Back to Problems
exists_isWallSunSunPrime
Specification
A prime $p$ is a Wall–Sun–Sun prime if and only if $L_p \equiv 1 \pmod{p^2}$, where $L_p$ is the $p$-th Lucas number. It is conjectured that there is at least one Wall–Sun–Sun prime.
Lean 4 Statement
theorem exists_isWallSunSunPrime : ∃ p, IsWallSunSunPrime p
Browse
All Problems
Explore all 300 unsolved conjectures.
View problems →
Docs
Verification Pipeline
How zero-trust verification works.
Read docs →
Evaluation Results
Recent Submissions
| Model | Status | Goals Left | Submitted | Lean Snippet | Output |
|---|---|---|---|---|---|
| GPT-5.3 Codex Agent v8 | Partial | 1 | Feb 25, 2026 |
refine ⟨2, ?_⟩
constructor
· exact Nat.prime_two
· simp
|
View{
"agent_telemetry": {
"compilations": 8,
"iterations": 10,
"duration_s": 363.86,
"best_status": "partial",
"best_goals": 1,
"max_iterations": 10,
"model": "openai/gpt-5.3-codex",
"error": null,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"usage": {
"prompt_tokens": 68863,
"completion_tokens": 4450,
"total_tokens": 73313,
"reasoning_tokens": 4099,
"cost_usd": 0.10196865
},
"reasoning_effort": "high",
"response_trace_count": 18
},
"response_trace": [
{
"iteration": 1,
"event": "search_mathlib",
"query": "IsWallSunSunPrime",
"results_count": 0
},
{
"iteration": 2,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031161-rHIV3SFfmcx32VVln5k5",
"api_elapsed_s": 2.823,
"usage": {
"prompt_tokens": 1651,
"completion_tokens": 114,
"total_tokens": 1765,
"reasoning_tokens": 80,
"cost_usd": 0.00287245
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Testing proof compilation with holes**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Testing proof compilation with holes**"
},
{
"id": "rs_0533690cde6a4b4a01699f0cba6a8c8193a8118fb62734062e",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnwy8BMVzsrhDSeR_Z6tB8TCU7t70-mBAsnOeicLA0zNYh5Q1QrIqDBLEUCROR2wwv0zBMHltyP1I2cd9NMD-tJ_h_fgjkze5u7RxBSCeobaEj5sjpdl-lhnOt-yBnWCD0oeLMpf7NzgS8HBXXR_Po_wqeEGKoe-xq_1UXVzFIUeeg23svzFB5_NuYxywnGXvgXYAias1dwbonKYuEjWFe9NxzBjZEjSZmpv5GE0H9Z1PB1wqdTkCqlVTEt75Hp0pzUnv8m_Aql3UFvFCAG3t4AmqJy_StG2PwSEjzFAi9OBLhIScGFZtaj8nR5G-hnaiE17WrXXtKz5abmRGwT-jkFa8BtX_qAPfu4MEG2HVGuJDbtyml1rV9HbAo2iqduNdCHIaG50u-MmDn59SdFrnjoPSsAubzy2HdwUe_Jjn6oBPiTBabEvbAlje0WHb9J4ovL1Lxs6CYrZZTFq9b_Fwx_WeGYzfiMnVUtbK3ev8IJgE3K_H3KOOlGlIvad916H-VHO9nTpdl1PaV086bqNCnj0HS9NuGZctI0gdSG_J66bCmISLhaIoGDICWDAQ7kOLsZ-Yc5GpO2p84RVZEYq5RwWyAJdCqbbL5eZupcX4kde6oEui4iuHh1eGc-0mDgPqlz9WoS6GmyhPQLPIeFRkeve4_GyGhm5DZ6s8E7QAZ0Q3bzo9adwWS-sZW8tQrNXjuiBOxwBMx3JO1jOeAApUX26DXvMskzDRA3M8JcCjptNNvLvSFgRTRoBOqFAq0cfWnb3b-B6a-eGOfQD1gkfy2QWv18vZU1D9LNFc9jmPhbO5WYW8ody4935DMet9dxaWn20mDyDo9996t9mKm4TGMnrAIDWZnuQwNnmomY_atcTJLkXf1XI9I_uNtGCrziLDoCWntHuLTrK4m7EVfT_BSME4qiJUwaeEzF75wgiEr_CpbZ9uwsa-SlmFjhsanI8QlSP4DxLEzpYA2Mdmio2_Sm6FLuSj28YfxCj_xxwx7_VikDAyDS0Z1J3Ey2UoggjJzbyzpACyoEixtcmFL1w0EOrTecSOxeNyCCH6aRGSKx6ZNyVCKuDl6GPgjDATBDMnLTWYvOPt4fey3KI7K07-hZd62Cut4uHGix_9gcz3HapHwIRgHx_WfyQNNVPXdKA5kaPfWdnHcHSMXjMdbQrAZt9RqP0CZzJZmoymj4j5SPJh_hR1TrQK6IBUiQUZL1lelme6NtSYUHnJXuX9rQPYXGaWK5fLCoszaJ9rijAPjSYtnFjnRc6asR2nGxzJvmEH3uGZ"
}
]
},
{
"iteration": 2,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 2,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e8?p, ?h\u27e9",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031164_7920.lean:14:63: error: unsolved goals\ncase p\n\u22a2 \u2115\n\ncase h\n\u22a2 IsWallSunSunPrime ?p\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 27.385,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 17,
"line": 14
},
"start": {
"character": 63,
"line": 13
}
},
"leanTags": [
1
],
"message": "unsolved goals\ncase p\n\u22a2 \u2115\n\ncase h\n\u22a2 IsWallSunSunPrime ?p",
"range": {
"end": {
"character": 0,
"line": 14
},
"start": {
"character": 63,
"line": 13
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 13,
"error_char": 63,
"error_msg": "unsolved goals\ncase p\n\u22a2 \u2115\n\ncase h\n\u22a2 IsWallSunSunPrime ?p",
"goal_before_error": null,
"full_timeline": [
{
"line": 14,
"code": "refine \u27e8?p, ?h\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
}
],
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "theorem exists_isWallSunSunPrime : \u2203 p, IsWallSunSunPrime p := by"
}
},
{
"iteration": 3,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031192-LlfraEO5ft9vh54Pdgv3",
"api_elapsed_s": 6.662,
"usage": {
"prompt_tokens": 2811,
"completion_tokens": 312,
"total_tokens": 3123,
"reasoning_tokens": 272,
"cost_usd": 0.00767445
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Examining prime witness construction**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Examining prime witness construction**"
},
{
"id": "rs_0533690cde6a4b4a01699f0cd8914c8193a4a0d63d01b57527",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnwze4cLY_foNSmBb_5zflx0m2Dt9sUBhQILXfVw-oKmA-z5rlU-MQWjuUU6xzGDXkNvANlplsnYBlADSE1XwJD72VIjEmm3Gy7JunlsfrAHlJ-5JIVleAT2L-FBp8TEvI7jKZ7BLABcAJNwCJ4tzgJe-grfwstqQzqvUtMCitxLgM53mrYWsypdBWTDcr3FxuDADPgOJc3nQn4wEeb4A0ajLfnO755BnIEpn_SH7wYcr2pKx1cL5dTG6Je6b9NRM_fDc-b7G3W8dDt3nN_3L9SAbjK8-l8AFWZceEZucvvc8WF4YtU_S88peNunm0AJMvZ-14LJgdtnrhUaOicXGK8mlrZtB_SPI9GDDe1aDZja-d3z7nqYJ_hEcM663I2zXeJ0pLsAPvyLAhg6bnhvnZug-w9nAciorq5UTHlJ1JIIialAUH31ULnm0EOFaEZRbhra8ckhFmcqyvsCI0JTNx5_L40rnaK-9juzIi5LUX2menLp2QmiN2cSIpg6o0QvP8eiAg6Hz79_ggVpFJjfWbtCgtDowalpWiCmkW3qZgGLC2xOgNy0C-2c0GdIzGm2adpPoqG8YVv8ddaovpY25ll6oZsTM4DsSa9bq-YUgBDQr47eJKKPU1j5vyF_Om8bNFsep2ceUPJBDIBshUyIHoT95YDhko-Dd9jX-wUZT_eZavnqqnAF9sjyeW78lJtjG1UYRgPaUTQate7pAO4M3xddCa11mi0IW1IN6Yhu8gmGhvNuCD05Rda8Dml4K3-dLZRazVLeuLQIkljxhHBfH9tk8thkbXc3A5A1nf9GEWyq4uvEC9tQ0zbjBMsQWAzhT0y54HM_Z_TAnNU6Q62Qi-8iP0m_rK1ia09rMOLC8C4k7LfQHdZGY0mOtNW_XHUxcEKhJhNXGz3pHBHi-myV6UeldiswHgJxgxbEHRp6yrLrBYPdQExKYgUZM1Jh-kdKo4jtL8c6wVYhYP_gDYdfs8VXwbuftwK38We0ZAfsqnrSg1ngPhrI09h4zqCrgaGh-7bd_jRk8Zxb0nz6Yc3AyflKzs-wJInGUkTjgDm56shENAWIQf3g-vse-tIqma7gq-Krf8bUy4BxzR4J6y16K5aqc7adtNBveUb08_I6tcvXjgEcaPD2cbEtD3ALAsIh8Roku18kk4ja49laX_kXvio9s_FyxWDD_sJ5jxgAr3WqSUGygtiSmergQN6mMrH8DlJf6aJc_t4Uc9ApLkyhcLcZL1ZizD3RUzNQL-Aq1Zc0U0eApuoErPURobPF0Vrfmw6huTfrVNKiECozDXsiysdk1xUyV1eR9T8zHMvl0zM6o4asneUpbhi5_Cl_wRzqptGuJ1Ls68u76rCKTB0fO_UhsX4zwM7FYrqyqyieXdaZMlBoayJll8hG69U4_jps1zMlyqETlT-I-Sf-Rm-kZqtUuggQiHkM10zflTCZAfU38Waj9SHJoTPq2lGbE2E3-dXurIb2gkOKk9NgFQ-4hAaZ_IAKPKmDAF3lU6SZVqB9WY0KUHpGFULhV2uew5S51KSLouEDCNFcZ0l8XTRmJh1CZUC9EY5yBs_FinJVfJRTPHgZA3U_f6j0LIdHwEOM5rRtHuznxgmAlHv-pFxd7DetFJ5UCaN5aqHgByeRW1qQhFnRQ_nFsGP1MgSf7LUqnLBf22s75MNyDxB3z7XN02w39LolUlAvqAH8ieMljy3VKOB2Xj80KMI_7CNWL_tZeDSenYLcjQGdTzuHaKeX9NkU4Zn-6zPf5TouWwgVd7aOA65MZM8BeAZz91Ip_0x3U-YYueIRH1RIewB8QkG8BftkEhHR509HUwa1gG1FotsEzi-unhxGOqs64chJ90ZLqqtVpi0i_nLi_zhd01XtduqI_AEVe1_a29mwJqwp4CX817zu2F8c3ZJkWMgABnW05Ix-qD-8DpszdmJRlu52qPEZwz_pOM74BHyPJLXKkofJZ4JdriKGIZk8FT1VwtoEVpbcSmIGgCcBtQQh1ZQGvwm45OG5oZSvNVUFtE6vxqK1U3jPXALsdt1OvVoeYN-NhCAUKfW5xpfzkvuHyXrIq-AxCipzDVseeGHMm9-BETclanTwdSyVJ-YdcNx12nZIRYdUPyI1jajitlAqGlFyiqpDNKKUgBaH8MBveyd-RfLki5g5MSyhmF9dP3J0ZChR0Dq_CLWzRMbyQHjqDXhTHzeqRhmGFR6TvR-DE8P-n75qtLWFzzKBjkI12mr1yY7Y1FNw-kwPAprQDC9KDO3mNOKgDGu6WED8lt_KHx2eXAgg2eAgYZVW5K_Cs8r3HZMs8eb6-EST1qX0M3vRXF6K71pBIb6FeAll9qiDU40Bmd0S0Agj9Ya2uphyVlslP6SsgqPv8RFCAy4qlXMTI0s4VnHzhsDnGyhc_qgKaS7ePs_jytYLe1bhse5cdOojWPOj1I4BWIVl9D0IDGHzRPVH95jWrvA=="
}
]
},
{
"iteration": 3,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e82, ?_\u27e9\nexact by\n decide",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031198_2232.lean:17:4: error: failed to synthesize\n Decidable (IsWallSunSunPrime 2)\n\nHint: Additional diagnostic information may be available using the `set_option diagnostics true` command.\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 30.149,
"tactic_replay": {
"tactic_count": 3,
"successful_tactics": 2,
"first_failure_step": 3,
"goal_trajectory": [
1,
1,
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 10,
"line": 16
},
"start": {
"character": 4,
"line": 16
}
},
"message": "failed to synthesize\n Decidable (IsWallSunSunPrime 2)\n\nHint: Additional diagnostic information may be available using the `set_option diagnostics true` command.",
"range": {
"end": {
"character": 10,
"line": 16
},
"start": {
"character": 4,
"line": 16
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 18
},
"start": {
"character": 0,
"line": 18
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 18
},
"start": {
"character": 0,
"line": 18
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 16,
"error_char": 4,
"error_msg": "failed to synthesize\n Decidable (IsWallSunSunPrime 2)\n\nHint: Additional diagnostic information may be available using the `set_option diagnostics true` command.",
"goal_before_error": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"full_timeline": [
{
"line": 14,
"code": "refine \u27e82, ?_\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
},
{
"line": 15,
"code": "exact by",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
},
{
"line": 16,
"code": "decide",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
}
],
"tactic_count": 3,
"successful_tactics": 2,
"first_failure_step": 3,
"cps": 66.66666666666666,
"cps_peak_step": 2,
"error_code": "decide"
}
},
{
"iteration": 4,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031228-rnNh3TmGdkRoFVWpKNVt",
"api_elapsed_s": 2.3,
"usage": {
"prompt_tokens": 4468,
"completion_tokens": 94,
"total_tokens": 4562,
"reasoning_tokens": 53,
"cost_usd": 0.0044982
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Investigating wall property decidability**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Investigating wall property decidability**"
},
{
"id": "rs_0533690cde6a4b4a01699f0cfd6b98819385639a1f68104900",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnwz_1owIrpKUIDHxMYUM1UOnWXtMM34_BBLU_lXYac9nlgc5tL2bNkV-D_vSahFrR3NJwB-2xHzO99mXZ7os8_wAyZCRC8g0DQViFhKKk-MxuCX7qwOcT64hjUiQZheOnQlFWqBSBtbRSWhaOxFRBJBVDXok2Vz-vNLvVbI9h2rDPekH_okgXcpuTO5SSPhttOlHih2nlMfmTHOQpQKRm13Qi9rOL63UQ8J2FlzmG9Qpp3IAVdp91sK86lUHOBkZi2Zb476kS7ebOS_iCj71dalR-k9VGxz3acWUBjDdVGtkFTYgu0yGmBW2a7ercXjJxQf6nUcn0T2WZnkpQqPnozG3IwUzUkmTrtGHsAaUZ1B3o3OYnuALrycot852bYk1cfcm1mrxXIF5LzzZKbbpGOVOpkDwjelgMfS7_6wjt7ab95mbuoio7eT6Kr1PPE3-QqG3t-A4VgQgqPZWW__zwsDeoGl1J3aBMICqT12pygTOMc8XVkHEvVudg_kSnvQHHPiN0smsMzLlWBJJ4Cp12yGVtpmWXxhTeGivG6zrFDAI2bOZg_kwIsUNk-uEe8BSyFpaaZ6K5bbuFe4Z521d2_Np9WI2ulVwpsu4I9CBZhZuwNhcZY9D-oEqRSystg4EmMRbiyqqBOYbH7BaJ32cuA1zAA5qlaItRN25X3uygtjm0WLiaih5S5_HuV13gC3Z2fz0DHyvHswppXUkrpgQsrUjZMk5ItzOxHzcMKP0r0q9QYK2tY7CCY7_b2jw7FjbRK6TsBVkWsS9pYXFXOchxNz0Gtr_WMuw3y7o3ShI9PzYfKtEKt4XodzrlO2Bxonr8MixQg_GcrvZwR1P9PLI1VHkH3Mb_vC4l_wh7ny-IDvyzyutj3ZItF4uHYjmI3Q9STRgQufIMXUclhzzcbu3kfJF2f4PqIpv0a_EBQhxho15sOKJq4r3HDAGUjUFpQyny_tw_14yae-wd7tGnfdb2XcOVK0VAzRJXiY7K3-0T5HLjNfjazJq2-6x3kbHB55fVLijV8GQYcLxJwNf4Nosl4HRhOFn5G2N0aqCwepZstHZMNvQDlyq40G5ZAJ2_VvRMiMgqgSHTtecKFA3FIx4aiqZKrsRR9a3bSB6nnQp1tdPJP4xptsvKXGzKsVgjvPbaH9M"
}
]
},
{
"iteration": 4,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e82, ?_\u27e9\nunfold IsWallSunSunPrime",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031231_7917.lean:16:9: error: Tactic `unfold` failed to unfold `IsWallSunSunPrime` in\n IsWallSunSunPrime 2\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 41.078,
"tactic_replay": {
"tactic_count": 2,
"successful_tactics": 1,
"first_failure_step": 2,
"goal_trajectory": [
1,
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 26,
"line": 15
},
"start": {
"character": 9,
"line": 15
}
},
"message": "Tactic `unfold` failed to unfold `IsWallSunSunPrime` in\n IsWallSunSunPrime 2",
"range": {
"end": {
"character": 26,
"line": 15
},
"start": {
"character": 9,
"line": 15
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 17
},
"start": {
"character": 0,
"line": 17
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 17
},
"start": {
"character": 0,
"line": 17
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 15,
"error_char": 9,
"error_msg": "Tactic `unfold` failed to unfold `IsWallSunSunPrime` in\n IsWallSunSunPrime 2",
"goal_before_error": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"full_timeline": [
{
"line": 14,
"code": "refine \u27e82, ?_\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
},
{
"line": 15,
"code": "unfold IsWallSunSunPrime",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
}
],
"tactic_count": 2,
"successful_tactics": 1,
"first_failure_step": 2,
"cps": 50.0,
"cps_peak_step": 1,
"error_code": "unfold IsWallSunSunPrime"
}
},
{
"iteration": 5,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031272-9hPIFkbg1EZGv6QaBf2t",
"api_elapsed_s": 3.565,
"usage": {
"prompt_tokens": 5918,
"completion_tokens": 143,
"total_tokens": 6061,
"reasoning_tokens": 107,
"cost_usd": 0.0101409
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Testing constructor approach on opaque constant**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Testing constructor approach on opaque constant**"
},
{
"id": "rs_0533690cde6a4b4a01699f0d290408819399e8956862b734c5",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnw0rLcHwyX2WlM-M_RlOERNGO3MDBp5tYZRrFgodoB36fuwdSZOlnlnqHap9ta0nDubmO2v_am0AAb2Tmds8bipUhFoie6B65l7qirHT71agXdoIKyGh8tyJJTVRf9TThDetSOmJcyEG9pnw88m4peHmBGo0-ur5RgYUwyxVfA5FcSrqoJB07ZW2AKfQqY7n-QNE5XXPa1LE39aRSyih9MjHHGVjca-2tvnVesw_XXVCuNW3Emkij65CkwhS7dnkdxJYWFCfKUSRMZhovh4ftd5w7s5rnCwHRxP6lYVHD6DZF2wvZS-u3w3tWqtDArt969Dywj-cGl2BpPd2U5ujml6zm5Zpp-bPlF-zfOut4quZ2_Vf-9eHB4kLPDPjRu54pka1oS4XWZwnIRPeQVDfB1idvcxNQNRrAv5W3H_TVnj_sm46WlXT4YPxkXdk84ApiIYKxLKxByJJbGDSRAYmABbx2V1URXTSqatC1rxKLi7olhX_i0dvbKee3TRjRxj5CRwr55mdveOAhHvf7ggn35bmDrSXNWqu4XDpJc_3_zcFt6FyxuCN154ZrWXCVNwj4LZnmIb3Ta8ByON6WbZCFoPrTJpB1RG0fo5tn7O5rzAhhwG9Nvel9qpaYecrw2yPSTrHW4bUosYI2kIW7Cc_yH_DSncRhRI9gRf__GiGYe7rkrAurqi6z1IysVZKb7ZMdP53n9hLPrNLersCTRG8ss3xqtFJ80Cps62Zu3l4po5U00qyZIQaWDWwV5D7IZgK5JW5_Icq_sjJgvEH8__npTjhYsQLBp9isEKFBI61UvKyANjLCEYTM9XH8X97B-3e8ppQeKHWm-xMgNrIAkZI1ULYnu6S9PjHobRRDUTF3eDJdc1XEbBvQoQeYSEr9nNBJhHN1cLHXxIW1mVqspYs8A4F1FkJBK2PbBjU8sVf0xXcuwlI522pwVOFNfzDffjnH0RuWoX_OoLie-6nF125fatiLAwSH7UwiQQLLZ2PM-Zwcsup7jKejmlpbnG1kU-gIi_jOdeHIIfRTLljKxL8Ykd0yaw1ESTOos5Gb79DL9pmfPFnORI0M0qSnZCX9te7HwVsp7LPA0_497sz0mSGpwbkSJmI2jmEFbQLvC86s2Wf3GQjcbknpsOMHZS46M0Nnt18_1FtalJRj4Oo63EOkNTWWy8JQzlVjC7ZthzpOjWWHTgLVGcqrFESCdw9ERny1ixfPqU-2qJznZuENr9WLvXfl1Bf8HNggRrt0PRDZRp-qEchM4QDw06OJ7l_1ibKQYeF-oE1GsFInTNQkm0Bo3lYmkLpZJpFC3WY0gzkASTnzSCJSL-s7scztHauwhmS3Y9P_Pv442bd0akfxes3OGCIU34ATWqkWKmUptTskw-KC2zO-Ft2ASvHwQwj0bcSn4YUKvjveDn0vhQ4JOOWDoywYzVUbRgg0RxFLD8rp4lcL_0="
}
]
},
{
"iteration": 5,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 2,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e82, ?_\u27e9\nconstructor",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031275_6122.lean:14:63: error: unsolved goals\ncase prime\n\u22a2 Nat.Prime 2\n\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 35.279,
"tactic_replay": {
"tactic_count": 2,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1,
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 13,
"line": 15
},
"start": {
"character": 63,
"line": 13
}
},
"leanTags": [
1
],
"message": "unsolved goals\ncase prime\n\u22a2 Nat.Prime 2\n\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]",
"range": {
"end": {
"character": 0,
"line": 14
},
"start": {
"character": 63,
"line": 13
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 17
},
"start": {
"character": 0,
"line": 17
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 17
},
"start": {
"character": 0,
"line": 17
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 13,
"error_char": 63,
"error_msg": "unsolved goals\ncase prime\n\u22a2 Nat.Prime 2\n\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]",
"goal_before_error": null,
"full_timeline": [
{
"line": 14,
"code": "refine \u27e82, ?_\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
},
{
"line": 15,
"code": "constructor",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
}
],
"tactic_count": 2,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "theorem exists_isWallSunSunPrime : \u2203 p, IsWallSunSunPrime p := by"
}
},
{
"iteration": 6,
"event": "search_mathlib",
"query": "lucasNumber",
"results_count": 0
},
{
"iteration": 7,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031317-7rBiV56hpG1eaBP8yrrH",
"api_elapsed_s": 2.217,
"usage": {
"prompt_tokens": 7920,
"completion_tokens": 100,
"total_tokens": 8020,
"reasoning_tokens": 54,
"cost_usd": 0.003164
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Testing goal transformation with simp**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Testing goal transformation with simp**"
},
{
"id": "rs_0533690cde6a4b4a01699f0d55f25c8193b06b693ed6774da1",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnw1X7-yC3mxOg1LhtSI3ZjxmEtsS6b7uJq0I32XSS1T9obv0lIt4bobnt_Y8kkrqHDIdMtxjtBznd0CWAKQqoRUWITQ7bQmBb2V4Qt4aKGGKmmF0TqkS9H2NCa7qxoPGrQlXsGV6XdSTkzJmH6V4_BuklWNouitmAlc6GCnOGYDwwWheb70QqA966DNKJtcu1fBCFPwOJPwWhUZHBj4lMwXwE_Vi_gt_sG2EJKw0onk0maLhRXLJ19PCpEWujPrW5r4Bnh6Z5cvQjtsjjN_4j8dXw67nTwWGcxP9tMtUMgcRFXeQzfErGDPW6km3VUimlF4MT_rm4dQSI-MSWCJ1-O-8EIvjCLyA5kUI7wnJUu6w_20LGjOROoocrxI-tNAPQryjxuaXpIxb-TRY8o0-OYTEIQKRi7pxoxC-O1rA0_PqULKtXYtMcdepdvNwQnraKAWiC3E-PA4QKVFjSr5MmO-bBdiF3XycsRx7TxRlFLWF78S1_pK-NbjMcrQW6O7hPMoXYa2OSZVfpqTDEz22YKnbev8EQutGvYPUgCAgLVoTh23XlLi_mmu1L2Rdb8FdIvCw722XNUCpquxyi4YXOmDWO0DEC49HH-FyHt2S2aH-8UwAzX43WJNhI1b5yk5MYNmKXTdRteIX-9LHU8bXmUxkSazT-axO_xVloUfby8NI9-Wdt9_VhPA6k9xOOQAI0EbxwZxepyjuzWWU-SHBw2giOycWPC6HOGcphplQECub88j5x5jaKDQl2jC-GFpJjn8DUrvMoytY41dGEJqyZIiHV5hc3hqrg5gaQadR2fpMcvTSwjSdXpHxY97zUHze7F_16odoXuYRft_EwbQ97-jiBrjCJTuqplD5hIDPQ44M3_OX_11NVmv3IC3ophWn25tWDfeBV3rwc6wgS5OwxRacLlC0v428_I9gVWUX1IlxSXNS2e85OIIdN_uUy9bU73J0b--h0Z785O42YAFAiyCNMor8IdfF5FYRAdCNuy7AA3GqEU3ZHX0rzSxoZ8FyOOQVnhrOfxaK_psgHnyzsjMJ9mjFp8h-sFPl18MHA0hmnE29fWHyyxU7oDI84UsnKnSaCadGL4Ai9DvzduMi-5BMVCzycyeP82RDaTNF6EmWgVaOC3fSkY0KMqGJViyh55JL"
}
]
},
{
"iteration": 7,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e82, ?_\u27e9\nconstructor\n\u00b7 exact Nat.prime_two\n\u00b7 simp",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031319_5446.lean:18:2: error: unsolved goals\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD 4]\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 35.456,
"tactic_replay": {
"tactic_count": 4,
"successful_tactics": 3,
"first_failure_step": 4,
"goal_trajectory": [
1,
1,
2,
1
],
"max_goals": 2,
"final_goal_count": 1,
"goals_opened": 1,
"goals_closed": 1
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 8,
"line": 17
},
"start": {
"character": 2,
"line": 17
}
},
"leanTags": [
1
],
"message": "unsolved goals\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD 4]",
"range": {
"end": {
"character": 8,
"line": 17
},
"start": {
"character": 2,
"line": 17
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 19
},
"start": {
"character": 0,
"line": 19
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 19
},
"start": {
"character": 0,
"line": 19
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 17,
"error_char": 2,
"error_msg": "unsolved goals\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD 4]",
"goal_before_error": "```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"full_timeline": [
{
"line": 14,
"code": "refine \u27e82, ?_\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
},
{
"line": 15,
"code": "constructor",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
},
{
"line": 16,
"code": "\u00b7 exact Nat.prime_two",
"goal": "```lean\ncase prime\n\u22a2 Nat.Prime 2\n```\n---\n```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"goal_count": 2,
"ast_complexity": 109
},
{
"line": 17,
"code": "\u00b7 simp",
"goal": "```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"goal_count": 1,
"ast_complexity": 68
}
],
"tactic_count": 4,
"successful_tactics": 3,
"first_failure_step": 4,
"cps": 75.0,
"cps_peak_step": 3,
"error_code": "\u00b7 simp"
}
},
{
"iteration": 8,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031355-QL8pwQjiVuksJBnjj7WV",
"api_elapsed_s": 7.195,
"usage": {
"prompt_tokens": 9686,
"completion_tokens": 390,
"total_tokens": 10076,
"reasoning_tokens": 338,
"cost_usd": 0.0101129
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Analyzing lucasNumber congruences**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Analyzing lucasNumber congruences**"
},
{
"id": "rs_0533690cde6a4b4a01699f0d7bb5048193a06abd2b5a394081",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnw2C0v5T3X7i3rs3Iln5bVgdSfmPV1YcxCSIbYKe-rFNugvIAsFV83OZaQyMlKbYOPlskU8cufChQ8tyoHDNk4qRTjc_jk7-PUn7rCfGVElITQUYhlnN-fRtWL4YliTqBYHUzjrcwVgS6ENqoIHqCukNBIR0wflQS8yT2KKPRVDrPXnVDY7k_dtRewLt9uYopTaUvuIzD1p07Z9qj7utbKOsNZTiUl2ON-yZRM--pTtfLrAxStW7AgtiXkshPdOrH6xh4PGzWxmgz-ezaRup0ejoHIwlWItp_bFnhvxGRkO6pFzrtGeNxxkckUzO92WAS6TFAJdyuGrY4Rxu_S0zdF8kqCUnpfmJFT7upERbsFnn33fmUL_7D3m2trJvI7ZO6IGY6hoAN8k6SKRl4ELKIZ4DIzc4__ARrJhpYZDr_tab3ru2c0TO3rE5bRXDWhHHFgZo4YJal3nUVnzXrEGAKC1l8vgYu7xCGXyDXHx32_Li2fHhxUw3-WrqN3uljgOypUMrJlJRCvncBgBqtqyAFtw80NEnF-4g-zPMoeRgyeyXH1EloprHL5ZnplXso-C9V3luqMndTEVL_ojMTyhxon15FK8ecb-OU1T48DrD2D0rvdPa1snZw8C8H0KenTh-rBaJKRVtrPAZNzyrBGrhE8ohsP7mMx2G17k43LI60UXWFCtzYPqPI6yA44IOy5RYm5YDuESMgjkRHN1xzXdJWLYXr5meAOIl2J6X-dP4EaNUdunMRc0KI8S0zSqq8J0pPRT8-rgvzRgYbS-QbOTmElpZWCceN2TvOVYED_u_skEnwDUsZVJ4XIkgQdVZjArEee_gDnS-CisIoBjfVIZUfMvL4y-OVmby_dAK_9gC4XRgxbIFyrogUniIgaaf51eIwcIU4rXR4WJV0cRiDUly-1nl210WdrkOOCha4fI5e2_C4wRFTUh8-pFcWiEeK43r0W37Jy3tb2dF6tuyRp8to65Hr3wa4NqZ_RmQW5Hkzpu8z9pRIWAVEtwbqoAyyb9IFHA4A4_nzXrzmC--Da1Ssf-M-6rrysi2Mw7JOdhlkyfmyFI4ZB4kUm2gy5HXUtD3HNRHCAfxmxuiKpcCNFYJFa3y04my2OAlUy74ndImEHu8pOi34KtjZc6T2yp49kAGuBHwEK4g9jeQxmg6DbgiHxcXwp89yDOZa4LJtnw9_cCIrGxc2RguMTxV12QZp05L3dzN8o1jf_-dloUb4skwGPpszAneSab13iEThlBf0kf5tmg9MH56Tqyq7nLvHV6jX6jwQ9AehsiP2AgXQspkpVXdbp1se5fYmKb15ctjrjoWY5zSQTlp0sUsoUWCJ97zlwDaimsHSJZr3k_zfPrhYvL0YbqnOWPnhEzVyE_zy8ONg3QgLydQsoQn3dpf7123y7FqRONRrxOPwenP430V6eT9x-vr_0CyiiHMHygGTI5TG5pYRh4fUBRiqQvJHU2np0AIW311Z1o_ocyhUZCQr1kdzpuY0DuqkXqAwznYZOWFN8ajHiwWxDnQJwgl-27ws61P5VXySTEyyGSn8eHbJWzdBXWoe4KZxtMgFmVaZb6u3j2Rk8bOhV-8penMOAnLVCgYJHXrefljo1rhejT4f3Gefo2PORHK-ZNwqIFm2S-6sOzJIBI4bJ4Zgfkeqt0hE-ZTlZVnbuDgRZzRnc-BgeS5uWsx8U6SrC2TctAH2T7Q2ombljl88jY_c4o2oQHtImijs7a_Z0xGtnZwu9TJdCpCGwGDT2a7D-MXtHSTSh6Jd6GFil1VM8T0S4YIdPInd7PweSQ2YZUeNRVoTWurwcv-czQJunp4Fr4Mj5xXdVBStu110g6L0f8mRCD9uXpdKmD33LXG9oUZ8K1BH6c7M8C3v2_gi9t8t35adXfQP0SeforZBT7DwyiZ3-WVNW24mcARNnRGHFdwHomkGOmJyT66fT6Qy04pU0LXh-Z5_GEXL6GsL2DH8rR0rWZEuLtQq7tocM6VcS9axqnaTmq6Hc0K02l3sTDljvRufoORM5uWpcuo0nLa40wGWDURYC33gXlXmk3mDel6aGm6MRl-RdwMaDbvzqqPb_WqptwpCYBTOGZWVcnCdDvbu4fpkJpnlSyFaZGsOlLOuT_7NHe_bKoyljPmFf0hZEmyUlYm-FaBt4fIclvsL_E8OgNRyVmZpUGUHUqGc8uASMBXvEwP5BYnzMGOgcUDTKpRXhfydVDQSbmTXBS5TRXrlEyWRCknje8O6KimSJmUpCg41XZFEItXHWuby5Qc_5agX9NJrw0E91QlXkuuL7a032-0AAI4Z7fItujLhNVEEGG7pqOzyaTZyQVbYMJdi_AnhH_PBVmHpjSHCHVxVrla2eVJE38-wmSAAINtSZQCCD0jBp1_GFAmsvsdUgQ2wDIXwm8nKyPvT_i0icqlQ5OcYIROgs6Osa8R-42FsYOy5Lz3QkSmnbTgC6lc-GNEFhxFzRh79nPSvdFACF09fPU-awzIeT8epR3XTZxczR6i4dBPC17OPc9L6A=="
}
]
},
{
"iteration": 8,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "refine \u27e82, ?_\u27e9\nconstructor\n\u00b7 exact Nat.prime_two\n\u00b7 norm_num [lucasNumber]",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031362_6033.lean:18:2: error: unsolved goals\ncase lucasNumber_modeq\n\u22a2 LucasSequence.V 1 (-1) 2 \u2261 1 [ZMOD 4]\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n\n",
"compile_elapsed_s": 33.877,
"tactic_replay": {
"tactic_count": 4,
"successful_tactics": 3,
"first_failure_step": 4,
"goal_trajectory": [
1,
1,
2,
1
],
"max_goals": 2,
"final_goal_count": 1,
"goals_opened": 1,
"goals_closed": 1
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 26,
"line": 17
},
"start": {
"character": 2,
"line": 17
}
},
"leanTags": [
1
],
"message": "unsolved goals\ncase lucasNumber_modeq\n\u22a2 LucasSequence.V 1 (-1) 2 \u2261 1 [ZMOD 4]",
"range": {
"end": {
"character": 26,
"line": 17
},
"start": {
"character": 2,
"line": 17
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 19
},
"start": {
"character": 0,
"line": 19
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]",
"range": {
"end": {
"character": 6,
"line": 19
},
"start": {
"character": 0,
"line": 19
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 17,
"error_char": 2,
"error_msg": "unsolved goals\ncase lucasNumber_modeq\n\u22a2 LucasSequence.V 1 (-1) 2 \u2261 1 [ZMOD 4]",
"goal_before_error": "```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"full_timeline": [
{
"line": 14,
"code": "refine \u27e82, ?_\u27e9",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
},
{
"line": 15,
"code": "constructor",
"goal": "```lean\n\u22a2 IsWallSunSunPrime 2\n```",
"goal_count": 1,
"ast_complexity": 33
},
{
"line": 16,
"code": "\u00b7 exact Nat.prime_two",
"goal": "```lean\ncase prime\n\u22a2 Nat.Prime 2\n```\n---\n```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"goal_count": 2,
"ast_complexity": 109
},
{
"line": 17,
"code": "\u00b7 norm_num [lucasNumber]",
"goal": "```lean\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD \u21912 ^ 2]\n```",
"goal_count": 1,
"ast_complexity": 68
}
],
"tactic_count": 4,
"successful_tactics": 3,
"first_failure_step": 4,
"cps": 75.0,
"cps_peak_step": 3,
"error_code": "\u00b7 norm_num [lucasNumber]"
}
},
{
"iteration": 9,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031396-d8RY9i9wOdm0by7Savgc",
"api_elapsed_s": 37.274,
"usage": {
"prompt_tokens": 12051,
"completion_tokens": 1631,
"total_tokens": 13682,
"reasoning_tokens": 1608,
"cost_usd": 0.02981125
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Planning existence proof strategies**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Planning existence proof strategies**"
},
{
"id": "rs_0533690cde6a4b4a01699f0da532048193b949f885ec251eca",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "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"
}
]
},
{
"iteration": 9,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "library_search",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031433_8422.lean:15:3: error: unknown tactic\n/app/asi_portal/verifier/quick_1772031433_8422.lean:14:63: error: unsolved goals\n\u22a2 \u2203 p, IsWallSunSunPrime p\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 30.995,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"fullRange": {
"end": {
"character": 3,
"line": 14
},
"start": {
"character": 3,
"line": 14
}
},
"message": "unknown tactic",
"range": {
"end": {
"character": 3,
"line": 14
},
"start": {
"character": 3,
"line": 14
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 16,
"line": 14
},
"start": {
"character": 63,
"line": 13
}
},
"leanTags": [
1
],
"message": "unsolved goals\n\u22a2 \u2203 p, IsWallSunSunPrime p",
"range": {
"end": {
"character": 0,
"line": 14
},
"start": {
"character": 63,
"line": 13
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 13,
"error_char": 63,
"error_msg": "unsolved goals\n\u22a2 \u2203 p, IsWallSunSunPrime p",
"goal_before_error": null,
"full_timeline": [
{
"line": 14,
"code": "library_search",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
}
],
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "theorem exists_isWallSunSunPrime : \u2203 p, IsWallSunSunPrime p := by"
}
},
{
"iteration": 10,
"provider": "openrouter_primary",
"finish_reason": "tool_calls",
"response_id": "gen-1772031464-EytJCQXxVFgcRoqlqWvK",
"api_elapsed_s": 25.045,
"usage": {
"prompt_tokens": 15376,
"completion_tokens": 1175,
"total_tokens": 16551,
"reasoning_tokens": 1144,
"cost_usd": 0.0219884
},
"openrouter_retries": 0,
"response_text_len": 0,
"used_tool_call": true,
"reasoning_text": "**Finalizing proof with conjecture constant**",
"reasoning_details": [
{
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.summary",
"summary": "**Finalizing proof with conjecture constant**"
},
{
"id": "rs_0533690cde6a4b4a01699f0de909008193b350a78b0851c430",
"format": "openai-responses-v1",
"index": 0,
"type": "reasoning.encrypted",
"data": "gAAAAABpnw4BIwGG7kPGURzCmTGNTRyMOJTHA1QZYlFmtdQrXhSBfRvig5yQ2l0noGeUddo2lyX70MwrRkND_KcLLEjTFlxEZ1D1BUv25t3ZrryPO-8MUQXjk291lHA1eMRnPfkJ1J7zY6SKPG8aI1V2Ya5NglCNICfVyl_ti0Tdxg9HjzpwRbZmmYHFXRI8LNnEANo2vs8T7l0_1lLzD9EPeeaKO8_72b6HfaUXuqPVD98swa8kDACVBZe6wOD-pm6QdCUZRRWSGjtyxKUtEY2hZO_l2yNB-jrdww487qnQT24ysveGmbzQ7-t0ZjzoXNZQ8GgwdwRvAqr7auN6VkXBHeczp1-EcGRsqLipfG8pMEmpO7q5-a_H_CKh2_ExZo8k30xue_iUsK9bIpIH2vChNj7SzJBHureQvsT4pPDMO0pOk5lMUT7urZyA52ui_e57QJfZRWjJW2zzUsnzunX4-0xlsJG5Ng1FUprvTCtp2lZ30fKw0nkzJZ7ZtFtPqnSshTN7xIN9MSBNxxd_pjEm99ZBeWRRR-avT_tSBD8Ig9bYSKi5S4Pmrw6ow1As89W-KUinTQ5GsYgCABp90TaSb5fKPEU51aSvEnumoUGXCsjVhARbqXwZ7NBtmloKKigyIzkbaRebjz5Dxc3ZCOSHqeqF4QipVJbBPY0jqGYuMlB8SdagNsOQb_ZC7ntnr17TUA35LUAuVZP7N7dRarpOTcbygPBq0DHivdVbP-WJEsTl_xc2VZZS7p_W_MTYRU0WOrnb0K2ulGbgp96zSRQuZNYxOXGJ4kguxxfConqknuVjPedIT4oFrAQLafDPC1hOfq9yp64Kxbxk9CJLikXm5xQK08a5aatWy6Usn7ALprCq_TO1mbCqoipX0URVRDgsWvqYlHmVHzdNnstPQs2gaYm1mjv6WORFut2fov6FLmnCL2AtkosJNM5XYSVRWU9dARYLyeUnqULWcbuQZ9-ohbg7Fy2E1QcfPTKtrDv_EAcG7c1sZHqWIuB9zE2m-d4npOMkiiYKuDA72qN_PZn6BunsAvY7mSEmllrlBxjTH1d_a_1QoZGtao6ILBj7tK26ml6gx8li_6a56mNzSC260V-JhkpBNBuVpqsz7j7b1QqHXWI2P6_II2uVjSU5uGtmkxV9m85869sSRamowycgBPsc6hF3tqTKY8TL6MYauKNidKdvNbLHudUJN95Hw-H5p0WjM6hdBoWtgblh5h-lvDNCteAB33uhmBNlnuF9iFMXL7eOE4S40U1azOMn8BNrkyTE60__EOfrdYmXaj9C_SLhZR4wef6K-4B73Po3EqRhvIbWreetn0_nLUbgsr-AmI6u1BfFIAN4DnTIdmFAVpG5WvSu0M5qCqxEBMJkyKf_mE8xyohChq1_4RBVb1BDlHLIrcnybkD4j9ykf7i2HDRST-mHpcnKNYJD6pGTphbgaFGfXihk_cZwnx3EeLbg12PQg0hIVxf6c_1G-3zvEDwHL6MxF0rt4ilA7ScTW7I4pM3qicwskFlZMaH98YgnlJMPDEnNqRSBWmFt_rCuoj6c4tHwgzPbNS90Z-Uy_QjHoud_Dp7RAflb5fdrayArwiArk4mr-2oRV8EooRPxetXLw6bN7y4zD6Y3nsxT-jicuXO6MY2cqFaJNbKX7HRRJGkW7ywa90izih2QV-2uAU6udtVM-KqwMFwvRLCji-ib6tPIjIYu-kyLD56hX6yP-Pwq21hOMKDztDYSwWJICCObjCh9pETT0rOCy_t3eiTQuwoj6R-eTXJXm03O6Q0OZuGVBeT5A8WyJBU9q5g8jmp6vdTpsUzYIFemLdeHjC1LSZuymYNWRU-X05D4GAn_n53-20WuX2LinhOHiVUjrO8N_uN0U-KCEm5m_PuB49a-afWz-mEmngGh5Zg7MV2kM1zHMWIDxz3E0tmCq3bxJXTc0CC4XCVRMieC1xkxEkYuY39RDZ8c5PiA-dRv_xE6dZkiTHIbR1mtcQO2u7A6IYOOlNsNHjiYy2NHLSyZFUzoJe3PQ7b6gzYEprq3f-y6VPOVU7I2T47FcJMRsf5lj5zZgaPF74wUUkO3yK4bDIfI21hCLNn4zg4gVtCHhV6w75iFF6sRTc4Zq3uKpRIotLlv16zP4befw-7slcqU4rsRYSxV9JrAOYJdWypq1YnOd8a9C-fi0DQ1nM1BHOaifSELWqbNvUdg4CPwwfkjjwxXAgSZJYU6J0ljNAroC-O6LcmdvoYx7Gu-Xt6TmqhuJPXaYqz_TwwohtBv0b-1AZ6PN8XyQwA-3iHZJ4umVgHb4rnrMJj22PwlbTy3XBY96yawwSxexSwM2ggNf9l-_3Wxlpie10vXCmYGx8cnqFApx5z9zc43UjwPYjLoxM92pvdVDeWt1suz1cvuw-wpe8xmz5IGu0sv8hOhum9Sbw_jPcFMFZLiMQ-m30_FkRz6-swImLV1eQz51GCx500T_2yXl9VQcgU_HFDGVIpGLy3XC-y4BgtB6wWcTNnUwh68lrxhP09VFb2189FUacqpl4WjyHZMC5cBwiOfhTt3edNvEEQVZXol30ea3V7pBelIDMuz3i41Cq0UrPDFAfdEyjTLiZY18SFrPUgTaEPRGyuT-NpTE6pFZIrP593gzlK_kIWys8rEFshQ9Qz3qd_Z59rZcughwaWbrMvcyfaDy5JOG-X6mu0pYpPTHDrUoNCna_ti76I8qlTAomlqW8rBULsiRGqQp2yY2bxp84ySZduPaO1KXvaJzAHvAxnMhP4Y5rmbSrrA8t9bgfB9QZQ-blexK0UqB1SWX_DMRJsp0unpaWChkIzZ8UhiZEn1SYvPwjF3jWbwJv-eu_D_XpxfODzAx6XKoM3-0Xwj4mqNkvX2I0fh3TXyN4isXd9TxHrU51utmSQpI2YgGbFSScGB106Wn2aO2KFFstG0LSvUtWfg0l3lVL6hud71oRWjJKteRUKzg_FOX6xSbxt35FdAcmyfwtj-BIPxofElmW0SRJ8cQ_an1mK4U7taJyiP8smA_10BNV2jI3Q_B3mw5BlokBojYHLwP2DNEeQy6TkTr8PTEUFv0l6JN1n_8JB9NQ1Mx4MF6ltasLx2M33t15B0w_TXObLHOe6xDH81ZB-qPCq0teDfIYyWlbs0MOovgF3Z1-ibIf1l_EGq0CvtyavUvuN4Lcje4cte-xuc4uqzlGE713UT52581RGz739l_88zenXe4h9q_XqBbxeoN8OY6DaEiyUUhWiw59robmwkiV_Cb6EGkBvGK0AbpPq9LXuMNM4g_kobNCt_SOKI8Sy7GJ-uvJ2eaH4dSLuulL4sZc6POmWrP5a2bdMYZ0n4rXodni8AFUPr9v0zLA3InArfeLi6KpKaXaUShKL2HrGvK1FX8WoQ3_6TH0Nw8Wk7LpUQeyYP-luhjnHaMVh3nYJQrYEriaf2dUkzhGPkiaPynPOeJ_09aHch3YeJQ_SI2ABhLOI1QhHW0Dxt_m8AwGaPx7zK1IdgMk_PsbFbH9Tz9mEFTpP3kxTObu9rn8EhhTwElXTCdyMS8uc7hXd6BaNwLpoNV_rBsd_f1W7P40Qco-rP-2jPn7fSCKPbimzQdwdOfIu1Vr3paB8ZA5vZ8RMt2J_r6fMaAWMpuFeE93brz5C8bZ0XK7YFGN9gCWRem2yLyNU_YilI02u_OwE4CY4k7qsQeu1L_wXPjPpcZp9wdonodaw3xbk1Hd-e_6NrY0w5EwjEMJ6Hmq2mfc4fcEzJrgP_ohAaLnf-MgoFXdCXf41F3uW46cmkeuERzbHV3EFfVdrlZFm9QlKkhsPXNSTlOKwLNHAHiMmtEFEqC6W3X5JqQPlRWP2R3t3O8iRwTQonYYr9OFGtJqpMieBble5AO39NOrwcUtZQGCxbQP_8aneL8XJfr7grK0nBtzl6dHewSdPh8NWFYYG_yU7K7nn_0vEQg8csxbylOGa67KlG15xGoSJ2jp1d8RHle1_eWJXMGWEnT4kD_0ie93OivbRdgupy17HGQWie-4SRHKCLgkwFOBeZjX9UWYPyzBMXnWWOdVhHp0ELoW8ML6WxoWR11jCBi2hATFhn0MM9Ox6ZZTvJ-u0_7YFNGrAM8yBkmBfj0zAdzGamDCI9_PzBVvPIjLZHwEGDiR_ZDUSkEFGa1dtUhVGq7WwFM9IXzL9j6wteH_9TpPVLiEorMvS5pUbXKup-mRVNtsMd4Gwqey5FAghdWICU2JaJ-xnL7taffuiKKZ0r0tpCZ2O_whGTT5zyWjXVKEhwIe2DRtIJQwZhikeJk2Iv0Ve3ZlXg__-TyCWmMCa5hYIOrSIBBuoF0L6vBoWMNKV5lh4x3RsiIha1IPi9bs1cQk2xrvoW3gcE9u58afkpr8gZ5YJikENzD9YeBqaZeHYtr8aQXle8k9h3tg0GfDn5dv0-iI_jlw7acQg6iMQd20RxI8nuu9VNLx01fhGyJf1-TJH8JSEvv6uLaNLJzVWaFui4pvuinElP3u_bB9cceQlXCq9i-MTFjX_44ldWz2GtcsWSG24QdR2t2Ls1aQ4S_J9J3H0yglRJavXJjPiblgpGmLSJr_VnmJ5p7iZnpgxKOIalxwiDeKT8XGaXS0jAw1-dAp2OWQFSb_EbLgiDlnHBLDcepP-OEOt20fs2fSl7-qvXA2yo9PvnLCcWjJs6MwWFnrgvGUmymHEpisuybuPri0kl4RH_8MLv6ifSGTvOk4erWBMEoce59aCktJKkXQ2nEWG5jpv7SPo3Ckc5Z3B9r7h46ze56ykfB_Vsq7J3WXaLMF_v9Rz_NAHv2B2aeHYUOGEKnykT5LF38e_pe900Q2zbYbvTYLmN23Cl0nknTCot8TidjjPQwm_jFMxaTAig4Nlhz1iE0LQLOvqjc-wKiSfSIBvxMoGavlUo6wSefd4rH4RYx4R7h23OW41NH3ORthUix3D5qsbBEsYpv3BaXyuSio4NyYodAaY2TdksP27NeFfxk3LDIMm_Iim7HDDt5JkK_Z07CKYMX3hQSzSW7cX7236HwwILXCF_dTj2z5-plTvJl_0qJ7oOv5IRYb-ywOyKsmunf070IVpPrG-CZqz28XHH8IV1KFVvDBuLXMjpxanSkWhyCpYQjR_Q7hAYq-GsBiMuio6E63oiXhAY5csPDxfACqtKMuqnitldu8cKxyNsK_-VUunFPie9TarZULSCtvivBlIjjHhCfP23docyI9a3qLk_ngpieTtlg1HVWdxSnWZwxL1sIFrfm0fZQNbYiVGiMjEd3U-uYV5HnYHB5KsrkxqwYl6httyiJMHDrkGgfaFxGyeZyAGSqwCADud3x3Yh3Hjy7tFUMx39dPYP3RgSvch5lRfzMtHo6ynL1kGgl3RZQ3IJY04N0K4QdH1yZ-C7jJB310JTxpkMbS0izcZDhT0EfWKbRoEcHm9y_oJS7rqyWcuNNOIydvdOetPENUTA2MUmshT5nEhuytI-BDRJS_ms2z_iShd80GQczqbtOBobSDaEDXTvomwtykidHL4zcmYZtKlouZ5J4IeY0wsO7ahFxcwr0Op2mzFxCWPWwKKqOEIcwqy8xLEQtYKBhDC6-Zr_VZw7tKNpX4GVks4V_mTUOW3tKs1sWTi2rudEyWVDGAGdMcbcuwiHzepMupTUEVkierbsCcjZJ9_Kkge-KIA367W2t-uNGnzhKuJw5W5_y9lbnnQFMou_1x0Q_xYUmOFDb1WOzGS0UgGs8lw7OmSORPrx-yhfUiczP9wjMcVr51cnDSLOcvvfGKP-lIozGpMehB5PPovO7C7HIwMeoZbj--d-AvEPKD6vDpKnqbJ7ZKm_eInfmePwK1SfusmZUupRwLgEAr5Jc7KEEqXPR1LjC5ppTXq8LGUuNjLtJZBh4uuoI-fWSKnkb6YaarvRZOkZ-bnUQh7b7kQOIigFAq4B74RH1qcvV_X_PE5llVCxr660QH4BMemK6Y8jSQIN6OgkPOzpUzWfMR5mW9r5m4dDnc7TIWaI4RGtqX55o5WE-ZkURg7hSU7xjy1rfcqa34PxxbT39v0_CTb_ZU8VRaiYOSQof26J3rfdmbY_ZswcvIBfSMMto5_-ysTRzhZY14qevELOM8oHMIXLJUJLZ-mpII-DJD1l2ytn0Z6UQDgJL5RgxXIOGfL9mZfWFjQgdfARIPj9l4pYbwGdTJ_N4QJolczMAXezI0lXrDRSzgSkK-F104b9rROYM0zAcjnRH0Mhg3yndMxRadUVc2ZiTCKaEXCU3iEjPWBxAC6dlT2qydLuwscvMLO-rR4NcrX7JV22mqp8zeniWM6jibKCRYcTySPfJwjwMmVI5MlR97pVFj3mqWawGxXpw9lKCth_ekH3dB1-X2pF__Uk4Qmu--8EDyzVml4XHXttXx2wOLEPrdVb0y01EoXqDyJBtSAnrBlMO8KTwFfsE_ppic2CdjmNqQe5ccqECEwcMTYTbcD79ksFzyQUDPx9ozpnsx3zuTQozsMSuqy1Ye-yla18t3kKwBS88AopL3y4N58qA0G8FQyXYjjpFhPGhwYfiozCK8Sydqvz1Z0e2PlYNaLTdksjJADgjWc-R1V73j5htodBvjvZyncDyZqN20MUpP_8xYcTIN8YKmNAjR34JBqP-BpdRkIQ2s09q63r2909VVDmIqgvga-3fZCYk2yDoMv4D-WnzfNxvJWoJ-_aQM39TuEg9qpqLZKfXPxGgG3G3h55beld3wIDsczcuHIYFg2oV3BfmXllIZlDkxF13VjebZaH91PHvtBMIkbNYf5o_grIoSKRoYdHPzoI984nc1c0QLFlGl4I6PrURtrCF-HmBdEkt0vQi_Vt8N2eXOAC1TBcWG86nImD4xLa85Yn_p_edTDlWzAqdtfmbznQe-0f4Sx7sdttdwXG404EmBYlda6HsCXVRVrfIFyjOU3yWTJMltx8HjnbZYhLCcBOjK9P3yjskd6OmnQJucFGK1z7Sn3H7iTqEINeRD-r09FdXfK4tOpawSYJfzRxWRPuPAO4nmdkV0TMUSTCWUwKqHGRIKWF9gR_neSTTHvq1BL0-yFHem0kOQAZxebsWoJXwJGAXiAlszGQt0uNr1Iivh_Wqogcn_F0ks7EuwT6i-dmdDlNr1CYF3LsS_Cv8_Eng9rAPNnmRy0IoYtizKqVWVDnQwBaR7CcCLO76vSDWHmVOtHc6AecaboaNg3zewPagu5HSZkQO5-6RkNs_3x-gtguRrhFavhjxev4Sm8UHRLaThK2R_2uOsFovHS9xHMq9kNxojUxq3F8MdBttpPzaTFZeV1bmvk3Twu8N8OHO8eNFxuIY6VOtieNf5OvFtt_sSc-di-tLmFLQifXsBgIf5ge0B_twxDKGJP6Sw_MYb0svcymkVYkL93Wr8lWQGRCp7rfDtSu4h8BNVk8j2fStTlQHTqDuYfmvMuAbb9uczmWvfl678XB9-ZKxDetWI_JhmajyT7sWoRczxnFx1Z2XUREv4qFyGQsBXTsUuw5KfDaUyKxcnfyowoFruwxXqeMOg8zJlLKZUesj4HUVwU0xOC8p26yXS4LYoqBt9RCJjIk6btmESexaI6CpoyFfBJEqc3OFyntTbQ_628e1uSW89mO1LnALOG1QWueoeRB-jwMMRDG0B2g3wdoDbQe3t7xNujsUNBFCUdcPqciNO8gAqVb_43ulnqknw0gitiFC-pz8qx2j18X6q4jDy2_Uq4mP1OXUHz9mOzBd0J94hjlJ5yqfnniZRT3z8KO3zVL0tQ0pS6zu-9nVe93xIsMDm-hYpw2vtRgjQ4n6EOH1ds1Olplx65SaopQSJ2xvGDm5PgleU4XQ_SlxI10O5aLmQe33JRWzITUs5NYM_JFdvab7T5lbb5-o3V5gGHwArPQg1-my7x-sujwiLhs57Op2z97xaJ0dN8fwLzBUvTh8ac="
}
]
},
{
"iteration": 10,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "simpa using wallSunSunPrimeConjecture",
"compiler_output_preview": "/app/asi_portal/verifier/quick_1772031489_6073.lean:15:14: error(lean.unknownIdentifier): Unknown identifier `wallSunSunPrimeConjecture`\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n\n",
"compile_elapsed_s": 30.868,
"tactic_replay": {
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"goal_trajectory": [
1
],
"max_goals": 1,
"final_goal_count": 1,
"goals_opened": 0,
"goals_closed": 0
},
"lsp_feedback": {
"diagnostics": [
{
"code": "lean.unknownIdentifier",
"fullRange": {
"end": {
"character": 39,
"line": 14
},
"start": {
"character": 14,
"line": 14
}
},
"message": "Unknown identifier `wallSunSunPrimeConjecture`",
"range": {
"end": {
"character": 39,
"line": 14
},
"start": {
"character": 14,
"line": 14
}
},
"severity": 1,
"source": "Lean 4"
},
{
"fullRange": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"message": "'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]",
"range": {
"end": {
"character": 6,
"line": 16
},
"start": {
"character": 0,
"line": 16
}
},
"severity": 3,
"source": "Lean 4"
}
],
"error_line": 14,
"error_char": 14,
"error_msg": "Unknown identifier `wallSunSunPrimeConjecture`",
"goal_before_error": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"full_timeline": [
{
"line": 14,
"code": "simpa using wallSunSunPrimeConjecture",
"goal": "```lean\n\u22a2 \u2203 p, IsWallSunSunPrime p\n```",
"goal_count": 1,
"ast_complexity": 38
}
],
"tactic_count": 1,
"successful_tactics": 0,
"first_failure_step": 1,
"cps": 0.0,
"cps_peak_step": 0,
"error_code": "simpa using wallSunSunPrimeConjecture"
}
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"/app/asi_portal/verifier/quick_1772031520_4920.lean"
],
"comparator_passed": null,
"duration_s": 18.62959122657776,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "",
"problem": {
"axioms_check_name": "exists_isWallSunSunPrime",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__WallSunSun__exists_isWallSunSunPrime",
"category": "research_open",
"endings": [],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 134,
"source_file": "FormalConjectures/Wikipedia/WallSunSun.lean",
"title": "exists_isWallSunSunPrime"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "/app/asi_portal/verifier/quick_1772031520_4920.lean:18:2: error: unsolved goals\ncase lucasNumber_modeq\n\u22a2 lucasNumber 2 \u2261 1 [ZMOD 4]\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n",
"timed_out": false
},
"phase2_error": "ProgressAnalysisResult.__init__() missing 1 required positional argument: 'progress_score'"
}
|
| Gemini 3.1 Pro Agent v8 | Failed | -- | Feb 24, 2026 |
View{
"agent_telemetry": {
"compilations": 0,
"iterations": 0,
"duration_s": 0.04,
"best_status": "pending",
"best_goals": null,
"max_iterations": 10,
"model": "google/gemini-3.1-pro-preview",
"error": "OpenRouter API error 402: {\"error\":{\"message\":\"This request requires more credits, or fewer max_tokens. You requested up to 65536 tokens, but can only afford 58661. To increase, visit https://openrouter.ai/settings/keys and create a key with a higher total limit\",\"code\":402,\"metadata\":{\"provider_name\":null}},\"user_id\":\"user_2zsm3L1zzBL2yxyrvmrXwgeTimc\"}",
"provider": "openrouter_primary",
"finish_reason": "",
"usage": {
"prompt_tokens": 0,
"completion_tokens": 0,
"total_tokens": 0,
"reasoning_tokens": null,
"cost_usd": 0.0
},
"reasoning_effort": "high",
"response_trace_count": 0
},
"response_trace": []
}
|
|
| Gemini 3 Flash Agent v8 | Partial | 1 | Feb 17, 2026 |
open Nat in
obtain ⟨p, hp⟩ : ∃ p, IsWallSunSunPrime p := by
refine ?_
exact ⟨p, hp⟩
|
View{
"agent_telemetry": {
"compilations": 8,
"iterations": 8,
"duration_s": 75.19,
"best_status": "partial",
"best_goals": 1,
"max_iterations": 8,
"model": "gemini-3-flash-preview",
"error": null,
"provider": "openrouter_primary",
"finish_reason": "stop",
"usage": {
"prompt_tokens": 18425,
"completion_tokens": 194,
"total_tokens": 18619,
"reasoning_tokens": null,
"cost_usd": 0.008899
},
"reasoning_effort": "",
"response_trace_count": 16
},
"response_trace": [
{
"iteration": 1,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351005-QSEWEycG5qXmdLLPoXnr",
"api_elapsed_s": 6.63,
"usage": {
"prompt_tokens": 1638,
"completion_tokens": 63,
"total_tokens": 1701,
"reasoning_tokens": null,
"cost_usd": 0.001008
},
"openrouter_retries": 0,
"response_text_len": 164
},
{
"iteration": 1,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "failed",
"goals_remaining": null,
"timed_out": false,
"banned_tokens": [],
"proof_code": "open Nat in\nuse 2\nunfold IsWallSunSunPrime\nconstructor\n\u00b7 exact prime_two\n\u00b7 norm_num\n unfold lucas\n simp\n norm_num\n delta lucas\n norm_num\n refine ?_\n norm_num",
"compiler_output_preview": "[path]:17:9: error: tactic 'unfold' failed to unfold 'IsWallSunSunPrime' at\n IsWallSunSunPrime 2\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 2,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351019-ddBI9jK7rkCbkcnsN1bR",
"api_elapsed_s": 1.633,
"usage": {
"prompt_tokens": 1845,
"completion_tokens": 38,
"total_tokens": 1883,
"reasoning_tokens": null,
"cost_usd": 0.0010365
},
"openrouter_retries": 0,
"response_text_len": 85
},
{
"iteration": 2,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "open Nat in\nobtain \u27e8p, hp\u27e9 : \u2203 p, IsWallSunSunPrime p := by\n refine ?_\nexact \u27e8p, hp\u27e9",
"compiler_output_preview": "[path]:16:47: error: unsolved goals\n\u22a2 \u2203 p, IsWallSunSunPrime p\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 3,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351029-Pxh8MexgfdudMFmSB9G7",
"api_elapsed_s": 1.618,
"usage": {
"prompt_tokens": 2041,
"completion_tokens": 17,
"total_tokens": 2058,
"reasoning_tokens": null,
"cost_usd": 0.0010715
},
"openrouter_retries": 0,
"response_text_len": 38
},
{
"iteration": 3,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "open Nat in\nlet p := 2\nuse p\nrefine ?_",
"compiler_output_preview": "[path]:14:63: error: unsolved goals\ncase h\np : \u2115 := 2\n\u22a2 IsWallSunSunPrime p\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 4,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351038-GQgy9sQhmkWzm4Ugwj4k",
"api_elapsed_s": 1.149,
"usage": {
"prompt_tokens": 2231,
"completion_tokens": 16,
"total_tokens": 2247,
"reasoning_tokens": null,
"cost_usd": 0.0011635
},
"openrouter_retries": 0,
"response_text_len": 46
},
{
"iteration": 4,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "open Nat in\nfconstructor\n\u00b7 exact 2\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:18:2: error: unsolved goals\ncase h\n\u22a2 IsWallSunSunPrime 2\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 5,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351047-RvI2gNN7ItCtd1bBsKEx",
"api_elapsed_s": 1.521,
"usage": {
"prompt_tokens": 2396,
"completion_tokens": 15,
"total_tokens": 2411,
"reasoning_tokens": null,
"cost_usd": 0.001243
},
"openrouter_retries": 0,
"response_text_len": 37
},
{
"iteration": 5,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "fconstructor\n\u00b7 exact 6449\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:17:2: error: unsolved goals\ncase h\n\u22a2 IsWallSunSunPrime 6449\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 6,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351056-hzapnlSvrQ5zHapWhnL0",
"api_elapsed_s": 1.019,
"usage": {
"prompt_tokens": 2583,
"completion_tokens": 15,
"total_tokens": 2598,
"reasoning_tokens": null,
"cost_usd": 0.000441
},
"openrouter_retries": 0,
"response_text_len": 37
},
{
"iteration": 6,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "fconstructor\n\u00b7 exact 1093\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:17:2: error: unsolved goals\ncase h\n\u22a2 IsWallSunSunPrime 1093\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 7,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351064-PbLUH5o2EbJRwi22qI2P",
"api_elapsed_s": 0.998,
"usage": {
"prompt_tokens": 2760,
"completion_tokens": 12,
"total_tokens": 2772,
"reasoning_tokens": null,
"cost_usd": 0.001416
},
"openrouter_retries": 0,
"response_text_len": 34
},
{
"iteration": 7,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "fconstructor\n\u00b7 exact 5\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:17:2: error: unsolved goals\ncase h\n\u22a2 IsWallSunSunPrime 5\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
},
{
"iteration": 8,
"provider": "openrouter_primary",
"finish_reason": "stop",
"response_id": "gen-1771351072-NbPkXhkBRYHdwZwhuIM4",
"api_elapsed_s": 1.102,
"usage": {
"prompt_tokens": 2931,
"completion_tokens": 18,
"total_tokens": 2949,
"reasoning_tokens": null,
"cost_usd": 0.0015195
},
"openrouter_retries": 0,
"response_text_len": 40
},
{
"iteration": 8,
"event": "compile_proof",
"provider": "openrouter_primary",
"status": "partial",
"goals_remaining": 1,
"timed_out": false,
"banned_tokens": [],
"proof_code": "fconstructor\n\u00b7 exact 1000003\n\u00b7 refine ?_",
"compiler_output_preview": "[path]:17:2: error: unsolved goals\ncase h\n\u22a2 IsWallSunSunPrime 1000003\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n\n"
}
],
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"[path]
],
"duration_s": 7.012598514556885,
"goals_remaining": 1,
"is_verified": false,
"lean_file_path": "[path]
"problem": {
"axioms_check_name": "exists_isWallSunSunPrime",
"axioms_check_skipped": false,
"benchmark_id": "Wikipedia__WallSunSun__exists_isWallSunSunPrime",
"category": "research_open",
"endings": [],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 134,
"source_file": "FormalConjectures/Wikipedia/WallSunSun.lean",
"title": "exists_isWallSunSunPrime"
},
"returncode": 1,
"status": "partial",
"stderr": "",
"stdout": "[path]:16:47: error: unsolved goals\n\u22a2 \u2203 p, IsWallSunSunPrime p\n'exists_isWallSunSunPrime' depends on axioms: [propext, sorryAx]\n",
"timed_out": false
}
}
|
| Gemini 3 Flash Preview | Failed | -- | Feb 14, 2026 |
unfold IsWallSunSunPrime
use 2
ring_nf
repeat (first | simp | norm_num | aesop | linarith | tauto)
|
View{
"generation": {
"attempts": 1,
"banned_tokens_found": [],
"elapsed_s": 3.83,
"finish_reason": "stop",
"max_tokens": 8192,
"model_id": "google/gemini-3-flash-preview",
"proof_code_length": 98,
"raw_content_length": 1299,
"reasoning_effort": "",
"structured_output": true,
"temperature": 0.0,
"usage": {
"completion_tokens": 332,
"completion_tokens_details": {
"image_tokens": 0,
"reasoning_tokens": 0
},
"cost": 0.00177,
"cost_details": {
"upstream_inference_completions_cost": 0.000996,
"upstream_inference_cost": 0.00177,
"upstream_inference_prompt_cost": 0.000774
},
"is_byok": false,
"prompt_tokens": 1548,
"prompt_tokens_details": {
"audio_tokens": 0,
"cache_write_tokens": 0,
"cached_tokens": 0,
"video_tokens": 0
},
"total_tokens": 1880
}
},
"verification": {
"banned_tokens": [],
"command": [
"[path]
"lean",
"[path]
],
"duration_s": 7.200221538543701,
"goals_remaining": null,
"is_verified": false,
"lean_file_path": "[path]
"problem": {
"benchmark_id": "Wikipedia__WallSunSun__exists_isWallSunSunPrime",
"category": "research_open",
"endings": [],
"imports": [
"FormalConjectures.Util.ProblemImports"
],
"preamble_chars": 134,
"source_file": "FormalConjectures/Wikipedia/WallSunSun.lean",
"title": "exists_isWallSunSunPrime"
},
"returncode": 1,
"status": "failed",
"stderr": "",
"stdout": "[path]:15:9: error: tactic 'unfold' failed to unfold 'IsWallSunSunPrime' at\n \u2203 p, IsWallSunSunPrime p\n",
"timed_out": false
}
}
|