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], [ 0.0, 0.2 ], [ 0.0, 0.0 ], [ 0.0, 0.0 ], [ 0.0, 0.16666666666666666 ], [ 0.0, 1.0 ], [ 0.0, 0.0 ], [ 0.0, 0.25 ], [ 0.0, 0.0 ], [ 0.0, 0.0 ], [ 0.0, 0.0 ], [ 0.0, 0.0 ], [ 0.0, 1.0 ], [ 0.0, 0.0 ], [ 0.0, 0.0 ], [ 0.0, 1.0 ], [ 0.0, 0.4 ], [ 0.0, 1.0 ], [ 0.0, 0.2 ], [ 0.0, 0.0 ], [ 0.0, 1.0 ], [ 0.0, 0.0 ], [ 0.0, 0.6666666666666666 ] ], "metric": "rate" }, "trajectory_sample": { "theorem": "AddCommMagma_x2eto_x5fisCommutative", "wild": { "depth": [ 1.0 ], "attempts": [ 1.0 ], "success_ratio": [ 1.0 ] }, "intervention": { "name": "block_infer_instance", "depth": [ 1.0 ], "attempts": [ 2.0 ], "success_ratio": [ 0.5 ] } }, "ged_sample": { "theorem": "AddCommMagma_x2eto_x5fisCommutative", "variants": [ "wild_type", "block_infer_instance", "block_intros" ], "matrix": [ [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ] ] }, "theorem_details": [ { "name": "AddCommMagma_x2eto_x5fisCommutative", "status": "Solved", "iterations": 1, "mean_ged": 0.0, "mean_ged_search_graph": 0.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_infer_instance", "block_intros" ], "ged_matrix": [ [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0 ] ], "history": [ { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : AddCommMagma G], Std.Commutative fun x1 x2 => x1 + x2", "outcome": "success" } ], "proof_term_stats": { "node_count": 43, "max_depth": 14, "kind_counts": [ { "label": "app", "count": 17 }, { "label": "lam", "count": 4 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 7 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.675", "expansion_count": 2, "nodes": { "cp1:_uniq.675": { "mvar_id": "cp1:_uniq.675", "goal_type": "\u2200 {G : Type u_3} [inst : AddCommMagma G], Std.Commutative fun x1 x2 => x1 + x2", "goal_sig": "2a2eb55d650a", "goal_sig_strict": "2a2eb55d650a", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { 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AddSemigroup \u03b1], Std.Associative fun x1 x2 => x1 + x2", "goal_sig": "0ab46aabcb29", "goal_sig_strict": "0ab46aabcb29", "visit_count": 3, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.3442.3" ] } }, "cp2:_uniq.3442.3": { "mvar_id": "cp2:_uniq.3442.3", "goal_type": "Std.Associative fun x1 x2 => x1 + x2", "goal_sig": "44a0b3f0499e", "goal_sig_strict": "28dd06c76198", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": {} } } } }, { "name": "AddSemigroup_x2eto_x5fisLawfulIdentity", "status": "Solved", "iterations": 1, "mean_ged": 0.0, "mean_ged_search_graph": 0.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_constructor", "block_intros", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "outcome": "blocked" }, { "tactic": "simp [AddMonoid", "goal": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "outcome": "blocked" }, { "tactic": "simp [add_comm", "goal": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "outcome": "blocked" }, { "tactic": "simp [add_zero", "goal": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "outcome": "success" } ], "proof_term_stats": { "node_count": 239, "max_depth": 18, "kind_counts": [ { "label": "app", "count": 109 }, { "label": "lam", "count": 10 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 13 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.6852", "expansion_count": 2, "nodes": { "cp1:_uniq.6852": { "mvar_id": "cp1:_uniq.6852", "goal_type": "\u2200 {M : Type u_4} [inst : AddZeroClass M], Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "goal_sig": "4ff34e0e9d18", "goal_sig_strict": "4ff34e0e9d18", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.6864.3" ] } }, "cp2:_uniq.6864.3": { "mvar_id": "cp2:_uniq.6864.3", "goal_type": "Std.LawfulIdentity (fun x1 x2 => x1 + x2) 0", "goal_sig": "14e69e2eb0d7", "goal_sig_strict": "3333658c0bc4", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "constructor": [] } } } } }, { "name": "CommMagma_x2eto_x5fisCommutative", "status": "Solved", "iterations": 1, "mean_ged": 0.0, "mean_ged_search_graph": 0.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_infer_instance", "block_intros", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0 ] ], "history": [ { "tactic": "simp only [mul", "goal": "\u2200 {G : Type u_3} [inst : CommMagma G], Std.Commutative fun x1 x2 => x1 * x2", "outcome": "blocked" }, { "tactic": "simp [mul_", "goal": "\u2200 {G : Type u_3} [inst : CommMagma G], Std.Commutative fun x1 x2 => x1 * x2", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : CommMagma G], Std.Commutative fun x1 x2 => x1 * x2", "outcome": "success" } ], "proof_term_stats": { "node_count": 43, "max_depth": 14, "kind_counts": [ { "label": "app", "count": 17 }, { "label": "lam", "count": 4 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 7 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.14618", "expansion_count": 2, "nodes": { "cp1:_uniq.14618": { "mvar_id": "cp1:_uniq.14618", "goal_type": "\u2200 {G : Type 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1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {\u03b1 : Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "blocked" }, { "tactic": "rfl", "goal": "\u2200 {\u03b1 : Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "blocked" }, { "tactic": "simp [DivisionMon", "goal": "\u2200 {\u03b1 : Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "success" } ], "proof_term_stats": { "node_count": 27, "max_depth": 10, "kind_counts": [ { "label": "app", "count": 9 }, { "label": "lam", "count": 4 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 4 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.19716", "expansion_count": 2, "nodes": { "cp1:_uniq.19716": { "mvar_id": "cp1:_uniq.19716", "goal_type": "\u2200 {\u03b1 : Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "goal_sig": "fcdb958230d6", "goal_sig_strict": "fcdb958230d6", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.19731.3" ] } }, "cp2:_uniq.19731.3": { "mvar_id": "cp2:_uniq.19731.3", "goal_type": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "goal_sig": "f3242f98ed58", "goal_sig_strict": "6b2079f7fd7f", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "congr": [] } } } } }, { "name": "IsRightCancelAdd_x2etoGrindAddRightCancel", "status": "Solved", "iterations": 1, "mean_ged": 3.5, "mean_ged_search_graph": 3.5, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_infer_instance", "block_intro" ], "ged_matrix": [ [ 0.0, 0.5714285714285714, 0.42857142857142855 ], [ 0.5714285714285714, 0.0, 1.0 ], [ 0.42857142857142855, 1.0, 0.0 ] ], "history": [ { "tactic": "intro \u03b1 _", "goal": "\u2200 (\u03b1 : Type u_5) [inst : AddSemigroup \u03b1] [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "outcome": "success" } ], "proof_term_stats": { "node_count": 35, 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r b c \u2192 p a b \u2192 p b c \u2192 p a c \u2192 f a c = f a b + f b c) \u2192\n \u2200 {a b c : \u03b1}, p a b \u2192 p b c \u2192 p a c \u2192 f a c = f a b + f b c", "goal_sig": "1fda03de5ebf", "goal_sig_strict": "1fda03de5ebf", "visit_count": 5, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1 \u03b2 _ _": [ "cp2:_uniq.483966.11" ] } }, "cp2:_uniq.483966.11": { "mvar_id": "cp2:_uniq.483966.11", "goal_type": "\u2200 (r : \u03b1 \u2192 \u03b1 \u2192 Prop) [IsTotal \u03b1 r] (f : \u03b1 \u2192 \u03b1 \u2192 \u03b2),\n Symmetric p\u271d \u2192\n (\u2200 {a b : \u03b1}, p\u271d a b \u2192 f a b + f b a = 0) \u2192\n (\u2200 {a b c : \u03b1}, r a b \u2192 r b c \u2192 p\u271d a b \u2192 p\u271d b c \u2192 p\u271d a c \u2192 f a c = f a b + f b c) \u2192\n \u2200 {a b c : \u03b1}, p\u271d a b \u2192 p\u271d b c \u2192 p\u271d a c \u2192 f a c = f a b + f b c", "goal_sig": "b9da55979b25", "goal_sig_strict": 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[zero_", "goal": "0 \u2022 a\u271d = 0", "outcome": "blocked" }, { "tactic": "ext", "goal": "0 \u2022 a\u271d = 0", "outcome": "failure" }, { "tactic": "rw [smul_def", "goal": "0 \u2022 a\u271d = 0", "outcome": "failure" }, { "tactic": "rw [zero_smul", "goal": "0 \u2022 a\u271d = 0", "outcome": "failure" }, { "tactic": "rw [smul_zero", "goal": "0 \u2022 a\u271d = 0", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.488191", "expansion_count": 2, "nodes": { "cp1:_uniq.488191": { "mvar_id": "cp1:_uniq.488191", "goal_type": "\u2200 {M : Type u_4} [inst : AddMonoid M] (P : Prop) [inst_1 : Decidable P] (a : M),\n (if P then 1 else 0) \u2022 a = if P then a else 0", "goal_sig": "a84c8af4ecab", "goal_sig_strict": "a84c8af4ecab", "visit_count": 6, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.488207.6" ] } }, "cp2:_uniq.488207.6": { "mvar_id": "cp2:_uniq.488207.6", "goal_type": "(if P\u271d 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