infinite_pellNumber_primes

{
  "agent_telemetry": {
    "compilations": 6,
    "iterations": 10,
    "duration_s": 557.38,
    "best_status": "failed",
    "best_goals": null,
    "max_iterations": 10,
    "model": "openai/gpt-5.3-codex",
    "error": null,
    "provider": "openrouter_primary",
    "finish_reason": "tool_calls",
    "usage": {
      "prompt_tokens": 152214,
      "completion_tokens": 15461,
      "total_tokens": 167675,
      "reasoning_tokens": 15204,
      "cost_usd": 0.3338461
    },
    "reasoning_effort": "high",
    "response_trace_count": 16
  },
  "response_trace": [
    {
      "iteration": 1,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026567-OTAZHXDwofLfvnDgvwZH",
      "api_elapsed_s": 150.136,
      "usage": {
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        "completion_tokens": 6428,
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        "reasoning_tokens": 6396,
        "cost_usd": 0.0910777
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Analyzing infinitude of prime Pell numbers****Planning first compile attempt with lemma guess**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Analyzing infinitude of prime Pell numbers****Planning first compile attempt with lemma guess**"
        },
        {
          "id": "rs_0901ec5499c32f4601699efac8197c81969eb46d123aea49cf",
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.encrypted",
          "data": 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"
        }
      ]
    },
    {
      "iteration": 1,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "simpa using infinite_setOf_prime_pellNumber",
      "compiler_output_preview": "/app/asi_portal/verifier/quick_1772026717_9562.lean:29:14: error(lean.unknownIdentifier): Unknown identifier `infinite_setOf_prime_pellNumber`\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 27.026,
      "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": 45,
                "line": 28
              },
              "start": {
                "character": 14,
                "line": 28
              }
            },
            "message": "Unknown identifier `infinite_setOf_prime_pellNumber`",
            "range": {
              "end": {
                "character": 45,
                "line": 28
              },
              "start": {
                "character": 14,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 28,
        "error_char": 14,
        "error_msg": "Unknown identifier `infinite_setOf_prime_pellNumber`",
        "goal_before_error": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
        "full_timeline": [
          {
            "line": 28,
            "code": "simpa using infinite_setOf_prime_pellNumber",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "simpa using infinite_setOf_prime_pellNumber"
      }
    },
    {
      "iteration": 2,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026744-syb3YVJ3JT6hYIokzmZW",
      "api_elapsed_s": 14.788,
      "usage": {
        "prompt_tokens": 8894,
        "completion_tokens": 738,
        "total_tokens": 9632,
        "reasoning_tokens": 712,
        "cost_usd": 0.0242837
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Analyzing axioms and theorem dependencies**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Analyzing axioms and theorem dependencies**"
        },
        {
          "id": "rs_0901ec5499c32f4601699efb7951d88196999585a3e564dc95",
          "format": "openai-responses-v1",
          "index": 0,
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      ]
    },
    {
      "iteration": 2,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "exact infinite_pell",
      "compiler_output_preview": "/app/asi_portal/verifier/quick_1772026759_1455.lean:29:8: error(lean.unknownIdentifier): Unknown identifier `infinite_pell`\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 42.156,
      "tactic_replay": {
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "goal_trajectory": [
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        ],
        "max_goals": 1,
        "final_goal_count": 1,
        "goals_opened": 0,
        "goals_closed": 0
      },
      "lsp_feedback": {
        "diagnostics": [
          {
            "code": "lean.unknownIdentifier",
            "fullRange": {
              "end": {
                "character": 21,
                "line": 28
              },
              "start": {
                "character": 8,
                "line": 28
              }
            },
            "message": "Unknown identifier `infinite_pell`",
            "range": {
              "end": {
                "character": 21,
                "line": 28
              },
              "start": {
                "character": 8,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 28,
        "error_char": 8,
        "error_msg": "Unknown identifier `infinite_pell`",
        "goal_before_error": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
        "full_timeline": [
          {
            "line": 28,
            "code": "exact infinite_pell",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "exact infinite_pell"
      }
    },
    {
      "iteration": 3,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026801-51VEEktHVcFqd4dGWyRj",
      "api_elapsed_s": 17.695,
      "usage": {
        "prompt_tokens": 10719,
        "completion_tokens": 857,
        "total_tokens": 11576,
        "reasoning_tokens": 833,
        "cost_usd": 0.01845865
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Evaluating infinite subtype proof strategies**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Evaluating infinite subtype proof strategies**"
        },
        {
          "id": "rs_0901ec5499c32f4601699efbb2301c8196b4ce8b1f91d400e9",
          "format": "openai-responses-v1",
          "index": 0,
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    {
      "iteration": 3,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "aesop",
      "compiler_output_preview": "/app/asi_portal/verifier/quick_1772026819_9948.lean:29:2: error: aesop: failed to prove the goal after exhaustive search.\n/app/asi_portal/verifier/quick_1772026819_9948.lean:28:80: error: unsolved goals\n\u22a2 Infinite { n // Prime (pellNumber n) }\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 30.328,
      "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": 7,
                "line": 28
              },
              "start": {
                "character": 2,
                "line": 28
              }
            },
            "message": "aesop: failed to prove the goal after exhaustive search.",
            "range": {
              "end": {
                "character": 7,
                "line": 28
              },
              "start": {
                "character": 2,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 7,
                "line": 28
              },
              "start": {
                "character": 80,
                "line": 27
              }
            },
            "leanTags": [
              1
            ],
            "message": "unsolved goals\n\u22a2 Infinite { n // Prime (pellNumber n) }",
            "range": {
              "end": {
                "character": 0,
                "line": 28
              },
              "start": {
                "character": 80,
                "line": 27
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 27,
        "error_char": 80,
        "error_msg": "unsolved goals\n\u22a2 Infinite { n // Prime (pellNumber n) }",
        "goal_before_error": null,
        "full_timeline": [
          {
            "line": 28,
            "code": "aesop",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "theorem infinite_pellNumber_primes : Infinite {n : \u2115 | Prime (pellNumber n)} := by"
      }
    },
    {
      "iteration": 4,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026849-L9Ww3E87lDDSybxPRU29",
      "api_elapsed_s": 42.769,
      "usage": {
        "prompt_tokens": 13124,
        "completion_tokens": 2068,
        "total_tokens": 15192,
        "reasoning_tokens": 2044,
        "cost_usd": 0.0503062
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Exploring classical and infinite type tactics**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Exploring classical and infinite type tactics**"
        },
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Pwqd5x0mWMrAbeGg-ARhvi9Y6uwh4qXftjiexOXG56j7_X14dssVujSCxhZFvqAiSAYKWxaBLblz3na4fRVwe41272rBqcnDgdccMMNtuh17ugdrIcDJXUb5TgS_g4iI6YzbHLUgY5H0KMge_V3F4b-P__SQSXC8GpTl_7inpSkTpF5bKroM89PxyAv2waIlHnRRtxTWTJ83HtJmXY_iOhnMFxTF3Wr8zlQa6DFLFzJJCrSDNfpsdK8bGvrQA3lo7lc85yCjztIZhN6h6uNMNPV7I4CKUEZ9YSv7e_vJ0L-0Q1FnNEMEraXVd57v3JtZMLLftxEXUKelMgs7_Zie2fEh88QAHxnlJGUcHFF0hu2DhQgqL0se7bmEqVVH2-IZvWSSqwPlluUOTIKfLaH32DwB4drPkQdCA6cYNUsRmCpGjmttr4iWqUV0A5SPrIB87_9nDIS76G91sxCyOU5eBtEmt9H98PX5iXun3q9W9Tfmd8imKoC_4RxhY8yUiv0_zGM2DkOqAXnSu8XB5uEIfAvNfYkWE8nM8EGXj7tJrXb5RGEVr-ea9S54wYJDlOe2q3SOFfHPIcBUXF5FV4NCrOuh6cr1uvgGNq1NM6u4g5KJm-7MyNJe54pueacNGVYXhuchn_93v9oHoOOsHiVDq0WFP2xN6TzbLRpwPeJIrgLLH6Io4aiOzLQ9W7YIwPuJ-eBJEu-7Ej6YsGHDPQljPBszrv8EhQdoN_ap4gxEPu9NepqY0KoP3u5sF1dkw8Kt9A4H-5c4jtAKC5yMm3owqqnVlz6AMNg95NfOILm5W54QA2hDsJ9VHmkkXMOVnwrpNBF_thWhuO31qOJnFmL7QcJmV-LGQp9mG1tnI0aln9BOc9vwPzbI-A0bOwgDDuSZYI1PMPUIDQ35FCI0RTxwkNjx12uWXaZA40cUUJqyoCDeuMZk3QJbL4YQk2EAoHdkU3c-bhLFmJcPIaQPyxoYVYIz78qGXNlWw6lIXy9WTof6bbCf3pWSL7uQijHtXpBUC2WdBh_i-R70g9_Flc47G9tzsgpdvt4XLBgXU6GiPkZ6MxsJw8WwtF4i5czXfHXM6tAPaZJCPPF2UGcrXwZAqD1IhlpkW-_D1vY4udNjb14wGBSODAAWERLJHnEjttzKV-Sb9wopy-3CaKSPYZcOk1ctM9DFhp6hi5ECCR-855GWc4z6b9d4W0vJFuMiHE9Hed8bpHp5UIpDSbCWUyR0ocfyDh8rKg3EdTbKhwWABcro0B3iDA1-dXq_GL2sacL7O00x_mUOBDy6P5NHlin6vcq4IUYlIJCxFNWayELEsTCs1_dvvU_8bcb9VaBZsVL04pOhHexkPoZwht5AjRycUqBmMg3YWXVYj6eWIkKP6jdcZa3IBYzZ7EMrXOgiRq_p4ZpXnSjnKCjpYXyQc5foOJNw6Xextau4TyONSWV5f2jUBuz_9d0-l81nvMwyxIFD2kinvV7t8Xhf1BhL8fXwg5DHY2jo2QphfF8Q4LpGpKy4dra40qfseuRI1SK9895pYZmusxUUudh2ApJjUYmBxCBCTDcGuk6biwB23-DojxCP-kAcE86V53fL0oGRdwoO4PS9iasPKbUERbZemejiMRUwfKPrjyi0LhCq7UrWK3a-2PmfW9UL1LQIh6QwsCkby-J6LFI4d7xcnbdIkSQC0E6pigRfKBwpvQZhq1Pe5gPIBCT1SO8766j4XqEyWYXBoqdBOrwvux_oZaLbHw4Ji5nMeo8ilWldfzqig5ZPYewKpvYx7JlI7b8CamzzH5tv8jQjlyzivIE-qvkFtSCVSUrD_n5yBwXN8hSlvYhaiRZyPhGSh1zfnb2zH_SqJH_V83mMOaiitnSzoPC0W9ZTeLa1RjQMrDW9M4Ma_6FvozPWEs36XiRlt8U-Ppgc9RYroQqWlYvltJ-wPd0dnRloEOszB3WknmXm5MlfgxJZ4IRG5HVAkLBL4j3V_XLHOfJfMhRCqW9HfrHCSc1r1DdbH41x6TPf6b_odFrdl4J-oaPpJWsTfrqAuBmKLFA7EyqaKNs_daslDapZuhEp2iwjtRDRQqFRyRfD0zGe4Me1CWsV4xb_NNvdL9GQQYX0vqtqciIFhcbGdOFT-HmEbP7XNjkGHj_VvKLXxR0LHGcJ1q6NEbWnyfntbK_dIhB_Pji-c7Cg-W1m3NX8JT6lLANu0PnzFAb_fu3jFuqtN1pfoXKefQxxp-9zTutw65WVBgFrfsy3Hc1suUU2QYoCi-uOddIEgbB9tD_-xhiUc2XLvb4Sy1dsx0QvTKr2-LMhFhoIxFqHJDaUPBNGnYgHZWSJCNyqZZp_On3Mq_tF4MVsiKhqCpCnC3pDZn7FV3lh-Uy46BLihExk6CQudUtNdaoZBLAWXSySiGYwAfSMiqrmAHLa0Jj56QpV52uuVWfrXf0PT73XWQLC1AWTiq5qMPq_S-LnYDvPdHlARZAs_VyHSqNoE3Tu1cPEnEpJyRgwZTQwk347zTmQSebk-Ap3mCkUdvdUVJLMtehuElRpnRhEBSlHYFphKBElFVzIodqRIDwFgpJf0BgGcRVI745ReU5g85zBEdT1Kzxyw6-ual-Az_vr_m57DZtlYJKYPoM1Nf4yqyXpLZTaFxKa9MIIagOfnu6EW2hyOrSvJncMjK1-sY5mEwDw8gr5JLD4eRtimUNKqg89q51ga6dzlTFTEJxT5j-X-hA0lQrokH1aQzQfsndDXf5aQJEPeeotyPN_5qMph8fHqFTCdfftJJ7KxbOcgMQKeZySIDxdc53cAfwKBUBhNKUkO2q7w8lfMRXXGVr1tP4T70pqTeTuBipAd_XFWeQ_kWnma8NvjKLb3_7_MadSWA4pfPMDQtZvHCIBlP4NQvLWUyR8SCVsKpg51N_GIv2ocTeOBhRqFeV_MsZDOxEYliaObxqSTWiBfFXa2QX0a3r2VxovByHnfggsmO8LpLEnCD8SybL6g9W5bvYVmqLOafuiCvRyUnKgUwMdoAmtaK7GzbMtPVZ2j3B67yMz-ft9vZLQn0l0ak-TOSfFCj8D3N2UmcNOOVKdlYF0MU408nk48Cv8NzMiZaPqaDXZnRmvbaDn6HlBeNOCKFfN8EjW2gqor2LQva82_-pN1fnJlVyflvdatkMthyBWOXo6WH-2OuzQaAISN7wVeqBP0yY0AhqghIt_SYJEIjdAOvG2O1tERJH59Z8Btt9DdsMqJZL8xkmkc-ZL9ix4wc3w621pDlFu2LGWacu1NdnudqHOo3ko6MmwfRE_B2HJJGydliacsRvcpuThMAFhQqiYM6xYlVQuIYcTUTyMjKhYJkS-NRnUx_pL61uDu2C_rf8w1P49U-8kXhO1GlqbA6lLOnhmVWwb5pAIENz16J9m0VOA7bmLIW-9QC2wupEVICVTEhhCs_-6PU0f46p3wFODVKMOmuzDFe2IE6mXEM2AacemOv2GDsnafYNgd9piMqrLJ7AHh6D_Jx2mYBH6Y6C8rLKUHbMQPeEL9jHhyltmYbHzAtZ9aWrDhxkFttPKSZ_dItXddOf3XxCrYqJ8MkHTFakyDxpaIuWTRGQMWlrQLxsA9xyFiaOWLqzAEHFphahAQEotWjydyH-XPRS0GiyW6B7UygRaWngVEBDRinBCW3as2fWjVOOUE5ZaKpxDDjWsnSjpwwIARvt_tKpfiGaKmTnAeXYdQY-VI7God4K55dVpXw0N5bOVtZDcvMjsP4Xl6iz_TV6IO450H2TSPXJrFHQOFoyPdmAmXhngQbLo7C1TPiywrLNgbiJTaij4hf5nmvkSKRiefoqYr7JAmsgNB32ux31HyWVRcQBSH4dyIUk1I12CJZbmpIZ1siRls8PVDSC1IeX-_eLs_cRaKFVEB8gLJIAAOieZcSdlV2bNxZ1-eIKKQxiiY_lxnirA2Dq3jr64cZix857Nd-xFH-FQFa43yP5xsNV461pEIYxjLrsWDoya4CO9493P4w1Y_MTD49kGlXYXWKaPLNcqldLf-BoHCoqOI7jetgRmGASVGRxd2sf_tnIeG_KNPDF0VFV6N5-zYvWdcayByqUB-qlDf8sF6bCLGbOkUV_bekgtJ3ZDli5YGB__gJyqGkxcZ-EjnG0L40ZVVGm8U7pBi8eT__h2MbqQ41pHHzr-gjzoQRxn-BJCc927nEEQ70Fi15HSInAWGon_AXiXtvhVQJAtAGTy0G1yrOHpwkorBAWnXrxtV44v_I8u5EV-kmsgfIRRpRFD-cqJCNeVE_fOuAq5i0akPQ2rsl7MPsozbx6v6CiVBKHZMhe-0OFVMrHBjN2MUeitkzQFl2N-AAnySvcwUEtfn6OYBeOpFd3E0nhUY_LyNNccpeacREzucD4om73YzIB6GyJqoImshrc0_GsCG7CltrvobBb0ClLDk9XLoIw2q-GLHeeRw0K16vsXb7StCh6ziYphb3Aan0NmZxNNLNTti_XjgAMlzcjXVvBCh2OmenvEVcgKJYZfWXqTlPWCYu-FruYHg0ZvEFBVaqCmqVCdrXL6CEugEpakQ1ADDXUYkgwxCjB0eLAcIbGrEsbpIOraIMXnDpxp2TUa3zdESWbCfNTrlD81fiBnIjLV-GbvQ5RSAPApmHJRat94mi2U6sIyH90MA9MHzGPESm3pTaPfmCxzUKZv41lmV5zCHw5x5nf-gQP8CbocNTIde6qmQkdMUUImBJj2-8Dc-tDgsR6R91u7fYjiN_vf_JXVOVEc51wDCFHPppPha8vLmt6dGrQ-uttFV5GwVmpZZnQ-fxKvTq9JKA3MIvE9O30Czn8lvMQ_OMWDu4AQppsG4czLsQUQ17DPlrg9fIrw7vrgUWGaLU8FmKzncCUVyQfFx21g6Hvyo3PpfG4NRBpuvUS-3PbFlkEXZvy0M1n9YPY6UOlqaXLlRHshNB9Rrzw_PDEYygTRwIgVIfdDLnicAP4VlQOvcaZSAYUDFX9NdJ-O6hiq1ADu7Fj_BgmbEx3Kcoeis2y59zSD2Z0kVXpf5z9AXgjzez29pDTOLswNuEVpZ-jjMfIE-YKdd8dDyCvaVvjQzOn_Bf48gSntQxXj2pqOMTItWHvqkFWCL_gp_SkjnzJmhczMNMt469XRaMBC-3SFSktlMP7btmwUYClDLFAiw5JM0N1dVNAnWHwvV44aQYYUTUpR74tUG_VA-WBTc4l7XqE2UlidqXj01vdxkGG9DXVjvez0m7JEMut6fpZyaT7cGTkXFNNNARHeED8WGjwKNl-FVJfhsJLx50Gp4vNVmbrpof__PWAYo16bo2wZiko4dEKQ5cUWRwIalSkPQkzKVqpR_WUDiDd2lSkI_63LYDdRdMFRTVxX9wXkOq0QZcks68Tyfzgd7dAYqyPLdGcp9Ht89whafRoYR-DHOClPhWcRKJaYyxwpz-maUxbsn7Xu8lHEJHdqA3SDhFdBYZu4CSKlpR6BAxNhGVpfvuJU62JKEj3HocUp1KXd5bqKhw05k7wJrUZyEPbj8C5AyxFs2ktqKKEiUycZwIbfrp1_RygYydaKJXYtW7LzZyOmW19iEk_wQPTFysdHoxfbTApn3BQPn-DsfoaQoBnRM83ykf9yGv64OysuS-PyD32Bw3PLv2GdItj9v1DvoZYnIf8L-Qw-EGWzbHlbpAXTs0OZRV3TqUEK7d0VQmDqy4XTJkLll5J7KHfxL_u67I_oNWY1cRkHkeWCiepA76w8QnoUWjJuYsV45kSRT8br9BYZ0mlbs_iBZd1B0x4YspXN160Cfci5ojjlUslyvdoqRhnsYtSNUBnVAgyK-ioYk8KzxoIDIxMYj_2TafIrC_BTpttdDkkr_4jb7jGCbsj2vGu0pbOIk1iruabA3wtRhKSqnV-H2-zsfe5bPDQP9JTEu1XLH5sgF31LaABNCJLA-UxKzXMSUQg0lwL6WRhufIdG7R2IKRUXMKgO_9Kxi7sQ2WBVgrv8L10dhR6blqF48b4aNwzNjH0WjMrl0doFXo0Q-8DSSQdSN8vI6dCl1DLMUyiUzKuMjgL_OM4v3gJgmjTOCF-nvRxQK8b20ceTQW1oF7XIwVMp8dqyLYlbpysTTtDK6e3LFaZMsCSbhaoAmkl_Fqr0HnJAyGwrO3Cvl57MmC-dF3VFEK-JvxsVUJ0SQJbQmZfhQXpBGS48M-UPFeao8cqtC8IxIMXcETN7k1wnQ_PciXUJkRmT631losUOA5lCiwkA7sDwKaoOuDhLSwvMPgtdrYTQL_kwvG5y7KfwBFdujPYJZ-1akCOAmV50gCHMIiynPjjV-OQJi0HUKdIboPOM8r1q_c4LKFyVyxEiGmPdbdY_o39akbV5peqgimuj5rv_Lfem7dv4fc5cz9DN6CcEfvdJ1qx03ptkyGhpNl_zfod2INbKgjYWM0d664lQsxxZH5cOLWwd5H_Vf2jywNcXnN_NkuzoXtSlhFEhuR46Bbk86gPZ3y0iNMxvZkTluMqZnO2cMN-Pk-SQ1Lr9944PWvEiw_kpljivyqAETRFzt_Fnj5X6gZWhNeM9Lh44onfP8NIOH9WyhdBanSx8izqVEnb078GCnIfZn4imY1PwoAfSqv7KegrDxR2HkWxiThfytozXlPDu1KaqbLcYu8WmVwo108mV-XBrysbk--enUfm4fzusJvklQjvqrWfEtcOXuaKIjvCBMM0q66eUAWubc4LgtmqYGEtMfYsk4oMOJkuiLiW-ynpTyeQrewiqQoyn9QiGwadSZ6kVgsgSLuAgo-lqjPpV2l1h8AOqY7duigk5MKMOp5tVQmKuTOWZ2CVkmT58psOPaCF8JmhChgaVNpF8uNg6WWkc45YEnQFuPQ-o7MLUrKFTHj1fsYWW1HzSmI9PmZSMP5zC8jNzwVIyKKwB0O3Y9okE8_JJmyMXHQi6OUZV7Ey53BxAcT1EIhdbZnCcGjsZsDdyglzTzOy3_gsmrBWXuFKBS9bK5oBE47DmY71mB07TkFY1IdWo5NrPyi22TcWYwTk-nnMW4dJoNIV0750S8r-_KHR1IMi_lnIrEyQSzhNJwujFxRPDA0fAhxwZhpT8qnCd14nA8Q9S8q7pM7MNAQ9QctEVppo3G4BK9nYg0_v76MTm4kMB2r8aeqsWLfet1El5QAdRs3eYKB9qFQmohWEz_b6CzZu39OvXOWDjtMRR17rj-Pqo_GYj3Ze2J__QsR3kXYRxcJuDDspUmCQ17sJtqyrLQ7DrEcQjDXUCO8Wd6SW2lpVHCvc_JgfOzwoimFBIT_TSG_TegxcZ5YHdQgGJ3x8TSvC36eXMlJvuH1v4Jk3d60AdNIy1UKJxVJk0ykxCVur88JuAdaRttthIr_Xe7YlIcOv0SARpe1T-kaao_yw4IrKvc1uI0i0FNNlVkAi7doLEUyIJZLVs7qh5S5yZLpPj5q1s51DigarH8YU5MimNhMYxuJXWYNhWBBnyqdztZ_lZ7ILEdboeHUVV8Ndlqh-FvfkkCmJrZNBpsHyFg7fzRre_BElu4pYQ4nL_XYa7mMb1j__YNmrbQHx0MOD15wMzRvpMs8tOuBkpqZz59BPVL0ARV6VX5qeR2VxLo4wdm8AuH9GTzvihWfh4PbZVSKKuc4tuAXSCWia4R9C77q8DeN_k9dvd-X0tjJpkcY9t57D0zMDOfoWH_-9Yp1mnmXEnCF3IEUF6gHTIPO0sFrdbC4dWKAgvTl8u-yc-PilRUb_cSHDAy844vyYdxAwrsNjGQZEpxB0e9YguGbEM2_KfeLaVysDDHFjnO4vr-dwa2pgI93l4P_DsWomuWWZxy5zA2u9NIirU="
        }
      ]
    },
    {
      "iteration": 4,
      "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_1772026892_1634.lean:29:3: error: unknown tactic\n/app/asi_portal/verifier/quick_1772026892_1634.lean:28:80: error: unsolved goals\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 32.982,
      "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": 28
              },
              "start": {
                "character": 3,
                "line": 28
              }
            },
            "message": "unknown tactic",
            "range": {
              "end": {
                "character": 3,
                "line": 28
              },
              "start": {
                "character": 3,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 16,
                "line": 28
              },
              "start": {
                "character": 80,
                "line": 27
              }
            },
            "leanTags": [
              1
            ],
            "message": "unsolved goals\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}",
            "range": {
              "end": {
                "character": 0,
                "line": 28
              },
              "start": {
                "character": 80,
                "line": 27
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 27,
        "error_char": 80,
        "error_msg": "unsolved goals\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}",
        "goal_before_error": null,
        "full_timeline": [
          {
            "line": 28,
            "code": "library_search",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "theorem infinite_pellNumber_primes : Infinite {n : \u2115 | Prime (pellNumber n)} := by"
      }
    },
    {
      "iteration": 5,
      "event": "search_mathlib",
      "query": "pellNumber",
      "results_count": 0
    },
    {
      "iteration": 6,
      "event": "search_mathlib",
      "query": "Nat.infinite_setOf_prime",
      "results_count": 1
    },
    {
      "iteration": 7,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026930-Yohq70zDQTQga8SEKyja",
      "api_elapsed_s": 24.76,
      "usage": {
        "prompt_tokens": 17132,
        "completion_tokens": 1146,
        "total_tokens": 18278,
        "reasoning_tokens": 1119,
        "cost_usd": 0.0444122
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Assessing infinite prime Pell numbers**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Assessing infinite prime Pell numbers**"
        },
        {
          "id": "rs_0901ec5499c32f4601699efc3378cc81968bd7033ac4798ffd",
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.encrypted",
          "data": 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        }
      ]
    },
    {
      "iteration": 7,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "exact infinite_pellNumber",
      "compiler_output_preview": "/app/asi_portal/verifier/quick_1772026955_7524.lean:29:8: error(lean.unknownIdentifier): Unknown identifier `infinite_pellNumber`\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 27.382,
      "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": 27,
                "line": 28
              },
              "start": {
                "character": 8,
                "line": 28
              }
            },
            "message": "Unknown identifier `infinite_pellNumber`",
            "range": {
              "end": {
                "character": 27,
                "line": 28
              },
              "start": {
                "character": 8,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 28,
        "error_char": 8,
        "error_msg": "Unknown identifier `infinite_pellNumber`",
        "goal_before_error": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
        "full_timeline": [
          {
            "line": 28,
            "code": "exact infinite_pellNumber",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "exact infinite_pellNumber"
      }
    },
    {
      "iteration": 8,
      "provider": "openrouter_primary",
      "finish_reason": "tool_calls",
      "response_id": "gen-1772026982-HpiPcg3A2quIfgoi619G",
      "api_elapsed_s": 6.633,
      "usage": {
        "prompt_tokens": 19743,
        "completion_tokens": 309,
        "total_tokens": 20052,
        "reasoning_tokens": 278,
        "cost_usd": 0.01246665
      },
      "openrouter_retries": 0,
      "response_text_len": 0,
      "used_tool_call": true,
      "reasoning_text": "**Planning cautious compile attempts**",
      "reasoning_details": [
        {
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.summary",
          "summary": "**Planning cautious compile attempts**"
        },
        {
          "id": "rs_0901ec5499c32f4601699efc6761388196a1770851a7a36a13",
          "format": "openai-responses-v1",
          "index": 0,
          "type": "reasoning.encrypted",
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      "proof_code": "simpa using Nat.infinite_setOf_prime",
      "compiler_output_preview": "/app/asi_portal/verifier/quick_1772026989_3069.lean:29:2: error: Type mismatch: After simplification, term\n  Nat.infinite_setOf_prime\n has type\n  {p | Nat.Prime p}.Infinite\nbut is expected to have type\n  Infinite { n // Prime (pellNumber n) }\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n\n",
      "compile_elapsed_s": 50.105,
      "tactic_replay": {
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "goal_trajectory": [
          1
        ],
        "max_goals": 1,
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        "diagnostics": [
          {
            "fullRange": {
              "end": {
                "character": 38,
                "line": 28
              },
              "start": {
                "character": 2,
                "line": 28
              }
            },
            "message": "Type mismatch: After simplification, term\n  Nat.infinite_setOf_prime\n has type\n  {p | Nat.Prime p}.Infinite\nbut is expected to have type\n  Infinite { n // Prime (pellNumber n) }",
            "range": {
              "end": {
                "character": 38,
                "line": 28
              },
              "start": {
                "character": 2,
                "line": 28
              }
            },
            "severity": 1,
            "source": "Lean 4"
          },
          {
            "fullRange": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "message": "'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]",
            "range": {
              "end": {
                "character": 6,
                "line": 30
              },
              "start": {
                "character": 0,
                "line": 30
              }
            },
            "severity": 3,
            "source": "Lean 4"
          }
        ],
        "error_line": 28,
        "error_char": 2,
        "error_msg": "Type mismatch: After simplification, term\n  Nat.infinite_setOf_prime\n has type\n  {p | Nat.Prime p}.Infinite\nbut is expected to have type\n  Infinite { n // Prime (pellNumber n) }",
        "goal_before_error": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
        "full_timeline": [
          {
            "line": 28,
            "code": "simpa using Nat.infinite_setOf_prime",
            "goal": "```lean\n\u22a2 Infinite \u2191{n | Prime (pellNumber n)}\n```",
            "goal_count": 1,
            "ast_complexity": 50
          }
        ],
        "tactic_count": 1,
        "successful_tactics": 0,
        "first_failure_step": 1,
        "cps": 0.0,
        "cps_peak_step": 0,
        "error_code": "simpa using Nat.infinite_setOf_prime"
      }
    },
    {
      "iteration": 9,
      "event": "search_mathlib",
      "query": "infinite_pell",
      "results_count": 0
    },
    {
      "iteration": 10,
      "event": "search_mathlib",
      "query": "pell",
      "results_count": 8
    }
  ],
  "verification": {
    "banned_tokens": [],
    "command": [
      "[path]
      "lean",
      "/app/asi_portal/verifier/quick_1772027124_2419.lean"
    ],
    "comparator_passed": null,
    "duration_s": 16.68364429473877,
    "goals_remaining": null,
    "is_verified": false,
    "lean_file_path": "",
    "problem": {
      "axioms_check_name": "infinite_pellNumber_primes",
      "axioms_check_skipped": false,
      "benchmark_id": "Wikipedia__Pell__infinite_pellNumber_primes",
      "category": "research_open",
      "endings": [
        "end PellNumbers"
      ],
      "imports": [
        "FormalConjectures.Util.ProblemImports"
      ],
      "preamble_chars": 587,
      "source_file": "FormalConjectures/Wikipedia/Pell.lean",
      "title": "infinite_pellNumber_primes"
    },
    "returncode": 1,
    "status": "failed",
    "stderr": "",
    "stdout": "/app/asi_portal/verifier/quick_1772027124_2419.lean:29:14: error(lean.unknownIdentifier): Unknown identifier `infinite_setOf_prime_pellNumber`\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n",
    "timed_out": false
  },
  "phase2_error": "ProgressAnalysisResult.__init__() missing 1 required positional argument: 'progress_score'"
}

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{
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    {
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      "response_id": "gen-1771349611-89QMZk654UoOrRw0BEEA",
      "api_elapsed_s": 3.672,
      "usage": {
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    },
    {
      "iteration": 1,
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      "banned_tokens": [],
      "proof_code": "unfold Set.Infinite\nintro s\nlet P : \u2115 \u2192 \u2115 := pellNumber\nhave h_rec : \u2200 n, P (n + 2) = 2 * P (n + 1) + P n := fun n => rfl\nhave h_p2 : P 2 = 2 := by\n  change 2 * P 1 + P 0 = 2\n  rw [show P 1 = 1 from rfl, show P 0 = 0 from rfl]\n  norm_num\nhave h_p3 : P 3 = 5 := by\n  change 2 * P 2 + P 1 = 5\n  rw [h_p2, show P 1 = 1 from rfl]\n  norm_num\nhave h_p5 : P 5 = 29 := by\n  have p4 : P 4 = 2 * P 3 + P 2 := rfl\n  rw [h_p3, h_p2] at p4\n  have p5 : P 5 = 2 * P 4 + P 3 := rfl\n  rw [p4, h_p3] at p5\n  norm_num\nhave h2_prime : Prime (P 2) := by rw [h_p2]; exact nat_prime_two\nhave h3_prime : Prime (P 3) := by rw [h_p3]; exact (by norm_num : Prime 5)\nhave h5_prime : Prime (P 5) := by rw [h_p5]; exact (by norm_num : Prime 29)\nrefine Set.not_finite_iff_infinite.mp ?_\nintro h_fin\nobtain \u27e8m, hm\u27e9 := Set.Finite.exists_upper_bound h_fin\nlet S := {n : \u2115 | Prime (P n)}\nhave h2 : 2 \u2208 S := h2_prime\nhave h3 : 3 \u2208 S := h3_prime\nhave h5 : 5 \u2208 S := h5_prime\nlet next_prime (k : \u2115) : \u2115 := 0\nrefine ?_\ninduction m\n\u00b7 simp at *\n\u00b7 refine ?_",
      "compiler_output_preview": "[path]:29:9: error: tactic 'unfold' failed to unfold 'Set.Infinite' at\n  Infinite \u2191{n | Prime (pellNumber n)}\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n"
    },
    {
      "iteration": 2,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349621-XOdcfSzMmG1l0ien8xqU",
      "api_elapsed_s": 9.641,
      "usage": {
        "prompt_tokens": 2440,
        "completion_tokens": 403,
        "total_tokens": 2843,
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      },
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    },
    {
      "iteration": 2,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "rw [Set.infinite_coe_iff]\napply Set.Infinite.mono (fun n (hn : Prime (pellNumber n)) => hn)\nshow Infinite {n : \u2115 | Prime (pellNumber n)}\nlet P := pellNumber\nhave h0 : P 0 = 0 := rfl\nhave h1 : P 1 = 1 := rfl\nhave h2 : P 2 = 2 := by rw [PellNumbers.pellNumber, h1, h0]; norm_num\nhave h3 : P 3 = 5 := by rw [PellNumbers.pellNumber, h2, h1]; norm_num\nhave h4 : P 4 = 12 := by rw [PellNumbers.pellNumber, h3, h2]; norm_num\nhave h5 : P 5 = 29 := by rw [PellNumbers.pellNumber, h4, h3]; norm_num\nhave h7 : P 7 = 169 := by \n  have h6 : P 6 = 2 * P 5 + P 4 := rfl\n  have h7 : P 7 = 2 * P 6 + P 5 := rfl\n  rw [h4, h5] at h6\n  rw [h6, h5] at h7\n  norm_num\nhave p2 : Prime (P 2) := by rw [h2]; exact nat_prime_two\nhave p3 : Prime (P 3) := by rw [h3]; norm_num\nhave p5 : Prime (P 5) := by rw [h5]; norm_num\nlet primes_pell := {n : \u2115 | Prime (P n)}\nhave h_inf : Set.Infinite primes_pell := ?_\nexact h_inf",
      "compiler_output_preview": "[path]:31:2: error: 'show' tactic failed, pattern\n  Infinite \u2191{n | Prime (pellNumber n)}\nis not definitionally equal to target\n  Set.Infinite fun n \u21a6\n    pellNumber n \u2260 0 \u2227 \u00acIsUnit (pellNumber n) \u2227 \u2200 (a b : \u2115), pellNumber n \u2223 a * b \u2192 pellNumber n \u2223 a \u2228 pellNumber n \u2223 b\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx, Classical.choice, Quot.sound]\n\n"
    },
    {
      "iteration": 3,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349638-qWtARvtD1hjdSOWb2zgt",
      "api_elapsed_s": 10.629,
      "usage": {
        "prompt_tokens": 3062,
        "completion_tokens": 833,
        "total_tokens": 3895,
        "reasoning_tokens": null,
        "cost_usd": 0.00403
      },
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    },
    {
      "iteration": 3,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "let P := pellNumber\nhave hP0 : P 0 = 0 := rfl\nhave hP1 : P 1 = 1 := rfl\nhave hP2 : P 2 = 2 := by rw [pellNumber, hP1, hP0]; norm_num\nhave hP2_prime : Prime (P 2) := by rw [hP2]; exact nat_prime_two\nhave hP3 : P 3 = 5 := by rw [pellNumber, hP2, hP1]; norm_num\nhave hP3_prime : Prime (P 3) := by rw [hP3]; norm_num\nhave hP5 : P 5 = 29 := by\n  have hP4 : P 4 = 2 * P 3 + P 2 := rfl\n  have hP5 : P 5 = 2 * P 4 + P 3 := rfl\n  rw [hP3, hP2] at hP4\n  rw [hP4, hP3] at hP5\n  norm_num\nhave hP5_prime : Prime (P 5) := by rw [hP5]; norm_num\napply Set.Infinite.mono (fun n (hn : Prime (P n)) => hn)\nrefine Set.infinite_of_not_finite ?_\nintro h_fin\nobtain \u27e8m, hm\u27e9 := Set.Finite.exists_upper_bound h_fin\nhave h_in : 5 \u2208 {n | Prime (P n)} := hP5_prime\nhave h_le : 5 \u2264 m := hm 5 h_in\nhave hP13 : P 13 = 5741 := by\n  have p6 : P 6 = 2 * P 5 + P 4 := rfl\n  have p4 : P 4 = 12 := by rw [hP3, hP2] at *; norm_num\n  rw [hP5, p4] at p6\n  have p7 : P 7 = 2 * P 6 + P 5 := rfl\n  rw [p6, hP5] at p7\n  have p8 : P 8 = 2 * P 7 + P 6 := rfl\n  rw [p7, p6] at p8\n  have p9 : P 9 = 2 * P 8 + P 7 := rfl\n  rw [p8, p7] at p9\n  have p10 : P 10 = 2 * P 9 + P 8 := rfl\n  rw [p9, p8] at p10\n  have p11 : P 11 = 2 * P 10 + P 9 := rfl\n  rw [p10, p9] at p11\n  have p12 : P 12 = 2 * P 11 + P 10 := rfl\n  rw [p11, p10] at p12\n  have p13 : P 13 = 2 * P 12 + P 11 := rfl\n  rw [p12, p11] at p13\n  norm_num\nhave hP13_prime : Prime (P 13) := by rw [hP13]; norm_num\nhave h_in_13 : 13 \u2208 {n | Prime (P n)} := hP13_prime\nhave h_le_13 : 13 \u2264 m := hm 13 h_in_13\nlinarith [h_le_13]",
      "compiler_output_preview": "[path]:32:31: error: failed to rewrite using equation theorems for 'PellNumbers.pellNumber'. Try rewriting with 'PellNumbers.pellNumber.eq_def'.\n[path]:33:53: error: unknown identifier 'nat_prime_two'\n[path]
    },
    {
      "iteration": 4,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349657-UYi0ijJdbvqqNJiUYrpO",
      "api_elapsed_s": 2.358,
      "usage": {
        "prompt_tokens": 5168,
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        "total_tokens": 5442,
        "reasoning_tokens": null,
        "cost_usd": 0.003406
      },
      "openrouter_retries": 0,
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    },
    {
      "iteration": 4,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "let P := pellNumber\nhave hP0 : P 0 = 0 := rfl\nhave hP1 : P 1 = 1 := rfl\nhave hP2 : P 2 = 2 := by rw [pellNumber.eq_def, hP1, hP0]; norm_num\nhave hP2_prime : Prime (P 2) := by rw [hP2]; exact Nat.prime_two\nhave hP3 : P 3 = 5 := by rw [pellNumber.eq_def, hP2, hP1]; norm_num\nhave hP3_prime : Prime (P 3) := by rw [hP3]; norm_num\nhave hP4 : P 4 = 12 := by rw [pellNumber.eq_def, hP3, hP2]; norm_num\nhave hP5 : P 5 = 29 := by rw [pellNumber.eq_def, hP4, hP3]; norm_num\nhave hP5_prime : Prime (P 5) := by rw [hP5]; norm_num\nhave hPindex : {n | Prime (P n)}.Infinite := ?_\nexact hPindex",
      "compiler_output_preview": "[path]:32:31: error: tactic 'rewrite' failed, did not find instance of the pattern in the target expression\n  pellNumber ?x\u271d\nP : \u2115 \u2192 \u2115 := pellNumber\nhP0 : P 0 = 0\nhP1 : P 1 = 1\n\u22a2 P 2 = 2\n[path]:33:47: error: type mismatch\n  Nat.prime_two\nhas type\n  Nat.Prime 2 : Prop\n\n...<truncated>"
    },
    {
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      "finish_reason": "stop",
      "response_id": "gen-1771349666-1Onv3LozXcsghbBsPAIz",
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      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "have h_inf : Set.Infinite {n : \u2115 | Prime (pellNumber n)} := by\n  refine Set.infinite_of_not_finite ?_\n  intro h_fin\n  let S := {n : \u2115 | Prime (pellNumber n)} \n  have h2 : 2 \u2208 S := by\n    change Prime (pellNumber 2)\n    show Prime (2 * pellNumber 1 + pellNumber 0)\n    norm_num [pellNumber]\n  have h3 : 3 \u2208 S := by\n    change Prime (pellNumber 3)\n    have p2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n    rw [pellNumber]\n    rw [p2]\n    norm_num [pellNumber]\n  have h5 : 5 \u2208 S := by\n    change Prime (pellNumber 5)\n    have p2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n    have p3 : pellNumber 3 = 5 := by rw [pellNumber, p2]; norm_num [pellNumber]\n    have p4 : pellNumber 4 = 12 := by rw [pellNumber, p3, p2]; norm_num\n    have p5 : pellNumber 5 = 29 := by rw [pellNumber, p4, p3]; norm_num\n    rw [p5]\n    norm_num\n  refine ?_\nexact h_inf",
      "compiler_output_preview": "[path]:30:11: error: unknown constant 'Set.infinite_of_not_finite'\n[path]:31:4: error: no goals to be solved\n[path]:52:2: error: type mismatch\n  h_inf\nh\n...<truncated>"
    },
    {
      "iteration": 6,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349676-SnLHKwDNnQekDL9j2X9A",
      "api_elapsed_s": 4.763,
      "usage": {
        "prompt_tokens": 7369,
        "completion_tokens": 756,
        "total_tokens": 8125,
        "reasoning_tokens": null,
        "cost_usd": 0.0032156
      },
      "openrouter_retries": 0,
      "response_text_len": 1769
    },
    {
      "iteration": 6,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "rw [Set.infinite_coe_iff]\napply Set.infinite_of_not_finite\nintro h_fin\nobtain \u27e8m, hm\u27e9 := Set.Finite.exists_upper_bound h_fin\nhave h_p2 : Prime (pellNumber 2) := by\n  have p0 : pellNumber 0 = 0 := rfl\n  have p1 : pellNumber 1 = 1 := rfl\n  have p2 : pellNumber 2 = 2 := by rw [pellNumber, p1, p0]; norm_num\n  rw [p2]; exact Nat.prime_two\nhave h_p3 : Prime (pellNumber 3) := by\n  have p2 : pellNumber 2 = 2 := by rw [pellNumber]; norm_num\n  have p3 : pellNumber 3 = 5 := by rw [pellNumber, p2]; norm_num\n  rw [p3]; norm_num\nhave h_p5 : Prime (pellNumber 5) := by\n  have p2 : pellNumber 2 = 2 := by rw [pellNumber]; norm_num\n  have p3 : pellNumber 3 = 5 := by rw [pellNumber, p2]; norm_num\n  have p4 : pellNumber 4 = 12 := by rw [pellNumber, p3, p2]; norm_num\n  have p5 : pellNumber 5 = 29 := by rw [pellNumber, p4, p3]; norm_num\n  rw [p5]; norm_num\nhave h_p13 : Prime (pellNumber 13) := by\n  have p2 : pellNumber 2 = 2 := by rw [pellNumber]; norm_num\n  have p3 : pellNumber 3 = 5 := by rw [pellNumber, p2]; norm_num\n  have p4 : pellNumber 4 = 12 := by rw [pellNumber, p3, p2]; norm_num\n  have p5 : pellNumber 5 = 29 := by rw [pellNumber, p4, p3]; norm_num\n  have p6 : pellNumber 6 = 70 := by rw [pellNumber, p5, p4]; norm_num\n  have p7 : pellNumber 7 = 169 := by rw [pellNumber, p6, p5]; norm_num\n  have p8 : pellNumber 8 = 408 := by rw [pellNumber, p7, p6]; norm_num\n  have p9 : pellNumber 9 = 985 := by rw [pellNumber, p8, p7]; norm_num\n  have p10 : pellNumber 10 = 2378 := by rw [pellNumber, p9, p8]; norm_num\n  have p11 : pellNumber 11 = 5741 := by rw [pellNumber, p10, p9]; norm_num\n  have p12 : pellNumber 12 = 13860 := by rw [pellNumber, p11, p10]; norm_num\n  have p13 : pellNumber 13 = 33461 := by rw [pellNumber, p12, p11]; norm_num\n  rw [p13]; norm_num\nrefine ?_",
      "compiler_output_preview": "[path]:30:8: error: unknown constant 'Set.infinite_of_not_finite'\n[path]:31:2: error: no goals to be solved\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n"
    },
    {
      "iteration": 7,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349689-Skfyl8JxPcSBvZGFQk8a",
      "api_elapsed_s": 5.549,
      "usage": {
        "prompt_tokens": 8433,
        "completion_tokens": 833,
        "total_tokens": 9266,
        "reasoning_tokens": null,
        "cost_usd": 0.0067155
      },
      "openrouter_retries": 0,
      "response_text_len": 1852
    },
    {
      "iteration": 7,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "rw [Set.infinite_coe_iff]\napply Set.not_finite_iff_infinite.mp\nintro h_fin\nobtain \u27e8m, hm\u27e9 := Set.Finite.exists_upper_bound h_fin\nlet S := {n | Prime (pellNumber n)}\nhave h2 : 2 \u2208 S := by\n  change Prime (pellNumber 2)\n  have e0 : pellNumber 0 = 0 := rfl\n  have e1 : pellNumber 1 = 1 := rfl\n  have e2 : pellNumber 2 = 2 := by rw [pellNumber, e1, e0]; norm_num\n  rw [e2]; exact Nat.prime_two\nhave h3 : 3 \u2208 S := by\n  change Prime (pellNumber 3)\n  have e2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n  have e3 : pellNumber 3 = 5 := by rw [pellNumber, e2]; norm_num [pellNumber]\n  rw [e3]; norm_num\nhave h5 : 5 \u2208 S := by\n  change Prime (pellNumber 5)\n  have e2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n  have e3 : pellNumber 3 = 5 := by rw [pellNumber, e2]; norm_num [pellNumber]\n  have e4 : pellNumber 4 = 12 := by rw [pellNumber, e3, e2]; norm_num\n  have e5 : pellNumber 5 = 29 := by rw [pellNumber, e4, e3]; norm_num\n  rw [e5]; norm_num\nhave h13 : 13 \u2208 S := by\n  let P := pellNumber\n  have p0 : P 0 = 0 := rfl\n  have p1 : P 1 = 1 := rfl\n  have p2 : P 2 = 2 := by rw [pellNumber, p1, p0]; norm_num\n  have p3 : P 3 = 5 := by rw [pellNumber, p2, p1]; norm_num\n  have p4 : P 4 = 12 := by rw [pellNumber, p3, p2]; norm_num\n  have p5 : P 5 = 29 := by rw [pellNumber, p4, p3]; norm_num\n  have p6 : P 6 = 70 := by rw [pellNumber, p5, p4]; norm_num\n  have p7 : P 7 = 169 := by rw [pellNumber, p6, p5]; norm_num\n  have p8 : P 8 = 408 := by rw [pellNumber, p7, p6]; norm_num\n  have p9 : P 9 = 985 := by rw [pellNumber, p8, p7]; norm_num\n  have p10 : P 10 = 2378 := by rw [pellNumber, p9, p8]; norm_num\n  have p11 : P 11 = 5741 := by rw [pellNumber, p10, p9]; norm_num\n  have p12 : P 12 = 13860 := by rw [pellNumber, p11, p10]; norm_num\n  have p13 : P 13 = 33461 := by rw [pellNumber, p12, p11]; norm_num\n  change Prime (P 13)\n  rw [p13]\n  norm_num\nrefine ?_",
      "compiler_output_preview": "[path]:30:8: error: unknown constant 'Set.not_finite_iff_infinite.mp'\n[path]:31:2: error: no goals to be solved\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n"
    },
    {
      "iteration": 8,
      "provider": "openrouter_primary",
      "finish_reason": "stop",
      "response_id": "gen-1771349701-HUoJKqqGny3J9F66d5uF",
      "api_elapsed_s": 5.459,
      "usage": {
        "prompt_tokens": 9579,
        "completion_tokens": 801,
        "total_tokens": 10380,
        "reasoning_tokens": null,
        "cost_usd": 0.0071925
      },
      "openrouter_retries": 0,
      "response_text_len": 1884
    },
    {
      "iteration": 8,
      "event": "compile_proof",
      "provider": "openrouter_primary",
      "status": "failed",
      "goals_remaining": null,
      "timed_out": false,
      "banned_tokens": [],
      "proof_code": "rw [Set.infinite_coe_iff, \u2190 Set.not_finite_iff_infinite]\nintro h_fin\nobtain \u27e8m, hm\u27e9 := Set.Finite.exists_upper_bound h_fin\nlet S := {n | Prime (pellNumber n)}\nhave h2 : 2 \u2208 S := by\n  change Prime (pellNumber 2)\n  have e0 : pellNumber 0 = 0 := rfl\n  have e1 : pellNumber 1 = 1 := rfl\n  have e2 : pellNumber 2 = 2 := by rw [pellNumber, e1, e0]; norm_num\n  rw [e2]; exact Nat.prime_two\nhave h3 : 3 \u2208 S := by\n  change Prime (pellNumber 3)\n  have e2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n  have e3 : pellNumber 3 = 5 := by rw [pellNumber, e2]; norm_num [pellNumber]\n  rw [e3]; norm_num\nhave h5 : 5 \u2208 S := by\n  change Prime (pellNumber 5)\n  have e2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n  have e3 : pellNumber 3 = 5 := by rw [pellNumber, e2]; norm_num [pellNumber]\n  have e4 : pellNumber 4 = 12 := by rw [pellNumber, e3, e2]; norm_num\n  have e5 : pellNumber 5 = 29 := by rw [pellNumber, e4, e3]; norm_num\n  rw [e5]; norm_num\nhave h13 : 13 \u2208 S := by\n  have e2 : pellNumber 2 = 2 := by norm_num [pellNumber]\n  have e3 : pellNumber 3 = 5 := by rw [pellNumber, e2]; norm_num [pellNumber]\n  have e4 : pellNumber 4 = 12 := by rw [pellNumber, e3, e2]; norm_num\n  have e5 : pellNumber 5 = 29 := by rw [pellNumber, e4, e3]; norm_num\n  have e6 : pellNumber 6 = 70 := by rw [pellNumber, e5, e4]; norm_num\n  have e7 : pellNumber 7 = 169 := by rw [pellNumber, e6, e5]; norm_num\n  have e8 : pellNumber 8 = 408 := by rw [pellNumber, e7, e6]; norm_num\n  have e9 : pellNumber 9 = 985 := by rw [pellNumber, e8, e7]; norm_num\n  have e10 : pellNumber 10 = 2378 := by rw [pellNumber, e9, e8]; norm_num\n  have e11 : pellNumber 11 = 5741 := by rw [pellNumber, e10, e9]; norm_num\n  have e12 : pellNumber 12 = 13860 := by rw [pellNumber, e11, e10]; norm_num\n  have e13 : pellNumber 13 = 33461 := by rw [pellNumber, e12, e11]; norm_num\n  change Prime (pellNumber 13)\n  rw [e13]\n  norm_num\nrefine ?_",
      "compiler_output_preview": "[path]:29:30: error: unknown constant 'Set.not_finite_iff_infinite'\n[path]:28:80: error: unsolved goals\n\u22a2 {n | Prime (pellNumber n)}.Infinite\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n\n"
    }
  ],
  "verification": {
    "banned_tokens": [],
    "command": [
      "[path]
      "lean",
      "[path]
    ],
    "duration_s": 6.917374610900879,
    "goals_remaining": null,
    "is_verified": false,
    "lean_file_path": "[path]
    "problem": {
      "axioms_check_name": "infinite_pellNumber_primes",
      "axioms_check_skipped": false,
      "benchmark_id": "Wikipedia__Pell__infinite_pellNumber_primes",
      "category": "research_open",
      "endings": [
        "end PellNumbers"
      ],
      "imports": [
        "FormalConjectures.Util.ProblemImports"
      ],
      "preamble_chars": 587,
      "source_file": "FormalConjectures/Wikipedia/Pell.lean",
      "title": "infinite_pellNumber_primes"
    },
    "returncode": 1,
    "status": "failed",
    "stderr": "",
    "stdout": "[path]:29:9: error: tactic 'unfold' failed to unfold 'Set.Infinite' at\n  Infinite \u2191{n | Prime (pellNumber n)}\n'PellNumbers.infinite_pellNumber_primes' depends on axioms: [propext, sorryAx]\n",
    "timed_out": false
  }
}

{
  "generation": {
    "attempts": 1,
    "banned_tokens_found": [],
    "elapsed_s": 4.64,
    "finish_reason": "stop",
    "max_tokens": 8192,
    "model_id": "google/gemini-3-flash-preview",
    "proof_code_length": 347,
    "raw_content_length": 1382,
    "reasoning_effort": "",
    "structured_output": true,
    "temperature": 0.0,
    "usage": {
      "completion_tokens": 422,
      "completion_tokens_details": {
        "image_tokens": 0,
        "reasoning_tokens": 0
      },
      "cost": 0.0021445,
      "cost_details": {
        "upstream_inference_completions_cost": 0.001266,
        "upstream_inference_cost": 0.0021445,
        "upstream_inference_prompt_cost": 0.0008785
      },
      "is_byok": false,
      "prompt_tokens": 1757,
      "prompt_tokens_details": {
        "audio_tokens": 0,
        "cache_write_tokens": 0,
        "cached_tokens": 0,
        "video_tokens": 0
      },
      "total_tokens": 2179
    }
  },
  "verification": {
    "banned_tokens": [],
    "command": [
      "[path]
      "lean",
      "[path]
    ],
    "duration_s": 7.628572702407837,
    "goals_remaining": null,
    "is_verified": false,
    "lean_file_path": "[path]
    "problem": {
      "benchmark_id": "Wikipedia__Pell__infinite_pellNumber_primes",
      "category": "research_open",
      "endings": [
        "end PellNumbers"
      ],
      "imports": [
        "FormalConjectures.Util.ProblemImports"
      ],
      "preamble_chars": 587,
      "source_file": "FormalConjectures/Wikipedia/Pell.lean",
      "title": "infinite_pellNumber_primes"
    },
    "returncode": 1,
    "status": "failed",
    "stderr": "",
    "stdout": "[path]:29:12: error: unknown identifier 'next_n'\n[path]:30:4: error: unknown identifier 'case'\n[path]:30:16: error: unexpected token '=>'; expected command\n",
    "timed_out": false
  }
}