{
  "model_id": "EPFL-LARA/lean-world-model-qwen3-4b-grpo",
  "backend": "transformers",
  "input": "import Mathlib\n\ntheorem demo (n : ℕ) : n + 0 = n := by sorry\n",
  "prompt": "Solve the following problem with Lean 4 code and explanatory comments:\n\n```lean4\nimport Mathlib\n\n\ntheorem demo (n : ℕ) : n + 0 = n := by sorry\n```\n\nReplace every sorry statement with an appropriate proof. Provide a complete solution in the lean4 code block, annotated with Lean 4 compiler feedback blocks in the form `/- <feedback> ... </feedback> -/` at the appropriate locations.\n",
  "response": "Here is the complete Lean 4 proof annotated with Lean 4 compiler feedback blocks:\n\n```lean4\nimport Mathlib\n\n-- Theorem: For any natural number n, n + 0 = n.\ntheorem demo (n : ℕ) : n + 0 = n := by\n  /- <feedback>\n  -- proof state:\n  n : ℕ\n  ⊢ n + 0 = n\n  </feedback> -/\n  induction n with\n  /- <feedback>\n  -- proof state:\n  case zero\n  ⊢ 0 + 0 = 0\n  </feedback> -/\n  | zero => rfl\n  /- <feedback>\n  -- proof state:\n  ih : n + 0 = n\n  case succ\n  ⊢ n + 1 + 0 = n + 1\n  </feedback> -/\n  | succ n ih => simp_all\n```\n",
  "lean_code": "import Mathlib\n\n-- Theorem: For any natural number n, n + 0 = n.\ntheorem demo (n : ℕ) : n + 0 = n := by\n  /- <feedback>\n  -- proof state:\n  n : ℕ\n  ⊢ n + 0 = n\n  </feedback> -/\n  induction n with\n  /- <feedback>\n  -- proof state:\n  case zero\n  ⊢ 0 + 0 = 0\n  </feedback> -/\n  | zero => rfl\n  /- <feedback>\n  -- proof state:\n  ih : n + 0 = n\n  case succ\n  ⊢ n + 1 + 0 = n + 1\n  </feedback> -/\n  | succ n ih => simp_all",
  "generation": {
    "seed": 0,
    "temperature": 0.3,
    "top_p": 0.95,
    "top_k": 0,
    "min_p": 0.0,
    "max_new_tokens": 2048,
    "add_special_tokens": false
  },
  "environment": {
    "torch": "2.9.0+cu129",
    "transformers": "4.57.3",
    "gpu": "NVIDIA H100 80GB",
    "dtype": "bfloat16"
  },
  "verification": {
    "lean_version": "4.15.0",
    "compiled": true,
    "original_theorem_type_checked": true,
    "contains_sorry": false
  },
  "weight_sha256": {
    "model-00001-of-00002.safetensors": "4524c20d5a992eb96bc1ed84eaa9e7d15347f232d9f8b21687228fd4912c4ede",
    "model-00002-of-00002.safetensors": "63dd64e9808d77f802c848b997c2cde09a1add8563259db29ce3b098133467b6"
  }
}