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Type u_1} [inst : DivisionMonoid \u03b1],\n DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "success" }, { "tactic": "rfl", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "blocked" }, { "tactic": "ext", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "failure" }, { "tactic": "funext", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "success" }, { "tactic": "apply Subtype.eq", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "failure" }, { "tactic": "dsimp [Division", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "failure" }, { "tactic": "dsimp only [Div", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "outcome": "failure" }, { "tactic": "congr", "goal": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.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.26631", "expansion_count": 2, "nodes": { "cp1:_uniq.26631": { "mvar_id": "cp1:_uniq.26631", "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.26646.3" ] } }, "cp2:_uniq.26646.3": { "mvar_id": "cp2:_uniq.26646.3", "goal_type": "DivisionMonoid.toDivInvOneMonoid =\n let __DivInvMonoid := inst\u271d.toDivInvMonoid;\n { toDivInvMonoid := __DivInvMonoid, inv_one := \u22ef }", "goal_sig": "f3242f98ed58", "goal_sig_strict": "10300c28d79e", "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": 3, "mean_ged": 2.3333333333333335, "mean_ged_search_graph": 2.3333333333333335, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_infer_instance", "block_intro", "control_null" ], "ged_matrix": [ [ 0.0, 0.5714285714285714, 0.42857142857142855, 0.0 ], [ 0.5714285714285714, 0.0, 1.0, 0.5714285714285714 ], [ 0.42857142857142855, 1.0, 0.0, 0.42857142857142855 ], [ 0.0, 0.5714285714285714, 0.42857142857142855, 0.0 ] ], "history": [ { "tactic": "intro \u03b1 _", "goal": "\u2200 (\u03b1 : Type u_5) [inst : AddSemigroup \u03b1] [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "outcome": "success" }, { "tactic": "simp [IsRightCancel", "goal": "\u2200 [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "outcome": "blocked" }, { "tactic": "simp only [IsRight", "goal": "\u2200 [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "outcome": "blocked" }, { "tactic": "intro", "goal": "\u2200 [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "outcome": "success" }, { "tactic": "infer_instance", "goal": "Lean.Grind.AddRightCancel \u03b1", "outcome": "success" } ], "proof_term_stats": { "node_count": 35, "max_depth": 9, "kind_counts": [ { "label": "app", "count": 14 }, { "label": "lam", "count": 3 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 6 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.28518", "expansion_count": 3, "nodes": { "cp1:_uniq.28518": { "mvar_id": "cp1:_uniq.28518", "goal_type": "\u2200 (\u03b1 : Type u_5) [inst : AddSemigroup \u03b1] [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "goal_sig": "2cb87b871c58", "goal_sig_strict": "2cb87b871c58", "visit_count": 3, "success_count": 3, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1 _": [ "cp2:_uniq.28526.5" ] } }, "cp2:_uniq.28526.5": { "mvar_id": "cp2:_uniq.28526.5", "goal_type": "\u2200 [IsRightCancelAdd \u03b1], Lean.Grind.AddRightCancel \u03b1", "goal_sig": "61934ae9bba4", "goal_sig_strict": "6eb86c844f7c", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "intro": [ "cp3:_uniq.28526.8" ] } }, "cp3:_uniq.28526.8": { "mvar_id": "cp3:_uniq.28526.8", "goal_type": "Lean.Grind.AddRightCancel \u03b1", "goal_sig": "f77c152a43bf", "goal_sig_strict": "8d4def0e39e8", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 2, "expansion_order": 2, "children": { "infer_instance": [] } } } } }, { "name": "Semigroup_x2eto_x5fisAssociative", "status": "Solved", "iterations": 2, "mean_ged": 0.6666666666666666, "mean_ged_search_graph": 0.6666666666666666, "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, 1.0, 0.0 ], [ 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} [inst : Semigroup \u03b1], Std.Associative fun x1 x2 => x1 * x2", "outcome": "success" }, { "tactic": "simp only [mul", "goal": "Std.Associative fun x1 x2 => x1 * x2", "outcome": "blocked" }, { "tactic": "intros", "goal": "Std.Associative fun x1 x2 => x1 * x2", "outcome": "success" }, { "tactic": "infer_instance", "goal": "Std.Associative 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.34451", "expansion_count": 2, "nodes": { "cp1:_uniq.34451": { "mvar_id": "cp1:_uniq.34451", "goal_type": "\u2200 {\u03b1 : Type u_1} [inst : Semigroup \u03b1], Std.Associative fun x1 x2 => x1 * x2", "goal_sig": "b2dd85793637", "goal_sig_strict": "b2dd85793637", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.34463.3" ] } }, "cp2:_uniq.34463.3": { "mvar_id": "cp2:_uniq.34463.3", "goal_type": "Std.Associative fun x1 x2 => x1 * x2", "goal_sig": "9df2984fb890", "goal_sig_strict": "687ff1743d1b", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "infer_instance": [] } } } } }, { "name": "Semigroup_x2eto_x5fisLawfulIdentity", "status": "Solved", "iterations": 2, "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 {M : Type u_4} [inst : MulOneClass M], Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {M : Type u_4} [inst : MulOneClass M], Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "outcome": "success" }, { "tactic": "simp only [mul", "goal": "Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "outcome": "blocked" }, { "tactic": "intros", "goal": "Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "outcome": "success" }, { "tactic": "infer_instance", "goal": "Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "outcome": "success" } ], "proof_term_stats": { "node_count": 67, "max_depth": 16, "kind_counts": [ { "label": "app", "count": 29 }, { "label": "lam", "count": 4 }, { "label": "forall", "count": 0 }, { "label": "unique_consts", "count": 11 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.40696", "expansion_count": 2, "nodes": { "cp1:_uniq.40696": { "mvar_id": "cp1:_uniq.40696", "goal_type": "\u2200 {M : Type u_4} [inst : MulOneClass M], Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "goal_sig": "0001b1607213", "goal_sig_strict": "0001b1607213", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.40708.3" ] } }, "cp2:_uniq.40708.3": { "mvar_id": "cp2:_uniq.40708.3", "goal_type": "Std.LawfulIdentity (fun x1 x2 => x1 * x2) 1", "goal_sig": "e282f2300c98", "goal_sig_strict": "60026d9f8a2e", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "infer_instance": [] } } } } }, { "name": "SubtractionMonoid_x2etoSubNegZeroMonoid_x2eeq_x5f1", "status": "Solved", "iterations": 2, "mean_ged": 0.0, "mean_ged_search_graph": 0.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_congr", "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 [Subtraction", "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": "simp", "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": "rfl", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "blocked" }, { "tactic": "simp", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "blocked" }, { "tactic": "ext", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "dsimp only [Sub", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "dsimp [Subt", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "funext", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "success" }, { "tactic": "apply SubtractionMonoid", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "cases SubNegMonoid.", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "congr", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \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.44448", "expansion_count": 2, "nodes": { "cp1:_uniq.44448": { "mvar_id": "cp1:_uniq.44448", "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", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.44463.3" ] } }, "cp2:_uniq.44463.3": { "mvar_id": "cp2:_uniq.44463.3", "goal_type": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst\u271d.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "goal_sig": "0f54c9c8d604", "goal_sig_strict": "b7d584420502", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "congr": [] } } } } }, { "name": "add_x5fadd_x5fadd_x5fcomm", "status": "Failed", "iterations": 7, "mean_ged": 0.42857142857142855, "mean_ged_search_graph": 0.42857142857142855, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_abel", "block_ac_rfl", "block_intros", "block_ring", "block_rw", "block_simp", "block_try" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 1.0, 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, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 ], [ 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0 ], [ 0.0, 0.0, 0.0, 1.0, 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, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 ], [ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "blocked" }, { "tactic": "simp [add_assoc", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "blocked" }, { "tactic": "simp only [add_comm", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "blocked" }, { "tactic": "simp only [add_ass", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "blocked" }, { "tactic": "simp only [add_left", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "outcome": "success" }, { "tactic": "simp only [add_", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "blocked" }, { "tactic": "simp [add_ass", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "blocked" }, { "tactic": "simp", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "blocked" }, { "tactic": "rw [add_assoc", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "abel", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "ac_rfl", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "try rw [add_", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "rw [add_comm,", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "rw [\u2190 add_", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" }, { "tactic": "ring", "goal": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.47339", "expansion_count": 1, "nodes": { "cp1:_uniq.47339": { "mvar_id": "cp1:_uniq.47339", "goal_type": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)", "goal_sig": "95ed15bec22b", "goal_sig_strict": "95ed15bec22b", "visit_count": 7, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.47357.7" ] } }, "cp2:_uniq.47357.7": { "mvar_id": "cp2:_uniq.47357.7", "goal_type": "a\u271d + b\u271d + (c\u271d + d\u271d) = a\u271d + c\u271d + (b\u271d + d\u271d)", "goal_sig": "7f6236953684", "goal_sig_strict": "d151b2e60012", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": {} } } } }, { "name": "add_x5fadd_x5fadd_x5fcomm_x27", "status": "Failed", "iterations": 7, "mean_ged": 0.125, "mean_ged_search_graph": 0.125, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_abel", "block_ac_rfl", "block_intros", "block_rfl", "block_ring", "block_rw", "block_simp", "block_try" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 1.0, 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 ], [ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0 ], [ 0.0, 0.0, 0.0, 1.0, 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 ], [ 0.0, 0.0, 0.0, 1.0, 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 ], [ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "outcome": "blocked" }, { "tactic": "simp [add_assoc", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "outcome": "blocked" }, { "tactic": "simp only [add_ass", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "outcome": "blocked" }, { "tactic": "simp only [add_comm", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "outcome": "success" }, { "tactic": "simp only [add_", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "blocked" }, { "tactic": "rfl", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "blocked" }, { "tactic": "simp [add_ass", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "blocked" }, { "tactic": "rw [add_assoc", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "rw [\u2190 add_", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "abel", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "rw [add_comm,", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "ac_rfl", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "ring", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" }, { "tactic": "try rw [add_", "goal": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.66483", "expansion_count": 1, "nodes": { "cp1:_uniq.66483": { "mvar_id": "cp1:_uniq.66483", "goal_type": "\u2200 {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + c + d = a + c + b + d", "goal_sig": "0e17b39fb3b2", "goal_sig_strict": "0e17b39fb3b2", "visit_count": 7, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.66501.7" ] } }, "cp2:_uniq.66501.7": { "mvar_id": "cp2:_uniq.66501.7", "goal_type": "a\u271d + b\u271d + c\u271d + d\u271d = a\u271d + c\u271d + b\u271d + d\u271d", "goal_sig": "020b04cbb60f", "goal_sig_strict": "ef86140e0a2e", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": {} } } } }, { "name": "add_x5fadd_x5fneg_x5fcancel_x27_x5fright", "status": "Solved", "iterations": 2, "mean_ged": 1.0, "mean_ged_search_graph": 1.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_abel", "block_intros", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "decide", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "simp [add_comm]", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "simp [add_left_", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "simp [sub_eq_", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "simp only [neg_add", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "simp only [add_left", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "outcome": "success" }, { "tactic": "simp", "goal": "a\u271d + (b\u271d + -a\u271d) = b\u271d", "outcome": "blocked" }, { "tactic": "simp [add_comm", "goal": "a\u271d + (b\u271d + -a\u271d) = b\u271d", "outcome": "blocked" }, { "tactic": "simp only [add_", "goal": "a\u271d + (b\u271d + -a\u271d) = b\u271d", "outcome": "blocked" }, { "tactic": "abel", "goal": "a\u271d + (b\u271d + -a\u271d) = b\u271d", "outcome": "success" } ], "proof_term_stats": { "node_count": 2253, "max_depth": 33, "kind_counts": [ { "label": "app", "count": 1119 }, { "label": "lam", "count": 4 }, { "label": "forall", "count": 3 }, { "label": "unique_consts", "count": 56 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.87264", "expansion_count": 2, "nodes": { "cp1:_uniq.87264": { "mvar_id": "cp1:_uniq.87264", "goal_type": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b + -a) = b", "goal_sig": "2b33fc8b73d1", "goal_sig_strict": "2b33fc8b73d1", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.87278.5" ] } }, "cp2:_uniq.87278.5": { "mvar_id": "cp2:_uniq.87278.5", "goal_type": "a\u271d + (b\u271d + -a\u271d) = b\u271d", "goal_sig": "675fd020867e", "goal_sig_strict": "203920d46c29", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "abel": [] } } } } }, { "name": "add_x5fadd_x5fsub_x5fcancel", "status": "Solved", "iterations": 2, "mean_ged": 1.0, "mean_ged_search_graph": 1.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_abel", "block_intros", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "simp [sub_eq_", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "simp only [sub_eq", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "decide", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "simp [add_comm]", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "simp only [add_ass", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "outcome": "success" }, { "tactic": "simp", "goal": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "outcome": "blocked" }, { "tactic": "simp only [add_", "goal": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "outcome": "blocked" }, { "tactic": "simp [add_comm", "goal": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "outcome": "blocked" }, { "tactic": "simp [sub_eq", "goal": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "outcome": "blocked" }, { "tactic": "abel", "goal": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "outcome": "success" } ], "proof_term_stats": { "node_count": 3495, "max_depth": 35, "kind_counts": [ { "label": "app", "count": 1739 }, { "label": "lam", "count": 5 }, { "label": "forall", "count": 3 }, { "label": "unique_consts", "count": 61 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.94720", "expansion_count": 2, "nodes": { "cp1:_uniq.94720": { "mvar_id": "cp1:_uniq.94720", "goal_type": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + c + (b - c) = a + b", "goal_sig": "94bfd7f9899b", "goal_sig_strict": "94bfd7f9899b", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.94736.6" ] } }, "cp2:_uniq.94736.6": { "mvar_id": "cp2:_uniq.94736.6", "goal_type": "a\u271d + c\u271d + (b\u271d - c\u271d) = a\u271d + b\u271d", "goal_sig": "cbbc983be051", "goal_sig_strict": "0418e6cebeb1", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "abel": [] } } } } }, { "name": "add_x5fcomm_x5fsub", "status": "Failed", "iterations": 9, "mean_ged": 1.25, "mean_ged_search_graph": 1.25, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_intros", "block_rfl", "block_rw", "block_simp" ], "ged_matrix": [ [ 0.0, 0.6, 0.0, 0.4, 0.0 ], [ 0.6, 0.0, 0.6, 1.0, 0.6 ], [ 0.0, 0.6, 0.0, 0.4, 0.0 ], [ 0.4, 1.0, 0.4, 0.0, 0.4 ], [ 0.0, 0.6, 0.0, 0.4, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionCommMonoid \u03b1] (a b c : \u03b1), a - b + c = a + (c - b)", "outcome": "blocked" }, { "tactic": "simp [sub_eq_", "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionCommMonoid \u03b1] (a b c : \u03b1), a - b + c = a + (c - b)", "outcome": "blocked" }, { "tactic": "simp only [sub_eq", "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionCommMonoid \u03b1] (a b c : \u03b1), a - b + c = a + (c - b)", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} [inst : SubtractionCommMonoid \u03b1] (a b c : \u03b1), a - b + c = a + (c - b)", "outcome": "success" }, { "tactic": "simp [sub_eq", "goal": "a\u271d - b\u271d + c\u271d = a\u271d + (c\u271d - b\u271d)", "outcome": "blocked" }, { "tactic": "rfl", "goal": "a\u271d - b\u271d + c\u271d = a\u271d + (c\u271d - b\u271d)", "outcome": "blocked" }, { 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"add_x5fsub_x5fsub_x5fcancel", "status": "Solved", "iterations": 2, "mean_ged": 1.0, "mean_ged_search_graph": 1.0, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_abel", "block_intros", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + b - (a - c) = b + c", "outcome": "blocked" }, { "tactic": "simp [sub_eq_", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + b - (a - c) = b + c", "outcome": "blocked" }, { "tactic": "simp only [sub_eq", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + b - (a - c) = b + c", "outcome": "blocked" }, { "tactic": "decide", "goal": "\u2200 {G : Type u_3} [inst : AddCommGroup G] (a b c : G), a + b - (a - c) = b + c", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {G : Type 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"cp4:_uniq.748684.48": { "mvar_id": "cp4:_uniq.748684.48", "goal_type": "a\u271d\u00b9 + Int.ofNat a\u271d \u2022 a\u271d\u00b9 = (Int.ofNat a\u271d + 1) \u2022 a\u271d\u00b9", "goal_sig": "789365e16e53", "goal_sig_strict": "fc2be2164d6d", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 3, "expansion_order": 3, "children": {} }, "cp4:_uniq.748684.62": { "mvar_id": "cp4:_uniq.748684.62", "goal_type": "a\u271d\u00b9 + Int.negSucc a\u271d \u2022 a\u271d\u00b9 = (Int.negSucc a\u271d + 1) \u2022 a\u271d\u00b9", "goal_sig": "ad1974c0dfe2", "goal_sig_strict": "a8c23114563d", "visit_count": 3, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 3, "expansion_order": 3, "children": { "norm_num": [ "cp5:_uniq.748684.1567" ] } }, "cp5:_uniq.748684.1567": { "mvar_id": "cp5:_uniq.748684.1567", "goal_type": "a\u271d\u00b9 + -((a\u271d + 1) \u2022 a\u271d\u00b9) = (Int.negSucc a\u271d + 1) \u2022 a\u271d\u00b9", "goal_sig": "27d360b02a32", "goal_sig_strict": "a0b3d9036f76", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 4, "expansion_order": 4, "children": {} } } } }, { "name": "additive_x5fof_x5fisTotal", "status": "Failed", "iterations": 7, "mean_ged": 10.75, "mean_ged_search_graph": 10.75, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_apply", "block_exact", "block_intros", "block_simp" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : AddMonoid \u03b2] (r : \u03b1 \u2192 \u03b1 \u2192 Prop) [IsTotal \u03b1 r] (f : \u03b1 \u2192 \u03b1 \u2192 \u03b2) (p : \u03b1 \u2192 Prop),\n (\u2200 {a b : \u03b1}, p a \u2192 p 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 a \u2192 p b \u2192 p c \u2192 f a c = f a b + f b c) \u2192\n \u2200 {a b c : \u03b1}, p a \u2192 p b \u2192 p c \u2192 f a c = f a b + f b c", "outcome": "success" }, { "tactic": "simp [a\u207b\u00b9", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "blocked" }, { "tactic": "exact a\u207b\u00b9 \ufffd", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "apply a\u00b3", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u207b\u00b9.2", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact IsTotal.total _ _ _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u207b\u00b9\u00b9", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "apply a\u271d\u00b9", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u207b\u00b9.1", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact IsTotal.total _ _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u207b\u00b9' (", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.761794", "expansion_count": 1, "nodes": { "cp1:_uniq.761794": { "mvar_id": "cp1:_uniq.761794", "goal_type": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : AddMonoid \u03b2] (r : \u03b1 \u2192 \u03b1 \u2192 Prop) [IsTotal \u03b1 r] (f : \u03b1 \u2192 \u03b1 \u2192 \u03b2) (p : \u03b1 \u2192 Prop),\n (\u2200 {a b : \u03b1}, p a \u2192 p 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 a \u2192 p b \u2192 p c \u2192 f a c = f a b + f b c) \u2192\n \u2200 {a b c : \u03b1}, p a \u2192 p b \u2192 p c \u2192 f a c = f a b + f b c", "goal_sig": "f63c8a0ed14e", "goal_sig_strict": "f63c8a0ed14e", "visit_count": 7, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.761866.16" ] } }, "cp2:_uniq.761866.16": { "mvar_id": "cp2:_uniq.761866.16", "goal_type": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "goal_sig": "0fbceb61aa40", "goal_sig_strict": "68ee8e17a850", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": {} } } } }, { "name": "additive_x5fof_x5fsymmetric_x5fof_x5fisTotal", "status": "Failed", "iterations": 9, "mean_ged": 2.5, "mean_ged_search_graph": 2.5, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_exact", "block_intro", "block_intros", "block_simpa" ], "ged_matrix": [ [ 0.0, 0.0, 0.3333333333333333, 0.7777777777777778, 0.0 ], [ 0.0, 0.0, 0.3333333333333333, 0.7777777777777778, 0.0 ], [ 0.3333333333333333, 0.3333333333333333, 0.0, 1.0, 0.3333333333333333 ], [ 0.7777777777777778, 0.7777777777777778, 1.0, 0.0, 0.7777777777777778 ], [ 0.0, 0.0, 0.3333333333333333, 0.7777777777777778, 0.0 ] ], "history": [ { "tactic": "intro \u03b1 \u03b2 _ _", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : AddMonoid \u03b2] (p r : \u03b1 \u2192 \u03b1 \u2192 Prop) [IsTotal \u03b1 r] (f : \u03b1 \u2192 \u03b1 \u2192 \u03b2),\n Symmetric p \u2192\n (\u2200 {a b : \u03b1}, p 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 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", "outcome": "success" }, { "tactic": "intros", "goal": "\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", "outcome": "success" }, { "tactic": "exact a\u271d\u00b9 a\u271d", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u271d\u00b3 a\u271d", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u271d\u00b9", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact add_comm _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact IsTotal.total a\u271d\u00b3", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u271d\u00b9 _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact IsTotal.total _ _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact a\u271d\u00b9 _ _ a\ufffd", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "simpa using a\u271d\u00b9 a\ufffd", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" }, { "tactic": "exact IsTotal.total _ _ _ _", "goal": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.776894", "expansion_count": 2, "nodes": { "cp1:_uniq.776894": { "mvar_id": "cp1:_uniq.776894", "goal_type": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : AddMonoid \u03b2] (p r : \u03b1 \u2192 \u03b1 \u2192 Prop) [IsTotal \u03b1 r] (f : \u03b1 \u2192 \u03b1 \u2192 \u03b2),\n Symmetric p \u2192\n (\u2200 {a b : \u03b1}, p 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 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": 9, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1 \u03b2 _ _": [ "cp2:_uniq.776964.11" ] } }, "cp2:_uniq.776964.11": { "mvar_id": "cp2:_uniq.776964.11", "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": "fb016293b05f", "visit_count": 3, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": { "intros": [ "cp3:_uniq.776964.25" ] } }, "cp3:_uniq.776964.25": { "mvar_id": "cp3:_uniq.776964.25", "goal_type": "f\u271d a\u271d\u00b3 c\u271d = f\u271d a\u271d\u00b3 b\u271d + f\u271d b\u271d c\u271d", "goal_sig": "12b69b5112cc", "goal_sig_strict": "7233a30603d4", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 2, "expansion_order": 2, "children": {} } } } }, { "name": "boole_x5fnsmul", "status": "Failed", "iterations": 10, "mean_ged": 1.375, "mean_ged_search_graph": 1.375, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_cases", "block_decide", "block_ext", "block_intros", "block_rfl", "block_rw", "block_simp", "block_split_ifs" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.7777777777777778, 0.7777777777777778, 0.7777777777777778, 0.7777777777777778, 0.0, 0.7777777777777778, 0.7777777777777778, 0.7777777777777778, 1.0 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.0, 0.0, 0.7777777777777778, 0.0, 0.0, 0.0, 0.4444444444444444 ], [ 0.4444444444444444, 0.4444444444444444, 0.4444444444444444, 0.4444444444444444, 1.0, 0.4444444444444444, 0.4444444444444444, 0.4444444444444444, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\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", "outcome": "blocked" }, { "tactic": "decide", "goal": "\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", "outcome": "blocked" }, { "tactic": "simp only 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"tactic": "simp", "goal": "(if P\u271d then 1 else 0) \u2022 a\u271d = if P\u271d then a\u271d else 0", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "(if P\u271d then 1 else 0) \u2022 a\u271d = if P\u271d then a\u271d else 0", "outcome": "blocked" }, { "tactic": "simp [smul_def", "goal": "(if P\u271d then 1 else 0) \u2022 a\u271d = if P\u271d then a\u271d else 0", "outcome": "blocked" }, { "tactic": "simp [smul_add", "goal": "(if P\u271d then 1 else 0) \u2022 a\u271d = if P\u271d then a\u271d else 0", "outcome": "blocked" }, { "tactic": "split_ifs", "goal": "(if P\u271d then 1 else 0) \u2022 a\u271d = if P\u271d then a\u271d else 0", "outcome": "success" }, { "tactic": "rfl", "goal": "1 \u2022 a\u271d = a\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "1 \u2022 a\u271d = a\u271d", "outcome": "blocked" }, { "tactic": "simp [smul_", "goal": "1 \u2022 a\u271d = a\u271d", "outcome": "blocked" }, { "tactic": "simp [one_sm", "goal": "1 \u2022 a\u271d = a\u271d", 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\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.790267", "expansion_count": 2, "nodes": { "cp1:_uniq.790267": { "mvar_id": "cp1:_uniq.790267", "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": 10, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.790283.6" ] } }, "cp2:_uniq.790283.6": { "mvar_id": "cp2:_uniq.790283.6", "goal_type": "(if P\u271d then 1 else 0) 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c\u271d = if h : p\u271d then a\u271d h ^ c\u271d else b\u271d h ^ c\u271d", "outcome": "success" }, { "tactic": "rfl", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp only [pow_def", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp [Pow.pow", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp only [Pow.", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp only [pow_apply", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "congr", "goal": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "outcome": "success" }, { "tactic": "rfl", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp [h]", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp_all", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp only [not_not", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "simp only [not_false", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "blocked" }, { "tactic": "congr", "goal": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "outcome": "success" } ], "proof_term_stats": { "node_count": 1409, "max_depth": 29, "kind_counts": [ { "label": "app", "count": 648 }, { "label": "lam", "count": 52 }, { "label": "forall", "count": 4 }, { "label": "unique_consts", "count": 14 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.938559", "expansion_count": 4, "nodes": { "cp1:_uniq.938559": { "mvar_id": "cp1:_uniq.938559", "goal_type": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : Pow \u03b1 \u03b2] (p : Prop) [inst_1 : Decidable p] (a : p \u2192 \u03b1) (b : \u00acp \u2192 \u03b1) (c : \u03b2),\n (if h : p then a h else b h) ^ c = if h : p then a h ^ c else b h ^ c", "goal_sig": "ce9ef822f82d", "goal_sig_strict": "ce9ef822f82d", "visit_count": 4, "success_count": 4, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.938591.9" ] } }, "cp2:_uniq.938591.9": { "mvar_id": "cp2:_uniq.938591.9", "goal_type": "(if h : p\u271d then a\u271d h else b\u271d h) ^ c\u271d = if h : p\u271d then a\u271d h ^ c\u271d else b\u271d h ^ c\u271d", "goal_sig": "b0404c3f2b70", "goal_sig_strict": "ee7266507280", "visit_count": 3, "success_count": 3, "is_terminal": false, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "split_ifs": [ "cp3:_uniq.938591.212", "cp3:_uniq.938591.429" ] } }, "cp3:_uniq.938591.212": { "mvar_id": "cp3:_uniq.938591.212", "goal_type": "a\u271d h\u271d ^ c\u271d = a\u271d h\u271d ^ c\u271d", "goal_sig": "8961886d9c84", "goal_sig_strict": "18f205c97901", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 2, "expansion_order": 2, "children": { "congr": [] } }, "cp3:_uniq.938591.429": { "mvar_id": "cp3:_uniq.938591.429", "goal_type": "b\u271d h\u271d ^ c\u271d = b\u271d h\u271d ^ c\u271d", "goal_sig": "8961886d9c84", "goal_sig_strict": "9c56c1ac0c46", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 2, "expansion_order": 2, "children": { "congr": [] } } } } }, { "name": "dite_x5fsmul", "status": "Solved", "iterations": 4, "mean_ged": 2.25, "mean_ged_search_graph": 2.25, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_congr", "block_intros", "block_split_ifs", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 0.5555555555555556, 0.4444444444444444, 0.0 ], [ 0.0, 0.0, 0.5555555555555556, 0.4444444444444444, 0.0 ], [ 0.5555555555555556, 0.5555555555555556, 0.0, 1.0, 0.5555555555555556 ], [ 0.4444444444444444, 0.4444444444444444, 1.0, 0.0, 0.4444444444444444 ], [ 0.0, 0.0, 0.5555555555555556, 0.4444444444444444, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : SMul \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) \u2022 a = if h : p then b h \u2022 a else c h \u2022 a", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : SMul \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) \u2022 a = if h : p then b h \u2022 a else c h \u2022 a", "outcome": "blocked" }, { "tactic": "decide", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : SMul \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) \u2022 a = if h : p then b h \u2022 a else c h \u2022 a", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : SMul \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) \u2022 a = if h : p then b h \u2022 a else c h \u2022 a", "outcome": "success" }, { "tactic": "simp [*]", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [dif", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [smul_", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "split_ifs", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "outcome": "success" }, { "tactic": "rfl", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [smul_", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [h]", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [smul_def", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [h, sm", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [\u2190 sm", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "congr", "goal": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "outcome": "success" }, { "tactic": "rfl", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [*]", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp [h]", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [h, sm", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp_all", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "simp only [not_not", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "blocked" }, { "tactic": "congr", "goal": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "outcome": "success" } ], "proof_term_stats": { "node_count": 1409, "max_depth": 29, "kind_counts": [ { "label": "app", "count": 648 }, { "label": "lam", "count": 52 }, { "label": "forall", "count": 4 }, { "label": "unique_consts", "count": 14 } ] }, "mcts_tree": { "root_mvar_id": "cp1:_uniq.940113", "expansion_count": 4, "nodes": { "cp1:_uniq.940113": { "mvar_id": "cp1:_uniq.940113", "goal_type": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : SMul \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) \u2022 a = if h : p then b h \u2022 a else c h \u2022 a", "goal_sig": "a22be9a216c9", "goal_sig_strict": "a22be9a216c9", "visit_count": 4, "success_count": 4, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intros": [ "cp2:_uniq.940145.9" ] } }, "cp2:_uniq.940145.9": { "mvar_id": "cp2:_uniq.940145.9", "goal_type": "(if h : p\u271d then b\u271d h else c\u271d h) \u2022 a\u271d = if h : p\u271d then b\u271d h \u2022 a\u271d else c\u271d h \u2022 a\u271d", "goal_sig": "fa9fe41ebd01", "goal_sig_strict": "f41f1c0a5e2e", "visit_count": 3, "success_count": 3, "is_terminal": false, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "split_ifs": [ "cp3:_uniq.940145.219", "cp3:_uniq.940145.443" ] } }, "cp3:_uniq.940145.219": { "mvar_id": "cp3:_uniq.940145.219", "goal_type": "b\u271d h\u271d \u2022 a\u271d = b\u271d h\u271d \u2022 a\u271d", "goal_sig": "f1f04f90184c", "goal_sig_strict": "8675aec4ef9b", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 2, "expansion_order": 2, "children": { "congr": [] } }, "cp3:_uniq.940145.443": { "mvar_id": "cp3:_uniq.940145.443", "goal_type": "c\u271d h\u271d \u2022 a\u271d = c\u271d h\u271d \u2022 a\u271d", "goal_sig": "f1f04f90184c", "goal_sig_strict": "a50296458e1f", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 2, "expansion_order": 2, "children": { "congr": [] } } } } }, { "name": "dite_x5fvadd", "status": "Solved", "iterations": 4, "mean_ged": 3.25, "mean_ged_search_graph": 3.25, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_congr", "block_intros", "block_split_ifs", "control_null" ], "ged_matrix": [ [ 0.0, 0.0, 0.5, 0.8, 0.0 ], [ 0.0, 0.0, 0.5, 0.8, 0.0 ], [ 0.5, 0.5, 0.0, 1.0, 0.5 ], [ 0.8, 0.8, 1.0, 0.0, 0.8 ], [ 0.0, 0.0, 0.5, 0.8, 0.0 ] ], "history": [ { "tactic": "simp", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : VAdd \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) +\u1d65 a = if h : p then b h +\u1d65 a else c h +\u1d65 a", "outcome": "blocked" }, { "tactic": "simp (config := {", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : VAdd \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) +\u1d65 a = if h : p then b h +\u1d65 a else c h +\u1d65 a", "outcome": "blocked" }, { "tactic": "simp [add_vadd", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : VAdd \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) +\u1d65 a = if h : p then b h +\u1d65 a else c h +\u1d65 a", "outcome": "blocked" }, { "tactic": "intros", "goal": "\u2200 {\u03b1 : Type u_1} {\u03b2 : Type u_2} [inst : VAdd \u03b2 \u03b1] (p : Prop) [inst_1 : Decidable p] (a : \u03b1) (b : p \u2192 \u03b2) (c : \u00acp \u2192 \u03b2),\n (if h : p then b h else c h) +\u1d65 a = if h : p then b h +\u1d65 a else c h +\u1d65 a", "outcome": "success" }, { "tactic": "simp [*]", "goal": "(if h : p\u271d then b\u271d h else c\u271d h) +\u1d65 a\u271d = if h : p\u271d then b\u271d h +\u1d65 a\u271d else c\u271d h +\u1d65 a\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "(if h : p\u271d then 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