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      "theorem": "AddSemigroup_x2eto_x5fisAssociative",
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      "(fun x => a\u271d + x)^[n\u271d] = fun x => n\u271d \u2022 a\u271d + x",
      "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
      "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
      "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
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      "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d",
      "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
      "Std.Associative fun x1 x2 => x1 + x2",
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      "(fun x => a\u271d + x)^[n\u271d] x\u271d = n\u271d \u2022 a\u271d + x\u271d",
      "SubtractionMonoid.toSubNegZeroMonoid =\n  let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n  { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
      "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b"
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      "apply div_eq_mul_inv",
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      "infer_instance"
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  "theorem_details": [
    {
      "name": "div_x5fdiv",
      "status": "Failed",
      "iterations": 8,
      "mean_ged": 2.3333333333333335,
      "mean_ged_search_graph": 2.3333333333333335,
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        {
          "tactic": "intros",
          "goal": "\u2200 {\u03b1 : Type u_1} [inst : DivisionCommMonoid \u03b1] (a b c : \u03b1), a / b / c = a / (b * c)",
          "outcome": "success"
        },
        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv]",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv, mul_div_assoc, \u2190 mul_assoc]",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "failure"
        },
        {
          "tactic": "norm_cast",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "success"
        },
        {
          "tactic": "letI := divisionRingOfDivisionCommMonoid \u03b1",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv]",
          "goal": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
          "outcome": "success"
        },
        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv]",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_assoc]",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "blocked"
        },
        {
          "tactic": "apply div_eq_mul_inv",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "failure"
        },
        {
          "tactic": "apply eq_inv_mul_of_mul_eq",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "failure"
        },
        {
          "tactic": "letI : DivisionCommGroup \u03b1 := DivInvMonoid.toDivisionCommGroup \u03b1",
          "goal": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
          "outcome": "failure"
        }
      ],
      "mcts_tree": {
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        "expansion_count": 2,
        "nodes": {
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            "mvar_id": "cp1:_uniq.2154",
            "goal_type": "\u2200 {\u03b1 : Type u_1} [inst : DivisionCommMonoid \u03b1] (a b c : \u03b1), a / b / c = a / (b * c)",
            "goal_sig": "00aeb42434d0",
            "goal_sig_strict": "00aeb42434d0",
            "visit_count": 8,
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            "is_terminal": false,
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            "children": {
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                "cp2:_uniq.2170.6"
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          },
          "cp2:_uniq.2170.6": {
            "mvar_id": "cp2:_uniq.2170.6",
            "goal_type": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)",
            "goal_sig": "595bb0eb2e12",
            "goal_sig_strict": "b0ea255c17ed",
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            "children": {
              "rw [div_eq_mul_inv]": [
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            }
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          "cp4:_uniq.2170.380": {
            "mvar_id": "cp4:_uniq.2170.380",
            "goal_type": "a\u271d / b\u271d * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)",
            "goal_sig": "7d2d7ae49fe4",
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          }
        }
      }
    },
    {
      "name": "SubtractionMonoid_x2etoSubNegZeroMonoid_x2eeq_x5f1",
      "status": "Failed",
      "iterations": 6,
      "mean_ged": 1.8,
      "mean_ged_search_graph": 1.8,
      "mean_ged_proof_graph": null,
      "mean_ged_trace_graph": null,
      "variants": [
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      "history": [
        {
          "tactic": "simp [SubtractionMonoid.toSubNegZeroMonoid]",
          "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionMonoid \u03b1],\n  SubtractionMonoid.toSubNegZeroMonoid =\n    let __SubNegMonoid := inst.toSubNegMonoid;\n    { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
          "outcome": "blocked"
        },
        {
          "tactic": "intros",
          "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionMonoid \u03b1],\n  SubtractionMonoid.toSubNegZeroMonoid =\n    let __SubNegMonoid := inst.toSubNegMonoid;\n    { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
          "outcome": "success"
        },
        {
          "tactic": "apply SubtractionMonoid.ext",
          "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n  let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n  { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
          "outcome": "failure"
        },
        {
          "tactic": "ext",
          "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n  let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n  { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
          "outcome": "failure"
        },
        {
          "tactic": "letI := inst",
          "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n  let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n  { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
          "outcome": "failure"
        }
      ],
      "mcts_tree": {
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        "nodes": {
          "cp1:_uniq.15336": {
            "mvar_id": "cp1:_uniq.15336",
            "goal_type": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionMonoid \u03b1],\n  SubtractionMonoid.toSubNegZeroMonoid =\n    let __SubNegMonoid := inst.toSubNegMonoid;\n    { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
            "goal_sig": "2754a5d665cf",
            "goal_sig_strict": "2754a5d665cf",
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            "success_count": 1,
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                "cp2:_uniq.15351.3"
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          },
          "cp2:_uniq.15351.3": {
            "mvar_id": "cp2:_uniq.15351.3",
            "goal_type": "SubtractionMonoid.toSubNegZeroMonoid =\n  let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n  { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }",
            "goal_sig": "0f54c9c8d604",
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    },
    {
      "name": "div_x5feq_x5fdiv_x5fiff_x5fdiv_x5feq_x5fdiv",
      "status": "Failed",
      "iterations": 6,
      "mean_ged": 2.4285714285714284,
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          "tactic": "intro G _ _ _",
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    {
      "name": "AddSemigroup_x2eto_x5fisAssociative",
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    {
      "name": "div_x5fdiv_x5fdiv_x5fcancel_x5fright",
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          "outcome": "blocked"
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          "tactic": "exact div_x5fdiv_x5fdiv_x5fcancel_x5fright_w30'",
          "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b",
          "outcome": "failure"
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        {
          "tactic": "apply div_x5fdiv_x5fdiv_x5fcancel_x5fright",
          "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b",
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        {
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          "outcome": "success"
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        {
          "tactic": "simp",
          "goal": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv]",
          "goal": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "apply div_x5fdiv_x5fdiv_x5fcancel_x5fright_w1",
          "goal": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv]",
          "goal": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
          "outcome": "success"
        },
        {
          "tactic": "simp only [inv_inv]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [mul_inv_rev, mul_assoc, mul_left_inv]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
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        {
          "tactic": "simp only [div_eq_mul_inv, mul_assoc, mul_inv_cancel_left]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
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        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
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          "tactic": "simp only [mul_inv_rev, mul_assoc, div_mul_cancel]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "blocked"
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          "tactic": "apply (mul_left_cancel\u2080 (div_eq_one_iff.mpr _) _).symm",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "failure"
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        {
          "tactic": "rw [mul_inv, mul_inv, div_inv, div_inv, div_inv]",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "failure"
        },
        {
          "tactic": "norm_cast",
          "goal": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
          "outcome": "success"
        }
      ],
      "mcts_tree": {
        "root_mvar_id": "cp1:_uniq.36807",
        "expansion_count": 2,
        "nodes": {
          "cp1:_uniq.36807": {
            "mvar_id": "cp1:_uniq.36807",
            "goal_type": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b",
            "goal_sig": "e26def4a1c18",
            "goal_sig_strict": "e26def4a1c18",
            "visit_count": 8,
            "success_count": 2,
            "is_terminal": false,
            "is_dead": true,
            "depth": 0,
            "expansion_order": 0,
            "children": {
              "intros": [
                "cp2:_uniq.36823.6"
              ]
            }
          },
          "cp2:_uniq.36823.6": {
            "mvar_id": "cp2:_uniq.36823.6",
            "goal_type": "a\u271d / c\u271d / (b\u271d / c\u271d) = a\u271d / b\u271d",
            "goal_sig": "97a72ac4ae2b",
            "goal_sig_strict": "7c58b5967fa0",
            "visit_count": 3,
            "success_count": 1,
            "is_terminal": false,
            "is_dead": true,
            "depth": 1,
            "expansion_order": 1,
            "children": {
              "rw [div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv]": [
                "cp3:_uniq.36823.459"
              ]
            }
          },
          "cp3:_uniq.36823.459": {
            "mvar_id": "cp3:_uniq.36823.459",
            "goal_type": "a\u271d * c\u271d\u207b\u00b9 * (b\u271d * c\u271d\u207b\u00b9)\u207b\u00b9 = a\u271d * b\u271d\u207b\u00b9",
            "goal_sig": "2df30d38e50c",
            "goal_sig_strict": "b611814f0a07",
            "visit_count": 1,
            "success_count": 0,
            "is_terminal": false,
            "is_dead": true,
            "depth": 2,
            "expansion_order": 2,
            "children": {}
          }
        }
      }
    },
    {
      "name": "div_x5feq_x5fiff_x5feq_x5fmul_x27",
      "status": "Failed",
      "iterations": 18,
      "mean_ged": 15.333333333333334,
      "mean_ged_search_graph": 15.333333333333334,
      "mean_ged_proof_graph": null,
      "mean_ged_trace_graph": null,
      "variants": [
        "wild_type",
        "block_apply_rules",
        "block_constructor",
        "block_ext",
        "block_have",
        "block_intros",
        "block_rfl",
        "block_rintro",
        "block_rw",
        "block_simp"
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      "ged_matrix": [
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      ],
      "history": [
        {
          "tactic": "simp only [div_eq_mul_inv]",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "blocked"
        },
        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_inv_rev]",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "blocked"
        },
        {
          "tactic": "have h := mul_inv_eq_iff_eq_mul",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "failure"
        },
        {
          "tactic": "intros",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
          "outcome": "success"
        },
        {
          "tactic": "simp [div_eq_mul_inv, mul_inv_cancel_right]",
          "goal": "a\u271d / b\u271d = c\u271d \u2194 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp [div_eq_iff_mul_eq, mul_comm]",
          "goal": "a\u271d / b\u271d = c\u271d \u2194 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "constructor",
          "goal": "a\u271d / b\u271d = c\u271d \u2194 a\u271d = b\u271d * c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_assoc, mul_comm c, mul_eq_iff_eq_inv_mul, eq_comm]",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_right_eq_self\u2080, inv_mul_cancel_right]",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_right_inv, mul_comm]",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_inv_cancel_right]",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "apply_rules [div_eq_iff, eq_mul_inv_iff_mul_eq, mul_right_cancel_iff]",
          "goal": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "simp",
          "goal": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp (config := { unfoldPartialApp := true }) [div_eq_mul_inv]",
          "goal": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp [div_eq_mul_inv]",
          "goal": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, inv_mul_cancel_right]",
          "goal": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "rintro rfl",
          "goal": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "rfl",
          "goal": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [mul_comm]",
          "goal": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp",
          "goal": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "simp only [div_eq_mul_inv, inv_mul_cancel_left]",
          "goal": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "ext",
          "goal": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "rw [div_eq_mul_inv, mul_assoc, mul_inv_cancel_right, one_mul]",
          "goal": "b\u271d * c\u271d / b\u271d = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, mul_assoc, mul_inv_cancel_left]",
          "goal": "b\u271d * c\u271d / b\u271d = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, mul_comm]",
          "goal": "b\u271d * c\u271d / b\u271d = c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "rw [\u2190 div_eq_mul_inv, \u2190 div_eq_mul_inv, inv_mul_cancel_left, mul_assoc]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_div_mul_left a b, div_eq_iff_mul_eq, mul_comm]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 div_eq_mul_inv]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, mul_comm]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_one a, div_mul_cancel]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 div_mul_right_eq_iff]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 @div_eq_mul_inv G, mul_assoc]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_iff_mul_eq]",
          "goal": "a\u271d = b\u271d * c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "simp [div_eq_iff]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "rw [\u2190 mul_inv_cancel_left]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_div_cancel_left b\u271d\u207b\u00b9 c\u271d, mul_comm]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 inv_mul_cancel_left]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, inv_mul_cancel_left]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, inv_mul_cancel_right]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 div_eq_mul_inv, mul_comm]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, mul_inv_cancel_left]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [mul_comm]",
          "goal": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
          "outcome": "success"
        },
        {
          "tactic": "simp only [eq_mul_inv_iff_mul_eq]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, mul_left_comm]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [mul_assoc, mul_inv_cancel_right]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [mul_assoc, mul_inv_cancel_left]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, inv_mul_cancel_left, mul_one]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [mul_inv_cancel_right]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_div_assoc, div_x5feq_x5fiff_x5feq_x5fmul_x27_w38, mul_inv_cancel_right]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 mul_assoc, mul_inv_cancel_left]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [eq_mul_inv_iff_mul_eq, mul_right_inv]",
          "goal": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
          "outcome": "failure"
        }
      ],
      "mcts_tree": {
        "root_mvar_id": "cp1:_uniq.41925",
        "expansion_count": 7,
        "nodes": {
          "cp1:_uniq.41925": {
            "mvar_id": "cp1:_uniq.41925",
            "goal_type": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c",
            "goal_sig": "86dc0a5e1af6",
            "goal_sig_strict": "86dc0a5e1af6",
            "visit_count": 18,
            "success_count": 7,
            "is_terminal": false,
            "is_dead": true,
            "depth": 0,
            "expansion_order": 0,
            "children": {
              "intros": [
                "cp2:_uniq.41947.6"
              ]
            }
          },
          "cp2:_uniq.41947.6": {
            "mvar_id": "cp2:_uniq.41947.6",
            "goal_type": "a\u271d / b\u271d = c\u271d \u2194 a\u271d = b\u271d * c\u271d",
            "goal_sig": "cb97102b018c",
            "goal_sig_strict": "cb145fd06b69",
            "visit_count": 14,
            "success_count": 6,
            "is_terminal": false,
            "is_dead": true,
            "depth": 1,
            "expansion_order": 1,
            "children": {
              "constructor": [
                "cp3:_uniq.41947.14",
                "cp3:_uniq.41947.15"
              ]
            }
          },
          "cp3:_uniq.41947.14": {
            "mvar_id": "cp3:_uniq.41947.14",
            "goal_type": "a\u271d / b\u271d = c\u271d \u2192 a\u271d = b\u271d * c\u271d",
            "goal_sig": "1133bad0c69a",
            "goal_sig_strict": "9a26489cfa16",
            "visit_count": 5,
            "success_count": 2,
            "is_terminal": false,
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            "depth": 2,
            "expansion_order": 2,
            "children": {
              "apply_rules [div_eq_iff, eq_mul_inv_iff_mul_eq, mul_right_cancel_iff]": [
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              ]
            }
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          "cp3:_uniq.41947.15": {
            "mvar_id": "cp3:_uniq.41947.15",
            "goal_type": "a\u271d = b\u271d * c\u271d \u2192 a\u271d / b\u271d = c\u271d",
            "goal_sig": "1133bad0c69a",
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            "visit_count": 7,
            "success_count": 3,
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            "expansion_order": 2,
            "children": {
              "rintro rfl": [
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            }
          },
          "cp4:_uniq.41947.526": {
            "mvar_id": "cp4:_uniq.41947.526",
            "goal_type": "(fun a => a\u271d) = fun a => b\u271d * c\u271d",
            "goal_sig": "9dc60bf9b161",
            "goal_sig_strict": "5b5c392b4826",
            "visit_count": 3,
            "success_count": 1,
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            "depth": 3,
            "expansion_order": 3,
            "children": {
              "ext": [
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              ]
            }
          },
          "cp5:_uniq.41947.30": {
            "mvar_id": "cp5:_uniq.41947.30",
            "goal_type": "b\u271d * c\u271d / b\u271d = c\u271d",
            "goal_sig": "259867bdb156",
            "goal_sig_strict": "0f30becd2065",
            "visit_count": 5,
            "success_count": 2,
            "is_terminal": false,
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            "depth": 3,
            "expansion_order": 4,
            "children": {
              "rw [div_eq_mul_inv, mul_comm]": [
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              ]
            }
          },
          "cp6:_uniq.41947.1101": {
            "mvar_id": "cp6:_uniq.41947.1101",
            "goal_type": "a\u271d = b\u271d * c\u271d",
            "goal_sig": "693ce18a4746",
            "goal_sig_strict": "1a0d2fcb5b78",
            "visit_count": 1,
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            "depth": 4,
            "expansion_order": 5,
            "children": {}
          },
          "cp7:_uniq.41947.1388": {
            "mvar_id": "cp7:_uniq.41947.1388",
            "goal_type": "b\u271d\u207b\u00b9 * (b\u271d * c\u271d) = c\u271d",
            "goal_sig": "de40bcc7162e",
            "goal_sig_strict": "ec1120de75cc",
            "visit_count": 3,
            "success_count": 1,
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              "rw [mul_comm]": [
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          "cp8:_uniq.41947.1427": {
            "mvar_id": "cp8:_uniq.41947.1427",
            "goal_type": "b\u271d * c\u271d * b\u271d\u207b\u00b9 = c\u271d",
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            "goal_sig_strict": "ad669bf9ce92",
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    {
      "name": "add_x5fzsmul",
      "status": "Failed",
      "iterations": 6,
      "mean_ged": 1.1666666666666667,
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        {
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        {
          "tactic": "simp [zsmul_add, add_smul]",
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          "tactic": "rw [\u2190 zsmul_one, \u2190 zsmul_one, add_smul]",
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          "outcome": "failure"
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        {
          "tactic": "induction m using Int.induction_on",
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          "outcome": "failure"
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        {
          "tactic": "rw [zsmul_def, add_comm, add_left_comm]",
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    {
      "name": "div_x5feq_x5fof_x5feq_x5fmul_x27",
      "status": "Failed",
      "iterations": 10,
      "mean_ged": 4.4,
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          "tactic": "intro G _ _ _ h",
          "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a = b * c \u2192 a / b = c",
          "outcome": "success"
        },
        {
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        },
        {
          "tactic": "simp only [div_eq_mul_inv, mul_comm]",
          "goal": "a\u271d = b\u271d * h \u2192 a\u271d / b\u271d = h",
          "outcome": "blocked"
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        {
          "tactic": "simp",
          "goal": "a\u271d = b\u271d * h \u2192 a\u271d / b\u271d = h",
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          "outcome": "failure"
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          "tactic": "have := div_x5feq_x5fof_x5feq_x5fmul_x27_of_x5feq_x5fof_x5feq_x5fmul_x27",
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          "outcome": "failure"
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        {
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          "outcome": "success"
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          "tactic": "simp [h]",
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          "outcome": "blocked"
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          "tactic": "rw [div_eq_mul_inv, h, inv_mul_cancel_right]",
          "goal": "a\u271d / b\u271d = h\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, h, mul_assoc, inv_mul_cancel_left, mul_one]",
          "goal": "a\u271d / b\u271d = h\u271d",
          "outcome": "failure"
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        {
          "tactic": "rw [div_eq_mul_inv, mul_comm, \u2190 inv_mul_cancel_left\u2080 b h, mul_assoc, mul_inv_cancel_right\u2080 b,\n    mul_one]",
          "goal": "a\u271d / b\u271d = h\u271d",
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        {
          "tactic": "rw [div_eq_mul_inv, h, mul_assoc, inv_mul_cancel_right]",
          "goal": "a\u271d / b\u271d = h\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [\u2190 div_eq_mul_inv, h, mul_inv_cancel_right]",
          "goal": "a\u271d / b\u271d = h\u271d",
          "outcome": "failure"
        },
        {
          "tactic": "rw [div_eq_mul_inv, h]",
          "goal": "a\u271d / b\u271d = h\u271d",
          "outcome": "success"
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        {
          "tactic": "simp [h]",
          "goal": "b\u271d * h\u271d * b\u271d\u207b\u00b9 = h\u271d",
          "outcome": "blocked"
        },
        {
          "tactic": "rw [h, mul_inv_cancel_right]",
          "goal": "b\u271d * h\u271d * b\u271d\u207b\u00b9 = h\u271d",
          "outcome": "failure"
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        {
          "tactic": "rw [h, mul_inv_cancel_left]",
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        {
          "tactic": "rw [h, mul_assoc, mul_inv_cancel_left]",
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          "outcome": "failure"
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        {
          "tactic": "rw [\u2190 mul_assoc, \u2190 h, mul_inv_cancel_right]",
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          "outcome": "blocked"
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          "outcome": "success"
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          "outcome": "failure"
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          "tactic": "apply add_iterate_eq_add_nsmul_left n a",
          "goal": "(fun x => a\u271d + x)^[n\u271d] = fun x => n\u271d \u2022 a\u271d + x",
          "outcome": "failure"
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          "tactic": "ext",
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          "outcome": "success"
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          "tactic": "simp [AddMonoid.add_comm, add_x5fleft_x5fiterate_w53]",
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          "outcome": "blocked"
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          "outcome": "blocked"
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          "tactic": "induction' n with n IH",
          "goal": "(fun x => a\u271d + x)^[n\u271d] x\u271d = n\u271d \u2022 a\u271d + x\u271d",
          "outcome": "failure"
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          "tactic": "unfold hasPow_fun.pow",
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          "outcome": "failure"
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          "tactic": "induction' n with n hn",
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          "outcome": "failure"
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        {
          "tactic": "rw [\u2190 add_iterate_succ, iterate_zero, iterate_succ, add_zero]",
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            "goal_type": "\u2200 {M : Type u_4} [inst : AddMonoid M] (a : M) (n : \u2115), (fun x => a + x)^[n] = fun x => n \u2022 a + x",
            "goal_sig": "1b91982fe9f8",
            "goal_sig_strict": "1b91982fe9f8",
            "visit_count": 8,
            "success_count": 2,
            "is_terminal": false,
            "is_dead": true,
            "depth": 0,
            "expansion_order": 0,
            "children": {
              "intros": [
                "cp2:_uniq.80483.5"
              ]
            }
          },
          "cp2:_uniq.80483.5": {
            "mvar_id": "cp2:_uniq.80483.5",
            "goal_type": "(fun x => a\u271d + x)^[n\u271d] = fun x => n\u271d \u2022 a\u271d + x",
            "goal_sig": "a73343ce15ac",
            "goal_sig_strict": "6255159bf54a",
            "visit_count": 3,
            "success_count": 1,
            "is_terminal": false,
            "is_dead": true,
            "depth": 1,
            "expansion_order": 1,
            "children": {
              "ext": [
                "cp3:_uniq.80483.76"
              ]
            }
          },
          "cp3:_uniq.80483.76": {
            "mvar_id": "cp3:_uniq.80483.76",
            "goal_type": "(fun x => a\u271d + x)^[n\u271d] x\u271d = n\u271d \u2022 a\u271d + x\u271d",
            "goal_sig": "ad3291af5f31",
            "goal_sig_strict": "e6f707864fb6",
            "visit_count": 1,
            "success_count": 0,
            "is_terminal": false,
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            "depth": 2,
            "expansion_order": 2,
            "children": {}
          }
        }
      }
    }
  ]
}