skipping the attempt for proving lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:31:37,854 - __main__ - INFO - Attempting to prove lemma: induction_1pxpownlt1pnx +2026-01-11 07:31:37,854 - __main__ - INFO - Attempt 3 for proving lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:31:37,854 - __main__ - INFO - Running the prover agent for lemma: induction_1pxpownlt1pnx (theorem_idx=237) with timeout: 600 seconds +2026-01-11 07:33:19,308 - __main__ - INFO - Prover Agent for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:33:19,475 - __main__ - INFO - Failed to prove lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:33:19,475 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1985_p6 + +2026-01-11 07:33:19,477 - __main__ - INFO - Attempting to prove lemma: induction_nfactltnexpnm1ngt3 +2026-01-11 07:33:19,477 - __main__ - INFO - Attempt 3 for proving lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:33:19,477 - __main__ - INFO - Running the prover agent for lemma: induction_nfactltnexpnm1ngt3 (theorem_idx=238) with timeout: 600 seconds +2026-01-11 07:34:37,270 - __main__ - INFO - Prover for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:34:37,270 - __main__ - INFO - Dumping proof search result: +theorem imo_2019_p1 + (f : ℤ → ℤ) : + ((∀ a b, f (2 * a) + (2 * f b) = f (f (a + b))) ↔ (∀ z, f z = 0 \/ ∃ c, ∀ z, f z = 2 * z + c)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2019_p1 + (f : ℤ → ℤ) : + ((∀ a b, f (2 * a) + (2 * f b) = f (f (a + b))) ↔ (∀ z, f z = 0 \/ ∃ c, ∀ z, f z = 2 * z + c)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 76 +SearchTimeInSecs: 506.0667564868927 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 98, 'attempt_idx': 2, 'total_queries': 98} + + + +2026-01-11 07:34:37,273 - __main__ - INFO - Attempting to prove lemma: induction_pord1p1on2powklt5on2 +2026-01-11 07:34:37,273 - __main__ - INFO - Attempt 3 for proving lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:34:37,273 - __main__ - INFO - Running the prover agent for lemma: induction_pord1p1on2powklt5on2 (theorem_idx=239) with timeout: 600 seconds +2026-01-11 07:35:42,709 - __main__ - INFO - Prover Agent for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:35:42,841 - __main__ - INFO - Failed to prove lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:35:42,841 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_2001_p6 + +2026-01-11 07:35:42,843 - __main__ - INFO - Attempting to prove lemma: induction_pprime_pdvdapowpma +2026-01-11 07:35:42,843 - __main__ - INFO - Attempt 3 for proving lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:35:42,843 - __main__ - INFO - Running the prover agent for lemma: induction_pprime_pdvdapowpma (theorem_idx=240) with timeout: 600 seconds +2026-01-11 07:36:01,193 - __main__ - INFO - Prover for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:36:01,193 - __main__ - INFO - Dumping proof search result: +theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := + +by + + + +ProofFile: None +LemmaName: theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 153.25966000556946 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 2, 'total_queries': 29} + + + +2026-01-11 07:36:01,195 - __main__ - INFO - Attempting to prove lemma: induction_prod1p1onk3le3m1onn +2026-01-11 07:36:01,195 - __main__ - INFO - Attempt 3 for proving lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:36:01,195 - __main__ - INFO - Running the prover agent for lemma: induction_prod1p1onk3le3m1onn (theorem_idx=241) with timeout: 600 seconds +2026-01-11 07:36:03,142 - __main__ - INFO - Prover for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:36:03,143 - __main__ - INFO - Dumping proof search result: +theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := + +by + + + +ProofFile: None +LemmaName: theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 3.25187611579895 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 2, 'total_queries': 6} + + + +2026-01-11 07:36:03,145 - __main__ - INFO - Attempting to prove lemma: induction_sumkexp3eqsumksq +2026-01-11 07:36:03,145 - __main__ - INFO - Attempt 3 for proving lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:36:03,145 - __main__ - INFO - Running the prover agent for lemma: induction_sumkexp3eqsumksq (theorem_idx=242) with timeout: 600 seconds +2026-01-11 07:40:08,031 - __main__ - INFO - Prover for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:40:08,031 - __main__ - INFO - Dumping proof search result: +theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := + +by + + + +ProofFile: None +LemmaName: theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 66 +SearchTimeInSecs: 490.77641010284424 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 64, 'attempt_idx': 2, 'total_queries': 72} + + + +2026-01-11 07:40:08,899 - __main__ - INFO - Prover for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:40:08,899 - __main__ - INFO - Dumping proof search result: +theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := + +by + + + +ProofFile: None +LemmaName: theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 235.1826252937317 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 32, 'attempt_idx': 2, 'total_queries': 132} + + + +2026-01-11 07:40:12,546 - __main__ - INFO - Prover for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:40:12,546 - __main__ - INFO - Dumping proof search result: +theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 322.8390865325928 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 2, 'total_queries': 37} + + + +2026-01-11 07:41:12,300 - __main__ - INFO - Prover for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:41:12,300 - __main__ - INFO - Dumping proof search result: +theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 65 +SearchTimeInSecs: 295.06475043296814 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 65, 'attempt_idx': 2, 'total_queries': 81} + + + +2026-01-11 07:41:12,341 - __main__ - INFO - Reloaded checkpoint info for attempt 4 +2026-01-11 07:41:12,449 - __main__ - INFO - Reloaded proof results for attempt 4 +2026-01-11 07:41:12,449 - __main__ - INFO - Getting all lemmas in file: data/test/miniF2F-lean4/MiniF2F/Test.lean with timeout: 3000 seconds +2026-01-11 07:41:12,511 - __main__ - INFO - Discovered 244 lemmas +2026-01-11 07:41:12,511 - __main__ - INFO - Lemma names: ['mathd_algebra_478', 'numbertheory_4x3m7y3neq2003', 'aime_1983_p1', 'amc12_2001_p5', 'mathd_algebra_141', 'mathd_numbertheory_3', 'imo_1969_p2', 'mathd_algebra_44', 'mathd_algebra_209', 'mathd_numbertheory_1124'] ... ['aime_1989_p8', 'mathd_numbertheory_296', 'mathd_algebra_142', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'mathd_algebra_400', 'aime_1995_p7', 'mathd_numbertheory_185', 'mathd_algebra_441', 'mathd_numbertheory_582', 'mathd_algebra_338'] +2026-01-11 07:41:12,539 - __main__ - INFO - Discovered 243 lemmas to prove in data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:12,539 - __main__ - INFO - Lemmas to prove in file data/test/miniF2F-lean4/MiniF2F/Test.lean: +['aime_1983_p2', 'aime_1989_p8', 'algebra_sqineq_at2malt1', 'amc12a_2002_p6', 'amc12a_2013_p4', 'amc12a_2021_p9', 'amc12b_2002_p19', 'amc12b_2002_p2', 'amc12b_2020_p2', 'amc12b_2020_p6', 'mathd_algebra_125', 'mathd_algebra_129', 'mathd_algebra_137', 'mathd_algebra_139', 'mathd_algebra_141', 'mathd_algebra_142', 'mathd_algebra_143', 'mathd_algebra_148', 'mathd_algebra_158', 'mathd_algebra_160', 'mathd_algebra_171', 'mathd_algebra_176', 'mathd_algebra_24', 'mathd_algebra_246', 'mathd_algebra_263', 'mathd_algebra_270', 'mathd_algebra_296', 'mathd_algebra_302', 'mathd_algebra_304', 'mathd_algebra_314', 'mathd_algebra_329', 'mathd_algebra_33', 'mathd_algebra_346', 'mathd_algebra_354', 'mathd_algebra_359', 'mathd_algebra_388', 'mathd_algebra_400', 'mathd_algebra_412', 'mathd_algebra_419', 'mathd_algebra_432', 'mathd_algebra_44', 'mathd_algebra_440', 'mathd_algebra_441', 'mathd_algebra_478', 'mathd_algebra_513', 'mathd_algebra_76', 'mathd_algebra_80', 'mathd_numbertheory_12', 'mathd_numbertheory_127', 'mathd_numbertheory_135', 'mathd_numbertheory_150', 'mathd_numbertheory_175', 'mathd_numbertheory_185', 'mathd_numbertheory_207', 'mathd_numbertheory_212', 'mathd_numbertheory_229', 'mathd_numbertheory_235', 'mathd_numbertheory_237', 'mathd_numbertheory_239', 'mathd_numbertheory_247', 'mathd_numbertheory_254', 'mathd_numbertheory_299', 'mathd_numbertheory_3', 'mathd_numbertheory_341', 'mathd_numbertheory_342', 'mathd_numbertheory_343', 'mathd_numbertheory_345', 'mathd_numbertheory_517', 'mathd_numbertheory_551', 'mathd_numbertheory_66', 'mathd_numbertheory_728', 'mathd_numbertheory_769', 'mathd_numbertheory_85', 'mathd_algebra_107', 'mathd_algebra_113', 'mathd_algebra_114', 'mathd_algebra_153', 'mathd_algebra_156', 'mathd_algebra_17', 'mathd_algebra_170', 'mathd_algebra_184', 'mathd_algebra_188', 'mathd_algebra_196', 'mathd_algebra_208', 'mathd_algebra_209', 'mathd_algebra_215', 'mathd_algebra_275', 'mathd_algebra_276', 'mathd_algebra_288', 'mathd_algebra_289', 'mathd_algebra_293', 'mathd_algebra_313', 'mathd_algebra_320', 'mathd_algebra_332', 'mathd_algebra_338', 'mathd_algebra_342', 'mathd_algebra_362', 'mathd_algebra_392', 'mathd_algebra_398', 'mathd_algebra_427', 'mathd_algebra_452', 'mathd_algebra_459', 'mathd_algebra_484', 'mathd_algebra_487', 'mathd_algebra_598', 'mathd_algebra_756', 'mathd_numbertheory_100', 'mathd_numbertheory_1124', 'mathd_numbertheory_222', 'mathd_numbertheory_227', 'mathd_numbertheory_233', 'mathd_numbertheory_234', 'mathd_numbertheory_277', 'mathd_numbertheory_293', 'mathd_numbertheory_296', 'mathd_numbertheory_314', 'mathd_numbertheory_320', 'mathd_numbertheory_321', 'mathd_numbertheory_328', 'mathd_numbertheory_34', 'mathd_numbertheory_353', 'mathd_numbertheory_427', 'mathd_numbertheory_430', 'mathd_numbertheory_435', 'mathd_numbertheory_447', 'mathd_numbertheory_451', 'mathd_numbertheory_457', 'mathd_numbertheory_483', 'mathd_numbertheory_495', 'mathd_numbertheory_5', 'mathd_numbertheory_521', 'mathd_numbertheory_541', 'mathd_numbertheory_552', 'mathd_numbertheory_559', 'mathd_numbertheory_582', 'mathd_numbertheory_618', 'mathd_numbertheory_711', 'mathd_numbertheory_764', 'mathd_numbertheory_765', 'mathd_numbertheory_99', 'numbertheory_2pownm1prime_nprime', 'numbertheory_3pow2pownm1mod2pownp3eq2pownp2', 'numbertheory_4x3m7y3neq2003', 'numbertheory_aoddbdiv4asqpbsqmod8eq1', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown', 'numbertheory_x5neqy2p4', 'aime_1983_p1', 'aime_1983_p3', 'aime_1984_p1', 'aime_1984_p7', 'aime_1987_p5', 'aime_1988_p8', 'aime_1990_p15', 'aime_1990_p4', 'aime_1991_p9', 'aime_1994_p3', 'aime_1995_p7', 'aime_1997_p9', 'aime_1999_p11', 'algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7', 'algebra_9onxpypzleqsum2onxpy', 'algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2', 'algebra_absapbon1pabsapbleqsumabsaon1pabsa', 'algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1', 'algebra_amgm_sum1toneqn_prod1tonleq1', 'algebra_amgm_sumasqdivbgeqsuma', 'algebra_apbmpcneq0_aeq0anbeq0anceq0', 'algebra_apbon2pownleqapownpbpowon2', 'algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3', 'algebra_bleqa_apbon2msqrtableqambsqon8b', 'algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778', 'algebra_ineq_nto1onlt2m1on', 'algebra_others_exirrpowirrrat', 'algebra_sqineq_unitcircatbpabsamblt1', 'algebra_sqineq_unitcircatbpamblt1', 'algebra_sum1onsqrt2to1onsqrt10000lt198', 'amc12_2000_p1', 'amc12_2000_p12', 'amc12_2000_p20', 'amc12_2000_p6', 'amc12_2001_p21', 'amc12_2001_p5', 'amc12a_2002_p13', 'amc12a_2003_p23', 'amc12a_2003_p5', 'amc12a_2008_p25', 'amc12a_2009_p6', 'amc12a_2009_p7', 'amc12a_2019_p12', 'amc12a_2020_p10', 'amc12a_2020_p15', 'amc12a_2020_p25', 'amc12a_2020_p4', 'amc12a_2020_p7', 'amc12a_2020_p9', 'amc12a_2021_p12', 'amc12a_2021_p14', 'amc12a_2021_p18', 'amc12a_2021_p19', 'amc12a_2021_p22', 'amc12a_2021_p25', 'amc12a_2021_p3', 'amc12a_2021_p8', 'amc12b_2002_p4', 'amc12b_2002_p7', 'amc12b_2020_p13', 'amc12b_2020_p21', 'amc12b_2020_p22', 'amc12b_2021_p1', 'amc12b_2021_p13', 'amc12b_2021_p18', 'amc12b_2021_p3', 'amc12b_2021_p4', 'amc12b_2021_p9', 'imo_1959_p1', 'imo_1960_p2', 'imo_1962_p2', 'imo_1963_p5', 'imo_1964_p2', 'imo_1965_p2', 'imo_1968_p5_1', 'imo_1969_p2', 'imo_1974_p3', 'imo_1977_p6', 'imo_1981_p6', 'imo_1982_p1', 'imo_1983_p6', 'imo_1984_p6', 'imo_1985_p6', 'imo_1992_p1', 'imo_1997_p5', 'imo_2001_p6', 'imo_2019_p1', 'imosl_2007_algebra_p6', 'induction_11div10tonmn1ton', 'induction_12dvd4expnp1p20', 'induction_1pxpownlt1pnx', 'induction_nfactltnexpnm1ngt3', 'induction_pord1p1on2powklt5on2', 'induction_pprime_pdvdapowpma', 'induction_prod1p1onk3le3m1onn', 'induction_sumkexp3eqsumksq'] +2026-01-11 07:41:12,540 - __main__ - INFO - Executing 243 theorems in parallel using 4 workers +2026-01-11 07:41:12,588 - __main__ - INFO - Attempting to prove lemma: aime_1983_p2 +2026-01-11 07:41:12,588 - __main__ - INFO - Attempt 4 for proving lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:12,589 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p2 (theorem_idx=0) with timeout: 600 seconds +2026-01-11 07:41:12,592 - __main__ - INFO - Attempting to prove lemma: aime_1989_p8 +2026-01-11 07:41:12,594 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,598 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_at2malt1 +2026-01-11 07:41:12,599 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,600 - __main__ - INFO - Attempting to prove lemma: amc12a_2013_p4 +2026-01-11 07:41:12,600 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,600 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p6 +2026-01-11 07:41:12,601 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,604 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p9 +2026-01-11 07:41:12,604 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,606 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p19 +2026-01-11 07:41:12,607 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,610 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p2 +2026-01-11 07:41:12,611 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,611 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p2 +2026-01-11 07:41:12,611 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,613 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p6 +2026-01-11 07:41:12,613 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,616 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_125 +2026-01-11 07:41:12,616 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,616 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_129 +2026-01-11 07:41:12,617 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,619 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_137 +2026-01-11 07:41:12,619 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,621 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_139 +2026-01-11 07:41:12,621 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,622 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_141 +2026-01-11 07:41:12,622 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:12,622 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_141 (theorem_idx=14) with timeout: 600 seconds +2026-01-11 07:41:12,624 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_142 +2026-01-11 07:41:12,624 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,625 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_143 +2026-01-11 07:41:12,625 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,627 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_148 +2026-01-11 07:41:12,627 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,628 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_158 +2026-01-11 07:41:12,629 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:12,629 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_158 (theorem_idx=18) with timeout: 600 seconds +2026-01-11 07:41:12,630 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_160 +2026-01-11 07:41:12,630 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,633 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_171 +2026-01-11 07:41:12,633 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,636 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_176 +2026-01-11 07:41:12,636 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,638 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_24 +2026-01-11 07:41:12,638 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,640 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_246 +2026-01-11 07:41:12,641 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:12,643 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_263 +2026-01-11 07:41:12,643 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:12,643 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_263 (theorem_idx=24) with timeout: 600 seconds +2026-01-11 07:41:25,792 - __main__ - INFO - Prover for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:41:25,792 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 5.835850954055786 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 3, 'total_queries': 15} + + + +2026-01-11 07:41:25,794 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_270 +2026-01-11 07:41:25,794 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,798 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_296 +2026-01-11 07:41:25,798 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,801 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_302 +2026-01-11 07:41:25,801 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,804 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_304 +2026-01-11 07:41:25,804 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,807 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_314 +2026-01-11 07:41:25,807 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,809 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_329 +2026-01-11 07:41:25,809 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,812 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_33 +2026-01-11 07:41:25,812 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,814 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_346 +2026-01-11 07:41:25,814 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,817 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_354 +2026-01-11 07:41:25,817 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,819 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_359 +2026-01-11 07:41:25,819 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,821 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_388 +2026-01-11 07:41:25,821 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,823 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_400 +2026-01-11 07:41:25,823 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,825 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_412 +2026-01-11 07:41:25,825 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,827 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_419 +2026-01-11 07:41:25,827 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,829 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_432 +2026-01-11 07:41:25,829 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,831 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_44 +2026-01-11 07:41:25,831 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,833 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_440 +2026-01-11 07:41:25,833 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,834 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_441 +2026-01-11 07:41:25,834 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,836 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_478 +2026-01-11 07:41:25,836 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,838 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_513 +2026-01-11 07:41:25,838 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,839 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_76 +2026-01-11 07:41:25,839 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:25,841 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_80 +2026-01-11 07:41:25,841 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:25,841 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_80 (theorem_idx=46) with timeout: 600 seconds +2026-01-11 07:41:54,991 - __main__ - INFO - Prover for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:41:54,992 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 16.455464124679565 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 9} + + + +2026-01-11 07:41:54,994 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_12 +2026-01-11 07:41:54,994 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:54,997 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_127 +2026-01-11 07:41:54,997 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:55,000 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_135 +2026-01-11 07:41:55,000 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:41:55,003 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_150 +2026-01-11 07:41:55,003 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:41:55,003 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_150 (theorem_idx=50) with timeout: 600 seconds +2026-01-11 07:42:01,795 - __main__ - INFO - Prover for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:42:01,795 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 35.04484581947327 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 3, 'total_queries': 22} + + + +2026-01-11 07:42:01,797 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_175 +2026-01-11 07:42:01,797 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,800 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_185 +2026-01-11 07:42:01,801 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,803 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_207 +2026-01-11 07:42:01,804 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,806 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_212 +2026-01-11 07:42:01,806 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,809 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_229 +2026-01-11 07:42:01,810 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,812 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_235 +2026-01-11 07:42:01,812 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,815 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_237 +2026-01-11 07:42:01,815 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,817 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_239 +2026-01-11 07:42:01,817 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,819 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_247 +2026-01-11 07:42:01,819 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,822 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_254 +2026-01-11 07:42:01,822 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,824 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_299 +2026-01-11 07:42:01,824 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,825 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_3 +2026-01-11 07:42:01,825 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,827 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_341 +2026-01-11 07:42:01,827 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,829 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_342 +2026-01-11 07:42:01,829 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,831 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_343 +2026-01-11 07:42:01,831 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,832 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_345 +2026-01-11 07:42:01,832 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,834 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_517 +2026-01-11 07:42:01,834 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,836 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_551 +2026-01-11 07:42:01,836 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,837 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_66 +2026-01-11 07:42:01,837 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,839 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_728 +2026-01-11 07:42:01,839 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,841 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_769 +2026-01-11 07:42:01,841 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,842 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_85 +2026-01-11 07:42:01,842 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,844 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_107 +2026-01-11 07:42:01,844 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,846 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_113 +2026-01-11 07:42:01,846 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:01,847 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_114 +2026-01-11 07:42:01,847 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:42:01,847 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_114 (theorem_idx=75) with timeout: 600 seconds +2026-01-11 07:42:14,333 - __main__ - INFO - Prover for lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:42:14,333 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := + +by +-- compute the two finite sums +have hsum1 : (∑ k in Finset.range 8, (2 * k + 1)) = 64 := by + norm_num +have hsum2 : (∑ k in Finset.range 5, (a + 2 * k)) = 5 * a + 20 := by + have hconst : ∑ k in Finset.range 5, a = 5 * a := by + simpa [Finset.sum_const_nat] + have hsumk : ∑ k in Finset.range 5, 2 * k = 20 := by + norm_num + calc + (∑ k in Finset.range 5, (a + 2 * k)) + = ∑ k in Finset.range 5, a + ∑ k in Finset.range 5, 2 * k := by + simpa [Finset.sum_add_distrib] + _ = 5 * a + 20 := by + simp [hconst, hsumk] +-- rewrite the hypothesis with the computed sums +have hcalc : (64 : ℤ) - (5 * a + 20) = 4 := by + have := h₁ + -- cast to integers before simplifying + simpa [hsum1, hsum2, Int.ofNat_add, Int.ofNat_mul] using this +-- solve the linear equation for a +linarith [hcalc] + + +ProofFile: None +LemmaName: theorem mathd_algebra_158 + (a : ℕ) + (h₀ : Even a) + (h₁ : ∑ k ∈ Finset.range 8, (2 * k + 1) - ∑ k ∈ Finset.range 5, (a + 2 * k) = (4:ℤ)) : + a = 8 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 27.654088735580444 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 3, 'total_queries': 103} + + + +2026-01-11 07:42:14,334 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_153 +2026-01-11 07:42:14,335 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:42:14,338 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_156 +2026-01-11 07:42:14,338 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:42:14,338 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_156 (theorem_idx=77) with timeout: 600 seconds +2026-01-11 07:43:06,958 - __main__ - INFO - Prover for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:43:06,958 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 45.33511471748352 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 3, 'total_queries': 113} + + + +2026-01-11 07:43:06,960 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_17 +2026-01-11 07:43:06,960 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:43:06,960 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_17 (theorem_idx=78) with timeout: 600 seconds +2026-01-11 07:44:54,593 - __main__ - INFO - Prover for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:44:54,593 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_156 + (x y : ℝ) + (f g : ℝ → ℝ) + (h₀ : ∀t, f t = t^4) + (h₁ : ∀t, g t = 5 * t^2 - 6) + (h₂ : f x = g x) + (h₃ : f y = g y) + (h₄ : x^2 < y^2) : + y^2 - x^2 = 1 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_156 + (x y : ℝ) + (f g : ℝ → ℝ) + (h₀ : ∀t, f t = t^4) + (h₁ : ∀t, g t = 5 * t^2 - 6) + (h₂ : f x = g x) + (h₃ : f y = g y) + (h₄ : x^2 < y^2) : + y^2 - x^2 = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 151.25685119628906 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 3, 'total_queries': 22} + + + +2026-01-11 07:44:54,595 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_170 +2026-01-11 07:44:54,595 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:44:54,599 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_184 +2026-01-11 07:44:54,599 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:44:54,599 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_184 (theorem_idx=80) with timeout: 600 seconds +2026-01-11 07:45:18,128 - __main__ - INFO - Prover for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:45:18,128 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 175.27341747283936 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 3, 'total_queries': 34} + + + +2026-01-11 07:45:18,130 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_188 +2026-01-11 07:45:18,131 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:45:18,134 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_196 +2026-01-11 07:45:18,134 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:45:18,137 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_208 +2026-01-11 07:45:18,137 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:45:18,137 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_208 (theorem_idx=83) with timeout: 600 seconds +2026-01-11 07:47:16,289 - __main__ - INFO - Prover for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:47:16,289 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 34 +SearchTimeInSecs: 109.21945714950562 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 3, 'total_queries': 38} + + + +2026-01-11 07:47:16,291 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_209 +2026-01-11 07:47:16,291 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:47:16,294 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_215 +2026-01-11 07:47:16,295 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:47:16,295 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_215 (theorem_idx=85) with timeout: 600 seconds +2026-01-11 07:47:44,759 - __main__ - INFO - Prover for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:47:44,759 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 74 +SearchTimeInSecs: 367.10493898391724 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 73, 'attempt_idx': 3, 'total_queries': 94} + + + +2026-01-11 07:47:44,761 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_275 +2026-01-11 07:47:44,761 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:47:44,761 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_275 (theorem_idx=86) with timeout: 600 seconds +2026-01-11 07:48:01,700 - __main__ - INFO - Prover for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:48:01,701 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 34.18983793258667 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 12} + + + +2026-01-11 07:48:01,703 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_276 +2026-01-11 07:48:01,703 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:48:01,703 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_276 (theorem_idx=87) with timeout: 600 seconds +2026-01-11 07:49:24,735 - __main__ - INFO - Prover for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:49:24,735 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_275 + (x : ℝ) + (h : ((11:ℝ)^(1 / 4))^(3 * x - 3) = 1 / 5) : + ((11:ℝ)^(1 / 4))^(6 * x + 2) = 121 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 87.77336239814758 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 3, 'total_queries': 23} + + + +2026-01-11 07:49:24,737 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_288 +2026-01-11 07:49:24,737 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:49:24,737 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_288 (theorem_idx=88) with timeout: 600 seconds +2026-01-11 07:51:07,794 - __main__ - INFO - Prover for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:51:07,794 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 171.59352159500122 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 3, 'total_queries': 44} + + + +2026-01-11 07:51:07,796 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_289 +2026-01-11 07:51:07,796 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:51:07,799 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_293 +2026-01-11 07:51:07,799 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:51:07,801 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_313 +2026-01-11 07:51:07,801 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:51:07,801 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_313 (theorem_idx=91) with timeout: 600 seconds +2026-01-11 07:53:07,067 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:53:07,225 - __main__ - INFO - Failed to prove lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:53:07,225 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_17 + +2026-01-11 07:53:07,227 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_320 +2026-01-11 07:53:07,227 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:53:07,227 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_320 (theorem_idx=92) with timeout: 600 seconds +2026-01-11 07:53:20,908 - __main__ - INFO - Prover for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:53:20,908 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 115.10545778274536 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 3, 'total_queries': 108} + + + +2026-01-11 07:53:20,910 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_332 +2026-01-11 07:53:20,910 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:53:20,910 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_332 (theorem_idx=93) with timeout: 600 seconds +2026-01-11 07:54:54,706 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:54:54,868 - __main__ - INFO - Failed to prove lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:54:54,868 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_184 + +2026-01-11 07:54:54,870 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_338 +2026-01-11 07:54:54,870 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:54:54,873 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_342 +2026-01-11 07:54:54,874 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:54:54,876 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_362 +2026-01-11 07:54:54,876 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:54:54,877 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_362 (theorem_idx=96) with timeout: 600 seconds +2026-01-11 07:58:36,880 - __main__ - INFO - Prover for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:58:36,880 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 200.20750331878662 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 3, 'total_queries': 17} + + + +2026-01-11 07:58:36,882 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_392 +2026-01-11 07:58:36,882 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:58:36,883 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_392 (theorem_idx=97) with timeout: 600 seconds +2026-01-11 07:58:59,005 - __main__ - INFO - Prover for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 07:58:59,005 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 319.91364216804504 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 39, 'attempt_idx': 3, 'total_queries': 50} + + + +2026-01-11 07:58:59,007 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_398 +2026-01-11 07:58:59,007 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:58:59,010 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_427 +2026-01-11 07:58:59,010 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:58:59,013 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_452 +2026-01-11 07:58:59,013 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:58:59,013 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_452 (theorem_idx=100) with timeout: 600 seconds +2026-01-11 07:59:24,815 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 07:59:24,993 - __main__ - INFO - Failed to prove lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:59:24,993 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_288 + +2026-01-11 07:59:24,998 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_459 +2026-01-11 07:59:24,998 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:59:25,003 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_484 +2026-01-11 07:59:25,003 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 07:59:25,008 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_487 +2026-01-11 07:59:25,008 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 07:59:25,008 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_487 (theorem_idx=103) with timeout: 600 seconds +2026-01-11 08:00:32,407 - __main__ - INFO - Prover for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:00:32,407 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 102.52062821388245 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 75} + + + +2026-01-11 08:00:32,409 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_598 +2026-01-11 08:00:32,409 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:00:32,413 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_756 +2026-01-11 08:00:32,413 - __main__ - INFO - Attempt 4 for proving lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:00:32,413 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_756 (theorem_idx=105) with timeout: 600 seconds +2026-01-11 08:03:07,371 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:03:07,528 - __main__ - INFO - Failed to prove lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:03:07,528 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_320 + +2026-01-11 08:03:07,530 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_100 +2026-01-11 08:03:07,530 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:03:07,531 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_100 (theorem_idx=106) with timeout: 600 seconds +2026-01-11 08:03:14,414 - __main__ - INFO - Prover for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:03:14,414 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 148.31831121444702 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 3, 'total_queries': 36} + + + +2026-01-11 08:03:14,416 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_1124 +2026-01-11 08:03:14,416 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:03:14,416 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_1124 (theorem_idx=107) with timeout: 600 seconds +2026-01-11 08:03:39,652 - __main__ - INFO - Prover for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:03:39,652 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 243.76024770736694 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 3, 'total_queries': 26} + + + +2026-01-11 08:03:39,654 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_222 +2026-01-11 08:03:39,654 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:03:39,658 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_227 +2026-01-11 08:03:39,658 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:03:39,658 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_227 (theorem_idx=109) with timeout: 600 seconds +2026-01-11 08:04:16,110 - __main__ - INFO - Prover for lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:04:16,110 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := + +by +-- Use the standard relation `gcd * lcm = n * m` +have h3 : n.gcd 40 * n.lcm 40 = n * 40 := Nat.gcd_mul_lcm n 40 +-- Rewrite with the given equalities +simp [h₁, h₂, mul_comm, mul_left_comm, mul_assoc] at h3 +-- `h3 : 10 * 280 = n * 40` +have h4 : n = 70 := by + apply Nat.eq_of_mul_eq_mul_left (by norm_num : 0 < 40) + -- we need `40 * n = 40 * 70` + -- rewrite `h3` to match the shape + have : n * 40 = 10 * 280 := h3.symm + -- simplify the right hand side + have : n * 40 = 70 * 40 := by + -- `10 * 280` and `70 * 40` are both `2800` + norm_num at this + simpa [mul_comm, mul_left_comm, mul_assoc] using this + -- commute factors to match `40 * n = 40 * 70` + simpa [mul_comm, mul_left_comm, mul_assoc] using this +exact h4 + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_100 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.gcd n 40 = 10) + (h₂ : Nat.lcm n 40 = 280) : + n = 70 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 44.87182021141052 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 3, 'total_queries': 23} + + + +2026-01-11 08:04:16,112 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_233 +2026-01-11 08:04:16,112 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:04:16,112 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_233 (theorem_idx=110) with timeout: 600 seconds +2026-01-11 08:04:40,056 - __main__ - INFO - Prover for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:04:40,057 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_227 + (x y n : ℕ+) + (h₀ : ↑x / (4:ℝ) + y / 6 = (x + y) / n) : + n = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 49.47034978866577 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 5} + + + +2026-01-11 08:04:40,059 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_234 +2026-01-11 08:04:40,059 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:04:40,059 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_234 (theorem_idx=111) with timeout: 600 seconds +2026-01-11 08:05:17,405 - __main__ - INFO - Prover for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:05:17,405 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 33 +SearchTimeInSecs: 45.116241455078125 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 3, 'total_queries': 39} + + + +2026-01-11 08:05:17,407 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_277 +2026-01-11 08:05:17,407 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:05:17,407 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_277 (theorem_idx=112) with timeout: 600 seconds +2026-01-11 08:07:28,380 - __main__ - INFO - Prover for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:07:28,380 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 143.87442541122437 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 3, 'total_queries': 98} + + + +2026-01-11 08:07:28,382 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_293 +2026-01-11 08:07:28,382 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:07:28,382 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_293 (theorem_idx=113) with timeout: 600 seconds +2026-01-11 08:08:59,114 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:08:59,272 - __main__ - INFO - Failed to prove lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:08:59,272 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_452 + +2026-01-11 08:08:59,274 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_296 +2026-01-11 08:08:59,275 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:08:59,275 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_296 (theorem_idx=114) with timeout: 600 seconds +2026-01-11 08:13:14,527 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:13:14,704 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:13:14,704 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_1124 + +2026-01-11 08:13:14,706 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_314 +2026-01-11 08:13:14,707 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:13:14,710 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_320 +2026-01-11 08:13:14,710 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:13:14,710 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_320 (theorem_idx=116) with timeout: 600 seconds +2026-01-11 08:13:32,452 - __main__ - INFO - Prover for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:13:32,452 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 247.59895658493042 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 12} + + + +2026-01-11 08:13:32,454 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_321 +2026-01-11 08:13:32,454 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:13:32,454 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_321 (theorem_idx=117) with timeout: 600 seconds +2026-01-11 08:14:09,699 - __main__ - INFO - Prover for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:14:09,699 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 36.762460231781006 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 36} + + + +2026-01-11 08:14:09,701 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_328 +2026-01-11 08:14:09,701 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:14:09,704 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_34 +2026-01-11 08:14:09,704 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:14:09,704 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_34 (theorem_idx=119) with timeout: 600 seconds +2026-01-11 08:14:33,974 - __main__ - INFO - Prover for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:14:33,974 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 45.004486322402954 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 3, 'total_queries': 57} + + + +2026-01-11 08:14:33,976 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_353 +2026-01-11 08:14:33,976 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:14:33,976 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_353 (theorem_idx=120) with timeout: 600 seconds +2026-01-11 08:14:40,735 - __main__ - INFO - Prover for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:14:40,735 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_277 + (m n : ℕ) + (h₀ : Nat.gcd m n = 6) + (h₁ : Nat.lcm m n = 126) : + 60 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 74 +SearchTimeInSecs: 554.2908208370209 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 74, 'attempt_idx': 3, 'total_queries': 74} + + + +2026-01-11 08:14:40,740 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_427 +2026-01-11 08:14:40,740 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:14:40,740 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_427 (theorem_idx=121) with timeout: 600 seconds +2026-01-11 08:16:24,836 - __main__ - INFO - Prover for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:16:24,836 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 101.69089245796204 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 3, 'total_queries': 56} + + + +2026-01-11 08:16:24,838 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_430 +2026-01-11 08:16:24,839 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:16:24,839 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_430 (theorem_idx=122) with timeout: 600 seconds +2026-01-11 08:17:28,507 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:17:28,698 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:17:28,698 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_293 + +2026-01-11 08:17:28,700 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_435 +2026-01-11 08:17:28,700 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:17:28,700 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_435 (theorem_idx=123) with timeout: 600 seconds +2026-01-11 08:18:20,239 - __main__ - INFO - Prover for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:18:20,239 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 236.65386080741882 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 37, 'attempt_idx': 3, 'total_queries': 51} + + + +2026-01-11 08:18:20,241 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_447 +2026-01-11 08:18:20,241 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:18:20,244 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_451 +2026-01-11 08:18:20,244 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:18:20,244 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_451 (theorem_idx=125) with timeout: 600 seconds +2026-01-11 08:19:12,740 - __main__ - INFO - Prover for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:19:12,740 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 159.2763752937317 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 3, 'total_queries': 37} + + + +2026-01-11 08:19:12,742 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_457 +2026-01-11 08:19:12,742 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:19:12,742 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_457 (theorem_idx=126) with timeout: 600 seconds +2026-01-11 08:20:26,838 - __main__ - INFO - Prover for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:20:26,839 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 61.047271490097046 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 3, 'total_queries': 59} + + + +2026-01-11 08:20:26,841 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_483 +2026-01-11 08:20:26,841 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:20:26,844 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_495 +2026-01-11 08:20:26,844 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:20:26,844 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_495 (theorem_idx=128) with timeout: 600 seconds +2026-01-11 08:20:54,029 - __main__ - INFO - Prover for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:20:54,029 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_451 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 2010 ≤ n ∧ n ≤ 2019 ∧ ∃ m, ((Nat.divisors m).card = 4 ∧ ∑ p ∈ (Nat.divisors m), p = n)) : + ∑ k ∈ S, k = 2016 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 145.1520128250122 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 3, 'total_queries': 73} + + + +2026-01-11 08:20:54,031 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_5 +2026-01-11 08:20:54,031 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:20:54,032 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_5 (theorem_idx=129) with timeout: 600 seconds +2026-01-11 08:22:17,716 - __main__ - INFO - Prover for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:22:17,716 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 72.65569591522217 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 3, 'total_queries': 16} + + + +2026-01-11 08:22:17,718 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_521 +2026-01-11 08:22:17,718 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:22:17,718 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_521 (theorem_idx=130) with timeout: 600 seconds +2026-01-11 08:23:08,493 - __main__ - INFO - Prover for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:23:08,493 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 324.60287857055664 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 3, 'total_queries': 73} + + + +2026-01-11 08:23:08,495 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_541 +2026-01-11 08:23:08,495 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:23:08,495 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_541 (theorem_idx=131) with timeout: 600 seconds +2026-01-11 08:24:08,232 - __main__ - INFO - Prover for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:24:08,232 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_495 + (a b : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a % 10 = 2) + (h₂ : b % 10 = 4) + (h₃ : Nat.gcd a b = 6) : + 108 ≤ Nat.lcm a b := + +by +-- The goal is actually false: consider a = 42, b = 24. They satisfy all hypotheses, +-- but a.lcm b = 84 < 108. Therefore the statement cannot be proven. No further +-- tactic can succeed. +apply? + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_495 + (a b : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a % 10 = 2) + (h₂ : b % 10 = 4) + (h₃ : Nat.gcd a b = 6) : + 108 ≤ Nat.lcm a b := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 190.75982761383057 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 3, 'total_queries': 10} + + + +2026-01-11 08:24:08,234 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_552 +2026-01-11 08:24:08,234 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:24:08,234 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_552 (theorem_idx=132) with timeout: 600 seconds +2026-01-11 08:24:40,297 - __main__ - INFO - Prover for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:24:40,297 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_521 + (m n : ℕ) + (h₀ : Even m) + (h₁ : Even n) + (h₂ : m - n = 2) + (h₃ : m * n = 288) : + m = 18 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_521 + (m n : ℕ) + (h₀ : Even m) + (h₁ : Even n) + (h₂ : m - n = 2) + (h₃ : m * n = 288) : + m = 18 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 119.6076307296753 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 3, 'total_queries': 15} + + + +2026-01-11 08:24:40,299 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_559 +2026-01-11 08:24:40,299 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:24:40,303 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_582 +2026-01-11 08:24:40,303 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:24:40,306 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_618 +2026-01-11 08:24:40,306 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:24:40,306 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_618 (theorem_idx=135) with timeout: 600 seconds +2026-01-11 08:24:40,872 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:24:41,033 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:24:41,033 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_427 + +2026-01-11 08:24:41,035 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_711 +2026-01-11 08:24:41,035 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:24:41,035 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_711 (theorem_idx=136) with timeout: 600 seconds +2026-01-11 08:26:45,331 - __main__ - INFO - Prover for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:26:45,331 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_711 + (m n : ℕ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 8) + (h₂ : Nat.lcm m n = 112) : + 72 ≤ m + n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 104.89353370666504 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 3, 'total_queries': 11} + + + +2026-01-11 08:26:45,333 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_764 +2026-01-11 08:26:45,333 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:26:45,333 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_764 (theorem_idx=137) with timeout: 600 seconds +2026-01-11 08:27:44,047 - __main__ - INFO - Prover for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:27:44,047 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 204.75499606132507 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 23, 'attempt_idx': 3, 'total_queries': 34} + + + +2026-01-11 08:27:44,050 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_765 +2026-01-11 08:27:44,050 - __main__ - INFO - Attempt 4 for proving lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:27:44,050 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_765 (theorem_idx=138) with timeout: 600 seconds +2026-01-11 08:28:40,696 - __main__ - INFO - Prover for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:28:40,696 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_618 + (n : ℕ) + (p : ℕ → ℕ) + (h₀ : ∀ x, p x = x^2 - x + 41) + (h₁ : 1 < Nat.gcd (p n) (p (n+1))) : + 41 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 226.60804986953735 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 3, 'total_queries': 49} + + + +2026-01-11 08:28:40,699 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_99 +2026-01-11 08:28:40,699 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:28:40,702 - __main__ - INFO - Attempting to prove lemma: numbertheory_2pownm1prime_nprime +2026-01-11 08:28:40,702 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:28:40,702 - __main__ - INFO - Running the prover agent for lemma: numbertheory_2pownm1prime_nprime (theorem_idx=140) with timeout: 600 seconds +2026-01-11 08:29:04,818 - __main__ - INFO - Prover for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:29:04,818 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 11.330840826034546 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 3, 'total_queries': 5} + + + +2026-01-11 08:29:04,820 - __main__ - INFO - Attempting to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 +2026-01-11 08:29:04,820 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:29:04,820 - __main__ - INFO - Running the prover agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 (theorem_idx=141) with timeout: 600 seconds +2026-01-11 08:32:22,385 - __main__ - INFO - Prover for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:32:22,386 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 268.11765480041504 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 27, 'attempt_idx': 3, 'total_queries': 44} + + + +2026-01-11 08:32:22,388 - __main__ - INFO - Attempting to prove lemma: numbertheory_4x3m7y3neq2003 +2026-01-11 08:32:22,388 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:32:22,388 - __main__ - INFO - Running the prover agent for lemma: numbertheory_4x3m7y3neq2003 (theorem_idx=142) with timeout: 600 seconds +2026-01-11 08:33:08,640 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:33:08,802 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:33:08,802 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_541 + +2026-01-11 08:33:08,804 - __main__ - INFO - Attempting to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 +2026-01-11 08:33:08,804 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:33:08,804 - __main__ - INFO - Running the prover agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 (theorem_idx=143) with timeout: 600 seconds +2026-01-11 08:34:48,681 - __main__ - INFO - Prover for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:34:48,681 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 469.7701563835144 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 56, 'attempt_idx': 3, 'total_queries': 60} + + + +2026-01-11 08:34:48,683 - __main__ - INFO - Attempting to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 +2026-01-11 08:34:48,683 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:34:48,683 - __main__ - INFO - Running the prover agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 (theorem_idx=144) with timeout: 600 seconds +2026-01-11 08:35:05,237 - __main__ - INFO - Prover for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:35:05,237 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + (n : ℕ) + (h₀ : 0 < n) : + (3^(2^n) - 1) % (2^(n + 3)) = 2^(n + 2) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 50 +SearchTimeInSecs: 342.0367419719696 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 49, 'attempt_idx': 3, 'total_queries': 49} + + + +2026-01-11 08:35:05,239 - __main__ - INFO - Attempting to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown +2026-01-11 08:35:05,239 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:35:05,240 - __main__ - INFO - Running the prover agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown (theorem_idx=145) with timeout: 600 seconds +2026-01-11 08:36:48,695 - __main__ - INFO - Prover for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:36:48,695 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 93.39576315879822 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 38} + + + +2026-01-11 08:36:48,697 - __main__ - INFO - Attempting to prove lemma: numbertheory_x5neqy2p4 +2026-01-11 08:36:48,697 - __main__ - INFO - Attempt 4 for proving lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:36:48,697 - __main__ - INFO - Running the prover agent for lemma: numbertheory_x5neqy2p4 (theorem_idx=146) with timeout: 600 seconds +2026-01-11 08:37:33,954 - __main__ - INFO - Prover for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:37:33,955 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 37.035444259643555 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 3, 'total_queries': 52} + + + +2026-01-11 08:37:33,957 - __main__ - INFO - Attempting to prove lemma: aime_1983_p1 +2026-01-11 08:37:33,957 - __main__ - INFO - Attempt 4 for proving lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:37:33,957 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p1 (theorem_idx=147) with timeout: 600 seconds +2026-01-11 08:39:40,297 - __main__ - INFO - Prover for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:39:40,297 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 119.41716599464417 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 3, 'total_queries': 32} + + + +2026-01-11 08:39:40,299 - __main__ - INFO - Attempting to prove lemma: aime_1983_p3 +2026-01-11 08:39:40,299 - __main__ - INFO - Attempt 4 for proving lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:39:40,299 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p3 (theorem_idx=148) with timeout: 600 seconds +2026-01-11 08:42:22,556 - __main__ - INFO - Prover Agent for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:42:22,716 - __main__ - INFO - Failed to prove lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:42:22,716 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_4x3m7y3neq2003 + +2026-01-11 08:42:22,718 - __main__ - INFO - Attempting to prove lemma: aime_1984_p1 +2026-01-11 08:42:22,718 - __main__ - INFO - Attempt 4 for proving lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:42:22,718 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p1 (theorem_idx=149) with timeout: 600 seconds +2026-01-11 08:43:08,989 - __main__ - INFO - Prover Agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:43:09,148 - __main__ - INFO - Failed to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:43:09,148 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 + +2026-01-11 08:43:09,150 - __main__ - INFO - Attempting to prove lemma: aime_1984_p7 +2026-01-11 08:43:09,150 - __main__ - INFO - Attempt 4 for proving lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:43:09,150 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p7 (theorem_idx=150) with timeout: 600 seconds +2026-01-11 08:43:16,244 - __main__ - INFO - Prover for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:43:16,244 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p1 + (u : ℕ → ℚ) + (h₀ : ∀ n, u (n + 1) = u n + 1) + (h₁ : ∑ k ∈ Finset.range 98, u k.succ = 137) : + ∑ k ∈ Finset.range 49, u (2 * k.succ) = 93 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 37.83251953125 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 94} + + + +2026-01-11 08:43:16,247 - __main__ - INFO - Attempting to prove lemma: aime_1987_p5 +2026-01-11 08:43:16,247 - __main__ - INFO - Attempt 4 for proving lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:43:16,247 - __main__ - INFO - Running the prover agent for lemma: aime_1987_p5 (theorem_idx=151) with timeout: 600 seconds +2026-01-11 08:44:35,227 - __main__ - INFO - Prover Agent for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:44:35,386 - __main__ - INFO - Failed to prove lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:44:35,386 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: aime_1983_p3 + +2026-01-11 08:44:35,388 - __main__ - INFO - Attempting to prove lemma: aime_1988_p8 +2026-01-11 08:44:35,388 - __main__ - INFO - Attempt 4 for proving lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:44:35,388 - __main__ - INFO - Running the prover agent for lemma: aime_1988_p8 (theorem_idx=152) with timeout: 600 seconds +2026-01-11 08:44:48,850 - __main__ - INFO - Prover Agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:44:49,011 - __main__ - INFO - Failed to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:44:49,011 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 + +2026-01-11 08:44:49,014 - __main__ - INFO - Attempting to prove lemma: aime_1990_p15 +2026-01-11 08:44:49,014 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:44:49,017 - __main__ - INFO - Attempting to prove lemma: aime_1990_p4 +2026-01-11 08:44:49,017 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:44:49,020 - __main__ - INFO - Attempting to prove lemma: aime_1991_p9 +2026-01-11 08:44:49,020 - __main__ - INFO - Attempt 4 for proving lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:44:49,020 - __main__ - INFO - Running the prover agent for lemma: aime_1991_p9 (theorem_idx=155) with timeout: 600 seconds +2026-01-11 08:45:22,534 - __main__ - INFO - Prover for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:45:22,534 - __main__ - INFO - Dumping proof search result: +theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 115.89762687683105 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 11} + + + +2026-01-11 08:45:22,536 - __main__ - INFO - Attempting to prove lemma: aime_1994_p3 +2026-01-11 08:45:22,536 - __main__ - INFO - Attempt 4 for proving lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:45:22,536 - __main__ - INFO - Running the prover agent for lemma: aime_1994_p3 (theorem_idx=156) with timeout: 600 seconds +2026-01-11 08:46:09,788 - __main__ - INFO - Prover for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:46:09,789 - __main__ - INFO - Dumping proof search result: +theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1984_p7 + (f : ℤ → ℤ) + (h₀ : ∀ n, 1000 ≤ n → f n = n - 3) + (h₁ : ∀ n, n < 1000 → f n = f (f (n + 5))) : + f 84 = 997 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 159.20022749900818 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 3, 'total_queries': 14} + + + +2026-01-11 08:46:09,791 - __main__ - INFO - Attempting to prove lemma: aime_1995_p7 +2026-01-11 08:46:09,791 - __main__ - INFO - Attempt 4 for proving lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:46:09,791 - __main__ - INFO - Running the prover agent for lemma: aime_1995_p7 (theorem_idx=157) with timeout: 600 seconds +2026-01-11 08:48:08,008 - __main__ - INFO - Prover for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:48:08,008 - __main__ - INFO - Dumping proof search result: +theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 175.33551502227783 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 3, 'total_queries': 21} + + + +2026-01-11 08:48:08,010 - __main__ - INFO - Attempting to prove lemma: aime_1997_p9 +2026-01-11 08:48:08,010 - __main__ - INFO - Attempt 4 for proving lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:48:08,010 - __main__ - INFO - Running the prover agent for lemma: aime_1997_p9 (theorem_idx=158) with timeout: 600 seconds +2026-01-11 08:49:26,061 - __main__ - INFO - Prover for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:49:26,061 - __main__ - INFO - Dumping proof search result: +theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 170.4938554763794 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 3, 'total_queries': 25} + + + +2026-01-11 08:49:26,063 - __main__ - INFO - Attempting to prove lemma: aime_1999_p11 +2026-01-11 08:49:26,063 - __main__ - INFO - Attempt 4 for proving lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:49:26,064 - __main__ - INFO - Running the prover agent for lemma: aime_1999_p11 (theorem_idx=159) with timeout: 600 seconds +2026-01-11 08:51:25,234 - __main__ - INFO - Prover for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:51:25,235 - __main__ - INFO - Dumping proof search result: +theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 96.06647253036499 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 3, 'total_queries': 8} + + + +2026-01-11 08:51:25,237 - __main__ - INFO - Attempting to prove lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 +2026-01-11 08:51:25,237 - __main__ - INFO - Attempt 4 for proving lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:51:25,237 - __main__ - INFO - Running the prover agent for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 (theorem_idx=160) with timeout: 600 seconds +2026-01-11 08:51:36,462 - __main__ - INFO - Prover for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:51:36,462 - __main__ - INFO - Dumping proof search result: +theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 362.55902004241943 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 42, 'attempt_idx': 3, 'total_queries': 42} + + + +2026-01-11 08:51:36,464 - __main__ - INFO - Attempting to prove lemma: algebra_9onxpypzleqsum2onxpy +2026-01-11 08:51:36,464 - __main__ - INFO - Attempt 4 for proving lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:51:36,465 - __main__ - INFO - Running the prover agent for lemma: algebra_9onxpypzleqsum2onxpy (theorem_idx=161) with timeout: 600 seconds +2026-01-11 08:54:35,576 - __main__ - INFO - Prover Agent for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:54:35,736 - __main__ - INFO - Failed to prove lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:54:35,737 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1988_p8 + +2026-01-11 08:54:35,739 - __main__ - INFO - Attempting to prove lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 +2026-01-11 08:54:35,739 - __main__ - INFO - Attempt 4 for proving lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:54:35,739 - __main__ - INFO - Running the prover agent for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 (theorem_idx=162) with timeout: 600 seconds +2026-01-11 08:55:13,058 - __main__ - INFO - Prover for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:55:13,058 - __main__ - INFO - Dumping proof search result: +theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 216.62501907348633 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 38, 'attempt_idx': 3, 'total_queries': 133} + + + +2026-01-11 08:55:13,060 - __main__ - INFO - Attempting to prove lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa +2026-01-11 08:55:13,061 - __main__ - INFO - Attempt 4 for proving lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:55:13,061 - __main__ - INFO - Running the prover agent for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa (theorem_idx=163) with timeout: 600 seconds +2026-01-11 08:58:08,197 - __main__ - INFO - Prover Agent for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 08:58:08,378 - __main__ - INFO - Failed to prove lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:58:08,378 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1997_p9 + +2026-01-11 08:58:08,381 - __main__ - INFO - Attempting to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 +2026-01-11 08:58:08,381 - __main__ - INFO - Attempt 4 for proving lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:58:08,381 - __main__ - INFO - Running the prover agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 (theorem_idx=164) with timeout: 600 seconds +2026-01-11 08:59:10,458 - __main__ - INFO - Prover for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:59:10,458 - __main__ - INFO - Dumping proof search result: +theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 54 +SearchTimeInSecs: 439.4584541320801 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 54, 'attempt_idx': 3, 'total_queries': 66} + + + +2026-01-11 08:59:10,460 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 +2026-01-11 08:59:10,460 - __main__ - INFO - Attempt 4 for proving lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:59:10,460 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 (theorem_idx=165) with timeout: 600 seconds +2026-01-11 08:59:48,056 - __main__ - INFO - Prover for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:59:48,056 - __main__ - INFO - Dumping proof search result: +theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 259.95355701446533 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 32, 'attempt_idx': 3, 'total_queries': 50} + + + +2026-01-11 08:59:48,058 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sumasqdivbgeqsuma +2026-01-11 08:59:48,059 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 08:59:48,062 - __main__ - INFO - Attempting to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 +2026-01-11 08:59:48,062 - __main__ - INFO - Attempt 4 for proving lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:59:48,062 - __main__ - INFO - Running the prover agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 (theorem_idx=167) with timeout: 600 seconds +2026-01-11 08:59:55,536 - __main__ - INFO - Prover for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 08:59:55,536 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 27.29350757598877 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 3, 'total_queries': 22} + + + +2026-01-11 08:59:55,538 - __main__ - INFO - Attempting to prove lemma: algebra_apbon2pownleqapownpbpowon2 +2026-01-11 08:59:55,538 - __main__ - INFO - Attempt 4 for proving lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 08:59:55,539 - __main__ - INFO - Running the prover agent for lemma: algebra_apbon2pownleqapownpbpowon2 (theorem_idx=168) with timeout: 600 seconds +2026-01-11 09:01:17,301 - __main__ - INFO - Prover for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:01:17,302 - __main__ - INFO - Dumping proof search result: +theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 46 +SearchTimeInSecs: 389.2683939933777 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 46, 'attempt_idx': 3, 'total_queries': 59} + + + +2026-01-11 09:01:17,304 - __main__ - INFO - Attempting to prove lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 +2026-01-11 09:01:17,304 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 09:01:17,307 - __main__ - INFO - Attempting to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b +2026-01-11 09:01:17,307 - __main__ - INFO - Attempt 4 for proving lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:01:17,307 - __main__ - INFO - Running the prover agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b (theorem_idx=170) with timeout: 600 seconds +2026-01-11 09:01:51,412 - __main__ - INFO - Prover for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:01:51,412 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 92.684490442276 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 3, 'total_queries': 21} + + + +2026-01-11 09:01:51,414 - __main__ - INFO - Attempting to prove lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 +2026-01-11 09:01:51,414 - __main__ - INFO - Attempt 4 for proving lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:01:51,414 - __main__ - INFO - Running the prover agent for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 (theorem_idx=171) with timeout: 600 seconds +2026-01-11 09:03:01,359 - __main__ - INFO - Prover for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:03:01,359 - __main__ - INFO - Dumping proof search result: +theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 50.777806520462036 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 43} + + + +2026-01-11 09:03:01,361 - __main__ - INFO - Attempting to prove lemma: algebra_ineq_nto1onlt2m1on +2026-01-11 09:03:01,361 - __main__ - INFO - Attempt 4 for proving lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:03:01,361 - __main__ - INFO - Running the prover agent for lemma: algebra_ineq_nto1onlt2m1on (theorem_idx=172) with timeout: 600 seconds +2026-01-11 09:04:12,371 - __main__ - INFO - Prover for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:04:12,372 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 254.8371241092682 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 3, 'total_queries': 33} + + + +2026-01-11 09:04:12,374 - __main__ - INFO - Attempting to prove lemma: algebra_others_exirrpowirrrat +2026-01-11 09:04:12,374 - __main__ - INFO - Attempt 4 for proving lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:04:12,374 - __main__ - INFO - Running the prover agent for lemma: algebra_others_exirrpowirrrat (theorem_idx=173) with timeout: 600 seconds +2026-01-11 09:05:43,431 - __main__ - INFO - Prover for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:05:43,431 - __main__ - INFO - Dumping proof search result: +theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := + +by + + + +ProofFile: None +LemmaName: theorem algebra_ineq_nto1onlt2m1on + (n : ℕ) : + (n : ℝ) ^ (1 / n : ℝ) < 2 - 1 / n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 145.33284091949463 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 62} + + + +2026-01-11 09:05:43,433 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpabsamblt1 +2026-01-11 09:05:43,433 - __main__ - INFO - Attempt 4 for proving lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:05:43,433 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpabsamblt1 (theorem_idx=174) with timeout: 600 seconds +2026-01-11 09:08:08,568 - __main__ - INFO - Prover Agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:08:08,728 - __main__ - INFO - Failed to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:08:08,728 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + +2026-01-11 09:08:08,730 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpamblt1 +2026-01-11 09:08:08,730 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 09:08:08,733 - __main__ - INFO - Attempting to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 +2026-01-11 09:08:08,733 - __main__ - INFO - Attempt 4 for proving lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:08:08,733 - __main__ - INFO - Running the prover agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 (theorem_idx=176) with timeout: 600 seconds +2026-01-11 09:09:11,792 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:09:11,792 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 200.6484718322754 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 3, 'total_queries': 34} + + + +2026-01-11 09:09:11,794 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p1 +2026-01-11 09:09:11,794 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:09:11,795 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p1 (theorem_idx=177) with timeout: 600 seconds +2026-01-11 09:11:17,443 - __main__ - INFO - Prover Agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:11:17,607 - __main__ - INFO - Failed to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:11:17,607 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b + +2026-01-11 09:11:17,609 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p12 +2026-01-11 09:11:17,610 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:11:17,610 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p12 (theorem_idx=178) with timeout: 600 seconds +2026-01-11 09:12:16,165 - __main__ - INFO - Prover for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:12:16,165 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 45.27299928665161 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 3, 'total_queries': 30} + + + +2026-01-11 09:12:16,167 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p20 +2026-01-11 09:12:16,167 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:12:16,167 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p20 (theorem_idx=179) with timeout: 600 seconds +2026-01-11 09:14:12,557 - __main__ - INFO - Prover Agent for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:14:12,718 - __main__ - INFO - Failed to prove lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:14:12,718 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_others_exirrpowirrrat + +2026-01-11 09:14:12,720 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p6 +2026-01-11 09:14:12,720 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:14:12,720 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p6 (theorem_idx=180) with timeout: 600 seconds +2026-01-11 09:14:37,261 - __main__ - INFO - Prover for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:14:37,261 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := + +by +field_simp [h₁, h₂, h₃] at * +ring +apply? + + +ProofFile: None +LemmaName: theorem amc12_2000_p20 + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) + (h₁ : x + 1/y = 4) + (h₂ : y + 1/z = 1) + (h₃ : z + 1/x = 7/3) : + x*y*z = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 96.90774011611938 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 3, 'total_queries': 33} + + + +2026-01-11 09:14:37,263 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p21 +2026-01-11 09:14:37,263 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:14:37,263 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p21 (theorem_idx=181) with timeout: 600 seconds +2026-01-11 09:15:08,853 - __main__ - INFO - Prover for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:15:08,853 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 338.84125566482544 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 3, 'total_queries': 28} + + + +2026-01-11 09:15:08,855 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p5 +2026-01-11 09:15:08,855 - __main__ - INFO - Attempt 4 for proving lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:15:08,855 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p5 (theorem_idx=182) with timeout: 600 seconds +2026-01-11 09:16:02,474 - __main__ - INFO - Prover for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:16:02,474 - __main__ - INFO - Dumping proof search result: +theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 55 +SearchTimeInSecs: 458.11684918403625 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 59, 'attempt_idx': 3, 'total_queries': 59} + + + +2026-01-11 09:16:02,476 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p13 +2026-01-11 09:16:02,476 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:16:02,476 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p13 (theorem_idx=183) with timeout: 600 seconds +2026-01-11 09:16:03,464 - __main__ - INFO - Prover for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:16:03,464 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 47.54695653915405 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 19} + + + +2026-01-11 09:16:03,466 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p23 +2026-01-11 09:16:03,466 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:16:03,467 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p23 (theorem_idx=184) with timeout: 600 seconds +2026-01-11 09:16:36,729 - __main__ - INFO - Prover for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:16:36,729 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 16.401692152023315 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 3, 'total_queries': 14} + + + +2026-01-11 09:16:36,731 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p5 +2026-01-11 09:16:36,731 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 09:16:36,734 - __main__ - INFO - Attempting to prove lemma: amc12a_2008_p25 +2026-01-11 09:16:36,734 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:16:36,734 - __main__ - INFO - Running the prover agent for lemma: amc12a_2008_p25 (theorem_idx=186) with timeout: 600 seconds +2026-01-11 09:17:17,013 - __main__ - INFO - Prover for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:17:17,013 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 166.07938075065613 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 3, 'total_queries': 18} + + + +2026-01-11 09:17:17,015 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p6 +2026-01-11 09:17:17,015 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:17:17,015 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p6 (theorem_idx=187) with timeout: 600 seconds +2026-01-11 09:17:47,689 - __main__ - INFO - Prover for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:17:47,689 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p21 + (a b c d : ℕ) + (h₀ : a * b * c * d = Nat.factorial 8) + (h₁ : a * b + a + b = 524) + (h₂ : b * c + b + c = 146) + (h₃ : c * d + c + d = 104) : + ↑a - ↑d = (10 : ℤ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 167.9265842437744 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 3, 'total_queries': 28} + + + +2026-01-11 09:17:47,691 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p7 +2026-01-11 09:17:47,691 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:17:47,691 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p7 (theorem_idx=188) with timeout: 600 seconds +2026-01-11 09:18:53,505 - __main__ - INFO - Prover for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:18:53,506 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p7 + (x : ℝ) + (n : ℕ) + (a : ℕ → ℝ) + (h₁ : ∀ m, a (m + 1) - a m = a (m + 2) - a (m + 1)) + (h₂ : a 1 = 2 * x - 3) + (h₃ : a 2 = 5 * x - 11) + (h₄ : a 3 = 3 * x + 1) + (h₅ : a n = 2009) : + n = 502 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2009_p7 + (x : ℝ) + (n : ℕ) + (a : ℕ → ℝ) + (h₁ : ∀ m, a (m + 1) - a m = a (m + 2) - a (m + 1)) + (h₂ : a 1 = 2 * x - 3) + (h₃ : a 2 = 5 * x - 11) + (h₄ : a 3 = 3 * x + 1) + (h₅ : a n = 2009) : + n = 502 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 42.842808961868286 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 22} + + + +2026-01-11 09:18:53,508 - __main__ - INFO - Attempting to prove lemma: amc12a_2019_p12 +2026-01-11 09:18:53,508 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:18:53,508 - __main__ - INFO - Running the prover agent for lemma: amc12a_2019_p12 (theorem_idx=189) with timeout: 600 seconds +2026-01-11 09:19:22,686 - __main__ - INFO - Prover for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:19:22,686 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 176.98326230049133 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 3, 'total_queries': 29} + + + +2026-01-11 09:19:22,688 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p10 +2026-01-11 09:19:22,688 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:19:22,688 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p10 (theorem_idx=190) with timeout: 600 seconds +2026-01-11 09:21:42,402 - __main__ - INFO - Prover for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:21:42,402 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2019_p12 (x y : ℕ) (h₀ : x ≠ 1 ∧ y ≠ 1) + (h₁ : Real.log x / Real.log 2 = Real.log 16 / Real.log y) (h₂ : x * y = 64) : + (Real.log (x / y) / Real.log 2) ^ 2 = 20 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2019_p12 (x y : ℕ) (h₀ : x ≠ 1 ∧ y ≠ 1) + (h₁ : Real.log x / Real.log 2 = Real.log 16 / Real.log y) (h₂ : x * y = 64) : + (Real.log (x / y) / Real.log 2) ^ 2 = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 149.23478412628174 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 3, 'total_queries': 13} + + + +2026-01-11 09:21:42,404 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p15 +2026-01-11 09:21:42,404 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:21:42,404 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p15 (theorem_idx=191) with timeout: 600 seconds +2026-01-11 09:24:24,620 - __main__ - INFO - Prover for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:24:24,620 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := + +by +have h12 : (12 : ℝ) = 2 ^ 2 * 3 := by norm_num +rw [h₀, h₁, h12] +simp [Real.rpow_mul, Real.mul_rpow, mul_comm, mul_left_comm, mul_assoc] + + +ProofFile: None +LemmaName: theorem amc12a_2009_p6 + (m n p q : ℝ) + (h₀ : p = 2 ^ m) + (h₁ : q = 3 ^ n) : + p^(2 * n) * (q^m) = 12^(m * n) := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 110 +SearchTimeInSecs: 403.50162148475647 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 3, 'total_queries': 141} + + + +2026-01-11 09:24:24,622 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p25 +2026-01-11 09:24:24,622 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:24:24,622 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p25 (theorem_idx=192) with timeout: 600 seconds +2026-01-11 09:26:36,917 - __main__ - INFO - Prover Agent for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:26:37,076 - __main__ - INFO - Failed to prove lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:26:37,076 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2008_p25 + +2026-01-11 09:26:37,078 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p4 +2026-01-11 09:26:37,078 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:26:37,078 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p4 (theorem_idx=193) with timeout: 600 seconds +2026-01-11 09:26:52,863 - __main__ - INFO - Prover for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:26:52,863 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 121.76873707771301 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 3, 'total_queries': 29} + + + +2026-01-11 09:26:52,865 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p7 +2026-01-11 09:26:52,865 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:26:52,865 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p7 (theorem_idx=194) with timeout: 600 seconds +2026-01-11 09:29:22,869 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:29:23,031 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:29:23,031 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p10 + +2026-01-11 09:29:23,033 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p9 +2026-01-11 09:29:23,033 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:29:23,033 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p9 (theorem_idx=195) with timeout: 600 seconds +2026-01-11 09:29:54,810 - __main__ - INFO - Prover for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:29:54,810 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 13.069554090499878 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 3, 'total_queries': 16} + + + +2026-01-11 09:29:54,812 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p12 +2026-01-11 09:29:54,812 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:29:54,812 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p12 (theorem_idx=196) with timeout: 600 seconds +2026-01-11 09:31:42,587 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:31:42,748 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:31:42,748 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2020_p15 + +2026-01-11 09:31:42,750 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p14 +2026-01-11 09:31:42,751 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:31:42,751 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p14 (theorem_idx=197) with timeout: 600 seconds +2026-01-11 09:32:12,832 - __main__ - INFO - Prover for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:32:12,832 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p4 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 1000 ≤ n ∧ n ≤ 9999 ∧ (∀ (d : ℕ), d ∈ Nat.digits 10 n → Even d) ∧ 5 ∣ n) : + S.card = 100 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 41 +SearchTimeInSecs: 320.0170328617096 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 3, 'total_queries': 77} + + + +2026-01-11 09:32:12,834 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p18 +2026-01-11 09:32:12,835 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:32:12,835 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p18 (theorem_idx=198) with timeout: 600 seconds +2026-01-11 09:33:01,830 - __main__ - INFO - Prover for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:33:01,830 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 63 +SearchTimeInSecs: 355.591819524765 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 59, 'attempt_idx': 3, 'total_queries': 77} + + + +2026-01-11 09:33:01,832 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p19 +2026-01-11 09:33:01,832 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:33:01,832 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p19 (theorem_idx=199) with timeout: 600 seconds +2026-01-11 09:33:09,303 - __main__ - INFO - Prover for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:33:09,303 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p14 : + (∑ k ∈ (Finset.Icc 1 20), (Real.logb (5^k) (3^(k^2)))) * (∑ k ∈ (Finset.Icc 1 100), (Real.logb (9^k) (25^k))) = 21000 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 71.87759232521057 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 3, 'total_queries': 38} + + + +2026-01-11 09:33:09,305 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p22 +2026-01-11 09:33:09,306 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:33:09,306 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p22 (theorem_idx=200) with timeout: 600 seconds +2026-01-11 09:33:12,856 - __main__ - INFO - Prover for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:33:12,856 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 178.0184850692749 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 3, 'total_queries': 59} + + + +2026-01-11 09:33:12,861 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p25 +2026-01-11 09:33:12,861 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:33:12,861 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p25 (theorem_idx=201) with timeout: 600 seconds +2026-01-11 09:34:22,271 - __main__ - INFO - Prover for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:34:22,272 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 41.76233696937561 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 18} + + + +2026-01-11 09:34:22,274 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p3 +2026-01-11 09:34:22,274 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 09:34:22,277 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p8 +2026-01-11 09:34:22,277 - __main__ - INFO - Attempt 4 for proving lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:34:22,277 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p8 (theorem_idx=203) with timeout: 600 seconds +2026-01-11 09:35:25,972 - __main__ - INFO - Prover for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:35:25,972 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p19 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ Real.pi ∧ Real.sin (Real.pi / 2 * Real.cos x) = Real.cos (Real.pi / 2 * Real.sin x)) : + S.card = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 125.81530094146729 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 16, 'attempt_idx': 3, 'total_queries': 29} + + + +2026-01-11 09:35:25,974 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p4 +2026-01-11 09:35:25,974 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:35:25,974 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p4 (theorem_idx=204) with timeout: 600 seconds +2026-01-11 09:35:54,641 - __main__ - INFO - Prover for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:35:54,641 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 75.1543231010437 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 3, 'total_queries': 21} + + + +2026-01-11 09:35:54,643 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p7 +2026-01-11 09:35:54,643 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:35:54,643 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p7 (theorem_idx=205) with timeout: 600 seconds +2026-01-11 09:39:12,731 - __main__ - INFO - Prover for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:39:12,731 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p7 + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : b = a + 1) + (h₂ : c = b + 1) + (h₃ : a * b * c = 8 * (a + b + c)) : + a^2 + (b^2 + c^2) = 77 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p7 + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : b = a + 1) + (h₂ : c = b + 1) + (h₃ : a * b * c = 8 * (a + b + c)) : + a^2 + (b^2 + c^2) = 77 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 184.807363986969 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 3, 'total_queries': 31} + + + +2026-01-11 09:39:12,733 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p13 +2026-01-11 09:39:12,733 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:39:12,733 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p13 (theorem_idx=206) with timeout: 600 seconds +2026-01-11 09:40:28,518 - __main__ - INFO - Prover for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:40:28,518 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 98 +SearchTimeInSecs: 478.80169892311096 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 92, 'attempt_idx': 3, 'total_queries': 192} + + + +2026-01-11 09:40:28,520 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p21 +2026-01-11 09:40:28,520 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:40:28,520 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p21 (theorem_idx=207) with timeout: 600 seconds +2026-01-11 09:43:09,465 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:43:09,645 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:43:09,645 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2021_p22 + +2026-01-11 09:43:09,647 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p22 +2026-01-11 09:43:09,647 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:43:09,647 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p22 (theorem_idx=208) with timeout: 600 seconds +2026-01-11 09:44:14,428 - __main__ - INFO - Prover for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:44:14,428 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 15 +SearchTimeInSecs: 213.94960856437683 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 3, 'total_queries': 19} + + + +2026-01-11 09:44:14,431 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p1 +2026-01-11 09:44:14,431 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:44:14,431 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p1 (theorem_idx=209) with timeout: 600 seconds +2026-01-11 09:44:25,762 - __main__ - INFO - Prover for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:44:25,762 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 287.8271083831787 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 38, 'attempt_idx': 3, 'total_queries': 54} + + + +2026-01-11 09:44:25,765 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p13 +2026-01-11 09:44:25,765 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:44:25,765 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p13 (theorem_idx=210) with timeout: 600 seconds +2026-01-11 09:45:03,384 - __main__ - INFO - Prover for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:45:03,384 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 12.364684343338013 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 3, 'total_queries': 2} + + + +2026-01-11 09:45:03,387 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p18 +2026-01-11 09:45:03,387 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:45:03,387 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p18 (theorem_idx=211) with timeout: 600 seconds +2026-01-11 09:45:26,165 - __main__ - INFO - Prover Agent for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:45:26,323 - __main__ - INFO - Failed to prove lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:45:26,323 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12b_2002_p4 + +2026-01-11 09:45:26,326 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p3 +2026-01-11 09:45:26,326 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:45:26,326 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p3 (theorem_idx=212) with timeout: 600 seconds +2026-01-11 09:47:01,227 - __main__ - INFO - Prover for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:47:01,227 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 38 +SearchTimeInSecs: 213.09468722343445 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 3, 'total_queries': 46} + + + +2026-01-11 09:47:01,229 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p4 +2026-01-11 09:47:01,229 - __main__ - INFO - Attempt 4 for proving lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:47:01,229 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p4 (theorem_idx=213) with timeout: 600 seconds +2026-01-11 09:48:17,333 - __main__ - INFO - Prover for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:48:17,333 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 176.38019680976868 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 3, 'total_queries': 39} + + + +2026-01-11 09:48:17,335 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p9 +2026-01-11 09:48:17,335 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 09:48:17,338 - __main__ - INFO - Attempting to prove lemma: imo_1959_p1 +2026-01-11 09:48:17,338 - __main__ - INFO - Attempt 4 for proving lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:48:17,338 - __main__ - INFO - Running the prover agent for lemma: imo_1959_p1 (theorem_idx=215) with timeout: 600 seconds +2026-01-11 09:48:46,394 - __main__ - INFO - Prover for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:48:46,394 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 248.47687602043152 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 33, 'attempt_idx': 3, 'total_queries': 58} + + + +2026-01-11 09:48:46,396 - __main__ - INFO - Attempting to prove lemma: imo_1960_p2 +2026-01-11 09:48:46,396 - __main__ - INFO - Attempt 4 for proving lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:48:46,396 - __main__ - INFO - Running the prover agent for lemma: imo_1960_p2 (theorem_idx=216) with timeout: 600 seconds +2026-01-11 09:48:55,661 - __main__ - INFO - Prover for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:48:55,661 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 201.88358664512634 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 3, 'total_queries': 33} + + + +2026-01-11 09:48:55,663 - __main__ - INFO - Attempting to prove lemma: imo_1962_p2 +2026-01-11 09:48:55,663 - __main__ - INFO - Attempt 4 for proving lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:48:55,663 - __main__ - INFO - Running the prover agent for lemma: imo_1962_p2 (theorem_idx=217) with timeout: 600 seconds +2026-01-11 09:50:59,525 - __main__ - INFO - Prover for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:50:59,525 - __main__ - INFO - Dumping proof search result: +theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 151.85390520095825 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 3, 'total_queries': 90} + + + +2026-01-11 09:50:59,527 - __main__ - INFO - Attempting to prove lemma: imo_1963_p5 +2026-01-11 09:50:59,527 - __main__ - INFO - Attempt 4 for proving lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:50:59,527 - __main__ - INFO - Running the prover agent for lemma: imo_1963_p5 (theorem_idx=218) with timeout: 600 seconds +2026-01-11 09:51:24,994 - __main__ - INFO - Prover for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:51:24,995 - __main__ - INFO - Dumping proof search result: +theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 136.29002690315247 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 3, 'total_queries': 13} + + + +2026-01-11 09:51:24,997 - __main__ - INFO - Attempting to prove lemma: imo_1964_p2 +2026-01-11 09:51:24,997 - __main__ - INFO - Attempt 4 for proving lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:51:24,997 - __main__ - INFO - Running the prover agent for lemma: imo_1964_p2 (theorem_idx=219) with timeout: 600 seconds +2026-01-11 09:56:20,655 - __main__ - INFO - Prover for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:56:20,655 - __main__ - INFO - Dumping proof search result: +theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 104 +SearchTimeInSecs: 312.7862708568573 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 82, 'attempt_idx': 3, 'total_queries': 117} + + + +2026-01-11 09:56:20,657 - __main__ - INFO - Attempting to prove lemma: imo_1965_p2 +2026-01-11 09:56:20,658 - __main__ - INFO - Attempt 4 for proving lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:56:20,658 - __main__ - INFO - Running the prover agent for lemma: imo_1965_p2 (theorem_idx=220) with timeout: 600 seconds +2026-01-11 09:57:01,402 - __main__ - INFO - Prover Agent for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:57:01,574 - __main__ - INFO - Failed to prove lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:57:01,574 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12b_2021_p4 + +2026-01-11 09:57:01,577 - __main__ - INFO - Attempting to prove lemma: imo_1968_p5_1 +2026-01-11 09:57:01,577 - __main__ - INFO - Attempt 4 for proving lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:57:01,577 - __main__ - INFO - Running the prover agent for lemma: imo_1968_p5_1 (theorem_idx=221) with timeout: 600 seconds +2026-01-11 09:58:17,961 - __main__ - INFO - Prover for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:58:17,961 - __main__ - INFO - Dumping proof search result: +theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 93.45941591262817 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 3, 'total_queries': 15} + + + +2026-01-11 09:58:17,963 - __main__ - INFO - Attempting to prove lemma: imo_1969_p2 +2026-01-11 09:58:17,963 - __main__ - INFO - Attempt 4 for proving lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:58:17,963 - __main__ - INFO - Running the prover agent for lemma: imo_1969_p2 (theorem_idx=222) with timeout: 600 seconds +2026-01-11 09:58:46,548 - __main__ - INFO - Prover Agent for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 09:58:46,708 - __main__ - INFO - Failed to prove lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:58:46,708 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1960_p2 + +2026-01-11 09:58:46,710 - __main__ - INFO - Attempting to prove lemma: imo_1974_p3 +2026-01-11 09:58:46,710 - __main__ - INFO - Attempt 4 for proving lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:58:46,711 - __main__ - INFO - Running the prover agent for lemma: imo_1974_p3 (theorem_idx=223) with timeout: 600 seconds +2026-01-11 09:59:41,896 - __main__ - INFO - Prover for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 09:59:41,896 - __main__ - INFO - Dumping proof search result: +theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 29.569283962249756 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 3, 'total_queries': 38} + + + +2026-01-11 09:59:41,898 - __main__ - INFO - Attempting to prove lemma: imo_1977_p6 +2026-01-11 09:59:41,898 - __main__ - INFO - Attempt 4 for proving lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 09:59:41,898 - __main__ - INFO - Running the prover agent for lemma: imo_1977_p6 (theorem_idx=224) with timeout: 600 seconds +2026-01-11 10:01:13,195 - __main__ - INFO - Prover for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:01:13,195 - __main__ - INFO - Dumping proof search result: +theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := + +by + + + +ProofFile: None +LemmaName: theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 167.93368816375732 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 3, 'total_queries': 24} + + + +2026-01-11 10:01:13,198 - __main__ - INFO - Attempting to prove lemma: imo_1981_p6 +2026-01-11 10:01:13,198 - __main__ - INFO - Attempt 4 for proving lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:01:13,198 - __main__ - INFO - Running the prover agent for lemma: imo_1981_p6 (theorem_idx=225) with timeout: 600 seconds +2026-01-11 10:01:25,182 - __main__ - INFO - Prover Agent for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:01:25,343 - __main__ - INFO - Failed to prove lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:01:25,343 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1964_p2 + +2026-01-11 10:01:25,345 - __main__ - INFO - Attempting to prove lemma: imo_1982_p1 +2026-01-11 10:01:25,345 - __main__ - INFO - Attempt 4 for proving lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:01:25,345 - __main__ - INFO - Running the prover agent for lemma: imo_1982_p1 (theorem_idx=226) with timeout: 600 seconds +2026-01-11 10:02:40,618 - __main__ - INFO - Prover Agent for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:02:40,783 - __main__ - INFO - Failed to prove lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:02:40,783 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: imo_1981_p6 + +2026-01-11 10:02:40,785 - __main__ - INFO - Attempting to prove lemma: imo_1983_p6 +2026-01-11 10:02:40,785 - __main__ - INFO - Attempt 4 for proving lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:02:40,785 - __main__ - INFO - Running the prover agent for lemma: imo_1983_p6 (theorem_idx=227) with timeout: 600 seconds +2026-01-11 10:04:01,766 - __main__ - INFO - Prover for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:04:01,766 - __main__ - INFO - Dumping proof search result: +theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 73.15809917449951 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 14} + + + +2026-01-11 10:04:01,769 - __main__ - INFO - Attempting to prove lemma: imo_1984_p6 +2026-01-11 10:04:01,769 - __main__ - INFO - Attempt 4 for proving lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:04:01,769 - __main__ - INFO - Running the prover agent for lemma: imo_1984_p6 (theorem_idx=228) with timeout: 600 seconds +2026-01-11 10:07:01,660 - __main__ - INFO - Prover Agent for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:07:02,023 - __main__ - INFO - Failed to prove lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:07:02,023 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1968_p5_1 + +2026-01-11 10:07:02,025 - __main__ - INFO - Attempting to prove lemma: imo_1985_p6 +2026-01-11 10:07:02,025 - __main__ - INFO - Attempt 4 for proving lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:07:02,025 - __main__ - INFO - Running the prover agent for lemma: imo_1985_p6 (theorem_idx=229) with timeout: 600 seconds +2026-01-11 10:08:55,873 - __main__ - INFO - Prover for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:08:55,873 - __main__ - INFO - Dumping proof search result: +theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 277.83394861221313 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 15, 'attempt_idx': 3, 'total_queries': 21} + + + +2026-01-11 10:08:55,875 - __main__ - INFO - Attempting to prove lemma: imo_1992_p1 +2026-01-11 10:08:55,876 - __main__ - INFO - Attempt 4 for proving lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:08:55,876 - __main__ - INFO - Running the prover agent for lemma: imo_1992_p1 (theorem_idx=230) with timeout: 600 seconds +2026-01-11 10:09:42,019 - __main__ - INFO - Prover Agent for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:09:42,378 - __main__ - INFO - Failed to prove lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:09:42,378 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1977_p6 + +2026-01-11 10:09:42,380 - __main__ - INFO - Attempting to prove lemma: imo_1997_p5 +2026-01-11 10:09:42,380 - __main__ - INFO - Attempt 4 for proving lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:09:42,380 - __main__ - INFO - Running the prover agent for lemma: imo_1997_p5 (theorem_idx=231) with timeout: 600 seconds +2026-01-11 10:11:25,526 - __main__ - INFO - Prover Agent for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:11:25,689 - __main__ - INFO - Failed to prove lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:11:25,690 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1982_p1 + +2026-01-11 10:11:25,692 - __main__ - INFO - Attempting to prove lemma: imo_2001_p6 +2026-01-11 10:11:25,692 - __main__ - INFO - Attempt 4 for proving lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:11:25,692 - __main__ - INFO - Running the prover agent for lemma: imo_2001_p6 (theorem_idx=232) with timeout: 600 seconds +2026-01-11 10:16:04,245 - __main__ - INFO - Prover for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:16:04,245 - __main__ - INFO - Dumping proof search result: +theorem imo_1985_p6 + (f : ℕ → NNReal → ℝ) + (h₀ : ∀ x, f 1 x = x) + (h₁ : ∀ x n, f (n + 1) x = f n x * (f n x + 1 / n)) : + ∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1985_p6 + (f : ℕ → NNReal → ℝ) + (h₀ : ∀ x, f 1 x = x) + (h₁ : ∀ x n, f (n + 1) x = f n x * (f n x + 1 / n)) : + ∃! a, ∀ n, 0 < n → 0 < f n a ∧ f n a < f (n + 1) a ∧ f (n + 1) a < 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 522.5528843402863 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 49, 'attempt_idx': 3, 'total_queries': 49} + + + +2026-01-11 10:16:04,247 - __main__ - INFO - Attempting to prove lemma: imo_2019_p1 +2026-01-11 10:16:04,247 - __main__ - INFO - Attempt 4 for proving lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:16:04,247 - __main__ - INFO - Running the prover agent for lemma: imo_2019_p1 (theorem_idx=233) with timeout: 600 seconds +2026-01-11 10:16:50,034 - __main__ - INFO - Prover for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:16:50,034 - __main__ - INFO - Dumping proof search result: +theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 47 +SearchTimeInSecs: 463.55218482017517 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 51, 'attempt_idx': 3, 'total_queries': 56} + + + +2026-01-11 10:16:50,036 - __main__ - INFO - Attempting to prove lemma: imosl_2007_algebra_p6 +2026-01-11 10:16:50,036 - __main__ - INFO - Attempt 4 for proving lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:16:50,036 - __main__ - INFO - Running the prover agent for lemma: imosl_2007_algebra_p6 (theorem_idx=234) with timeout: 600 seconds +2026-01-11 10:17:26,010 - __main__ - INFO - Prover Agent for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:17:26,171 - __main__ - INFO - Failed to prove lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:17:26,171 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: imo_2019_p1 + +2026-01-11 10:17:26,173 - __main__ - INFO - Attempting to prove lemma: induction_11div10tonmn1ton +2026-01-11 10:17:26,174 - __main__ - INFO - Attempt 4 for proving lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:17:26,174 - __main__ - INFO - Running the prover agent for lemma: induction_11div10tonmn1ton (theorem_idx=235) with timeout: 600 seconds +2026-01-11 10:17:26,792 - __main__ - INFO - Prover for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:17:26,792 - __main__ - INFO - Dumping proof search result: +theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 346.9028878211975 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 41, 'attempt_idx': 3, 'total_queries': 41} + + + +2026-01-11 10:17:26,794 - __main__ - INFO - Attempting to prove lemma: induction_12dvd4expnp1p20 +2026-01-11 10:17:26,794 - __main__ - INFO - Skipping the attempt for proving lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:17:26,797 - __main__ - INFO - Attempting to prove lemma: induction_1pxpownlt1pnx +2026-01-11 10:17:26,798 - __main__ - INFO - Attempt 4 for proving lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:17:26,798 - __main__ - INFO - Running the prover agent for lemma: induction_1pxpownlt1pnx (theorem_idx=237) with timeout: 600 seconds +2026-01-11 10:18:47,164 - __main__ - INFO - Prover for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:18:47,164 - __main__ - INFO - Dumping proof search result: +theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := + +by + + + +ProofFile: None +LemmaName: theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 62.07256555557251 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 3, 'total_queries': 12} + + + +2026-01-11 10:18:47,166 - __main__ - INFO - Attempting to prove lemma: induction_nfactltnexpnm1ngt3 +2026-01-11 10:18:47,166 - __main__ - INFO - Attempt 4 for proving lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:18:47,166 - __main__ - INFO - Running the prover agent for lemma: induction_nfactltnexpnm1ngt3 (theorem_idx=238) with timeout: 600 seconds +2026-01-11 10:19:18,621 - __main__ - INFO - Prover for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:19:18,621 - __main__ - INFO - Dumping proof search result: +theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 122.35734057426453 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 24} + + + +2026-01-11 10:19:18,623 - __main__ - INFO - Attempting to prove lemma: induction_pord1p1on2powklt5on2 +2026-01-11 10:19:18,623 - __main__ - INFO - Attempt 4 for proving lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:19:18,623 - __main__ - INFO - Running the prover agent for lemma: induction_pord1p1on2powklt5on2 (theorem_idx=239) with timeout: 600 seconds +2026-01-11 10:19:42,520 - __main__ - INFO - Prover Agent for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:19:42,682 - __main__ - INFO - Failed to prove lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:19:42,682 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1997_p5 + +2026-01-11 10:19:42,684 - __main__ - INFO - Attempting to prove lemma: induction_pprime_pdvdapowpma +2026-01-11 10:19:42,684 - __main__ - INFO - Attempt 4 for proving lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:19:42,684 - __main__ - INFO - Running the prover agent for lemma: induction_pprime_pdvdapowpma (theorem_idx=240) with timeout: 600 seconds +2026-01-11 10:20:09,901 - __main__ - INFO - Prover for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:20:09,901 - __main__ - INFO - Dumping proof search result: +theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := + +by + + + +ProofFile: None +LemmaName: theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 10.665962934494019 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 3, 'total_queries': 7} + + + +2026-01-11 10:20:09,903 - __main__ - INFO - Attempting to prove lemma: induction_prod1p1onk3le3m1onn +2026-01-11 10:20:09,903 - __main__ - INFO - Attempt 4 for proving lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:20:09,903 - __main__ - INFO - Running the prover agent for lemma: induction_prod1p1onk3le3m1onn (theorem_idx=241) with timeout: 600 seconds +2026-01-11 10:20:56,253 - __main__ - INFO - Prover for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:20:56,253 - __main__ - INFO - Dumping proof search result: +theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := + +by + + + +ProofFile: None +LemmaName: theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 120.01647281646729 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 3, 'total_queries': 32} + + + +2026-01-11 10:20:56,255 - __main__ - INFO - Attempting to prove lemma: induction_sumkexp3eqsumksq +2026-01-11 10:20:56,255 - __main__ - INFO - Attempt 4 for proving lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:20:56,255 - __main__ - INFO - Running the prover agent for lemma: induction_sumkexp3eqsumksq (theorem_idx=242) with timeout: 600 seconds +2026-01-11 10:22:56,355 - __main__ - INFO - Prover for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:22:56,356 - __main__ - INFO - Dumping proof search result: +theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 16 +SearchTimeInSecs: 106.43127655982971 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 3, 'total_queries': 79} + + + +2026-01-11 10:23:24,532 - __main__ - INFO - Prover for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:23:24,533 - __main__ - INFO - Dumping proof search result: +theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 233.25762677192688 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 3, 'total_queries': 39} + + + +2026-01-11 10:24:20,995 - __main__ - INFO - Prover for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:24:20,995 - __main__ - INFO - Dumping proof search result: +theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := + +by + + + +ProofFile: None +LemmaName: theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 238.61876392364502 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 3, 'total_queries': 61} + + + +2026-01-11 10:27:26,952 - __main__ - INFO - Prover Agent for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:27:27,113 - __main__ - INFO - Failed to prove lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,113 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: induction_1pxpownlt1pnx + +2026-01-11 10:27:27,142 - __main__ - INFO - Reloaded checkpoint info for attempt 5 +2026-01-11 10:27:27,235 - __main__ - INFO - Reloaded proof results for attempt 5 +2026-01-11 10:27:27,235 - __main__ - INFO - Getting all lemmas in file: data/test/miniF2F-lean4/MiniF2F/Test.lean with timeout: 3000 seconds +2026-01-11 10:27:27,296 - __main__ - INFO - Discovered 244 lemmas +2026-01-11 10:27:27,296 - __main__ - INFO - Lemma names: ['mathd_algebra_478', 'numbertheory_4x3m7y3neq2003', 'aime_1983_p1', 'amc12_2001_p5', 'mathd_algebra_141', 'mathd_numbertheory_3', 'imo_1969_p2', 'mathd_algebra_44', 'mathd_algebra_209', 'mathd_numbertheory_1124'] ... ['aime_1989_p8', 'mathd_numbertheory_296', 'mathd_algebra_142', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'mathd_algebra_400', 'aime_1995_p7', 'mathd_numbertheory_185', 'mathd_algebra_441', 'mathd_numbertheory_582', 'mathd_algebra_338'] +2026-01-11 10:27:27,327 - __main__ - INFO - Discovered 243 lemmas to prove in data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,328 - __main__ - INFO - Lemmas to prove in file data/test/miniF2F-lean4/MiniF2F/Test.lean: +['aime_1983_p2', 'aime_1989_p8', 'algebra_sqineq_at2malt1', 'amc12a_2002_p6', 'amc12a_2013_p4', 'amc12a_2021_p9', 'amc12b_2002_p19', 'amc12b_2002_p2', 'amc12b_2020_p2', 'amc12b_2020_p6', 'mathd_algebra_125', 'mathd_algebra_129', 'mathd_algebra_137', 'mathd_algebra_139', 'mathd_algebra_141', 'mathd_algebra_142', 'mathd_algebra_143', 'mathd_algebra_148', 'mathd_algebra_158', 'mathd_algebra_160', 'mathd_algebra_171', 'mathd_algebra_176', 'mathd_algebra_24', 'mathd_algebra_246', 'mathd_algebra_263', 'mathd_algebra_270', 'mathd_algebra_296', 'mathd_algebra_302', 'mathd_algebra_304', 'mathd_algebra_314', 'mathd_algebra_329', 'mathd_algebra_33', 'mathd_algebra_346', 'mathd_algebra_354', 'mathd_algebra_359', 'mathd_algebra_388', 'mathd_algebra_400', 'mathd_algebra_412', 'mathd_algebra_419', 'mathd_algebra_432', 'mathd_algebra_44', 'mathd_algebra_440', 'mathd_algebra_441', 'mathd_algebra_478', 'mathd_algebra_513', 'mathd_algebra_76', 'mathd_algebra_80', 'mathd_numbertheory_12', 'mathd_numbertheory_127', 'mathd_numbertheory_135', 'mathd_numbertheory_150', 'mathd_numbertheory_175', 'mathd_numbertheory_185', 'mathd_numbertheory_207', 'mathd_numbertheory_212', 'mathd_numbertheory_229', 'mathd_numbertheory_235', 'mathd_numbertheory_237', 'mathd_numbertheory_239', 'mathd_numbertheory_247', 'mathd_numbertheory_254', 'mathd_numbertheory_299', 'mathd_numbertheory_3', 'mathd_numbertheory_341', 'mathd_numbertheory_342', 'mathd_numbertheory_343', 'mathd_numbertheory_345', 'mathd_numbertheory_517', 'mathd_numbertheory_551', 'mathd_numbertheory_66', 'mathd_numbertheory_728', 'mathd_numbertheory_769', 'mathd_numbertheory_85', 'mathd_algebra_107', 'mathd_algebra_113', 'mathd_algebra_114', 'mathd_algebra_153', 'mathd_algebra_156', 'mathd_algebra_17', 'mathd_algebra_170', 'mathd_algebra_184', 'mathd_algebra_188', 'mathd_algebra_196', 'mathd_algebra_208', 'mathd_algebra_209', 'mathd_algebra_215', 'mathd_algebra_275', 'mathd_algebra_276', 'mathd_algebra_288', 'mathd_algebra_289', 'mathd_algebra_293', 'mathd_algebra_313', 'mathd_algebra_320', 'mathd_algebra_332', 'mathd_algebra_338', 'mathd_algebra_342', 'mathd_algebra_362', 'mathd_algebra_392', 'mathd_algebra_398', 'mathd_algebra_427', 'mathd_algebra_452', 'mathd_algebra_459', 'mathd_algebra_484', 'mathd_algebra_487', 'mathd_algebra_598', 'mathd_algebra_756', 'mathd_numbertheory_100', 'mathd_numbertheory_1124', 'mathd_numbertheory_222', 'mathd_numbertheory_227', 'mathd_numbertheory_233', 'mathd_numbertheory_234', 'mathd_numbertheory_277', 'mathd_numbertheory_293', 'mathd_numbertheory_296', 'mathd_numbertheory_314', 'mathd_numbertheory_320', 'mathd_numbertheory_321', 'mathd_numbertheory_328', 'mathd_numbertheory_34', 'mathd_numbertheory_353', 'mathd_numbertheory_427', 'mathd_numbertheory_430', 'mathd_numbertheory_435', 'mathd_numbertheory_447', 'mathd_numbertheory_451', 'mathd_numbertheory_457', 'mathd_numbertheory_483', 'mathd_numbertheory_495', 'mathd_numbertheory_5', 'mathd_numbertheory_521', 'mathd_numbertheory_541', 'mathd_numbertheory_552', 'mathd_numbertheory_559', 'mathd_numbertheory_582', 'mathd_numbertheory_618', 'mathd_numbertheory_711', 'mathd_numbertheory_764', 'mathd_numbertheory_765', 'mathd_numbertheory_99', 'numbertheory_2pownm1prime_nprime', 'numbertheory_3pow2pownm1mod2pownp3eq2pownp2', 'numbertheory_4x3m7y3neq2003', 'numbertheory_aoddbdiv4asqpbsqmod8eq1', 'numbertheory_exk2powkeqapb2mulbpa2_aeq1', 'numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown', 'numbertheory_x5neqy2p4', 'aime_1983_p1', 'aime_1983_p3', 'aime_1984_p1', 'aime_1984_p7', 'aime_1987_p5', 'aime_1988_p8', 'aime_1990_p15', 'aime_1990_p4', 'aime_1991_p9', 'aime_1994_p3', 'aime_1995_p7', 'aime_1997_p9', 'aime_1999_p11', 'algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7', 'algebra_9onxpypzleqsum2onxpy', 'algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2', 'algebra_absapbon1pabsapbleqsumabsaon1pabsa', 'algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1', 'algebra_amgm_sum1toneqn_prod1tonleq1', 'algebra_amgm_sumasqdivbgeqsuma', 'algebra_apbmpcneq0_aeq0anbeq0anceq0', 'algebra_apbon2pownleqapownpbpowon2', 'algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3', 'algebra_bleqa_apbon2msqrtableqambsqon8b', 'algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778', 'algebra_ineq_nto1onlt2m1on', 'algebra_others_exirrpowirrrat', 'algebra_sqineq_unitcircatbpabsamblt1', 'algebra_sqineq_unitcircatbpamblt1', 'algebra_sum1onsqrt2to1onsqrt10000lt198', 'amc12_2000_p1', 'amc12_2000_p12', 'amc12_2000_p20', 'amc12_2000_p6', 'amc12_2001_p21', 'amc12_2001_p5', 'amc12a_2002_p13', 'amc12a_2003_p23', 'amc12a_2003_p5', 'amc12a_2008_p25', 'amc12a_2009_p6', 'amc12a_2009_p7', 'amc12a_2019_p12', 'amc12a_2020_p10', 'amc12a_2020_p15', 'amc12a_2020_p25', 'amc12a_2020_p4', 'amc12a_2020_p7', 'amc12a_2020_p9', 'amc12a_2021_p12', 'amc12a_2021_p14', 'amc12a_2021_p18', 'amc12a_2021_p19', 'amc12a_2021_p22', 'amc12a_2021_p25', 'amc12a_2021_p3', 'amc12a_2021_p8', 'amc12b_2002_p4', 'amc12b_2002_p7', 'amc12b_2020_p13', 'amc12b_2020_p21', 'amc12b_2020_p22', 'amc12b_2021_p1', 'amc12b_2021_p13', 'amc12b_2021_p18', 'amc12b_2021_p3', 'amc12b_2021_p4', 'amc12b_2021_p9', 'imo_1959_p1', 'imo_1960_p2', 'imo_1962_p2', 'imo_1963_p5', 'imo_1964_p2', 'imo_1965_p2', 'imo_1968_p5_1', 'imo_1969_p2', 'imo_1974_p3', 'imo_1977_p6', 'imo_1981_p6', 'imo_1982_p1', 'imo_1983_p6', 'imo_1984_p6', 'imo_1985_p6', 'imo_1992_p1', 'imo_1997_p5', 'imo_2001_p6', 'imo_2019_p1', 'imosl_2007_algebra_p6', 'induction_11div10tonmn1ton', 'induction_12dvd4expnp1p20', 'induction_1pxpownlt1pnx', 'induction_nfactltnexpnm1ngt3', 'induction_pord1p1on2powklt5on2', 'induction_pprime_pdvdapowpma', 'induction_prod1p1onk3le3m1onn', 'induction_sumkexp3eqsumksq'] +2026-01-11 10:27:27,328 - __main__ - INFO - Executing 243 theorems in parallel using 4 workers +2026-01-11 10:27:27,379 - __main__ - INFO - Attempting to prove lemma: aime_1983_p2 +2026-01-11 10:27:27,380 - __main__ - INFO - Attempt 5 for proving lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,380 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p2 (theorem_idx=0) with timeout: 600 seconds +2026-01-11 10:27:27,383 - __main__ - INFO - Attempting to prove lemma: aime_1989_p8 +2026-01-11 10:27:27,384 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,386 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_at2malt1 +2026-01-11 10:27:27,387 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,387 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p6 +2026-01-11 10:27:27,388 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,388 - __main__ - INFO - Attempting to prove lemma: amc12a_2013_p4 +2026-01-11 10:27:27,388 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,393 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p9 +2026-01-11 10:27:27,393 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,395 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p19 +2026-01-11 10:27:27,395 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,398 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p2 +2026-01-11 10:27:27,398 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,400 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p2 +2026-01-11 10:27:27,400 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,403 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p6 +2026-01-11 10:27:27,403 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,406 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_125 +2026-01-11 10:27:27,406 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,407 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_129 +2026-01-11 10:27:27,408 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,410 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_137 +2026-01-11 10:27:27,410 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,411 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_139 +2026-01-11 10:27:27,411 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,413 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_141 +2026-01-11 10:27:27,413 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,413 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_141 (theorem_idx=14) with timeout: 600 seconds +2026-01-11 10:27:27,414 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_142 +2026-01-11 10:27:27,415 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,416 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_143 +2026-01-11 10:27:27,416 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,419 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_148 +2026-01-11 10:27:27,419 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,419 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_158 +2026-01-11 10:27:27,419 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,422 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_160 +2026-01-11 10:27:27,422 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,423 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_171 +2026-01-11 10:27:27,423 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,425 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_176 +2026-01-11 10:27:27,425 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,427 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_24 +2026-01-11 10:27:27,427 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,427 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_246 +2026-01-11 10:27:27,428 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,429 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_263 +2026-01-11 10:27:27,429 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,429 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_263 (theorem_idx=24) with timeout: 600 seconds +2026-01-11 10:27:27,430 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_270 +2026-01-11 10:27:27,430 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,432 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_296 +2026-01-11 10:27:27,432 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,435 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_302 +2026-01-11 10:27:27,435 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,437 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_304 +2026-01-11 10:27:27,437 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,438 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_314 +2026-01-11 10:27:27,439 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,440 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_329 +2026-01-11 10:27:27,440 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,442 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_33 +2026-01-11 10:27:27,442 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,444 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_346 +2026-01-11 10:27:27,444 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,445 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_354 +2026-01-11 10:27:27,445 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,447 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_359 +2026-01-11 10:27:27,447 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,449 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_388 +2026-01-11 10:27:27,449 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,450 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_400 +2026-01-11 10:27:27,450 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,452 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_412 +2026-01-11 10:27:27,452 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,454 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_419 +2026-01-11 10:27:27,454 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,455 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_432 +2026-01-11 10:27:27,455 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,457 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_44 +2026-01-11 10:27:27,457 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,459 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_440 +2026-01-11 10:27:27,459 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,460 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_441 +2026-01-11 10:27:27,460 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,462 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_478 +2026-01-11 10:27:27,462 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,464 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_513 +2026-01-11 10:27:27,464 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,465 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_76 +2026-01-11 10:27:27,465 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:27,467 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_80 +2026-01-11 10:27:27,467 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:27,467 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_80 (theorem_idx=46) with timeout: 600 seconds +2026-01-11 10:27:50,566 - __main__ - INFO - Prover for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:27:50,566 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_263 + (y : ℝ) + (h₀ : 0 ≤ 19 + 3 * y) + (h₁ : Real.sqrt (19 + 3 * y) = 7) : + y = 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 9.821609735488892 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 4, 'total_queries': 13} + + + +2026-01-11 10:27:50,568 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_12 +2026-01-11 10:27:50,568 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,571 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_127 +2026-01-11 10:27:50,571 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,574 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_135 +2026-01-11 10:27:50,574 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,577 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_150 +2026-01-11 10:27:50,577 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:50,577 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_150 (theorem_idx=50) with timeout: 600 seconds +2026-01-11 10:27:50,746 - __main__ - INFO - Prover for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:27:50,746 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_141 + (a b : ℝ) + (h₁ : (a * b)=180) + (h₂ : 2 * (a + b)=54) : + (a^2 + b^2) = 369 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 15.942838430404663 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 8} + + + +2026-01-11 10:27:50,748 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_175 +2026-01-11 10:27:50,748 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,751 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_185 +2026-01-11 10:27:50,751 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,754 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_207 +2026-01-11 10:27:50,754 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,757 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_212 +2026-01-11 10:27:50,757 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,760 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_229 +2026-01-11 10:27:50,760 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,762 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_235 +2026-01-11 10:27:50,762 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,765 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_237 +2026-01-11 10:27:50,765 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,767 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_239 +2026-01-11 10:27:50,767 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,769 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_247 +2026-01-11 10:27:50,769 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,771 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_254 +2026-01-11 10:27:50,771 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,773 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_299 +2026-01-11 10:27:50,773 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,775 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_3 +2026-01-11 10:27:50,775 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,777 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_341 +2026-01-11 10:27:50,777 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,779 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_342 +2026-01-11 10:27:50,779 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,780 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_343 +2026-01-11 10:27:50,780 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,782 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_345 +2026-01-11 10:27:50,782 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,784 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_517 +2026-01-11 10:27:50,784 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,785 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_551 +2026-01-11 10:27:50,785 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,787 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_66 +2026-01-11 10:27:50,787 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,789 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_728 +2026-01-11 10:27:50,789 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,791 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_769 +2026-01-11 10:27:50,791 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,793 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_85 +2026-01-11 10:27:50,793 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,794 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_107 +2026-01-11 10:27:50,794 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,796 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_113 +2026-01-11 10:27:50,796 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:27:50,798 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_114 +2026-01-11 10:27:50,798 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:27:50,798 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_114 (theorem_idx=75) with timeout: 600 seconds +2026-01-11 10:28:38,244 - __main__ - INFO - Prover for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:28:38,244 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_80 + (x : ℝ) + (h₀ : x ≠ -1) + (h₁ : (x - 9) / (x + 1) = 2) : + x = -11 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 58.33587694168091 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 4, 'total_queries': 24} + + + +2026-01-11 10:28:38,246 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_153 +2026-01-11 10:28:38,246 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:28:38,249 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_156 +2026-01-11 10:28:38,249 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:28:38,249 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_156 (theorem_idx=77) with timeout: 600 seconds +2026-01-11 10:29:26,520 - __main__ - INFO - Prover for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:29:26,520 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p2 + (x p : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < p ∧ p < 15) + (h₁ : p ≤ x ∧ x ≤ 15) + (h₂ : f x = abs (x - p) + abs (x - 15) + abs (x - p - 15)) : + 15 ≤ f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 92.94658041000366 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 4, 'total_queries': 90} + + + +2026-01-11 10:29:26,522 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_17 +2026-01-11 10:29:26,523 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:29:26,523 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_17 (theorem_idx=78) with timeout: 600 seconds +2026-01-11 10:29:53,498 - __main__ - INFO - Prover for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:29:53,498 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_150 + (n : ℕ) + (h₀ : ¬ Nat.Prime (7 + 30 * n)) : + 6 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 94.75075840950012 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 38} + + + +2026-01-11 10:29:53,500 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_170 +2026-01-11 10:29:53,500 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:29:53,503 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_184 +2026-01-11 10:29:53,503 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:29:53,503 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_184 (theorem_idx=80) with timeout: 600 seconds +2026-01-11 10:32:37,308 - __main__ - INFO - Prover for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:32:37,308 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := + +by +simp [h₀] at *; norm_num +have h : (64 : ℝ) ^ (1 / 3 : ℝ) = 4 := by + norm_num +simp [h] at * +norm_num +rw [h] at * +simp +-- First prove the cube root of 64 is 4, then use it to simplify the goal +have h64 : (64 : ℝ) ^ (1 / 3 : ℝ) = 4 := by + norm_num +-- Now rewrite the goal using h64 and simplify +simp [h64] at * +simp [h64] +simp [mul_comm, mul_left_comm, mul_assoc, h64] at * + + +ProofFile: None +LemmaName: theorem mathd_algebra_114 + (a : ℝ) + (h₀ : a = 8) : + (16 * (a^2) ^ (1 / 3 : ℝ)) ^ (1 / 3 : ℝ) = 4 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 126 +SearchTimeInSecs: 267.116069316864 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 4, 'total_queries': 113} + + + +2026-01-11 10:32:37,310 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_188 +2026-01-11 10:32:37,310 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:32:37,314 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_196 +2026-01-11 10:32:37,314 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:32:37,316 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_208 +2026-01-11 10:32:37,317 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:32:37,317 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_208 (theorem_idx=83) with timeout: 600 seconds +2026-01-11 10:34:37,716 - __main__ - INFO - Prover for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:34:37,716 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_208 : + Real.sqrt 1000000 - 1000000^(1/3) = 900 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 29 +SearchTimeInSecs: 111.21766805648804 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 4, 'total_queries': 52} + + + +2026-01-11 10:34:37,718 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_209 +2026-01-11 10:34:37,718 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:34:37,721 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_215 +2026-01-11 10:34:37,721 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:34:37,722 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_215 (theorem_idx=85) with timeout: 600 seconds +2026-01-11 10:35:30,933 - __main__ - INFO - Prover for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:35:30,933 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_215 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ (x + 3)^2 = 121) : + ∑ k ∈ S, k = -6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 42.37070894241333 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 12} + + + +2026-01-11 10:35:30,936 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_275 +2026-01-11 10:35:30,936 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:35:30,936 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_275 (theorem_idx=86) with timeout: 600 seconds +2026-01-11 10:35:45,837 - __main__ - INFO - Prover for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:35:45,837 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_184 + (a b : NNReal) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : (a^2) = 6*b) + (h₂ : (a^2) = 54/b) : + a = 3 * NNReal.sqrt 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 341.2322850227356 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 40, 'attempt_idx': 4, 'total_queries': 40} + + + +2026-01-11 10:35:45,842 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_276 +2026-01-11 10:35:45,843 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:35:45,843 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_276 (theorem_idx=87) with timeout: 600 seconds +2026-01-11 10:38:24,018 - __main__ - INFO - Prover for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:38:24,018 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_276 + (a b : ℤ) + (h₀ : ∀ x : ℝ, 10 * x^2 - x - 24 = (a * x - 8) * (b * x + 3)) : + a * b + b = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 143.75377368927002 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 4, 'total_queries': 33} + + + +2026-01-11 10:38:24,020 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_288 +2026-01-11 10:38:24,020 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:38:24,020 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_288 (theorem_idx=88) with timeout: 600 seconds +2026-01-11 10:38:38,423 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:38:38,582 - __main__ - INFO - Failed to prove lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:38:38,582 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_156 + +2026-01-11 10:38:38,584 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_289 +2026-01-11 10:38:38,584 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:38:38,588 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_293 +2026-01-11 10:38:38,588 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:38:38,591 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_313 +2026-01-11 10:38:38,591 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:38:38,591 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_313 (theorem_idx=91) with timeout: 600 seconds +2026-01-11 10:39:26,704 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:39:26,866 - __main__ - INFO - Failed to prove lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:39:26,866 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_17 + +2026-01-11 10:39:26,868 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_320 +2026-01-11 10:39:26,868 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:39:26,868 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_320 (theorem_idx=92) with timeout: 600 seconds +2026-01-11 10:41:41,327 - __main__ - INFO - Prover for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:41:41,327 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := + +by +simp [h₀, h₁, h₂] at * +field_simp +field_simp [h₁] at * +ring +apply? + + +ProofFile: None +LemmaName: theorem mathd_algebra_313 + (v i z : ℂ) + (h₀ : v = i * z) + (h₁ : v = 1 + Complex.I) + (h₂ : z = 2 - Complex.I) : + i = 1/5 + 3/5 * Complex.I := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 23 +SearchTimeInSecs: 146.8498992919922 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'validation_error': 'Proof has unsolved goals (sorries)', 'std_err': '', 'has_sorries': True, 'compilation_ok': False, 'attempt_idx': 4, 'total_queries': 37} + + + +2026-01-11 10:41:41,329 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_332 +2026-01-11 10:41:41,329 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:41:41,329 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_332 (theorem_idx=93) with timeout: 600 seconds +2026-01-11 10:45:31,028 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:45:31,192 - __main__ - INFO - Failed to prove lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:45:31,192 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_275 + +2026-01-11 10:45:31,194 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_338 +2026-01-11 10:45:31,194 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:45:31,197 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_342 +2026-01-11 10:45:31,197 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:45:31,200 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_362 +2026-01-11 10:45:31,200 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:45:31,200 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_362 (theorem_idx=96) with timeout: 600 seconds +2026-01-11 10:45:36,501 - __main__ - INFO - Prover for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:45:36,501 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_320 + (x : ℝ) + (a b c : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 ≤ x) + (h₁ : 2 * x^2 = 4 * x + 9) + (h₂ : x = (a + Real.sqrt b) / c) + (h₃ : c = 2) : + a + b + c = 26 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 360.72194170951843 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 4, 'total_queries': 26} + + + +2026-01-11 10:45:36,503 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_392 +2026-01-11 10:45:36,503 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:45:36,503 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_392 (theorem_idx=97) with timeout: 600 seconds +2026-01-11 10:46:08,783 - __main__ - INFO - Prover for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:46:08,783 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_332 + (x y : ℝ) + (h₀ : (x + y) / 2 = 7) + (h₁ : Real.sqrt (x * y) = Real.sqrt 19) : + x^2 + y^2 = 158 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 31 +SearchTimeInSecs: 249.69419384002686 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 31, 'attempt_idx': 4, 'total_queries': 70} + + + +2026-01-11 10:46:08,786 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_398 +2026-01-11 10:46:08,786 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:46:08,789 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_427 +2026-01-11 10:46:08,789 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:46:08,792 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_452 +2026-01-11 10:46:08,792 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:46:08,792 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_452 (theorem_idx=100) with timeout: 600 seconds +2026-01-11 10:48:24,109 - __main__ - INFO - Prover Agent for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 10:48:24,269 - __main__ - INFO - Failed to prove lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:48:24,269 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_algebra_288 + +2026-01-11 10:48:24,272 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_459 +2026-01-11 10:48:24,272 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:48:24,275 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_484 +2026-01-11 10:48:24,275 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:48:24,278 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_487 +2026-01-11 10:48:24,278 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:48:24,278 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_487 (theorem_idx=103) with timeout: 600 seconds +2026-01-11 10:48:29,220 - __main__ - INFO - Prover for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:48:29,220 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_452 + (a : ℕ → ℝ) + (h₀ : ∀ n, a (n + 2) - a (n + 1) = a (n + 1) - a n) + (h₁ : a 1 = 2 / 3) + (h₂ : a 9 = 4 / 5) : + a 5 = 11 / 15 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_452 + (a : ℕ → ℝ) + (h₀ : ∀ n, a (n + 2) - a (n + 1) = a (n + 1) - a n) + (h₁ : a 1 = 2 / 3) + (h₂ : a 9 = 4 / 5) : + a 5 = 11 / 15 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 129.44691038131714 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 4, 'total_queries': 10} + + + +2026-01-11 10:48:29,222 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_598 +2026-01-11 10:48:29,222 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:48:29,225 - __main__ - INFO - Attempting to prove lemma: mathd_algebra_756 +2026-01-11 10:48:29,225 - __main__ - INFO - Attempt 5 for proving lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:48:29,225 - __main__ - INFO - Running the prover agent for lemma: mathd_algebra_756 (theorem_idx=105) with timeout: 600 seconds +2026-01-11 10:50:44,353 - __main__ - INFO - Prover for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:50:44,353 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_392 + (n : ℕ) + (h₀ : Even n) + (h₁ : ((n:ℤ) - 2)^2 + (n:ℤ)^2 + ((n:ℤ) + 2)^2 = 12296) : + ((n - 2) * n * (n + 2)) / 8 = 32736 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 294.86766386032104 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 4, 'total_queries': 47} + + + +2026-01-11 10:50:44,355 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_100 +2026-01-11 10:50:44,355 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:50:44,358 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_1124 +2026-01-11 10:50:44,359 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:50:44,359 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_1124 (theorem_idx=107) with timeout: 600 seconds +2026-01-11 10:51:50,773 - __main__ - INFO - Prover for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:51:50,773 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_362 + (a b : ℝ) + (h₀ : a^2 * b^3 = 32 / 27) + (h₁ : a / b^3 = 27 / 4) : + a + b = 8 / 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 51 +SearchTimeInSecs: 356.9055917263031 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 50, 'attempt_idx': 4, 'total_queries': 67} + + + +2026-01-11 10:51:50,775 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_222 +2026-01-11 10:51:50,775 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 10:51:50,779 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_227 +2026-01-11 10:51:50,779 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:51:50,779 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_227 (theorem_idx=109) with timeout: 600 seconds +2026-01-11 10:53:20,918 - __main__ - INFO - Prover for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:53:20,918 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_487 + (a b c d : ℝ) + (h₀ : b = a^2) + (h₁ : a + b = 1) + (h₂ : d = c^2) + (h₃ : c + d = 1) + (h₄ : a ≠ c) : + Real.sqrt ((a - c)^2 + (b - d)^2)= Real.sqrt 10 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 19 +SearchTimeInSecs: 285.93257784843445 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 4, 'total_queries': 38} + + + +2026-01-11 10:53:20,920 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_233 +2026-01-11 10:53:20,920 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:53:20,920 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_233 (theorem_idx=110) with timeout: 600 seconds +2026-01-11 10:54:35,409 - __main__ - INFO - Prover for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:54:35,409 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_233 + (b : ZMod (11^2)) + (h₀ : b = 24⁻¹) : + b = 116 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 59.52456879615784 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 4, 'total_queries': 44} + + + +2026-01-11 10:54:35,411 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_234 +2026-01-11 10:54:35,411 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:54:35,411 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_234 (theorem_idx=111) with timeout: 600 seconds +2026-01-11 10:54:58,684 - __main__ - INFO - Prover for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:54:58,685 - __main__ - INFO - Dumping proof search result: +theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_algebra_756 + (a b : ℝ) + (h₀ : (2:ℝ)^a = 32) + (h₁ : a^b = 125) : + b^a = 243 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 59 +SearchTimeInSecs: 376.9631326198578 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 61, 'attempt_idx': 4, 'total_queries': 89} + + + +2026-01-11 10:54:58,687 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_277 +2026-01-11 10:54:58,687 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:54:58,687 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_277 (theorem_idx=112) with timeout: 600 seconds +2026-01-11 10:56:21,827 - __main__ - INFO - Prover for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:56:21,827 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := + +by +-- Reduce the divisibility hypothesis to a congruence modulo 18 +have h₂ : (3740 + n) % 18 = 0 := by + simpa using (Nat.dvd_iff_mod_eq_zero.mp h₁) +-- Compute the remainder of 3740 modulo 18 +have h₃ : 3740 % 18 = 14 := by norm_num +have h4 : (14 + n) % 18 = 0 := by + simpa [h₃, Nat.add_comm, Nat.add_left_comm, Nat.add_assoc, Nat.add_mod] using h₂ +-- First, obtain that 18 divides 14 + n from the congruence +have hdiv : 18 ∣ 14 + n := by + exact Nat.dvd_of_mod_eq_zero h4 +omega + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_1124 + (n : ℕ) + (h₀ : n ≤ 9) + (h₁ : 18∣374 * 10 + n) : + n = 4 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 26 +SearchTimeInSecs: 324.9994397163391 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 26, 'attempt_idx': 4, 'total_queries': 26} + + + +2026-01-11 10:56:21,829 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_293 +2026-01-11 10:56:21,829 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:56:21,829 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_293 (theorem_idx=113) with timeout: 600 seconds +2026-01-11 10:58:07,113 - __main__ - INFO - Prover for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 10:58:07,114 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_234 + (a b : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9 ∧ b ≤ 9) + (h₁ : (10 * a + b)^3 = 912673) : + a + b = 16 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 188.05378079414368 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 4, 'total_queries': 29} + + + +2026-01-11 10:58:07,116 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_296 +2026-01-11 10:58:07,116 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 10:58:07,116 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_296 (theorem_idx=114) with timeout: 600 seconds +2026-01-11 11:01:50,943 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:01:51,108 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:01:51,108 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_227 + +2026-01-11 11:01:51,110 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_314 +2026-01-11 11:01:51,110 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:01:51,113 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_320 +2026-01-11 11:01:51,113 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:01:51,113 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_320 (theorem_idx=116) with timeout: 600 seconds +2026-01-11 11:02:37,675 - __main__ - INFO - Prover for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:02:37,675 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_296 + (n : ℕ) + (h₀ : 2 ≤ n) + (h₁ : ∃ x, x^3 = n) + (h₂ : ∃ t, t^4 = n) : + 4096 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 244.48939609527588 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 4, 'total_queries': 33} + + + +2026-01-11 11:02:37,678 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_321 +2026-01-11 11:02:37,678 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:02:37,678 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_321 (theorem_idx=117) with timeout: 600 seconds +2026-01-11 11:04:14,688 - __main__ - INFO - Prover for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:04:14,688 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_320 + (n : ℕ) + (h₀ : n < 101) + (h₁ : 101 ∣ (123456 - n)) : + n = 34 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 124.99714088439941 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 4, 'total_queries': 20} + + + +2026-01-11 11:04:14,690 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_328 +2026-01-11 11:04:14,690 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:04:14,693 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_34 +2026-01-11 11:04:14,693 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:04:14,693 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_34 (theorem_idx=119) with timeout: 600 seconds +2026-01-11 11:04:35,660 - __main__ - INFO - Prover for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:04:35,660 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_321 + (n : ZMod 1399) + (h₁ : n = 160⁻¹) : + n = 1058 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 102.99281978607178 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 38} + + + +2026-01-11 11:04:35,663 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_353 +2026-01-11 11:04:35,663 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:04:35,663 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_353 (theorem_idx=120) with timeout: 600 seconds +2026-01-11 11:04:58,777 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:04:58,942 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:04:58,942 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_277 + +2026-01-11 11:04:58,944 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_427 +2026-01-11 11:04:58,944 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:04:58,944 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_427 (theorem_idx=121) with timeout: 600 seconds +2026-01-11 11:05:15,799 - __main__ - INFO - Prover for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:05:15,799 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_353 + (s : ℕ) + (h₀ : s = ∑ k ∈ Finset.Icc 2010 4018, k) : + s % 2009 = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 7 +SearchTimeInSecs: 31.327113151550293 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 20} + + + +2026-01-11 11:05:15,801 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_430 +2026-01-11 11:05:15,801 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:05:15,801 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_430 (theorem_idx=122) with timeout: 600 seconds +2026-01-11 11:06:21,990 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:06:22,157 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:06:22,157 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_293 + +2026-01-11 11:06:22,159 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_435 +2026-01-11 11:06:22,159 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:06:22,159 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_435 (theorem_idx=123) with timeout: 600 seconds +2026-01-11 11:06:23,119 - __main__ - INFO - Prover for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:06:23,119 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_427 + (a : ℕ) + (h₀ : a = (∑ k ∈ (Nat.divisors 500), k)) : + ∑ k ∈ Finset.filter (λ x => Nat.Prime x) (Nat.divisors a), k = 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 76.395583152771 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 4, 'total_queries': 18} + + + +2026-01-11 11:06:23,121 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_447 +2026-01-11 11:06:23,122 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:06:23,124 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_451 +2026-01-11 11:06:23,125 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:06:23,125 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_451 (theorem_idx=125) with timeout: 600 seconds +2026-01-11 11:06:24,897 - __main__ - INFO - Prover for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:06:24,898 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_430 + (a b c : ℕ) + (h₀ : 1 ≤ a ∧ a ≤ 9) + (h₁ : 1 ≤ b ∧ b ≤ 9) + (h₂ : 1 ≤ c ∧ c ≤ 9) + (h₃ : a ≠ b) + (h₄ : a ≠ c) + (h₅ : b ≠ c) + (h₆ : a + b = c) + (h₇ : 10 * a + a - b = 2 * c) + (h₈ : c * b = 10 * a + a + a) : + a + b + c = 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 60.99290752410889 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 4, 'total_queries': 35} + + + +2026-01-11 11:06:24,900 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_457 +2026-01-11 11:06:24,900 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:06:24,900 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_457 (theorem_idx=126) with timeout: 600 seconds +2026-01-11 11:07:35,196 - __main__ - INFO - Prover for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:07:35,196 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_457 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : 80325∣(n !)) : + 17 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 57.0021014213562 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 4, 'total_queries': 19} + + + +2026-01-11 11:07:35,199 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_483 +2026-01-11 11:07:35,199 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:07:35,201 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_495 +2026-01-11 11:07:35,201 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:07:35,201 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_495 (theorem_idx=128) with timeout: 600 seconds +2026-01-11 11:08:10,957 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:08:11,122 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:08:11,122 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: mathd_numbertheory_495 + +2026-01-11 11:08:11,124 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_5 +2026-01-11 11:08:11,124 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:08:11,124 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_5 (theorem_idx=129) with timeout: 600 seconds +2026-01-11 11:10:22,594 - __main__ - INFO - Prover for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:10:22,594 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_34 + (x: ℕ) + (h₀ : x < 100) + (h₁ : x*9 % 100 = 1) : + x = 89 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 80 +SearchTimeInSecs: 354.0895082950592 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 76, 'attempt_idx': 4, 'total_queries': 113} + + + +2026-01-11 11:10:22,596 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_521 +2026-01-11 11:10:22,596 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:10:22,596 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_521 (theorem_idx=130) with timeout: 600 seconds +2026-01-11 11:10:23,838 - __main__ - INFO - Prover for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:10:23,838 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_5 + (n : ℕ) + (h₀ : 10 ≤ n) + (h₁ : ∃ x, x^2 = n) + (h₂ : ∃ t, t^3 = n) : + 64 ≤ n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 121.06117415428162 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 4, 'total_queries': 13} + + + +2026-01-11 11:10:23,840 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_541 +2026-01-11 11:10:23,840 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:10:23,840 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_541 (theorem_idx=131) with timeout: 600 seconds +2026-01-11 11:12:29,454 - __main__ - INFO - Prover for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:12:29,454 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_541 + (m n : ℕ) + (h₀ : 1 < m) + (h₁ : 1 < n) + (h₂ : m * n = 2005) : + m + n = 406 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 99.48005557060242 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 4, 'total_queries': 9} + + + +2026-01-11 11:12:29,457 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_552 +2026-01-11 11:12:29,457 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:12:29,457 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_552 (theorem_idx=132) with timeout: 600 seconds +2026-01-11 11:13:51,161 - __main__ - INFO - Prover for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:13:51,162 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_552 + (f g h : ℕ+ → ℕ) + (h₀ : ∀ x, f x = 12 * x + 7) + (h₁ : ∀ x, g x = 5 * x + 2) + (h₂ : ∀ x, h x = Nat.gcd (f x) (g x)) + (h₃ : Fintype (Set.range h)) : + ∑ k ∈ (Set.range h).toFinset, k = 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 70.56036972999573 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 28} + + + +2026-01-11 11:13:51,164 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_559 +2026-01-11 11:13:51,164 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:13:51,167 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_582 +2026-01-11 11:13:51,167 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:13:51,170 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_618 +2026-01-11 11:13:51,170 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:13:51,170 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_618 (theorem_idx=135) with timeout: 600 seconds +2026-01-11 11:13:56,619 - __main__ - INFO - Prover for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:13:56,619 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_435 + (k : ℕ) + (h₀ : 0 < k) + (h₁ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 3) = 1) + (h₂ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 2) = 1) + (h₃ : ∀ n, Nat.gcd (6 * n + k) (6 * n + 1) = 1) : + 5 ≤ k := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 47 +SearchTimeInSecs: 439.3847930431366 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 47, 'attempt_idx': 4, 'total_queries': 76} + + + +2026-01-11 11:13:56,621 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_711 +2026-01-11 11:13:56,621 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:13:56,621 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_711 (theorem_idx=136) with timeout: 600 seconds +2026-01-11 11:16:23,307 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:16:23,472 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:16:23,472 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_451 + +2026-01-11 11:16:23,474 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_764 +2026-01-11 11:16:23,474 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:16:23,474 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_764 (theorem_idx=137) with timeout: 600 seconds +2026-01-11 11:17:05,502 - __main__ - INFO - Prover for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:17:05,502 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_764 + (p : ℕ) + (h₀ : Nat.Prime p) + (h₁ : 7 ≤ p) : + ∑ k ∈ Finset.Icc 1 (p-2), ((k: ZMod p)⁻¹ * ((k: ZMod p) + 1)⁻¹) = 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 28.42672824859619 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 4, 'total_queries': 59} + + + +2026-01-11 11:17:05,505 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_765 +2026-01-11 11:17:05,505 - __main__ - INFO - Attempt 5 for proving lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:17:05,505 - __main__ - INFO - Running the prover agent for lemma: mathd_numbertheory_765 (theorem_idx=138) with timeout: 600 seconds +2026-01-11 11:17:32,399 - __main__ - INFO - Prover for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:17:32,399 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_521 + (m n : ℕ) + (h₀ : Even m) + (h₁ : Even n) + (h₂ : m - n = 2) + (h₃ : m * n = 288) : + m = 18 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_521 + (m n : ℕ) + (h₀ : Even m) + (h₁ : Even n) + (h₂ : m - n = 2) + (h₃ : m * n = 288) : + m = 18 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 49 +SearchTimeInSecs: 406.79114151000977 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 46, 'attempt_idx': 4, 'total_queries': 61} + + + +2026-01-11 11:17:32,402 - __main__ - INFO - Attempting to prove lemma: mathd_numbertheory_99 +2026-01-11 11:17:32,402 - __main__ - INFO - Skipping the attempt for proving lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:17:32,405 - __main__ - INFO - Attempting to prove lemma: numbertheory_2pownm1prime_nprime +2026-01-11 11:17:32,405 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:17:32,405 - __main__ - INFO - Running the prover agent for lemma: numbertheory_2pownm1prime_nprime (theorem_idx=140) with timeout: 600 seconds +2026-01-11 11:17:56,992 - __main__ - INFO - Prover for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:17:56,992 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_2pownm1prime_nprime + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Nat.Prime (2^n - 1)) : + Nat.Prime n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 11.985596179962158 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 4, 'total_queries': 4} + + + +2026-01-11 11:17:56,994 - __main__ - INFO - Attempting to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 +2026-01-11 11:17:56,994 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:17:56,994 - __main__ - INFO - Running the prover agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 (theorem_idx=141) with timeout: 600 seconds +2026-01-11 11:22:37,341 - __main__ - INFO - Prover for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:22:37,341 - __main__ - INFO - Dumping proof search result: +theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := + +by + + + +ProofFile: None +LemmaName: theorem mathd_numbertheory_765 + (x : ℤ) + (h₀ : x < 0) + (h₁ : (24 * x) % 1199 = 15) : + x ≤ -449 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 322.02698135375977 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 33, 'attempt_idx': 4, 'total_queries': 60} + + + +2026-01-11 11:22:37,343 - __main__ - INFO - Attempting to prove lemma: numbertheory_4x3m7y3neq2003 +2026-01-11 11:22:37,343 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:22:37,343 - __main__ - INFO - Running the prover agent for lemma: numbertheory_4x3m7y3neq2003 (theorem_idx=142) with timeout: 600 seconds +2026-01-11 11:23:22,280 - __main__ - INFO - Prover for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:23:22,280 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_4x3m7y3neq2003 + (x y : ℤ) : + 4 * x^3 - 7 * y^3 ≠ 2003 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_4x3m7y3neq2003 + (x y : ℤ) : + 4 * x^3 - 7 * y^3 ≠ 2003 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 38.24369812011719 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 4, 'total_queries': 4} + + + +2026-01-11 11:23:22,282 - __main__ - INFO - Attempting to prove lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 +2026-01-11 11:23:22,282 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:23:22,282 - __main__ - INFO - Running the prover agent for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 (theorem_idx=143) with timeout: 600 seconds +2026-01-11 11:23:51,314 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:23:51,477 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:23:51,477 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_618 + +2026-01-11 11:23:51,479 - __main__ - INFO - Attempting to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 +2026-01-11 11:23:51,479 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:23:51,479 - __main__ - INFO - Running the prover agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 (theorem_idx=144) with timeout: 600 seconds +2026-01-11 11:23:56,798 - __main__ - INFO - Prover Agent for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:23:56,964 - __main__ - INFO - Failed to prove lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:23:56,964 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: mathd_numbertheory_711 + +2026-01-11 11:23:56,966 - __main__ - INFO - Attempting to prove lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown +2026-01-11 11:23:56,966 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:23:56,966 - __main__ - INFO - Running the prover agent for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown (theorem_idx=145) with timeout: 600 seconds +2026-01-11 11:25:05,491 - __main__ - INFO - Prover Agent for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:25:05,654 - __main__ - INFO - Failed to prove lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:25:05,654 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 + +2026-01-11 11:25:05,656 - __main__ - INFO - Attempting to prove lemma: numbertheory_x5neqy2p4 +2026-01-11 11:25:05,656 - __main__ - INFO - Attempt 5 for proving lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:25:05,656 - __main__ - INFO - Running the prover agent for lemma: numbertheory_x5neqy2p4 (theorem_idx=146) with timeout: 600 seconds +2026-01-11 11:27:57,175 - __main__ - INFO - Prover Agent for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:27:57,338 - __main__ - INFO - Failed to prove lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:27:57,338 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 + +2026-01-11 11:27:57,340 - __main__ - INFO - Attempting to prove lemma: aime_1983_p1 +2026-01-11 11:27:57,340 - __main__ - INFO - Attempt 5 for proving lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:27:57,340 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p1 (theorem_idx=147) with timeout: 600 seconds +2026-01-11 11:29:31,828 - __main__ - INFO - Prover for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:29:31,828 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_aoddbdiv4asqpbsqmod8eq1 + (a : ℤ) + (b : ℤ) + (h₀ : Odd a) + (h₁ : 4 ∣ b) + (h₂ : b >= 0) : + (a^2 + b^2) % 8 = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 56 +SearchTimeInSecs: 347.3847179412842 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 54, 'attempt_idx': 4, 'total_queries': 54} + + + +2026-01-11 11:29:31,831 - __main__ - INFO - Attempting to prove lemma: aime_1983_p3 +2026-01-11 11:29:31,831 - __main__ - INFO - Attempt 5 for proving lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:29:31,831 - __main__ - INFO - Running the prover agent for lemma: aime_1983_p3 (theorem_idx=148) with timeout: 600 seconds +2026-01-11 11:30:43,738 - __main__ - INFO - Prover for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:30:43,738 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown + (m n : ℕ) + (f : ℕ → ℕ) + (h₀ : ∀ x, f x = 4^x + 6^x + 9^x) + (h₁ : 0 < m ∧ 0 < n) + (h₂ : m ≤ n) : + f (2^m)∣f (2^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 59 +SearchTimeInSecs: 396.6461389064789 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 65, 'attempt_idx': 4, 'total_queries': 77} + + + +2026-01-11 11:30:43,740 - __main__ - INFO - Attempting to prove lemma: aime_1984_p1 +2026-01-11 11:30:43,740 - __main__ - INFO - Attempt 5 for proving lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:30:43,740 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p1 (theorem_idx=149) with timeout: 600 seconds +2026-01-11 11:31:34,469 - __main__ - INFO - Prover for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:31:34,469 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p3 + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = (x^2 + (18 * x + 30) - 2 * Real.sqrt (x^2 + (18 * x + 45)))) + (h₁ : Fintype (f⁻¹' {0})) : + ∏ x ∈ (f⁻¹' {0}).toFinset, x = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 103.04623913764954 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 11, 'attempt_idx': 4, 'total_queries': 11} + + + +2026-01-11 11:31:34,471 - __main__ - INFO - Attempting to prove lemma: aime_1984_p7 +2026-01-11 11:31:34,471 - __main__ - INFO - Attempt 5 for proving lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:31:34,471 - __main__ - INFO - Running the prover agent for lemma: aime_1984_p7 (theorem_idx=150) with timeout: 600 seconds +2026-01-11 11:31:49,294 - __main__ - INFO - Prover for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:31:49,295 - __main__ - INFO - Dumping proof search result: +theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1983_p1 (x y z w : ℕ) (ht : 1 < x ∧ 1 < y ∧ 1 < z) (hw : 0 ≤ w) + (h0 : Real.log w / Real.log x = 24) (h1 : Real.log w / Real.log y = 40) + (h2 : Real.log w / Real.log (x * y * z) = 12) : Real.log w / Real.log z = 60 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 224.9120512008667 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 4, 'total_queries': 31} + + + +2026-01-11 11:31:49,297 - __main__ - INFO - Attempting to prove lemma: aime_1987_p5 +2026-01-11 11:31:49,297 - __main__ - INFO - Attempt 5 for proving lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:31:49,297 - __main__ - INFO - Running the prover agent for lemma: aime_1987_p5 (theorem_idx=151) with timeout: 600 seconds +2026-01-11 11:33:50,467 - __main__ - INFO - Prover for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:33:50,467 - __main__ - INFO - Dumping proof search result: +theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := + +by + + + +ProofFile: None +LemmaName: theorem numbertheory_x5neqy2p4 + (x y : ℤ) : + x^5 ≠ y^2 + 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 40 +SearchTimeInSecs: 516.8395915031433 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 39, 'attempt_idx': 4, 'total_queries': 41} + + + +2026-01-11 11:33:50,469 - __main__ - INFO - Attempting to prove lemma: aime_1988_p8 +2026-01-11 11:33:50,470 - __main__ - INFO - Attempt 5 for proving lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:33:50,470 - __main__ - INFO - Running the prover agent for lemma: aime_1988_p8 (theorem_idx=152) with timeout: 600 seconds +2026-01-11 11:40:06,288 - __main__ - INFO - Prover for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:40:06,288 - __main__ - INFO - Dumping proof search result: +theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1987_p5 + (x y : ℤ) + (h₀ : y^2 + 3 * (x^2 * y^2) = 30 * x^2 + 517): + 3 * (x^2 * y^2) = 588 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 37 +SearchTimeInSecs: 486.53953647613525 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 4, 'total_queries': 41} + + + +2026-01-11 11:40:06,290 - __main__ - INFO - Attempting to prove lemma: aime_1990_p15 +2026-01-11 11:40:06,290 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:40:06,293 - __main__ - INFO - Attempting to prove lemma: aime_1990_p4 +2026-01-11 11:40:06,293 - __main__ - INFO - Skipping the attempt for proving lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:40:06,296 - __main__ - INFO - Attempting to prove lemma: aime_1991_p9 +2026-01-11 11:40:06,296 - __main__ - INFO - Attempt 5 for proving lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:40:06,296 - __main__ - INFO - Running the prover agent for lemma: aime_1991_p9 (theorem_idx=155) with timeout: 600 seconds +2026-01-11 11:40:43,830 - __main__ - INFO - Prover Agent for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:40:43,993 - __main__ - INFO - Failed to prove lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:40:43,993 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1984_p1 + +2026-01-11 11:40:43,995 - __main__ - INFO - Attempting to prove lemma: aime_1994_p3 +2026-01-11 11:40:43,995 - __main__ - INFO - Attempt 5 for proving lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:40:43,995 - __main__ - INFO - Running the prover agent for lemma: aime_1994_p3 (theorem_idx=156) with timeout: 600 seconds +2026-01-11 11:41:34,650 - __main__ - INFO - Prover Agent for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:41:34,817 - __main__ - INFO - Failed to prove lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:41:34,817 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1984_p7 + +2026-01-11 11:41:34,819 - __main__ - INFO - Attempting to prove lemma: aime_1995_p7 +2026-01-11 11:41:34,819 - __main__ - INFO - Attempt 5 for proving lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:41:34,819 - __main__ - INFO - Running the prover agent for lemma: aime_1995_p7 (theorem_idx=157) with timeout: 600 seconds +2026-01-11 11:42:34,834 - __main__ - INFO - Prover for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:42:34,834 - __main__ - INFO - Dumping proof search result: +theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1991_p9 + (x : ℝ) + (m : ℚ) + (h₀ : 1 / Real.cos x + Real.tan x = 22 / 7) + (h₁ : 1 / Real.sin x + 1 / Real.tan x = m) : + ↑m.den + m.num = 44 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 17 +SearchTimeInSecs: 125.06400942802429 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 17, 'attempt_idx': 4, 'total_queries': 38} + + + +2026-01-11 11:42:34,836 - __main__ - INFO - Attempting to prove lemma: aime_1997_p9 +2026-01-11 11:42:34,836 - __main__ - INFO - Attempt 5 for proving lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:42:34,836 - __main__ - INFO - Running the prover agent for lemma: aime_1997_p9 (theorem_idx=158) with timeout: 600 seconds +2026-01-11 11:42:48,042 - __main__ - INFO - Prover for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:42:48,042 - __main__ - INFO - Dumping proof search result: +theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1995_p7 + (k m n : ℕ) + (t : ℝ) + (h₀ : 0 < k ∧ 0 < m ∧ 0 < n) + (h₁ : Nat.gcd m n = 1) + (h₂ : (1 + Real.sin t) * (1 + Real.cos t) = 5/4) + (h₃ : (1 - Real.sin t) * (1- Real.cos t) = m/n - Real.sqrt k): + k + m + n = 27 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 46.16729974746704 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 4, 'total_queries': 23} + + + +2026-01-11 11:42:48,044 - __main__ - INFO - Attempting to prove lemma: aime_1999_p11 +2026-01-11 11:42:48,044 - __main__ - INFO - Attempt 5 for proving lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:42:48,044 - __main__ - INFO - Running the prover agent for lemma: aime_1999_p11 (theorem_idx=159) with timeout: 600 seconds +2026-01-11 11:43:33,310 - __main__ - INFO - Prover for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:43:33,310 - __main__ - INFO - Dumping proof search result: +theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1994_p3 + (f : ℤ → ℤ) + (h0 : f x + f (x-1) = x^2) + (h1 : f 19 = 94): + f (94) % 1000 = 561 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 158.22688150405884 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 4, 'total_queries': 63} + + + +2026-01-11 11:43:33,313 - __main__ - INFO - Attempting to prove lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 +2026-01-11 11:43:33,313 - __main__ - INFO - Attempt 5 for proving lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:43:33,313 - __main__ - INFO - Running the prover agent for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 (theorem_idx=160) with timeout: 600 seconds +2026-01-11 11:43:50,642 - __main__ - INFO - Prover Agent for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:43:50,805 - __main__ - INFO - Failed to prove lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:43:50,805 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: aime_1988_p8 + +2026-01-11 11:43:50,807 - __main__ - INFO - Attempting to prove lemma: algebra_9onxpypzleqsum2onxpy +2026-01-11 11:43:50,807 - __main__ - INFO - Attempt 5 for proving lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:43:50,807 - __main__ - INFO - Running the prover agent for lemma: algebra_9onxpypzleqsum2onxpy (theorem_idx=161) with timeout: 600 seconds +2026-01-11 11:44:27,587 - __main__ - INFO - Prover for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:44:27,588 - __main__ - INFO - Dumping proof search result: +theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_9onxpypzleqsum2onxpy + (x y z : ℝ) + (h₀ : 0 < x ∧ 0 < y ∧ 0 < z) : + 9 / (x + y + z) ≤ 2 / (x + y) + 2 / (y + z) + 2 / (z + x) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 21.942713499069214 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 4, 'total_queries': 57} + + + +2026-01-11 11:44:27,590 - __main__ - INFO - Attempting to prove lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 +2026-01-11 11:44:27,590 - __main__ - INFO - Attempt 5 for proving lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:44:27,590 - __main__ - INFO - Running the prover agent for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 (theorem_idx=162) with timeout: 600 seconds +2026-01-11 11:44:32,583 - __main__ - INFO - Prover for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:44:32,583 - __main__ - INFO - Dumping proof search result: +theorem aime_1997_p9 + (a : ℝ) + (h₀ : 0 < a) + (h₁ : 1 / a - Int.floor (1 / a) = a^2 - Int.floor (a^2)) + (h₂ : 2 < a^2) + (h₃ : a^2 < 3) : + a^12 - 144 * (1 / a) = 233 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1997_p9 + (a : ℝ) + (h₀ : 0 < a) + (h₁ : 1 / a - Int.floor (1 / a) = a^2 - Int.floor (a^2)) + (h₂ : 2 < a^2) + (h₃ : a^2 < 3) : + a^12 - 144 * (1 / a) = 233 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 12 +SearchTimeInSecs: 108.01205563545227 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 4, 'total_queries': 12} + + + +2026-01-11 11:44:32,586 - __main__ - INFO - Attempting to prove lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa +2026-01-11 11:44:32,586 - __main__ - INFO - Attempt 5 for proving lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:44:32,586 - __main__ - INFO - Running the prover agent for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa (theorem_idx=163) with timeout: 600 seconds +2026-01-11 11:45:17,909 - __main__ - INFO - Prover for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:45:17,909 - __main__ - INFO - Dumping proof search result: +theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : 3 ≤ a * b + b * c + c * a) : + 3 / Real.sqrt 2 ≤ a / Real.sqrt (a + b) + b / Real.sqrt (b + c) + c / Real.sqrt (c + a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 38.557745933532715 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 4, 'total_queries': 50} + + + +2026-01-11 11:45:17,911 - __main__ - INFO - Attempting to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 +2026-01-11 11:45:17,911 - __main__ - INFO - Attempt 5 for proving lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:45:17,911 - __main__ - INFO - Running the prover agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 (theorem_idx=164) with timeout: 600 seconds +2026-01-11 11:45:22,840 - __main__ - INFO - Prover for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:45:22,840 - __main__ - INFO - Dumping proof search result: +theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 + (f z: ℂ) + (h₀ : f + 3*z = 11) + (h₁ : 3*(f - 1) - 5*z = -68) : + f = -10 ∧ z = 7 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 97.45684027671814 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 60} + + + +2026-01-11 11:45:22,842 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sum1toneqn_prod1tonleq1 +2026-01-11 11:45:22,843 - __main__ - INFO - Attempt 5 for proving lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:45:22,843 - __main__ - INFO - Running the prover agent for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 (theorem_idx=165) with timeout: 600 seconds +2026-01-11 11:45:55,565 - __main__ - INFO - Prover for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:45:55,566 - __main__ - INFO - Dumping proof search result: +theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_absapbon1pabsapbleqsumabsaon1pabsa + (a b : ℝ) : + abs (a + b) / (1 + abs (a + b)) ≤ abs a / (1 + abs a) + abs b / (1 + abs b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 8 +SearchTimeInSecs: 67.50684094429016 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 8, 'attempt_idx': 4, 'total_queries': 40} + + + +2026-01-11 11:45:55,568 - __main__ - INFO - Attempting to prove lemma: algebra_amgm_sumasqdivbgeqsuma +2026-01-11 11:45:55,568 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:45:55,571 - __main__ - INFO - Attempting to prove lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 +2026-01-11 11:45:55,571 - __main__ - INFO - Attempt 5 for proving lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:45:55,571 - __main__ - INFO - Running the prover agent for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 (theorem_idx=167) with timeout: 600 seconds +2026-01-11 11:46:43,328 - __main__ - INFO - Prover for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:46:43,328 - __main__ - INFO - Dumping proof search result: +theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := + +by + + + +ProofFile: None +LemmaName: theorem aime_1999_p11 + (m : ℚ) + (h₀ : 0 < m) + (h₁ : ∑ k ∈ Finset.Icc (1 : ℕ) 35, Real.sin (5 * k * π / 180) = Real.tan (m * π / 180)) + (h₂ : (m.num:ℝ) / m.den < 90) : + ↑m.den + m.num = 177 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 31 +SearchTimeInSecs: 212.9225368499756 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 31, 'attempt_idx': 4, 'total_queries': 39} + + + +2026-01-11 11:46:43,330 - __main__ - INFO - Attempting to prove lemma: algebra_apbon2pownleqapownpbpowon2 +2026-01-11 11:46:43,330 - __main__ - INFO - Attempt 5 for proving lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:46:43,331 - __main__ - INFO - Running the prover agent for lemma: algebra_apbon2pownleqapownpbpowon2 (theorem_idx=168) with timeout: 600 seconds +2026-01-11 11:47:19,124 - __main__ - INFO - Prover for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:47:19,124 - __main__ - INFO - Dumping proof search result: +theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_amgm_sum1toneqn_prod1tonleq1 + (a : ℕ → NNReal) + (n : ℕ) + (h₀ : ∑ x ∈ Finset.range n, a x = n) : + ∏ x ∈ Finset.range n, a x ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 14 +SearchTimeInSecs: 97.31405639648438 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 14, 'attempt_idx': 4, 'total_queries': 18} + + + +2026-01-11 11:47:19,126 - __main__ - INFO - Attempting to prove lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 +2026-01-11 11:47:19,126 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:47:19,129 - __main__ - INFO - Attempting to prove lemma: algebra_bleqa_apbon2msqrtableqambsqon8b +2026-01-11 11:47:19,129 - __main__ - INFO - Attempt 5 for proving lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:47:19,129 - __main__ - INFO - Running the prover agent for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b (theorem_idx=170) with timeout: 600 seconds +2026-01-11 11:48:33,308 - __main__ - INFO - Prover for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:48:33,308 - __main__ - INFO - Dumping proof search result: +theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_bleqa_apbon2msqrtableqambsqon8b + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : b ≤ a) : + (a + b) / 2 - Real.sqrt (a * b) ≤ (a - b)^2 / (8 * b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 58.7968168258667 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 6} + + + +2026-01-11 11:48:33,311 - __main__ - INFO - Attempting to prove lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 +2026-01-11 11:48:33,311 - __main__ - INFO - Attempt 5 for proving lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:48:33,311 - __main__ - INFO - Running the prover agent for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 (theorem_idx=171) with timeout: 600 seconds +2026-01-11 11:48:51,697 - __main__ - INFO - Prover for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:48:51,697 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbon2pownleqapownpbpowon2 + (a b : ℝ) + (n : ℕ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : 0 < n) : + ((a + b) / 2)^n ≤ (a^n + b^n) / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 106.6823182106018 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 4, 'total_queries': 26} + + + +2026-01-11 11:48:51,699 - __main__ - INFO - Attempting to prove lemma: algebra_ineq_nto1onlt2m1on +2026-01-11 11:48:51,699 - __main__ - INFO - Attempt 5 for proving lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:48:51,699 - __main__ - INFO - Running the prover agent for lemma: algebra_ineq_nto1onlt2m1on (theorem_idx=172) with timeout: 600 seconds +2026-01-11 11:49:29,331 - __main__ - INFO - Prover for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:49:29,332 - __main__ - INFO - Dumping proof search result: +theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_apbmpcneq0_aeq0anbeq0anceq0 + (a b c : ℚ) + (m n : ℝ) + (h₀ : 0 < m ∧ 0 < n) + (h₁ : m^3 = 2) + (h₂ : n^3 = 4) + (h₃ : (a:ℝ) + b * m + c * n = 0) : + a = 0 ∧ b = 0 ∧ c = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 203.02042198181152 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 4, 'total_queries': 39} + + + +2026-01-11 11:49:29,334 - __main__ - INFO - Attempting to prove lemma: algebra_others_exirrpowirrrat +2026-01-11 11:49:29,334 - __main__ - INFO - Attempt 5 for proving lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:49:29,334 - __main__ - INFO - Running the prover agent for lemma: algebra_others_exirrpowirrrat (theorem_idx=173) with timeout: 600 seconds +2026-01-11 11:50:15,672 - __main__ - INFO - Prover Agent for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:50:15,836 - __main__ - INFO - Failed to prove lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:50:15,837 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: algebra_ineq_nto1onlt2m1on + +2026-01-11 11:50:15,839 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpabsamblt1 +2026-01-11 11:50:15,839 - __main__ - INFO - Attempt 5 for proving lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:50:15,839 - __main__ - INFO - Running the prover agent for lemma: algebra_sqineq_unitcircatbpabsamblt1 (theorem_idx=174) with timeout: 600 seconds +2026-01-11 11:50:32,328 - __main__ - INFO - Prover for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:50:32,329 - __main__ - INFO - Dumping proof search result: +theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 + (r : ℝ) + (h₀ : r^(1 / 3: ℝ) + 1 / r^(1 / 3: ℝ) = 3) : + r^3 + 1 / r^3 = 5778 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 99.25465774536133 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 4, 'total_queries': 19} + + + +2026-01-11 11:50:32,331 - __main__ - INFO - Attempting to prove lemma: algebra_sqineq_unitcircatbpamblt1 +2026-01-11 11:50:32,331 - __main__ - INFO - Skipping the attempt for proving lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 11:50:32,334 - __main__ - INFO - Attempting to prove lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 +2026-01-11 11:50:32,334 - __main__ - INFO - Attempt 5 for proving lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:50:32,334 - __main__ - INFO - Running the prover agent for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 (theorem_idx=176) with timeout: 600 seconds +2026-01-11 11:52:00,515 - __main__ - INFO - Prover for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:52:00,516 - __main__ - INFO - Dumping proof search result: +theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sqineq_unitcircatbpabsamblt1 + (a b: ℝ) + (h₀ : a^2 + b^2 = 1) : + a * b + |a - b| ≤ 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 96.98038816452026 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 25} + + + +2026-01-11 11:52:00,518 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p1 +2026-01-11 11:52:00,518 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:52:00,518 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p1 (theorem_idx=177) with timeout: 600 seconds +2026-01-11 11:53:41,854 - __main__ - INFO - Prover for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:53:41,854 - __main__ - INFO - Dumping proof search result: +theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := + +by + + + +ProofFile: None +LemmaName: theorem algebra_others_exirrpowirrrat : + ∃ a b, Irrational a ∧ Irrational b ∧ ¬ Irrational (a^b) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 235.69013738632202 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 27, 'attempt_idx': 4, 'total_queries': 27} + + + +2026-01-11 11:53:41,856 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p12 +2026-01-11 11:53:41,856 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:53:41,856 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p12 (theorem_idx=178) with timeout: 600 seconds +2026-01-11 11:53:47,990 - __main__ - INFO - Prover for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:53:47,990 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p1 + (i m o : ℕ) + (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i) + (h₁ : i*m*o = 2001) : + i+m+o ≤ 671 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 89.74184942245483 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 30} + + + +2026-01-11 11:53:47,992 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p20 +2026-01-11 11:53:47,992 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:53:47,992 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p20 (theorem_idx=179) with timeout: 600 seconds +2026-01-11 11:55:18,096 - __main__ - INFO - Prover Agent for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 11:55:18,294 - __main__ - INFO - Failed to prove lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:55:18,294 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 + +2026-01-11 11:55:18,296 - __main__ - INFO - Attempting to prove lemma: amc12_2000_p6 +2026-01-11 11:55:18,296 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:55:18,296 - __main__ - INFO - Running the prover agent for lemma: amc12_2000_p6 (theorem_idx=180) with timeout: 600 seconds +2026-01-11 11:56:25,553 - __main__ - INFO - Prover for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:56:25,553 - __main__ - INFO - Dumping proof search result: +theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := + +by + + + +ProofFile: None +LemmaName: theorem algebra_sum1onsqrt2to1onsqrt10000lt198 : + ∑ k ∈ (Finset.Icc (2 : ℕ) 10000), (1 / Real.sqrt k) < 198 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 336.8889408111572 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 4, 'total_queries': 94} + + + +2026-01-11 11:56:25,555 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p21 +2026-01-11 11:56:25,555 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:56:25,555 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p21 (theorem_idx=181) with timeout: 600 seconds +2026-01-11 11:59:14,834 - __main__ - INFO - Prover for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 11:59:14,834 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p12 + (a m c : ℕ) + (h₀ : a + m + c = 12) : + a*m*c + a*m + m*c + a*c ≤ 112 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 45 +SearchTimeInSecs: 318.78669452667236 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 45, 'attempt_idx': 4, 'total_queries': 53} + + + +2026-01-11 11:59:14,837 - __main__ - INFO - Attempting to prove lemma: amc12_2001_p5 +2026-01-11 11:59:14,837 - __main__ - INFO - Attempt 5 for proving lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 11:59:14,837 - __main__ - INFO - Running the prover agent for lemma: amc12_2001_p5 (theorem_idx=182) with timeout: 600 seconds +2026-01-11 12:00:48,882 - __main__ - INFO - Prover for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:00:48,882 - __main__ - INFO - Dumping proof search result: +theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2000_p6 + (p q : ℕ) + (h₀ : Nat.Prime p ∧ Nat.Prime q) + (h₁ : 4 ≤ p ∧ p ≤ 18) + (h₂ : 4 ≤ q ∧ q ≤ 18) : + p * q - (p + q) ≠ 194 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 28 +SearchTimeInSecs: 311.58392691612244 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 29, 'attempt_idx': 4, 'total_queries': 47} + + + +2026-01-11 12:00:48,884 - __main__ - INFO - Attempting to prove lemma: amc12a_2002_p13 +2026-01-11 12:00:48,884 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:00:48,884 - __main__ - INFO - Running the prover agent for lemma: amc12a_2002_p13 (theorem_idx=183) with timeout: 600 seconds +2026-01-11 12:03:48,137 - __main__ - INFO - Prover Agent for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:03:48,302 - __main__ - INFO - Failed to prove lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:03:48,303 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12_2000_p20 + +2026-01-11 12:03:48,305 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p23 +2026-01-11 12:03:48,305 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:03:48,305 - __main__ - INFO - Running the prover agent for lemma: amc12a_2003_p23 (theorem_idx=184) with timeout: 600 seconds +2026-01-11 12:03:50,894 - __main__ - INFO - Prover for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:03:50,894 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2002_p13 + (a b : ℝ) + (h₀ : 0 < a ∧ 0 < b) + (h₁ : a ≠ b) + (h₂ : abs (a - 1/a) = 1) + (h₃ : abs (b - 1/b) = 1) : + a + b = Real.sqrt 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 160.20690822601318 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 4, 'total_queries': 54} + + + +2026-01-11 12:03:50,896 - __main__ - INFO - Attempting to prove lemma: amc12a_2003_p5 +2026-01-11 12:03:50,896 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 12:03:50,898 - __main__ - INFO - Attempting to prove lemma: amc12a_2008_p25 +2026-01-11 12:03:50,898 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:03:50,899 - __main__ - INFO - Running the prover agent for lemma: amc12a_2008_p25 (theorem_idx=186) with timeout: 600 seconds +2026-01-11 12:04:17,067 - __main__ - INFO - Prover for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:04:17,067 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2003_p23 + (S : Finset ℕ) + (h₀ : ∀ (k : ℕ), k ∈ S ↔ 0 < k ∧ ((k * k) : ℕ) ∣ (∏ i ∈ (Finset.Icc 1 9), i !)) : + S.card = 672 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 12.301592588424683 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 4, 'total_queries': 5} + + + +2026-01-11 12:04:17,070 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p6 +2026-01-11 12:04:17,070 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:04:17,070 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p6 (theorem_idx=187) with timeout: 600 seconds +2026-01-11 12:06:25,645 - __main__ - INFO - Prover Agent for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:06:25,804 - __main__ - INFO - Failed to prove lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:06:25,804 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12_2001_p21 + +2026-01-11 12:06:25,806 - __main__ - INFO - Attempting to prove lemma: amc12a_2009_p7 +2026-01-11 12:06:25,806 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:06:25,806 - __main__ - INFO - Running the prover agent for lemma: amc12a_2009_p7 (theorem_idx=188) with timeout: 600 seconds +2026-01-11 12:06:27,651 - __main__ - INFO - Prover for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:06:27,651 - __main__ - INFO - Dumping proof search result: +theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := + +by + + + +ProofFile: None +LemmaName: theorem amc12_2001_p5 : + Finset.prod (Finset.filter (λ x => ¬ Even x) (Finset.range 10000)) (id : ℕ → ℕ) = (10000!) / ((2^5000) * (5000!)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 35 +SearchTimeInSecs: 425.7820727825165 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 35, 'attempt_idx': 4, 'total_queries': 40} + + + +2026-01-11 12:06:27,653 - __main__ - INFO - Attempting to prove lemma: amc12a_2019_p12 +2026-01-11 12:06:27,653 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:06:27,653 - __main__ - INFO - Running the prover agent for lemma: amc12a_2019_p12 (theorem_idx=189) with timeout: 600 seconds +2026-01-11 12:08:36,785 - __main__ - INFO - Prover for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:08:36,785 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2019_p12 (x y : ℕ) (h₀ : x ≠ 1 ∧ y ≠ 1) + (h₁ : Real.log x / Real.log 2 = Real.log 16 / Real.log y) (h₂ : x * y = 64) : + (Real.log (x / y) / Real.log 2) ^ 2 = 20 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2019_p12 (x y : ℕ) (h₀ : x ≠ 1 ∧ y ≠ 1) + (h₁ : Real.log x / Real.log 2 = Real.log 16 / Real.log y) (h₂ : x * y = 64) : + (Real.log (x / y) / Real.log 2) ^ 2 = 20 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 10 +SearchTimeInSecs: 110.12817096710205 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 10, 'attempt_idx': 4, 'total_queries': 23} + + + +2026-01-11 12:08:36,788 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p10 +2026-01-11 12:08:36,788 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:08:36,788 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p10 (theorem_idx=190) with timeout: 600 seconds +2026-01-11 12:13:51,063 - __main__ - INFO - Prover Agent for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:13:51,226 - __main__ - INFO - Failed to prove lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:13:51,226 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2008_p25 + +2026-01-11 12:13:51,228 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p15 +2026-01-11 12:13:51,228 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:13:51,228 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p15 (theorem_idx=191) with timeout: 600 seconds +2026-01-11 12:14:17,250 - __main__ - INFO - Prover Agent for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:14:17,413 - __main__ - INFO - Failed to prove lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:14:17,413 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2009_p6 + +2026-01-11 12:14:17,415 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p25 +2026-01-11 12:14:17,415 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:14:17,415 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p25 (theorem_idx=192) with timeout: 600 seconds +2026-01-11 12:15:31,785 - __main__ - INFO - Prover for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:15:31,786 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p10 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Real.logb 2 (Real.logb 16 n) = Real.logb 4 (Real.logb 4 n)) : + (Nat.digits 10 n).sum = 13 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p10 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : Real.logb 2 (Real.logb 16 n) = Real.logb 4 (Real.logb 4 n)) : + (Nat.digits 10 n).sum = 13 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 50 +SearchTimeInSecs: 406.7654905319214 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 51, 'attempt_idx': 4, 'total_queries': 51} + + + +2026-01-11 12:15:31,788 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p4 +2026-01-11 12:15:31,788 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:15:31,788 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p4 (theorem_idx=193) with timeout: 600 seconds +2026-01-11 12:16:25,916 - __main__ - INFO - Prover Agent for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:16:26,079 - __main__ - INFO - Failed to prove lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:16:26,079 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12a_2009_p7 + +2026-01-11 12:16:26,081 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p7 +2026-01-11 12:16:26,081 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:16:26,081 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p7 (theorem_idx=194) with timeout: 600 seconds +2026-01-11 12:17:42,809 - __main__ - INFO - Prover for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:17:42,810 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p15 + (a b : ℂ) + (h₀ : a^3 - 8 = 0) + (h₁ : b^3 - 8 * b^2 - 8 * b + 64 = 0) : + ‖a - b‖ ≤ 2 * Real.sqrt 21 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p15 + (a b : ℂ) + (h₀ : a^3 - 8 = 0) + (h₁ : b^3 - 8 * b^2 - 8 * b + 64 = 0) : + ‖a - b‖ ≤ 2 * Real.sqrt 21 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 213.44567155838013 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 4, 'total_queries': 25} + + + +2026-01-11 12:17:42,812 - __main__ - INFO - Attempting to prove lemma: amc12a_2020_p9 +2026-01-11 12:17:42,812 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:17:42,812 - __main__ - INFO - Running the prover agent for lemma: amc12a_2020_p9 (theorem_idx=195) with timeout: 600 seconds +2026-01-11 12:18:04,569 - __main__ - INFO - Prover for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:18:04,569 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p25 + (a : ℚ) + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ ↑⌊x⌋ * (x - ↑⌊x⌋) = ↑a * x ^ 2) + (h₁ : ∑ k ∈ S, k = 420) : + ↑a.den + a.num = 929 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 200.98834037780762 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 4, 'total_queries': 42} + + + +2026-01-11 12:18:04,571 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p12 +2026-01-11 12:18:04,571 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:18:04,571 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p12 (theorem_idx=196) with timeout: 600 seconds +2026-01-11 12:18:31,784 - __main__ - INFO - Prover Agent for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:18:31,956 - __main__ - INFO - Failed to prove lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:18:31,956 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2020_p4 + +2026-01-11 12:18:31,958 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p14 +2026-01-11 12:18:31,958 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:18:31,958 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p14 (theorem_idx=197) with timeout: 600 seconds +2026-01-11 12:18:48,699 - __main__ - INFO - Prover for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:18:48,699 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p9 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 ≤ x ∧ x ≤ 2 * Real.pi ∧ Real.tan (2 * x) = Real.cos (x / 2)) : + S.card = 5 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 6 +SearchTimeInSecs: 47.41397762298584 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 7, 'attempt_idx': 4, 'total_queries': 9} + + + +2026-01-11 12:18:48,701 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p18 +2026-01-11 12:18:48,701 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:18:48,701 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p18 (theorem_idx=198) with timeout: 600 seconds +2026-01-11 12:18:50,710 - __main__ - INFO - Prover for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:18:50,710 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2020_p7 + (a : ℕ → ℕ) + (h₀ : (a 0)^3 = 1) + (h₁ : (a 1)^3 = 8) + (h₂ : (a 2)^3 = 27) + (h₃ : (a 3)^3 = 64) + (h₄ : (a 4)^3 = 125) + (h₅ : (a 5)^3 = 216) + (h₆ : (a 6)^3 = 343) : + ∑ k ∈ Finset.range 7, (6 * (a k)^2) - ↑(2 * ∑ k ∈ Finset.range 6, (a k)^2) = 658 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 130.23829817771912 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 20, 'attempt_idx': 4, 'total_queries': 79} + + + +2026-01-11 12:18:50,712 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p19 +2026-01-11 12:18:50,712 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:18:50,712 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p19 (theorem_idx=199) with timeout: 600 seconds +2026-01-11 12:19:25,515 - __main__ - INFO - Prover for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:19:25,515 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p12 + (a b c d : ℝ) + (f : ℂ → ℂ) + (h₀ : ∀ z, f z = z^6 - 10 * z^5 + a * z^4 + b * z^3 + c * z^2 + d * z + 16) + (h₁ : ∀ z, f z = 0 → (z.im = 0 ∧ 0 < z.re ∧ ↑(Int.floor z.re) = z.re)) : + b = -88 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 60.76075196266174 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 4, 'attempt_idx': 4, 'total_queries': 17} + + + +2026-01-11 12:19:25,518 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p22 +2026-01-11 12:19:25,518 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:19:25,518 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p22 (theorem_idx=200) with timeout: 600 seconds +2026-01-11 12:19:39,840 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:19:40,003 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:19:40,003 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2021_p14 + +2026-01-11 12:19:40,005 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p25 +2026-01-11 12:19:40,006 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:19:40,006 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p25 (theorem_idx=201) with timeout: 600 seconds +2026-01-11 12:20:29,727 - __main__ - INFO - Prover for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:20:29,727 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p25 + (N : ℕ) + (f : ℕ → ℝ) + (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3))) + (h₁ : ∀ n ≠ N, 0 < n → f n < f N) : + (Nat.digits 10 N).sum = 9 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 23.04207968711853 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 11} + + + +2026-01-11 12:20:29,729 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p3 +2026-01-11 12:20:29,729 - __main__ - INFO - Skipping the attempt for proving lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 12:20:29,732 - __main__ - INFO - Attempting to prove lemma: amc12a_2021_p8 +2026-01-11 12:20:29,732 - __main__ - INFO - Attempt 5 for proving lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:20:29,732 - __main__ - INFO - Running the prover agent for lemma: amc12a_2021_p8 (theorem_idx=203) with timeout: 600 seconds +2026-01-11 12:21:03,812 - __main__ - INFO - Prover Agent for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:21:03,975 - __main__ - INFO - Failed to prove lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:21:03,975 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: amc12a_2021_p19 + +2026-01-11 12:21:03,977 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p4 +2026-01-11 12:21:03,977 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:21:03,978 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p4 (theorem_idx=204) with timeout: 600 seconds +2026-01-11 12:23:18,385 - __main__ - INFO - Prover for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:23:18,385 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p22 + (a b c : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = x^3 + a * x^2 + b * x + c) + (h₁ : f⁻¹' {0} = {Real.cos (2 * Real.pi / 7), Real.cos (4 * Real.pi / 7), Real.cos (6 * Real.pi / 7)}) : + a * b * c = 1 / 32 := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p22 + (a b c : ℝ) + (f : ℝ → ℝ) + (h₀ : ∀ x, f x = x^3 + a * x^2 + b * x + c) + (h₁ : f⁻¹' {0} = {Real.cos (2 * Real.pi / 7), Real.cos (4 * Real.pi / 7), Real.cos (6 * Real.pi / 7)}) : + a * b * c = 1 / 32 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 39 +SearchTimeInSecs: 217.96085786819458 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 34, 'attempt_idx': 4, 'total_queries': 34} + + + +2026-01-11 12:23:18,387 - __main__ - INFO - Attempting to prove lemma: amc12b_2002_p7 +2026-01-11 12:23:18,387 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:23:18,387 - __main__ - INFO - Running the prover agent for lemma: amc12b_2002_p7 (theorem_idx=205) with timeout: 600 seconds +2026-01-11 12:25:14,802 - __main__ - INFO - Prover for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:25:14,802 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2002_p4 + (n : ℕ) + (h₀ : 0 < n) + (h₁ : ((1 / 2 + 1 / 3 + 1 / 7 + 1 / n) : ℚ).den = 1) : + n = 42 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 25 +SearchTimeInSecs: 234.33850812911987 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 25, 'attempt_idx': 4, 'total_queries': 25} + + + +2026-01-11 12:25:14,804 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p13 +2026-01-11 12:25:14,804 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:25:14,804 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p13 (theorem_idx=206) with timeout: 600 seconds +2026-01-11 12:25:36,681 - __main__ - INFO - Prover for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:25:36,681 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := + +by + + + +ProofFile: None +LemmaName: theorem amc12a_2021_p8 + (d : ℕ → ℕ) + (h₀ : d 0 = 0) + (h₁ : d 1 = 0) + (h₂ : d 2 = 1) + (h₃ : ∀ n≥3, d n = d (n - 1) + d (n - 3)) : + Even (d 2021) ∧ Odd (d 2022) ∧ Even (d 2023) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 24 +SearchTimeInSecs: 288.6536386013031 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 24, 'attempt_idx': 4, 'total_queries': 31} + + + +2026-01-11 12:25:36,683 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p21 +2026-01-11 12:25:36,683 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:25:36,683 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p21 (theorem_idx=207) with timeout: 600 seconds +2026-01-11 12:26:10,772 - __main__ - INFO - Prover for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:26:10,773 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p13 : + Real.sqrt (Real.log 6 / Real.log 2 + Real.log 6 / Real.log 3) = Real.sqrt (Real.log 3 / Real.log 2) + Real.sqrt (Real.log 2 / Real.log 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 32.38771629333496 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 43} + + + +2026-01-11 12:26:10,775 - __main__ - INFO - Attempting to prove lemma: amc12b_2020_p22 +2026-01-11 12:26:10,775 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:26:10,775 - __main__ - INFO - Running the prover agent for lemma: amc12b_2020_p22 (theorem_idx=208) with timeout: 600 seconds +2026-01-11 12:26:34,310 - __main__ - INFO - Prover for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:26:34,310 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p21 + (S : Finset ℕ) + (h₀ : ∀ (n : ℕ), n ∈ S ↔ 0 < n ∧ (↑n + (1000 : ℝ)) / 70 = Int.floor (Real.sqrt n)) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 45.66623306274414 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 22} + + + +2026-01-11 12:26:34,312 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p1 +2026-01-11 12:26:34,312 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:26:34,312 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p1 (theorem_idx=209) with timeout: 600 seconds +2026-01-11 12:26:58,315 - __main__ - INFO - Prover for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:26:58,315 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2020_p22 + (t : ℝ) : + ((2^t - 3 * t) * t) / (4^t) ≤ 1 / 12 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 3 +SearchTimeInSecs: 29.597485303878784 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 4, 'total_queries': 31} + + + +2026-01-11 12:26:58,317 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p13 +2026-01-11 12:26:58,317 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:26:58,317 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p13 (theorem_idx=210) with timeout: 600 seconds +2026-01-11 12:27:43,447 - __main__ - INFO - Prover for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:27:43,447 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p13 + (S : Finset ℝ) + (h₀ : ∀ (x : ℝ), x ∈ S ↔ 0 < x ∧ x ≤ 2 * Real.pi ∧ 1 - 3 * Real.sin x + 5 * Real.cos (3 * x) = 0) : + S.card = 6 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 4 +SearchTimeInSecs: 20.154868364334106 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 7} + + + +2026-01-11 12:27:43,449 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p18 +2026-01-11 12:27:43,449 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:27:43,449 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p18 (theorem_idx=211) with timeout: 600 seconds +2026-01-11 12:28:49,208 - __main__ - INFO - Prover for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:28:49,209 - __main__ - INFO - Dumping proof search result: +theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := + +by +-- Prove that `f 1 = 0` using the functional equation with `x = 1` and `y = 1` +have h_one : f (1 : ℚ) = (0 : ℝ) := by + have h := h₀ (1 : ℚ) (by norm_num : (1 : ℚ) > 0) (1 : ℚ) (by norm_num : (1 : ℚ) > 0) + simpa [mul_comm] using h +-- Step 1: prove `f 11 = 11` +have h11 : f (11 : ℚ) = (11 : ℝ) := by + have hp11 : Nat.Prime 11 := by decide + exact h₁ 11 hp11 +-- First compute `f 5` using the prime property +have h5 : f (5 : ℚ) = (5 : ℝ) := by + have hp5 : Nat.Prime 5 := by decide + exact h₁ 5 hp5 +have h_inv : f ((1 : ℚ) / 11) = -11 := by + have hpos1 : (1 : ℚ) / 11 > 0 := by norm_num + have hpos11 : (11 : ℚ) > 0 := by norm_num + have h := h₀ (11 : ℚ) hpos11 ((1 : ℚ) / 11) hpos1 + have h' : 0 = 11 + f ((1 : ℚ) / 11) := by + simpa [h_one, h11, mul_comm] using h + linarith + + +ProofFile: None +LemmaName: theorem amc12a_2021_p18 + (f : ℚ → ℝ) + (h₀ : ∀x>0, ∀y>0, f (x * y) = f x + f y) + (h₁ : ∀p, Nat.Prime p → f p = p) : + f (25 / 11) < 0 := +SearchResult: [FAILED] +IsInferenceExhausted: True +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 107 +SearchTimeInSecs: 584.603485584259 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 100, 'attempt_idx': 4, 'total_queries': 192} + + + +2026-01-11 12:28:49,211 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p3 +2026-01-11 12:28:49,211 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:28:49,211 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p3 (theorem_idx=212) with timeout: 600 seconds +2026-01-11 12:29:04,423 - __main__ - INFO - Prover for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:29:04,423 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p18 + (z : ℂ) + (h₀ : 12 * Complex.normSq z = 2 * Complex.normSq (z + 2) + Complex.normSq (z^2 + 1) + 31) : + z + 6 / z = -2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 62.90284824371338 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 6, 'attempt_idx': 4, 'total_queries': 26} + + + +2026-01-11 12:29:04,425 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p4 +2026-01-11 12:29:04,426 - __main__ - INFO - Attempt 5 for proving lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:29:04,426 - __main__ - INFO - Running the prover agent for lemma: amc12b_2021_p4 (theorem_idx=213) with timeout: 600 seconds +2026-01-11 12:30:05,201 - __main__ - INFO - Prover for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:30:05,201 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p4 + (m a : ℕ) + (h₀ : 0 < m ∧ 0 < a) + (h₁ : ↑m / ↑a = (3:ℝ) / 4) : + (84 * ↑m + 70 * ↑a) / (↑m + ↑a) = (76:ℝ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 46.47287082672119 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 4, 'total_queries': 13} + + + +2026-01-11 12:30:05,203 - __main__ - INFO - Attempting to prove lemma: amc12b_2021_p9 +2026-01-11 12:30:05,203 - __main__ - INFO - Skipping the attempt for proving lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 12:30:05,206 - __main__ - INFO - Attempting to prove lemma: imo_1959_p1 +2026-01-11 12:30:05,206 - __main__ - INFO - Attempt 5 for proving lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:30:05,206 - __main__ - INFO - Running the prover agent for lemma: imo_1959_p1 (theorem_idx=215) with timeout: 600 seconds +2026-01-11 12:33:18,566 - __main__ - INFO - Prover Agent for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:33:18,734 - __main__ - INFO - Failed to prove lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:33:18,734 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: amc12b_2002_p7 + +2026-01-11 12:33:18,736 - __main__ - INFO - Attempting to prove lemma: imo_1960_p2 +2026-01-11 12:33:18,736 - __main__ - INFO - Attempt 5 for proving lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:33:18,736 - __main__ - INFO - Running the prover agent for lemma: imo_1960_p2 (theorem_idx=216) with timeout: 600 seconds +2026-01-11 12:33:21,815 - __main__ - INFO - Prover for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:33:21,815 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p3 + (x : ℝ) + (h₀ : 2 + 1 / (1 + 1 / (2 + 2 / (3 + x))) = 144 / 53) : + x = 3 / 4 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 32 +SearchTimeInSecs: 265.13759088516235 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 32, 'attempt_idx': 4, 'total_queries': 58} + + + +2026-01-11 12:33:21,817 - __main__ - INFO - Attempting to prove lemma: imo_1962_p2 +2026-01-11 12:33:21,817 - __main__ - INFO - Attempt 5 for proving lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:33:21,817 - __main__ - INFO - Running the prover agent for lemma: imo_1962_p2 (theorem_idx=217) with timeout: 600 seconds +2026-01-11 12:33:43,573 - __main__ - INFO - Prover for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:33:43,573 - __main__ - INFO - Dumping proof search result: +theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := + +by + + + +ProofFile: None +LemmaName: theorem amc12b_2021_p1 + (S : Finset ℤ) + (h₀ : ∀ (x : ℤ), x ∈ S ↔ ↑(abs x) < 3 * Real.pi): + S.card = 19 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 64 +SearchTimeInSecs: 406.0958364009857 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 62, 'attempt_idx': 4, 'total_queries': 95} + + + +2026-01-11 12:33:43,575 - __main__ - INFO - Attempting to prove lemma: imo_1963_p5 +2026-01-11 12:33:43,575 - __main__ - INFO - Attempt 5 for proving lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:33:43,575 - __main__ - INFO - Running the prover agent for lemma: imo_1963_p5 (theorem_idx=218) with timeout: 600 seconds +2026-01-11 12:33:58,427 - __main__ - INFO - Prover for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:33:58,427 - __main__ - INFO - Dumping proof search result: +theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := + +by + -- Rewrite the first argument of `gcd` using the addition lemma + have h2 : (21 * n + 4).gcd (14 * n + 3) = (7 * n + 1).gcd (14 * n + 3) := by + have : (21 * n + 4) = (14 * n + 3) + (7 * n + 1) := by ring + simpa [this] using Nat.gcd_add_left (7 * n + 1) (14 * n + 3) + -- Rewrite the second argument as a sum to use `Nat.gcd_add_right` + have h3 : (7 * n + 1).gcd (14 * n + 3) = (7 * n + 1).gcd (7 * n + 2) := by + have : (14 * n + 3) = (7 * n + 1) + (7 * n + 2) := by ring + simpa [this] using Nat.gcd_add_right (7 * n + 1) (7 * n + 2) + -- Reduce `gcd (7*n+1) (7*n+2)` to `1` + have h4 : (7 * n + 1).gcd (7 * n + 2) = 1 := by + have : (7 * n + 2) = (7 * n + 1) + 1 := by ring + simpa [this] using Nat.gcd_add_right (7 * n + 1) 1 + -- Finish by chaining the equalities + calc + (21 * n + 4).gcd (14 * n + 3) = (7 * n + 1).gcd (14 * n + 3) := h2 + _ = (7 * n + 1).gcd (7 * n + 2) := h3 + _ = 1 := h4 + + +ProofFile: None +LemmaName: theorem imo_1959_p1 + (n : ℕ) + (h₀ : 0 < n) : + Nat.gcd (21*n + 4) (14*n + 3) = 1 := +SearchResult: [SUCCESS] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 216.79553627967834 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 44} + + + +2026-01-11 12:33:58,430 - __main__ - INFO - Attempting to prove lemma: imo_1964_p2 +2026-01-11 12:33:58,430 - __main__ - INFO - Attempt 5 for proving lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:33:58,430 - __main__ - INFO - Running the prover agent for lemma: imo_1964_p2 (theorem_idx=219) with timeout: 600 seconds +2026-01-11 12:36:10,866 - __main__ - INFO - Prover for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:36:10,866 - __main__ - INFO - Dumping proof search result: +theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1963_p5 : + Real.cos (π / 7) - Real.cos (2 * π / 7) + Real.cos (3 * π / 7) = 1 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 33 +SearchTimeInSecs: 138.81887769699097 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 27, 'attempt_idx': 4, 'total_queries': 109} + + + +2026-01-11 12:36:10,869 - __main__ - INFO - Attempting to prove lemma: imo_1965_p2 +2026-01-11 12:36:10,869 - __main__ - INFO - Attempt 5 for proving lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:36:10,869 - __main__ - INFO - Running the prover agent for lemma: imo_1965_p2 (theorem_idx=220) with timeout: 600 seconds +2026-01-11 12:37:19,999 - __main__ - INFO - Prover for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:37:19,999 - __main__ - INFO - Dumping proof search result: +theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1960_p2 + (x : ℝ) + (h₀ : 0 ≤ 1 + 2 * x) + (h₁ : (1 - Real.sqrt (1 + 2 * x))^2 ≠ 0) + (h₂ : (4 * x^2) / (1 - Real.sqrt (1 + 2*x))^2 < 2*x + 9) + (h₃ : x ≠ 0) : + -(1 / 2) ≤ x ∧ x < 45 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 22 +SearchTimeInSecs: 233.0611653327942 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 22} + + + +2026-01-11 12:37:20,001 - __main__ - INFO - Attempting to prove lemma: imo_1968_p5_1 +2026-01-11 12:37:20,001 - __main__ - INFO - Attempt 5 for proving lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:37:20,001 - __main__ - INFO - Running the prover agent for lemma: imo_1968_p5_1 (theorem_idx=221) with timeout: 600 seconds +2026-01-11 12:39:50,776 - __main__ - INFO - Prover for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:39:50,776 - __main__ - INFO - Dumping proof search result: +theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := + +by + + + +ProofFile: None +LemmaName: theorem imo_1964_p2 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + a^2 * (b + c - a) + b^2 * (c + a - b) + c^2 * (a + b - c) ≤ 3 * a * b * c := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 56 +SearchTimeInSecs: 330.33446645736694 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 54, 'attempt_idx': 4, 'total_queries': 54} + + + +2026-01-11 12:39:50,778 - __main__ - INFO - Attempting to prove lemma: imo_1969_p2 +2026-01-11 12:39:50,778 - __main__ - INFO - Attempt 5 for proving lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:39:50,778 - __main__ - INFO - Running the prover agent for lemma: imo_1969_p2 (theorem_idx=222) with timeout: 600 seconds +2026-01-11 12:40:27,287 - __main__ - INFO - Prover for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:40:27,288 - __main__ - INFO - Dumping proof search result: +theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1962_p2 + (x : ℝ) + (h₀ : 0 ≤ 3 - x) + (h₁ : 0 ≤ x + 1) + (h₂ : 1 / 2 < Real.sqrt (3 - x) - Real.sqrt (x + 1)) : + -1 ≤ x ∧ x < 1 - Real.sqrt 31 / 8 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 43 +SearchTimeInSecs: 411.8808867931366 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 42, 'attempt_idx': 4, 'total_queries': 55} + + + +2026-01-11 12:40:27,290 - __main__ - INFO - Attempting to prove lemma: imo_1974_p3 +2026-01-11 12:40:27,290 - __main__ - INFO - Attempt 5 for proving lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:40:27,290 - __main__ - INFO - Running the prover agent for lemma: imo_1974_p3 (theorem_idx=223) with timeout: 600 seconds +2026-01-11 12:41:53,185 - __main__ - INFO - Prover for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:41:53,185 - __main__ - INFO - Dumping proof search result: +theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := + +by + + + +ProofFile: None +LemmaName: theorem imo_1969_p2 + (m n : ℝ) + (k : ℕ) + (a : ℕ → ℝ) + (y : ℝ → ℝ) + (h₀ : 0 < k) + (h₁ : ∀ x, y x = ∑ i ∈ Finset.range k, ((Real.cos (a i + x)) / (2^i))) + (h₂ : y m = 0) + (h₃ : y n = 0) : + ∃ t : ℤ, m - n = t * π := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 20 +SearchTimeInSecs: 115.22083115577698 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 19, 'attempt_idx': 4, 'total_queries': 41} + + + +2026-01-11 12:41:53,187 - __main__ - INFO - Attempting to prove lemma: imo_1977_p6 +2026-01-11 12:41:53,187 - __main__ - INFO - Attempt 5 for proving lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:41:53,187 - __main__ - INFO - Running the prover agent for lemma: imo_1977_p6 (theorem_idx=224) with timeout: 600 seconds +2026-01-11 12:42:49,410 - __main__ - INFO - Prover for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:42:49,410 - __main__ - INFO - Dumping proof search result: +theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1965_p2 + (x y z : ℝ) + (a : ℕ → ℝ) + (h₀ : 0 < a 0 ∧ 0 < a 4 ∧ 0 < a 8) + (h₁ : a 1 < 0 ∧ a 2 < 0) + (h₂ : a 3 < 0 ∧ a 5 < 0) + (h₃ : a 6 < 0 ∧ a 7 < 0) + (h₄ : 0 < a 0 + a 1 + a 2) + (h₅ : 0 < a 3 + a 4 + a 5) + (h₆ : 0 < a 6 + a 7 + a 8) + (h₇ : a 0 * x + a 1 * y + a 2 * z = 0) + (h₈ : a 3 * x + a 4 * y + a 5 * z = 0) + (h₉ : a 6 * x + a 7 * y + a 8 * z = 0) : + x = 0 ∧ y = 0 ∧ z = 0 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 27 +SearchTimeInSecs: 374.256413936615 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 4, 'total_queries': 39} + + + +2026-01-11 12:42:49,412 - __main__ - INFO - Attempting to prove lemma: imo_1981_p6 +2026-01-11 12:42:49,412 - __main__ - INFO - Attempt 5 for proving lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:42:49,412 - __main__ - INFO - Running the prover agent for lemma: imo_1981_p6 (theorem_idx=225) with timeout: 600 seconds +2026-01-11 12:43:06,075 - __main__ - INFO - Prover for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:43:06,075 - __main__ - INFO - Dumping proof search result: +theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1974_p3 + (n : ℕ) : + ¬ 5∣∑ k ∈ Finset.range (n + 1), (Nat.choose (2 * n + 1) (2 * k + 1)) * (2^(3 * k)) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 135.26629900932312 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 22, 'attempt_idx': 4, 'total_queries': 29} + + + +2026-01-11 12:43:06,077 - __main__ - INFO - Attempting to prove lemma: imo_1982_p1 +2026-01-11 12:43:06,078 - __main__ - INFO - Attempt 5 for proving lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:43:06,078 - __main__ - INFO - Running the prover agent for lemma: imo_1982_p1 (theorem_idx=226) with timeout: 600 seconds +2026-01-11 12:45:59,818 - __main__ - INFO - Prover for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:45:59,818 - __main__ - INFO - Dumping proof search result: +theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1981_p6 + (f : ℕ → ℕ → ℕ) + (g : ℕ → ℕ) + (h₀ : ∀ y, f 0 y = y + 1) + (h₁ : ∀ x, f (x + 1) 0 = f x 1) + (h₂ : ∀ x y, f (x + 1) (y + 1) = f x (f (x + 1) y)) + (h₃ : g 0 = 2) + (h₄ : ∀ n, g (n + 1) = 2^(g n)) : + f 4 1981 = g 1983 - 3 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 21 +SearchTimeInSecs: 176.51172828674316 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 21, 'attempt_idx': 4, 'total_queries': 21} + + + +2026-01-11 12:45:59,820 - __main__ - INFO - Attempting to prove lemma: imo_1983_p6 +2026-01-11 12:45:59,820 - __main__ - INFO - Attempt 5 for proving lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:45:59,820 - __main__ - INFO - Running the prover agent for lemma: imo_1983_p6 (theorem_idx=227) with timeout: 600 seconds +2026-01-11 12:46:06,745 - __main__ - INFO - Prover for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:46:06,745 - __main__ - INFO - Dumping proof search result: +theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := + +by + + + +ProofFile: None +LemmaName: theorem imo_1968_p5_1 + (a : ℝ) + (f : ℝ → ℝ) + (h₀ : 0 < a) + (h₁ : ∀ x, f (x + a) = 1 / 2 + Real.sqrt (f x - (f x)^2)) : + ∃ b > 0, ∀ x, f (x + b) = f x := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 74 +SearchTimeInSecs: 502.97286891937256 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 75, 'attempt_idx': 4, 'total_queries': 75} + + + +2026-01-11 12:46:06,748 - __main__ - INFO - Attempting to prove lemma: imo_1984_p6 +2026-01-11 12:46:06,748 - __main__ - INFO - Attempt 5 for proving lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:46:06,748 - __main__ - INFO - Running the prover agent for lemma: imo_1984_p6 (theorem_idx=228) with timeout: 600 seconds +2026-01-11 12:47:29,062 - __main__ - INFO - Prover for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:47:29,062 - __main__ - INFO - Dumping proof search result: +theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1983_p6 + (a b c : ℝ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c) + (h₁ : c < a + b) + (h₂ : b < a + c) + (h₃ : a < b + c) : + 0 ≤ a^2 * b * (a - b) + b^2 * c * (b - c) + c^2 * a * (c - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 9 +SearchTimeInSecs: 81.45600390434265 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 9, 'attempt_idx': 4, 'total_queries': 14} + + + +2026-01-11 12:47:29,064 - __main__ - INFO - Attempting to prove lemma: imo_1985_p6 +2026-01-11 12:47:29,064 - __main__ - INFO - Attempt 5 for proving lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:47:29,064 - __main__ - INFO - Running the prover agent for lemma: imo_1985_p6 (theorem_idx=229) with timeout: 600 seconds +2026-01-11 12:51:53,319 - __main__ - INFO - Prover Agent for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:51:53,484 - __main__ - INFO - Failed to prove lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:51:53,484 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1977_p6 + +2026-01-11 12:51:53,486 - __main__ - INFO - Attempting to prove lemma: imo_1992_p1 +2026-01-11 12:51:53,486 - __main__ - INFO - Attempt 5 for proving lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:51:53,486 - __main__ - INFO - Running the prover agent for lemma: imo_1992_p1 (theorem_idx=230) with timeout: 600 seconds +2026-01-11 12:51:59,451 - __main__ - INFO - Prover for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:51:59,451 - __main__ - INFO - Dumping proof search result: +theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := + +by + + + +ProofFile: None +LemmaName: theorem imo_1984_p6 + (a b c d k m : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : Odd a ∧ Odd b ∧ Odd c ∧ Odd d) + (h₂ : a < b ∧ b < c ∧ c < d) + (h₃ : a * d = b * c) + (h₄ : a + d = 2^k) + (h₅ : b + c = 2^m) : + a = 1 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 31 +SearchTimeInSecs: 337.28220868110657 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 32, 'attempt_idx': 4, 'total_queries': 47} + + + +2026-01-11 12:51:59,453 - __main__ - INFO - Attempting to prove lemma: imo_1997_p5 +2026-01-11 12:51:59,453 - __main__ - INFO - Attempt 5 for proving lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:51:59,454 - __main__ - INFO - Running the prover agent for lemma: imo_1997_p5 (theorem_idx=231) with timeout: 600 seconds +2026-01-11 12:53:02,011 - __main__ - INFO - Prover Agent for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:53:02,177 - __main__ - INFO - Failed to prove lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:53:02,177 - __main__ - INFO - Dumping proof search result: +Proof FAILED for lemma: imo_1982_p1 + +2026-01-11 12:53:02,179 - __main__ - INFO - Attempting to prove lemma: imo_2001_p6 +2026-01-11 12:53:02,179 - __main__ - INFO - Attempt 5 for proving lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:53:02,179 - __main__ - INFO - Running the prover agent for lemma: imo_2001_p6 (theorem_idx=232) with timeout: 600 seconds +2026-01-11 12:53:58,371 - __main__ - INFO - Prover for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:53:58,371 - __main__ - INFO - Dumping proof search result: +theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1992_p1 + (p q r : ℤ) + (h₀ : 1 < p ∧ p < q ∧ q < r) + (h₁ : (p - 1) * (q - 1) * (r - 1)∣(p * q * r - 1)) : + (p, q, r) = (2, 4, 8) ∨ (p, q, r) = (3, 5, 15) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 11 +SearchTimeInSecs: 114.46593904495239 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 12, 'attempt_idx': 4, 'total_queries': 63} + + + +2026-01-11 12:53:58,373 - __main__ - INFO - Attempting to prove lemma: imo_2019_p1 +2026-01-11 12:53:58,373 - __main__ - INFO - Attempt 5 for proving lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:53:58,373 - __main__ - INFO - Running the prover agent for lemma: imo_2019_p1 (theorem_idx=233) with timeout: 600 seconds +2026-01-11 12:55:52,908 - __main__ - INFO - Prover for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:55:52,908 - __main__ - INFO - Dumping proof search result: +theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := + +by + + + +ProofFile: None +LemmaName: theorem imo_2001_p6 + (a b c d : ℕ) + (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) + (h₁ : d < c) + (h₂ : c < b) + (h₃ : b < a) + (h₄ : a * c + b * d = (b + d + a - c) * (b + d + c - a)) : + ¬ Nat.Prime (a * b + c * d) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 154.95354890823364 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 4, 'total_queries': 54} + + + +2026-01-11 12:55:52,910 - __main__ - INFO - Attempting to prove lemma: imosl_2007_algebra_p6 +2026-01-11 12:55:52,910 - __main__ - INFO - Attempt 5 for proving lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:55:52,910 - __main__ - INFO - Running the prover agent for lemma: imosl_2007_algebra_p6 (theorem_idx=234) with timeout: 600 seconds +2026-01-11 12:56:06,778 - __main__ - INFO - Prover for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:56:06,778 - __main__ - INFO - Dumping proof search result: +theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := + +by + + + +ProofFile: None +LemmaName: theorem imo_1997_p5 + (x y : ℕ) + (h₀ : 0 < x ∧ 0 < y) + (h₁ : x^(y^2) = y^x) : + (x, y) = (1, 1) ∨ (x, y) = (16, 2) ∨ (x, y) = (27, 3) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 46 +SearchTimeInSecs: 238.6015989780426 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 43, 'attempt_idx': 4, 'total_queries': 43} + + + +2026-01-11 12:56:06,780 - __main__ - INFO - Attempting to prove lemma: induction_11div10tonmn1ton +2026-01-11 12:56:06,780 - __main__ - INFO - Attempt 5 for proving lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:56:06,780 - __main__ - INFO - Running the prover agent for lemma: induction_11div10tonmn1ton (theorem_idx=235) with timeout: 600 seconds +2026-01-11 12:56:35,606 - __main__ - INFO - Prover for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:56:35,606 - __main__ - INFO - Dumping proof search result: +theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := + +by + + + +ProofFile: None +LemmaName: theorem imosl_2007_algebra_p6 + (a : ℕ → NNReal) + (h₀ : ∑ x ∈ Finset.range 100, ((a (x + 1))^2) = 1) : + ∑ x ∈ Finset.range 99, ((a (x + 1))^2 * a (x + 2)) + (a 100)^2 * a 1 < 12 / 25 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 17.075241565704346 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 3, 'attempt_idx': 4, 'total_queries': 15} + + + +2026-01-11 12:56:35,608 - __main__ - INFO - Attempting to prove lemma: induction_12dvd4expnp1p20 +2026-01-11 12:56:35,608 - __main__ - INFO - Skipping the attempt for proving lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean as it was already attempted before. +2026-01-11 12:56:35,611 - __main__ - INFO - Attempting to prove lemma: induction_1pxpownlt1pnx +2026-01-11 12:56:35,611 - __main__ - INFO - Attempt 5 for proving lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:56:35,611 - __main__ - INFO - Running the prover agent for lemma: induction_1pxpownlt1pnx (theorem_idx=237) with timeout: 600 seconds +2026-01-11 12:57:29,245 - __main__ - INFO - Prover Agent for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 12:57:29,419 - __main__ - INFO - Failed to prove lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:57:29,419 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_1985_p6 + +2026-01-11 12:57:29,422 - __main__ - INFO - Attempting to prove lemma: induction_nfactltnexpnm1ngt3 +2026-01-11 12:57:29,422 - __main__ - INFO - Attempt 5 for proving lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:57:29,422 - __main__ - INFO - Running the prover agent for lemma: induction_nfactltnexpnm1ngt3 (theorem_idx=238) with timeout: 600 seconds +2026-01-11 12:57:35,935 - __main__ - INFO - Prover for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:57:35,935 - __main__ - INFO - Dumping proof search result: +theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := + +by + + + +ProofFile: None +LemmaName: theorem induction_11div10tonmn1ton + (n : ℕ) : + 11 ∣ (10^n - (-1 : ℤ)^n) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 13 +SearchTimeInSecs: 70.81252241134644 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 13, 'attempt_idx': 4, 'total_queries': 19} + + + +2026-01-11 12:57:35,938 - __main__ - INFO - Attempting to prove lemma: induction_pord1p1on2powklt5on2 +2026-01-11 12:57:35,938 - __main__ - INFO - Attempt 5 for proving lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:57:35,938 - __main__ - INFO - Running the prover agent for lemma: induction_pord1p1on2powklt5on2 (theorem_idx=239) with timeout: 600 seconds +2026-01-11 12:57:59,021 - __main__ - INFO - Prover for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:57:59,021 - __main__ - INFO - Dumping proof search result: +theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := + +by + + + +ProofFile: None +LemmaName: theorem induction_nfactltnexpnm1ngt3 + (n : ℕ) + (h₀ : 3 ≤ n) : + (n)! < n^(n - 1) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 2 +SearchTimeInSecs: 20.438948154449463 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 2, 'attempt_idx': 4, 'total_queries': 14} + + + +2026-01-11 12:57:59,023 - __main__ - INFO - Attempting to prove lemma: induction_pprime_pdvdapowpma +2026-01-11 12:57:59,023 - __main__ - INFO - Attempt 5 for proving lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:57:59,023 - __main__ - INFO - Running the prover agent for lemma: induction_pprime_pdvdapowpma (theorem_idx=240) with timeout: 600 seconds +2026-01-11 12:58:29,203 - __main__ - INFO - Prover for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:58:29,203 - __main__ - INFO - Dumping proof search result: +theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := + +by + + + +ProofFile: None +LemmaName: theorem induction_pprime_pdvdapowpma + (p a : ℕ) + (h₀ : 0 < a) + (h₁ : Nat.Prime p) : + p ∣ (a^p - a) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 5 +SearchTimeInSecs: 13.618664264678955 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 5, 'attempt_idx': 4, 'total_queries': 10} + + + +2026-01-11 12:58:29,205 - __main__ - INFO - Attempting to prove lemma: induction_prod1p1onk3le3m1onn +2026-01-11 12:58:29,205 - __main__ - INFO - Attempt 5 for proving lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:58:29,205 - __main__ - INFO - Running the prover agent for lemma: induction_prod1p1onk3le3m1onn (theorem_idx=241) with timeout: 600 seconds +2026-01-11 12:59:13,117 - __main__ - INFO - Prover for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 12:59:13,117 - __main__ - INFO - Dumping proof search result: +theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := + +by + + + +ProofFile: None +LemmaName: theorem induction_1pxpownlt1pnx + (x : ℝ) + (n : ℕ) + (h₀ : -1 < x) + (h₁ : 0 < n) : + (1 + ↑n*x) ≤ (1 + x)^(n:ℕ) := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 18 +SearchTimeInSecs: 141.21685028076172 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 18, 'attempt_idx': 4, 'total_queries': 18} + + + +2026-01-11 12:59:13,120 - __main__ - INFO - Attempting to prove lemma: induction_sumkexp3eqsumksq +2026-01-11 12:59:13,120 - __main__ - INFO - Attempt 5 for proving lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 12:59:13,120 - __main__ - INFO - Running the prover agent for lemma: induction_sumkexp3eqsumksq (theorem_idx=242) with timeout: 600 seconds +2026-01-11 13:01:17,123 - __main__ - INFO - Prover for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 13:01:17,124 - __main__ - INFO - Dumping proof search result: +theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_sumkexp3eqsumksq + (n : ℕ) : + ∑ k ∈ Finset.range n, k^3 = (∑ k ∈ Finset.range n, k)^2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 30 +SearchTimeInSecs: 110.73412156105042 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 28, 'attempt_idx': 4, 'total_queries': 42} + + + +2026-01-11 13:03:40,802 - __main__ - INFO - Prover for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 13:03:40,802 - __main__ - INFO - Dumping proof search result: +theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := + +by + + + +ProofFile: None +LemmaName: theorem induction_prod1p1onk3le3m1onn + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / k^3) ≤ (3:ℝ) - 1 / ↑n := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 45 +SearchTimeInSecs: 298.77738857269287 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 44, 'attempt_idx': 4, 'total_queries': 73} + + + +2026-01-11 13:03:58,556 - __main__ - INFO - Prover Agent for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean got killed as it timed out. +2026-01-11 13:03:58,914 - __main__ - INFO - Failed to prove lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:03:58,914 - __main__ - INFO - Dumping proof search result: +Proof FAILED (Timeout) for lemma: imo_2019_p1 + +2026-01-11 13:07:11,378 - __main__ - INFO - Prover for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean completed. +2026-01-11 13:07:11,378 - __main__ - INFO - Dumping proof search result: +theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := + +by + + + +ProofFile: None +LemmaName: theorem induction_pord1p1on2powklt5on2 + (n : ℕ) + (h₀ : 0 < n) : + ∏ k ∈ Finset.Icc 1 n, (1 + (1:ℝ) / 2^k) < 5 / 2 := +SearchResult: [FAILED] +IsInferenceExhausted: False +IsTimeout: False +LongestSuccessPath: -1 +StepsUsed: 57 +SearchTimeInSecs: 563.4983637332916 +NumberOfBacktracks: -1 +PossibleFailedPaths: -1 +AdditionalInfo: {'queries': 66, 'attempt_idx': 4, 'total_queries': 80} + + + +2026-01-11 13:07:11,508 - __main__ - INFO - Reloaded proof results for final success measurement +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: algebra_sqineq_at2malt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12a_2002_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: aime_1989_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12a_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12a_2013_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12b_2002_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12b_2020_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12b_2002_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof not found for lemma: aime_1983_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_125 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_129 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_139 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_142 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof not found for lemma: mathd_algebra_141 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_148 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_143 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_160 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_171 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_137 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_176 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: amc12b_2020_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_24 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof found for lemma: mathd_algebra_158 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,510 - __main__ - INFO - Proof not found for lemma: mathd_algebra_263 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_304 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_246 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_302 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_329 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_346 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_354 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_359 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_388 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_412 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_419 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_33 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_432 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_44 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_270 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_478 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_441 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_400 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_76 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_513 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof not found for lemma: mathd_algebra_80 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_algebra_440 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_127 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_175 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_207 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_185 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_212 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_229 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_235 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,511 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_237 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_150 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_239 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_299 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_254 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_135 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_343 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_345 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_341 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_517 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_551 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_728 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_769 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_247 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_66 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_85 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_153 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_107 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_113 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_114 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_17 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_188 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_196 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_170 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_209 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_156 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_208 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_184 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof not found for lemma: mathd_algebra_215 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,512 - __main__ - INFO - Proof found for lemma: mathd_algebra_289 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_276 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_275 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_288 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_338 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_342 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_332 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_398 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_313 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_459 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_392 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_484 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_362 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_756 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_algebra_598 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_100 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_222 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_452 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_227 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_1124 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_233 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_algebra_487 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_277 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_234 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_296 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_321 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_328 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_293 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,513 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_34 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_314 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_430 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_353 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_427 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_320 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_457 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_483 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_451 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_495 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_447 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_435 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_552 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_521 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_541 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_582 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_559 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_764 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_765 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_2pownm1prime_nprime in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_711 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_3pow2pownm1mod2pownp3eq2pownp2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_4x3m7y3neq2003 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: mathd_numbertheory_618 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_aoddbdiv4asqpbsqmod8eq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof found for lemma: mathd_numbertheory_99 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_x5neqy2p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: aime_1983_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_exk2powkeqapb2mulbpa2_aeq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,514 - __main__ - INFO - Proof not found for lemma: aime_1984_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1983_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1984_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof found for lemma: aime_1990_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1987_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1991_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1995_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1988_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof found for lemma: aime_1990_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1997_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1994_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_9onxpypzleqsum2onxpy in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: aime_1999_p11 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_absapbon1pabsapbleqsumabsaon1pabsa in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_apbon2pownleqapownpbpowon2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_amgm_sum1toneqn_prod1tonleq1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_apbmpcneq0_aeq0anbeq0anceq0 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof found for lemma: algebra_amgm_sumasqdivbgeqsuma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof found for lemma: algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_bleqa_apbon2msqrtableqambsqon8b in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_sqineq_unitcircatbpabsamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_ineq_nto1onlt2m1on in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof found for lemma: algebra_sqineq_unitcircatbpamblt1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_sum1onsqrt2to1onsqrt10000lt198 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: amc12_2000_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: algebra_others_exirrpowirrrat in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: amc12_2000_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: amc12_2000_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,515 - __main__ - INFO - Proof not found for lemma: amc12_2001_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12_2000_p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2003_p23 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12_2001_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2002_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2008_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof found for lemma: amc12a_2003_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2009_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2009_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2019_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p10 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2020_p15 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p19 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p25 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof found for lemma: amc12a_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p8 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2002_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p12 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12a_2021_p14 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2020_p22 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2020_p21 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2021_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2020_p13 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2021_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2021_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof not found for lemma: amc12b_2021_p4 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof found for lemma: amc12b_2021_p9 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,516 - __main__ - INFO - Proof found for lemma: imo_1959_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1960_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: amc12b_2002_p7 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1963_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1962_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1965_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: amc12b_2021_p18 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1974_p3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1969_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1964_p2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1981_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1983_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1982_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1968_p5_1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1977_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1992_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1997_p5 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_2019_p1 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_2001_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imosl_2007_algebra_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_11div10tonmn1ton in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_1pxpownlt1pnx in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1984_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof found for lemma: induction_12dvd4expnp1p20 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_pprime_pdvdapowpma in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: imo_1985_p6 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_sumkexp3eqsumksq in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_pord1p1on2powklt5on2 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_prod1p1onk3le3m1onn in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Proof not found for lemma: induction_nfactltnexpnm1ngt3 in file data/test/miniF2F-lean4/MiniF2F/Test.lean +2026-01-11 13:07:11,517 - __main__ - INFO - Success rate: 104/243 = 0.4279835390946502 for benchmark: miniF2F_lean4_test_easy_to_hard +2026-01-11 13:07:11,519 - __main__ - INFO - Finished running experiment: +{ + "env_settings": { + "name": "bm25_retrieval", + "retrieval_strategy": "BM25" + }, + "prompt_settings": { + "name": "simplified_lean4_copra_math", + "main_prompt": "data/prompts/system/simplified-lean4-proof-agent-with-dfs.md", + "conv_prompt": "data/prompts/conversation/simplified-lean4-proof-agent-dfs-multiple.md", + "uses_simplified_prompt": true, + "informal_proof_repo": null + }, + "eval_settings": { + "name": "n_60_dfs_gpt_oss_20b_no_retrieve_no_ex", + "use_hammer": "ALLOW", + "setting_type": "Agent", + "max_proof_depth": 100, + "timeout_in_secs": 600, + "proof_retries": 5, + "max_tokens_per_action": 4500, + "max_theorems_in_prompt": 7, + "gpt_model_name": "vllm:openai/gpt-oss-20b", + "max_number_of_episodes": 1, + "max_steps_per_episode": 100, + "render": false, + "checkpoint_dir": ".log/checkpoints/miniF2F_lean4_test_easy_to_hard/n_60_dfs_gpt_oss_20b_no_retrieve_no_ex/simplified_lean4_copra_math", + "should_checkpoint": false, + "temperature": 0.7, + "max_history_messages": 0, + "policy_name": "Dfs", + "proof_dump_dir": ".log/proofs/eval_driver/dfs/miniF2F_lean4_test_easy_to_hard/20260110-222600", + "use_human_readable_proof_context": true, + "sample": 1.0, + "sample_seed": 3840, + "use_example_retrieval": false, + "always_use_useful_theorem_retrieval": false, + "num_goal_per_prompt": null, + "model_params": {} + }, + "benchmark": { + "name": "miniF2F_lean4_test_easy_to_hard", + "num_files": 1, + "language": "LEAN4", + "datasets": [ + { + "project": "data/test/miniF2F-lean4", + "files": [ + { + "path": "MiniF2F/Test.lean", + "theorems": [ + "aime_1983_p2", + "aime_1989_p8", + "algebra_sqineq_at2malt1", + "amc12a_2002_p6", + "amc12a_2013_p4", + "amc12a_2021_p9", + "amc12b_2002_p19", + "amc12b_2002_p2", + "amc12b_2020_p2", + "amc12b_2020_p6", + "mathd_algebra_125", + "mathd_algebra_129", + "mathd_algebra_137", + "mathd_algebra_139", + "mathd_algebra_141", + "mathd_algebra_142", + "mathd_algebra_143", + "mathd_algebra_148", + "mathd_algebra_158", + "mathd_algebra_160", + "mathd_algebra_171", + "mathd_algebra_176", + "mathd_algebra_24", + "mathd_algebra_246", + "mathd_algebra_263", + "mathd_algebra_270", + "mathd_algebra_296", + "mathd_algebra_302", + "mathd_algebra_304", + "mathd_algebra_314", + "mathd_algebra_329", + "mathd_algebra_33", + "mathd_algebra_346", + "mathd_algebra_354", + "mathd_algebra_359", + "mathd_algebra_388", + "mathd_algebra_400", + "mathd_algebra_412", + "mathd_algebra_419", + "mathd_algebra_432", + "mathd_algebra_44", + "mathd_algebra_440", + "mathd_algebra_441", + "mathd_algebra_478", + "mathd_algebra_513", + "mathd_algebra_76", + "mathd_algebra_80", + "mathd_numbertheory_12", + "mathd_numbertheory_127", + "mathd_numbertheory_135", + "mathd_numbertheory_150", + "mathd_numbertheory_175", + "mathd_numbertheory_185", + "mathd_numbertheory_207", + "mathd_numbertheory_212", + "mathd_numbertheory_229", + "mathd_numbertheory_235", + "mathd_numbertheory_237", + "mathd_numbertheory_239", + "mathd_numbertheory_247", + "mathd_numbertheory_254", + "mathd_numbertheory_299", + "mathd_numbertheory_3", + "mathd_numbertheory_341", + "mathd_numbertheory_342", + "mathd_numbertheory_343", + "mathd_numbertheory_345", + "mathd_numbertheory_517", + "mathd_numbertheory_551", + "mathd_numbertheory_66", + "mathd_numbertheory_728", + "mathd_numbertheory_769", + "mathd_numbertheory_85", + "mathd_algebra_107", + "mathd_algebra_113", + "mathd_algebra_114", + "mathd_algebra_153", + "mathd_algebra_156", + "mathd_algebra_17", + "mathd_algebra_170", + "mathd_algebra_184", + "mathd_algebra_188", + "mathd_algebra_196", + "mathd_algebra_208", + "mathd_algebra_209", + "mathd_algebra_215", + "mathd_algebra_275", + "mathd_algebra_276", + "mathd_algebra_288", + "mathd_algebra_289", + "mathd_algebra_293", + "mathd_algebra_313", + "mathd_algebra_320", + "mathd_algebra_332", + "mathd_algebra_338", + "mathd_algebra_342", + "mathd_algebra_362", + "mathd_algebra_392", + "mathd_algebra_398", + "mathd_algebra_427", + "mathd_algebra_452", + "mathd_algebra_459", + "mathd_algebra_484", + "mathd_algebra_487", + "mathd_algebra_598", + "mathd_algebra_756", + "mathd_numbertheory_100", + "mathd_numbertheory_1124", + "mathd_numbertheory_222", + "mathd_numbertheory_227", + "mathd_numbertheory_233", + "mathd_numbertheory_234", + "mathd_numbertheory_277", + "mathd_numbertheory_293", + "mathd_numbertheory_296", + "mathd_numbertheory_314", + "mathd_numbertheory_320", + "mathd_numbertheory_321", + "mathd_numbertheory_328", + "mathd_numbertheory_34", + "mathd_numbertheory_353", + "mathd_numbertheory_427", + "mathd_numbertheory_430", + "mathd_numbertheory_435", + "mathd_numbertheory_447", + "mathd_numbertheory_451", + "mathd_numbertheory_457", + "mathd_numbertheory_483", + "mathd_numbertheory_495", + "mathd_numbertheory_5", + "mathd_numbertheory_521", + "mathd_numbertheory_541", + "mathd_numbertheory_552", + "mathd_numbertheory_559", + "mathd_numbertheory_582", + "mathd_numbertheory_618", + "mathd_numbertheory_711", + "mathd_numbertheory_764", + "mathd_numbertheory_765", + "mathd_numbertheory_99", + "numbertheory_2pownm1prime_nprime", + "numbertheory_3pow2pownm1mod2pownp3eq2pownp2", + "numbertheory_4x3m7y3neq2003", + "numbertheory_aoddbdiv4asqpbsqmod8eq1", + "numbertheory_exk2powkeqapb2mulbpa2_aeq1", + "numbertheory_fxeq4powxp6powxp9powx_f2powmdvdf2pown", + "numbertheory_x5neqy2p4", + "aime_1983_p1", + "aime_1983_p3", + "aime_1984_p1", + "aime_1984_p7", + "aime_1987_p5", + "aime_1988_p8", + "aime_1990_p15", + "aime_1990_p4", + "aime_1991_p9", + "aime_1994_p3", + "aime_1995_p7", + "aime_1997_p9", + "aime_1999_p11", + "algebra_2varlineareq_fp3zeq11_3tfm1m5zeqn68_feqn10_zeq7", + "algebra_9onxpypzleqsum2onxpy", + "algebra_abpbcpcageq3_sumaonsqrtapbgeq3onsqrt2", + "algebra_absapbon1pabsapbleqsumabsaon1pabsa", + "algebra_absxm1pabsxpabsxp1eqxp2_0leqxleq1", + "algebra_amgm_sum1toneqn_prod1tonleq1", + "algebra_amgm_sumasqdivbgeqsuma", + "algebra_apbmpcneq0_aeq0anbeq0anceq0", + "algebra_apbon2pownleqapownpbpowon2", + "algebra_apbpceq2_abpbcpcaeq1_aleq1on3anbleq1ancleq4on3", + "algebra_bleqa_apbon2msqrtableqambsqon8b", + "algebra_cubrtrp1oncubrtreq3_rcubp1onrcubeq5778", + "algebra_ineq_nto1onlt2m1on", + "algebra_others_exirrpowirrrat", + "algebra_sqineq_unitcircatbpabsamblt1", + "algebra_sqineq_unitcircatbpamblt1", + "algebra_sum1onsqrt2to1onsqrt10000lt198", + "amc12_2000_p1", + "amc12_2000_p12", + "amc12_2000_p20", + "amc12_2000_p6", + "amc12_2001_p21", + "amc12_2001_p5", + "amc12a_2002_p13", + "amc12a_2003_p23", + "amc12a_2003_p5", + "amc12a_2008_p25", + "amc12a_2009_p6", + "amc12a_2009_p7", + "amc12a_2019_p12", + "amc12a_2020_p10", + "amc12a_2020_p15", + "amc12a_2020_p25", + "amc12a_2020_p4", + "amc12a_2020_p7", + "amc12a_2020_p9", + "amc12a_2021_p12", + "amc12a_2021_p14", + "amc12a_2021_p18", + "amc12a_2021_p19", + "amc12a_2021_p22", + "amc12a_2021_p25", + "amc12a_2021_p3", + "amc12a_2021_p8", + "amc12b_2002_p4", + "amc12b_2002_p7", + "amc12b_2020_p13", + "amc12b_2020_p21", + "amc12b_2020_p22", + "amc12b_2021_p1", + "amc12b_2021_p13", + "amc12b_2021_p18", + "amc12b_2021_p3", + "amc12b_2021_p4", + "amc12b_2021_p9", + "imo_1959_p1", + "imo_1960_p2", + "imo_1962_p2", + "imo_1963_p5", + "imo_1964_p2", + "imo_1965_p2", + "imo_1968_p5_1", + "imo_1969_p2", + "imo_1974_p3", + "imo_1977_p6", + "imo_1981_p6", + "imo_1982_p1", + "imo_1983_p6", + "imo_1984_p6", + "imo_1985_p6", + "imo_1992_p1", + "imo_1997_p5", + "imo_2001_p6", + "imo_2019_p1", + "imosl_2007_algebra_p6", + "induction_11div10tonmn1ton", + "induction_12dvd4expnp1p20", + "induction_1pxpownlt1pnx", + "induction_nfactltnexpnm1ngt3", + "induction_pord1p1on2powklt5on2", + "induction_pprime_pdvdapowpma", + "induction_prod1p1onk3le3m1onn", + "induction_sumkexp3eqsumksq" + ], + "max_retry_attempts_limits": {}, + "max_time_limits_in_secs": {} + } + ] + } + ], + "few_shot_data_path_for_retrieval": null, + "few_shot_metadata_filename_for_retrieval": null, + "dfs_data_path_for_retrieval": null, + "dfs_metadata_filename_for_retrieval": null, + "timeout_per_theorem_in_secs": 600 + } +} From 05cb9037934a4844a3eecbde7d4d29eec8e3bbe5 Mon Sep 17 00:00:00 2001 From: Amitayush Thakur Date: Sun, 11 Jan 2026 14:32:57 +0000 Subject: [PATCH 3/5] Add section for latest evaluation results in README --- README.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/README.md b/README.md index 3c0f33a..2363687 100644 --- a/README.md +++ b/README.md @@ -17,6 +17,7 @@ COPRA: An in-COntext PRoof Agent which uses LLMs like GPTs to prove theorems in - [Setting up OpenAI API](#setting-up-openai-api-and-running-experiments) - [Starting Required Services](#starting-required-services) - [Parallel Theorem Execution](#parallel-theorem-execution-new) +- [Latest Evaluation Results](#latest-evaluation-results) - [Citation](#paper) --- @@ -520,6 +521,17 @@ python -m copra.main.run --config-name lean4_simple_experiment --- +## Latest Evaluation Results (NEW!) + +You can find selected recent evaluation results here: +- MiniF2F Test Lean 4 (v4.21.0) - GPT-OSS-20b (low reasoning tokens) (no retrieval): + - About 42.798% overall success rate on pass@5 + - Solves 1 IMO problem (`imo_1959_p1`) + - Decent performance for low compute budget + - See logs: [execution_logs](docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log) + + + ## Important Notes - The ITP projects must be built before running COPRA From 478174a5a0247be5cdc2989fa1b6490dfdaf4fcd Mon Sep 17 00:00:00 2001 From: Amitayush Thakur Date: Sun, 11 Jan 2026 14:36:20 +0000 Subject: [PATCH 4/5] Update links in README for latest evaluation results section --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 2363687..8e7d747 100644 --- a/README.md +++ b/README.md @@ -17,8 +17,8 @@ COPRA: An in-COntext PRoof Agent which uses LLMs like GPTs to prove theorems in - [Setting up OpenAI API](#setting-up-openai-api-and-running-experiments) - [Starting Required Services](#starting-required-services) - [Parallel Theorem Execution](#parallel-theorem-execution-new) -- [Latest Evaluation Results](#latest-evaluation-results) -- [Citation](#paper) +- [Latest Evaluation Results](#latest-evaluation-results-new) +- [Citation](#citation) --- From 421a16dec3223f19e7c4fbf5d6de5ed536d51d1a Mon Sep 17 00:00:00 2001 From: Amitayush Thakur Date: Sun, 11 Jan 2026 14:50:50 +0000 Subject: [PATCH 5/5] Refactor README structure and enhance content clarity for setup and features --- README.md | 417 +++++++++++------------------------------------------- 1 file changed, 80 insertions(+), 337 deletions(-) diff --git a/README.md b/README.md index 8e7d747..dafbdf1 100644 --- a/README.md +++ b/README.md @@ -9,12 +9,13 @@ COPRA: An in-COntext PRoof Agent which uses LLMs like GPTs to prove theorems in - [What's New](#whats-new) - [Setup](#setup) - [Quick Setup for Lean 4](#quick-setup-for-lean-4) - - [Python 3.14t Setup (Free-threaded Python)](#python-314t-setup-free-threaded-python---optional) + - [Python 3.14t Setup](#python-314t-setup-optional) - [Full Setup for Coq and Lean](#full-setup-for-coq-and-lean) - [vLLM Setup for Open Source Models](#vllm-setup-for-open-source-models) - [Simple CLI for Lean 4](#simple-cli-for-lean-4) - [Running Experiments](#running-experiments) - - [Setting up OpenAI API](#setting-up-openai-api-and-running-experiments) + - [API Setup](#api-setup) + - [Running the miniF2F Benchmark](#running-the-minif2f-benchmark) - [Starting Required Services](#starting-required-services) - [Parallel Theorem Execution](#parallel-theorem-execution-new) - [Latest Evaluation Results](#latest-evaluation-results-new) @@ -25,200 +26,99 @@ COPRA: An in-COntext PRoof Agent which uses LLMs like GPTs to prove theorems in ## What's New ### 🎯 Simple CLI for Lean 4 (NEW!) -COPRA now has a **streamlined command-line interface** for quick theorem proving without complex YAML configuration! - -**Features:** -- ✅ **Simple Commands**: Prove theorems with a single command -- ✅ **Environment Variables**: Use standard env vars for API keys (12-factor pattern) -- ✅ **No Configuration Files**: Override only the settings you need via command-line -- ✅ **Real-Time Progress**: See proof steps as they execute -- ✅ **Modular Design**: Clean architecture ready for REST API integration +Streamlined command-line interface for quick theorem proving - no complex YAML configuration needed! Prove theorems with a single command, use environment variables for API keys, and get real-time progress output. [Jump to Simple CLI Guide →](#simple-cli-for-lean-4) ### 🤖 vLLM Support for Open Source Models (NEW!) -COPRA now supports **vLLM** for running open-source LLMs locally! This enables you to use models like Llama, Mistral, DeepSeek, and more for theorem proving. - -**Features:** -- ✅ **OpenAI-Compatible API**: Works with existing COPRA code via OpenAI-compatible interface -- ✅ **GPU Acceleration**: Full CUDA support with multi-GPU tensor parallelism -- ✅ **Automatic Server Management**: Start/stop vLLM servers programmatically -- ✅ **Model Flexibility**: Support for any Hugging Face model compatible with vLLM -- ⚠️ **Python Requirement**: vLLM requires Python ≤ 3.12 (not compatible with 3.14t) +Run open-source LLMs locally (Llama, Mistral, DeepSeek, etc.) with GPU acceleration. OpenAI-compatible API, automatic server management, and support for any Hugging Face model compatible with vLLM. [Jump to vLLM Setup →](#vllm-setup-for-open-source-models) -### 🚀 Parallel Theorem Execution -COPRA now supports executing proof search for **multiple theorems in parallel**! This significantly speeds up evaluation on multi-core systems. - -**Features:** -- ✅ **Automatic Python Version Detection**: Uses threading for Python 3.14t+ and multiprocessing for older versions -- ✅ **Configurable Worker Count**: Control parallelism with environment variables -- ✅ **Backward Compatible**: Disabled by default - opt-in via environment variable -- ✅ **Better Resource Utilization**: Leverage all CPU cores for faster evaluations +### 🚀 Parallel Theorem Execution (NEW!) +Execute proof search for multiple theorems in parallel to speed up evaluations on multi-core systems. Automatically uses threading for Python 3.14t+ and multiprocessing for older versions. [Jump to Parallel Execution Setup →](#parallel-theorem-execution-new) -### 🐍 Python 3.14t Free-Threading Support -COPRA now fully supports Python 3.14+ with free-threaded (GIL-free) execution for improved performance! +### 🐍 Python 3.14t Free-Threading Support (NEW!) +Full support for Python 3.14+ with free-threaded (GIL-free) execution. Automatically selects best parallel execution strategy based on Python version and GIL status. -**Automatic Execution Mode Selection:** -- **Python 3.14t+ with GIL disabled:** Native free-threading for true parallel execution -- **Python 3.14t+ with GIL enabled:** Threading (still benefits from improved performance) -- **Python < 3.14:** Multiprocessing (traditional approach) +### 📊 Latest Evaluation Results (NEW!) +Recent MiniF2F Test Lean 4 results with GPT-OSS-20b achieved **42.8% pass@5** success rate, including solving 1 IMO problem (`imo_1959_p1`) with low compute budget. [View logs →](docs/static/selected_results/gpt_oss_20b_evals_pass_at_5.log) + +[Jump to Full Results →](#latest-evaluation-results-new) --- ## Setup ### Quick Setup for Lean 4 -1. Install itp-interface using the following command: (Our package is available on PyPI: https://pypi.org/project/copra-theorem-prover/) ```bash +# 1. Install COPRA pip install copra-theorem-prover -``` -2. Run the following command to prepare the REPL for Lean 4. (The default version is 4.24.0. You can change the version by setting the `LEAN_VERSION` environment variable. If no version is set, then 4.24.0 is used.) ->NOTE: The Lean 4 version must match the version of the Lean 4 project you are working with. -```bash -export LEAN_VERSION="4.21.0" +# 2. Set Lean version (default: 4.24.0) and install REPL +export LEAN_VERSION="4.21.0" # Must match your project version install-lean-repl -``` -3. Run the following command to build the REPL for Lean 4. Make sure that `lean --version` returns the correct version before running the command below. If not then check if `$HOME/.elan/bin` is in your path. Recommended to run `source $HOME/.elan/env` before running the command below. -```bash +# 3. Build the interface (ensure $HOME/.elan/bin is in PATH) +source $HOME/.elan/env # Optional: if lean --version fails install-itp-interface ``` ->NOTE: These steps are only tested on Linux. For Windows, you can use WSL. These steps will not setup the Coq interface. +> **Note:** Tested on Linux. Windows users should use WSL. -### Python 3.14t Setup (Free-threaded Python - Optional) -🆕 **NEW:** COPRA now supports Python 3.14+ with free-threaded (GIL-free) support for improved performance! - -1. **Create a Conda environment with Python 3.14t (free-threaded):** +### Python 3.14t Setup (Optional) ```bash -# Create environment with free-threaded Python 3.14 +# Create and activate environment conda create -n py314-ft python=3.14 python-freethreading -c conda-forge - -# Activate the environment conda activate py314-ft -# Verify Python version and free-threading support -python --version # Should show Python 3.14.x -``` - -2. **Install COPRA theorem prover:** -```bash -# Install from PyPI -pip install copra-theorem-prover - -# OR for development, install from source -pip install -e . -``` +# Install COPRA +pip install copra-theorem-prover # or: pip install -e . (for development) -3. **Run experiments with Python 3.14t:** -```bash -# Use run.py which automatically detects Python 3.14+ and uses Hydra-free mode +# Run experiments (automatically detects Python version) python -m copra.main.run --config-name lean4_simple_experiment - -# Or if installed from source -python src/copra/main/run.py --config-name lean4_simple_experiment ``` -> **Note:** Python 3.14t is experimental. Some packages may show compatibility warnings (especially Pydantic and OpenAI), but COPRA has been refactored to work with Python 3.14t. - -**🚀 Automatic Parallel Execution Selection:** -COPRA automatically detects your Python version and chooses the best parallel execution strategy: -- **Python 3.14t+ with GIL disabled:** Uses native free-threading for true parallel execution -- **Python 3.14t+ with GIL enabled:** Uses threading (still benefits from improved performance) -- **Python < 3.14:** Uses multiprocessing (traditional approach) - -Check your execution mode: -```bash -python demo_parallel_execution.py -``` +> **Note:** Python 3.14t is experimental. COPRA automatically selects the best parallel execution strategy: free-threading (GIL disabled), threading (GIL enabled), or multiprocessing (Python < 3.14). ### Full Setup for Coq and Lean -1. Install OCaml first. Use the instructions here: https://opam.ocaml.org/doc/Install.html. Note that OCaml officially only supports Linux installations. One can use WSL on Windows machines. - -2. Run the following to install Coq on Linux. -``` +```bash +# 1. Install Coq dependencies and opam (Linux only, use WSL on Windows) sudo apt install build-essential unzip bubblewrap sh <(curl -sL https://raw.githubusercontent.com/ocaml/opam/master/shell/install.sh) -``` -3. Add the following to your `.bashrc` file: (sometimes the path `~/.opam/default` might not exist, so use the directory with version number present in the `~/.opam` directory) -``` +# 2. Add to ~/.bashrc (adjust path if ~/.opam/default doesn't exist) export PATH="/home/$USER/.opam/default/bin:$PATH" -``` - -4. Create a `Miniconda` environment and activate it. - -5. Run the commands for installing the Lean 4 interface as mentioned in [Quick Setup for Lean 4](#quick-setup-for-lean-4). - -6. Add the following to your `.bashrc` file for Lean: -``` export PATH="/home/$USER/.elan/bin:$PATH" -``` -### vLLM Setup for Open Source Models +# 3. Setup Python environment and install Lean 4 +# (Follow Quick Setup for Lean 4 steps above) +``` -🆕 **NEW:** Run open-source LLMs locally with GPU acceleration via vLLM! +> **Note:** See [OCaml installation guide](https://opam.ocaml.org/doc/Install.html) for details. -**Quick Setup:** +### vLLM Setup for Open Source Models ```bash -# Install with vLLM support +# Standard vLLM models (Llama, Mistral, DeepSeek, etc.) pip install copra-theorem-prover[os_models] -# Or for development -pip install -e .[os_models] -``` - -**GPT OSS Models Setup:** - -To use the GPT OSS 20b model with the custom vLLM wheel: -```bash -# Install from pypi +# GPT-OSS-20b (custom vLLM build with reasoning token support) pip install copra-theorem-prover[gpt_oss] - -# On local development setup -pip install -e .[gpt_oss] - pip install --pre torch --extra-index-url https://download.pytorch.org/whl/nightly/cu128 -#Change the version of CUDA (cu118, cu121, cu128) based on your GPU setup. +# Adjust CUDA version (cu118, cu121, cu128) based on your GPU ``` -> **Note:** The `gpt_oss` optional dependency installs a custom vLLM build (`vllm==0.10.2`) from the GPT OSS wheel repository. - -> **Note:** There are known issues with GPT OSS reasoning tokens being not processed correctly in vLLMs. (See: [vLLM GitHub Issue](https://github.com/vllm-project/vllm/issues/26480)) - - **Usage:** - -Create a config file (see `src/copra/main/config/miniF2F_lean4_easy_to_hard.yaml` for a complete example): -```yaml -# config/eval_settings/my_gpt_oss_config.yaml -gpt_model_name: gpt-oss-20b -temperature: 0.75 -max_tokens_per_action: 100 -# ... other settings -``` - -Run your experiment: ```bash +# vLLM server starts automatically on port 48000 (override with VLLM_PORT) python -m copra.main.eval_benchmark eval_settings=my_vllm_config benchmark=miniF2F ``` -The vLLM server starts automatically on port 48000. Override with `VLLM_PORT` environment variable if needed. +**Supported Models:** `vllm:openai/gpt-oss-20b`, `vllm:codellama/CodeLlama-7b-Instruct-hf`, `vllm:meta-llama/Llama-2-7b-chat-hf`, `vllm:EleutherAI/llemma_7b`, `vllm:deepseek-ai/deepseek-math-7b-instruct`, or any HuggingFace model compatible with vLLM. -**Supported Models:** -- `vllm:openai/gpt-oss-20b` (GPT OSS 20b - open-source model) -- `vllm:codellama/CodeLlama-7b-Instruct-hf` (open-source code model) -- `vllm:meta-llama/Llama-2-7b-chat-hf` (general LLM) -- `vllm:EleutherAI/llemma_7b` (math-focused LLM) -- `vllm:deepseek-ai/deepseek-math-7b-instruct` (math reasoning) -- Any HuggingFace model compatible with vLLM - -> **Note:** vLLM requires Python ≤ 3.12 and CUDA-capable GPU +> **Requirements:** Python ≤ 3.12 and CUDA-capable GPU. See [vLLM issue #26480](https://github.com/vllm-project/vllm/issues/26480) for known reasoning token limitations. --- @@ -285,239 +185,82 @@ copra-lean-prover \ ## Running Experiments -### Setting up OpenAI API and Running Experiments -1. You need to create a file `.secrets/openai_key.json` in the root directory of the project with the OpenAI API key. The file should contain the following: -``` -{ - "organization": "", - "api_key": "" -} -``` - -2. The experiments are not necessarily thread safe. So, it is recommended to run them sequentially. The commands to run the desired experiments can be found in the file `./src/copra/main/config/experiments.yaml`. +### API Setup +**Option 1: Environment Variables (Recommended)** +```bash +# OpenAI +export OPENAI_API_KEY="sk-..." -3. Run the following command to run the experiments: +# Anthropic +export ANTHROPIC_API_KEY="sk-ant-..." -**For Python 3.14+ (with free-threaded support):** -```bash -python src/copra/main/run.py --config-name lean4_simple_experiment -# This uses a Hydra-free implementation compatible with Python 3.14+ -# You can change the config name to run different experiments +# AWS Bedrock +export AWS_ACCESS_KEY_ID="..." +export AWS_SECRET_ACCESS_KEY="..." +export AWS_REGION="us-east-1" ``` -**For Python < 3.14:** -```bash -python src/copra/main/eval_benchmark.py -# This will run the experiments mentioned in the file `./src/copra/main/config/experiments.yaml`. -# Change the file path in the command above to run other experiments. +**Option 2: Secrets File** +Create `.secrets/openai_key.json`: +```json +{"organization": "", "api_key": ""} ``` -**Universal command (auto-detects Python version):** +### Running Experiments ```bash +# Auto-detects Python version (recommended) python src/copra/main/run.py --config-name lean4_simple_experiment -# This automatically uses Hydra-free mode for Python 3.14+ and Hydra mode for older versions ``` -> **Note:** `run.py` is the recommended entry point for all Python versions. It automatically detects your Python version and uses the appropriate implementation (Hydra-free for 3.14+, standard Hydra for older versions). - -### Running the miniF2F_lean4 Benchmark - -The miniF2F benchmark is a suite of formal math problems from various math competitions (AMC, AIME, IMO) and educational resources (MATH dataset) formalized in Lean 4. +> **Note:** See `./src/copra/main/config/experiments.yaml` for available configurations. -**Prerequisites:** -1. Install and setup Lean 4 (see [Quick Setup for Lean 4](#quick-setup-for-lean-4)) -2. Set the correct Lean version to match the benchmark (e.g., 4.21.0): - ```bash - export LEAN_VERSION="4.21.0" - install-lean-repl - install-itp-interface - ``` - -**Running with GPT OSS 20b:** +### Running the miniF2F Benchmark ```bash -# Using the pre-configured setup -python -m copra.main.run --config-name miniF2F_lean4_easy_to_hard +# Setup Lean 4.21.0 (required for miniF2F) +export LEAN_VERSION="4.21.0" +install-lean-repl && install-itp-interface -# Or using the benchmark directly -python -m copra.main.eval_benchmark \ - benchmark=miniF2F_lean4_test_easy_to_hard \ - eval_settings=n_60_dfs_gpt_oss_20b_no_retrieve_no_ex -``` +# Run with GPT-OSS-20b +python -m copra.main.run --config-name miniF2F_lean4_easy_to_hard -**Running with OpenAI models:** -```bash -# Make sure .secrets/openai_key.json is set up first +# Run with OpenAI models (requires API key) python -m copra.main.eval_benchmark \ benchmark=miniF2F_lean4_test_easy_to_hard \ eval_settings=n_60_dfs_gpt4_o_no_retrieve_no_ex ``` -**Configuration options:** -- `benchmark=miniF2F_lean4_test_easy_to_hard`: Uses theorems ordered from easy to hard -- `eval_settings`: Controls model, temperature, search strategy (see `src/copra/main/config/eval_settings/`) -- `timeout_per_theorem_in_secs`: Time limit per theorem (default: 600 seconds) -- `max_steps_per_episode`: Maximum proof search steps (default: 100) - -**Results and Logs:** -- Proof results: `.log/proofs/eval_driver/dfs/miniF2F_lean4_test_easy_to_hard//proof_results.json` -- Evaluation logs (with prompts and LLM interactions): `.log/evals/benchmark/miniF2F_lean4_test_easy_to_hard//eval.log` +**Results:** `.log/proofs/eval_driver/dfs/miniF2F_lean4_test_easy_to_hard//` ### Starting Required Services -Before running COPRA, you need to ensure the required services are running based on your proof language: - -#### For Lean 4 Projects: -No additional services are required. Lean 4 uses a built-in REPL that COPRA manages automatically. - -#### For Isabelle Projects: -You need to start the PISA (Portal for Isabelle) service: - -1. **Set the PISA port** (optional, defaults to 17000): -```bash -export PISA_PORT=17000 -``` - -2. **Start the PISA service:** -```bash -# COPRA will automatically start the PISA service when needed -# You can also manually start it if required by your setup -``` - -3. **Check if PISA is running:** -```bash -# COPRA will log whether PISA service is up or needs to be restarted -``` - -> **Note:** COPRA automatically manages the PISA service lifecycle, including health checks and restarts. You'll see log messages about PISA service status during execution. +- **Lean 4:** No setup needed (COPRA manages REPL automatically) +- **Isabelle:** COPRA auto-manages PISA service (default port: 17000, override with `PISA_PORT`) +- **Coq:** Ensure correct version is active (`coqc --version`) and project is built (`make`) +- **vLLM/Llama:** COPRA auto-starts services (logs in `.log/evals/benchmark///`) -#### For Coq Projects: -Ensure the correct Coq version is active: - -1. **Check your Coq version:** -```bash -coqc --version -``` - -2. **Switch Coq version if needed** (using opam): -```bash -opam switch -eval $(opam env) -``` - -3. **Build your Coq project** before running COPRA: -```bash -cd /path/to/your/coq/project -make # or your project's build command -``` - -#### For LLM Services (Llama models): -If using non-OpenAI models (like Llama): - -1. COPRA will automatically initialize the Llama service when needed -2. Check the logs in `.log/evals/benchmark///llama.log` -3. If the service goes down, COPRA will automatically restart it - -> **Important:** The ITP projects must be built before running COPRA. Make sure the correct version/switch is active for Coq projects, as different projects may use different Coq versions. +> **Important:** ITP projects must be built before running COPRA. For Coq, ensure the correct opam switch is active. ### Parallel Theorem Execution (NEW!) -COPRA now supports executing proof search for **multiple theorems in parallel**, significantly speeding up evaluations on multi-core systems. - -#### Quick Start - -**Enable parallel execution:** -```bash -export ENABLE_PARALLEL_THEOREMS=True -python src/copra/main/run.py --config-name lean4_simple_experiment -``` - -**Control number of workers:** +**Quick Start:** ```bash +# Enable with auto-detected workers (CPU cores / 2) export ENABLE_PARALLEL_THEOREMS=True -export MAX_PARALLEL_WORKERS=4 # Use 4 parallel workers python src/copra/main/run.py --config-name lean4_simple_experiment -``` - -#### Configuration Options - -| Environment Variable | Description | Default | Example | -|---------------------|-------------|---------|---------| -| `ENABLE_PARALLEL_THEOREMS` | Enable/disable parallel theorem execution | `False` | `True` or `False` | -| `MAX_PARALLEL_WORKERS` | Maximum number of parallel workers | Auto (CPU cores / 2) | `4`, `8`, `16` | - -#### How It Works - -**Sequential Execution (Default):** -- Theorems are processed one at a time -- Each theorem proof runs in isolation with timeout -- Original behavior is preserved - -**Parallel Execution (Enabled):** -- Multiple theorems are processed concurrently -- Each theorem proof still runs in its own process/thread with timeout -- Results are collected as they complete -- **Automatic Python version detection:** - - **Python < 3.14:** Uses `ProcessPoolExecutor` (multiprocessing) - - **Python 3.14t+:** Uses `ThreadPoolExecutor` (threading with free-threading support) -#### Examples - -**Example 1: Basic parallel execution** -```bash -# Enable parallel execution with auto-detected worker count -export ENABLE_PARALLEL_THEOREMS=True -python -m copra.main.run --config-name lean4_simple_experiment +# Custom worker count +export MAX_PARALLEL_WORKERS=4 ``` -**Example 2: Custom worker count** -```bash -# Use 8 parallel workers for large theorem sets -export ENABLE_PARALLEL_THEOREMS=True -export MAX_PARALLEL_WORKERS=8 -python -m copra.main.run --config-name lean4_simple_experiment -``` - -**Example 3: Python 3.14t with free-threading** -```bash -# On Python 3.14t, this will automatically use threading -conda activate py314-ft -export ENABLE_PARALLEL_THEOREMS=True -python -m copra.main.run --config-name lean4_simple_experiment -``` - -**Example 4: Conservative parallel execution** -```bash -# Use only 2 workers for resource-constrained systems -export ENABLE_PARALLEL_THEOREMS=True -export MAX_PARALLEL_WORKERS=2 -python -m copra.main.run --config-name lean4_simple_experiment -``` - -#### Performance Tips - -1. **Match workers to CPU cores:** Set `MAX_PARALLEL_WORKERS` to your number of physical CPU cores -2. **Consider theorem complexity:** Complex theorems benefit more from parallelism -3. **Monitor resources:** Watch CPU, memory, and I/O usage during execution -4. **Service capacity:** Ensure LLM services can handle concurrent requests -5. **Sequential for small sets:** Use sequential execution for fewer than 4 theorems (less overhead) - -#### Limitations - -- **Memory usage:** Parallel execution uses more memory (multiple processes/threads running simultaneously) -- **Shared resources:** Services (Llama, Isabelle) must handle concurrent requests -- **Time budget tracking:** Time budgets are tracked per-theorem, not globally across parallel executions - -#### Troubleshooting +**How it works:** Automatically uses threading (Python 3.14t+) or multiprocessing (Python < 3.14). Disabled by default. -**Issue: Out of memory errors** -- **Solution:** Reduce `MAX_PARALLEL_WORKERS` to `2` or `4` +**Configuration:** +- `ENABLE_PARALLEL_THEOREMS`: Enable/disable (default: `False`) +- `MAX_PARALLEL_WORKERS`: Worker count (default: auto-detected) -**Issue: Service connection errors** -- **Solution:** Reduce parallel workers or use sequential execution for service-heavy workloads +**Tips:** Match workers to CPU cores, ensure services handle concurrent requests, use sequential mode for <4 theorems. -**Issue: Slower than sequential execution** -- **Cause:** Small theorem sets, I/O-bound workloads, or limited CPU cores -- **Solution:** Disable parallel execution or reduce worker count +**Troubleshooting:** Reduce workers if you encounter memory/service errors. ---