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"name": "block_rfl", "ged": 2.0, "ged_family": "ged_search_graph", "ged_search_graph": 2.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "add_x5feq_x5fzero_x5fiff_x5fneg_x5feq", "name": "block_simp", "ged": 0.0, "ged_family": "ged_search_graph", "ged_search_graph": 0.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5fdiv_x5fdiv_x5fcancel_x5fright", "name": "block_apply", "ged": 9.0, "ged_family": "ged_search_graph", "ged_search_graph": 9.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": -10.0, "delta_max_depth": -5.0, "delta_backtracks": -6.0, "recovery_iterations": null }, { "theorem": "div_x5fdiv_x5fdiv_x5fcancel_x5fright", "name": "block_have", "ged": 8.0, 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"ged_search_graph": 7.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": -8.0, "delta_max_depth": -4.0, "delta_backtracks": -5.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fiff_x5feq_x5fmul_x27", "name": "block_classical", "ged": 0.0, "ged_family": "ged_search_graph", "ged_search_graph": 0.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fiff_x5feq_x5fmul_x27", "name": "block_have", "ged": 12.0, "ged_family": "ged_search_graph", "ged_search_graph": 12.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": true, "delta_iterations": 4.0, "delta_max_depth": 6.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fiff_x5feq_x5fmul_x27", "name": "block_simp", "ged": 2.0, "ged_family": "ged_search_graph", "ged_search_graph": 2.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "add_x5fzsmul", "name": "block_decide", "ged": 0.0, "ged_family": "ged_search_graph", "ged_search_graph": 0.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "add_x5fzsmul", "name": "block_intros", "ged": 1.0, "ged_family": "ged_search_graph", "ged_search_graph": 1.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": true, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "add_x5fzsmul", "name": "block_simp", "ged": 0.0, "ged_family": "ged_search_graph", "ged_search_graph": 0.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": true, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fof_x5feq_x5fmul_x27", "name": "block_intro", "ged": 3.0, "ged_family": "ged_search_graph", "ged_search_graph": 3.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fof_x5feq_x5fmul_x27", "name": "block_rw", "ged": 4.0, "ged_family": "ged_search_graph", "ged_search_graph": 4.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": true, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null }, { "theorem": "div_x5feq_x5fof_x5feq_x5fmul_x27", "name": "block_simpa", "ged": 2.0, "ged_family": "ged_search_graph", "ged_search_graph": 2.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 2.0, "delta_max_depth": 1.0, "delta_backtracks": 1.0, "recovery_iterations": null }, { "theorem": "add_x5fleft_x5fiterate", "name": "block_intros", "ged": 4.0, "ged_family": "ged_search_graph", "ged_search_graph": 4.0, "ged_proof_graph": null, "ged_trace_graph": null, "solved": false, "delta_iterations": 0.0, "delta_max_depth": 0.0, "delta_backtracks": 0.0, "recovery_iterations": null } ], "ged_histogram": { "bins": [ 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5 ], "counts": [ 8.0, 3.0, 6.0, 1.0, 4.0, 4.0, 0.0, 1.0, 2.0, 2.0, 0.0, 1.0 ] }, "ged_histogram_search": { "bins": [ 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5 ], "counts": [ 8.0, 3.0, 6.0, 1.0, 4.0, 4.0, 0.0, 1.0, 2.0, 2.0, 0.0, 1.0 ] }, "ged_histogram_proof": { "bins": [], "counts": [] }, "ged_histogram_trace": { "bins": [], "counts": [] }, "recovery_histogram": { "bins": [], "counts": [] }, "trajectory_sample": { "theorem": "div_x5fdiv", "wild": { "depth": [ 1.0, 4.0, 3.0, 2.0, 1.0 ], "attempts": [ 1.0, 5.0, 0.0, 0.0, 0.0 ], "success_ratio": [ 1.0, 0.0, 0.0, 0.0, 0.0 ] }, "intervention": { "name": "block_intro", "depth": [ 1.0, 3.0, 2.0, 1.0 ], "attempts": [ 2.0, 0.0, 0.0, 0.0 ], "success_ratio": [ 0.5, 0.0, 0.0, 0.0 ] } }, "ged_sample": { "theorem": "div_x5fdiv", "variants": [ "wild_type", "block_intro", "block_rw", "block_simp" ], "matrix": [ [ 0.0, 0.8, 1.0, 1.0 ], [ 0.8, 0.0, 0.8, 0.8 ], [ 1.0, 0.8, 0.0, 0.0 ], [ 1.0, 0.8, 0.0, 0.0 ] ] }, "goal_tactic_heatmap": { "rows": [ "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c : G}, a / b = c \u2194 a = b * c", "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b", "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "\u2200 {G : Type u_3} [inst : AddGroup G] (a : G) (m n : \u2124), (m + n) \u2022 a = m \u2022 a + n \u2022 a", "\u2200 {\u03b1 : Type u_1} [inst : AddSemigroup \u03b1], Std.Associative fun x1 x2 => x1 + x2", "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "\u2200 {\u03b1 : Type u_1} [inst : SubtractionMonoid \u03b1],\n SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d" ], "cols": [ "intros", "simp [div_eq_mul_inv]", "simp only [div_eq_mul_inv]", "intro \u03b1", "intro G _ _ _", "intro \u03b1 _", "simp", "simp [mul_assoc]", "intro \u03b1 _ _ _", "simp only [div_eq_mul_inv, mul_inv_rev]" ], "matrix": [ [ 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, 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, 0.0 ], [ 1.0, 0.0, 0.0, 0.0, 0.5, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ 0.75, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ], [ 1.0, 0.0, 0.0, 0.5, 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 ], [ 1.0, 0.0, 0.0, 0.6666666666666666, 0.0, 0.5, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] ], "metric": "success_rate" }, "rescue_matrix": { "rows": [ "block_decide", "block_intros", "block_intro", "block_have", "block_simp", "block_rw", "block_apply", "block_ext", "block_first", "block_try", "block_rfl", "block_classical", "block_infer_instance", "control_null", "block_simpa" ], "cols": [ "rescue_rate", "wild_solved_rate" ], "matrix": [ [ 0.5, 0.0 ], [ 0.5, 0.0 ], [ 0.3333333333333333, 0.5 ], [ 0.3333333333333333, 0.0 ], [ 0.16666666666666666, 0.0 ], [ 0.0, 1.0 ], [ 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, 1.0 ], [ 0.0, 0.0 ] ], "metric": "rate" }, "theorem_details": [ { "name": "div_x5fdiv", "status": "Failed", "iterations": 5, "mean_ged": 4.666666666666667, "mean_ged_search_graph": 4.666666666666667, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_intro", "block_rw", "block_simp" ], "ged_matrix": [ [ 0.0, 0.8, 1.0, 1.0 ], [ 0.8, 0.0, 0.8, 0.8 ], [ 1.0, 0.8, 0.0, 0.0 ], [ 1.0, 0.8, 0.0, 0.0 ] ], "history": [ { "tactic": "intro \u03b1 _ _ _", "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\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "a\u271d * b\u271d\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "outcome": "blocked" }, { "tactic": "simp only [\u2190 div_eq_mul_inv, div_mul_div_cancel]", "goal": "a\u271d * b\u271d\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_inv_rev]", "goal": "a\u271d * b\u271d\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "outcome": "blocked" }, { "tactic": "rw [div_eq_mul_inv, mul_assoc, mul_inv_cancel_right\u2080 (zero_lt_one.trans_le (zero_le_one : 0 < 1)),\n mul_one]", "goal": "a\u271d * b\u271d\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.2154", "expansion_count": 3, "nodes": { "cp1:_uniq.2154": { "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": 7, "success_count": 3, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1 _ _ _": [ "cp2:_uniq.2170.11" ] } }, "cp2:_uniq.2170.11": { "mvar_id": "cp2:_uniq.2170.11", "goal_type": "\u2200 (c : \u03b1), a\u271d / b\u271d / c = a\u271d / (b\u271d * c)", "goal_sig": "a7820483e5ba", "goal_sig_strict": "29d5893c402b", "visit_count": 5, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": { "intros": [ "cp3:_uniq.2170.14" ] } }, "cp3:_uniq.2170.14": { "mvar_id": "cp3:_uniq.2170.14", "goal_type": "a\u271d / b\u271d / c\u271d = a\u271d / (b\u271d * c\u271d)", "goal_sig": "595bb0eb2e12", "goal_sig_strict": "f39038042727", "visit_count": 3, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 2, "expansion_order": 2, "children": { "rw [div_eq_mul_inv, div_eq_mul_inv]": [ "cp4:_uniq.2170.467" ] } }, "cp4:_uniq.2170.467": { "mvar_id": "cp4:_uniq.2170.467", "goal_type": "a\u271d * b\u271d\u207b\u00b9 * c\u271d\u207b\u00b9 = a\u271d / (b\u271d * c\u271d)", "goal_sig": "72cd07610eb4", "goal_sig_strict": "3ce6fd56c5fa", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 3, "expansion_order": 3, "children": {} } } } }, { "name": "SubtractionMonoid_x2etoSubNegZeroMonoid_x2eeq_x5f1", "status": "Failed", "iterations": 5, "mean_ged": 4.666666666666667, "mean_ged_search_graph": 4.666666666666667, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_apply", "block_ext", "block_intro" ], "ged_matrix": [ [ 0.0, 1.0, 0.8, 1.0 ], [ 1.0, 0.0, 0.6, 0.0 ], [ 0.8, 0.6, 0.0, 0.6 ], [ 1.0, 0.0, 0.6, 0.0 ] ], "history": [ { "tactic": "intro \u03b1", "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": "ext", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" }, { "tactic": "apply ext", "goal": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.8829", "expansion_count": 3, "nodes": { "cp1:_uniq.8829": { "mvar_id": "cp1:_uniq.8829", "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": 7, "success_count": 3, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1": [ "cp2:_uniq.8844.2" ] } }, "cp2:_uniq.8844.2": { "mvar_id": "cp2:_uniq.8844.2", "goal_type": "\u2200 [inst : SubtractionMonoid \u03b1],\n SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "goal_sig": "41b89678652b", "goal_sig_strict": "4cb2d9f383fc", "visit_count": 5, "success_count": 2, "is_terminal": false, "is_dead": true, "depth": 1, "expansion_order": 1, "children": { "letI := Classical.decEq \u03b1": [ "cp3:_uniq.8844.12" ] } }, "cp3:_uniq.8844.12": { "mvar_id": "cp3:_uniq.8844.12", "goal_type": "\u2200 [inst : SubtractionMonoid \u03b1],\n SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "goal_sig": "3aff9f6aa18f", "goal_sig_strict": "9ef4d22b8243", "visit_count": 3, "success_count": 1, "is_terminal": false, "is_dead": true, "depth": 2, "expansion_order": 2, "children": { "intro inst": [ "cp4:_uniq.8844.15" ] } }, "cp4:_uniq.8844.15": { "mvar_id": "cp4:_uniq.8844.15", "goal_type": "SubtractionMonoid.toSubNegZeroMonoid =\n let __SubNegMonoid := inst.toSubNegMonoid;\n { toSubNegMonoid := __SubNegMonoid, neg_zero := \u22ef }", "goal_sig": "0bf122f9500a", "goal_sig_strict": "9741632382b3", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 3, "expansion_order": 3, "children": {} } } } }, { "name": "div_x5feq_x5fdiv_x5fiff_x5fdiv_x5feq_x5fdiv", "status": "Failed", "iterations": 1, "mean_ged": 0.4, "mean_ged_search_graph": 0.4, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_first", "block_have", "block_rw", "block_simp", "block_try" ], "ged_matrix": [ [ 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ], [ 1.0, 1.0, 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp [div_eq_mul_inv]", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_iff_eq_mul]", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "blocked" }, { "tactic": "try { rfl }", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "success" }, { "tactic": "have := div_x5feq_x5fdiv_x5fiff_x5fdiv_x5feq_x5fdiv_w9", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "failure" }, { "tactic": "first | rintro \u27e8\u27e9 | rintro \u27e8\u27e9 | rintro \u27e8\u27e9 | rintro \u27e8\u27e9", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "failure" }, { "tactic": "rw [div_eq_iff_eq_mul, div_eq_iff_eq_mul]", "goal": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "outcome": "failure" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.10114", "expansion_count": 0, "nodes": { "cp1:_uniq.10114": { "mvar_id": "cp1:_uniq.10114", "goal_type": "\u2200 {G : Type u_3} [inst : CommGroup G] {a b c d : G}, a / b = c / d \u2194 a / c = b / d", "goal_sig": "49e00c39610d", "goal_sig_strict": "2b10d298e309", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": {} } } } }, { "name": "AddSemigroup_x2eto_x5fisAssociative", "status": "Solved", "iterations": 1, "mean_ged": 1.3333333333333333, "mean_ged_search_graph": 1.3333333333333333, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_infer_instance", "block_intro", "control_null" ], "ged_matrix": [ [ 0.0, 0.5, 0.5, 1.0 ], [ 0.5, 0.0, 0.0, 1.0 ], [ 0.5, 0.0, 0.0, 1.0 ], [ 1.0, 1.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp [AddSemigroup_x2eto_x5fisAssociative_w14]", "goal": "\u2200 {\u03b1 : Type u_1} [inst : AddSemigroup \u03b1], Std.Associative fun x1 x2 => x1 + x2", "outcome": "blocked" }, { "tactic": "intro \u03b1", "goal": "\u2200 {\u03b1 : Type u_1} [inst : AddSemigroup \u03b1], 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.15486", "expansion_count": 2, "nodes": { "cp1:_uniq.15486": { "mvar_id": "cp1:_uniq.15486", "goal_type": "\u2200 {\u03b1 : Type u_1} [inst : AddSemigroup \u03b1], Std.Associative fun x1 x2 => x1 + x2", "goal_sig": "0ab46aabcb29", "goal_sig_strict": "0ab46aabcb29", "visit_count": 2, "success_count": 2, "is_terminal": false, "is_dead": false, "depth": 0, "expansion_order": 0, "children": { "intro \u03b1": [ "cp2:_uniq.15498.2" ] } }, "cp2:_uniq.15498.2": { "mvar_id": "cp2:_uniq.15498.2", "goal_type": "\u2200 [inst : AddSemigroup \u03b1], Std.Associative fun x1 x2 => x1 + x2", "goal_sig": "3191d17dd457", "goal_sig_strict": "51544471af3a", "visit_count": 1, "success_count": 1, "is_terminal": true, "is_dead": false, "depth": 1, "expansion_order": 1, "children": { "infer_instance": [] } } } } }, { "name": "add_x5feq_x5fzero_x5fiff_x5fneg_x5feq", "status": "Failed", "iterations": 1, "mean_ged": 1.3333333333333333, "mean_ged_search_graph": 1.3333333333333333, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_decide", "block_rfl", "block_simp" ], "ged_matrix": [ [ 0.0, 1.0, 1.0, 0.0 ], [ 1.0, 0.0, 1.0, 1.0 ], [ 1.0, 1.0, 0.0, 1.0 ], [ 0.0, 1.0, 1.0, 0.0 ] ], "history": [ { "tactic": "simp only [\u2190 sub_eq_zero]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "decide", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "rfl", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp [eq_comm]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp [eq_iff_true_of_subsingleton]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp [add_neg_eq_sub]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp [add_comm]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp only [AddGroup.neg_eq_iff_add_eq_zero]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" }, { "tactic": "simp only [eq_iff_iff, add_left_neg]", "goal": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "outcome": "blocked" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.21695", "expansion_count": 0, "nodes": { "cp1:_uniq.21695": { "mvar_id": "cp1:_uniq.21695", "goal_type": "\u2200 {G : Type u_3} [inst : AddGroup G] {a b : G}, a + b = 0 \u2194 -a = b", "goal_sig": "434160c49fe0", "goal_sig_strict": "434160c49fe0", "visit_count": 1, "success_count": 0, "is_terminal": false, "is_dead": true, "depth": 0, "expansion_order": 0, "children": {} } } } }, { "name": "div_x5fdiv_x5fdiv_x5fcancel_x5fright", "status": "Failed", "iterations": 11, "mean_ged": 8.2, "mean_ged_search_graph": 8.2, "mean_ged_proof_graph": null, "mean_ged_trace_graph": null, "variants": [ "wild_type", "block_apply", "block_have", "block_intro", "block_rw", "block_simp" ], "ged_matrix": [ [ 0.0, 1.0, 0.8888888888888888, 0.8888888888888888, 1.0, 0.7777777777777778 ], [ 1.0, 0.0, 0.2222222222222222, 0.2222222222222222, 0.0, 0.2222222222222222 ], [ 0.8888888888888888, 0.2222222222222222, 0.0, 0.0, 0.2222222222222222, 0.1111111111111111 ], [ 0.8888888888888888, 0.2222222222222222, 0.0, 0.0, 0.2222222222222222, 0.1111111111111111 ], [ 1.0, 0.0, 0.2222222222222222, 0.2222222222222222, 0.0, 0.2222222222222222 ], [ 0.7777777777777778, 0.2222222222222222, 0.1111111111111111, 0.1111111111111111, 0.2222222222222222, 0.0 ] ], "history": [ { "tactic": "simp only [div_eq_mul_inv, div_eq_mul_inv, mul_assoc, inv_div, mul_inv_cancel_right, mul_comm]", "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_inv_rev]", "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b", "outcome": "blocked" }, { "tactic": "intro G _ _ _", "goal": "\u2200 {G : Type u_3} [inst : Group G] (a b c : G), a / c / (b / c) = a / b", "outcome": "success" }, { "tactic": "simp", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [mul_assoc]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [div_eq_mul_inv]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_inv_rev, mul_assoc, mul_inv_cancel_left]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_inv_rev, mul_assoc]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv, inv_inv]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "rw [mul_right_inv, mul_left_inv]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "apply mul_left_cancel\u2080", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "rw [mul_inv_rev]", "goal": "a\u271d * c\u207b\u00b9 * (b\u271d * c\u207b\u00b9)\u207b\u00b9 = a\u271d / b\u271d", "outcome": "success" }, { "tactic": "simp only [div_eq_mul_inv, mul_assoc]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [mul_div_cancel_left]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [div_eq_mul_inv]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "rw [mul_div_cancel_left, mul_div_cancel_left]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "rw [div_eq_mul_inv, mul_assoc, inv_div, mul_assoc]", "goal": "a\u271d * b\u271d\u207b\u00b9 = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "simp [div_eq_mul_inv]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [mul_inv_rev, div_eq_mul_inv, mul_assoc]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [\u2190 mul_assoc, div_mul_cancel]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [div_eq_mul_inv, mul_assoc]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [mul_assoc]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_inv_rev, inv_inv]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "have : c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = b\u271d\u207b\u00b9 := by", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "rw [mul_assoc, mul_inv_cancel_left]", "goal": "a\u271d * c\u207b\u00b9 * (c\u207b\u00b9\u207b\u00b9 * b\u271d\u207b\u00b9) = a\u271d / b\u271d", "outcome": "success" }, { "tactic": "simp only [div_eq_mul_inv, mul_assoc, mul_inv_cancel_left]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_assoc, mul_left_comm (a\u271d : G), mul_inv_cancel_left]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_assoc, inv_mul_cancel_right]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, div_eq_mul_inv, mul_assoc, mul_left_comm b, mul_comm c]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [div_eq_mul_inv]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_assoc, inv_mul_cancel_left]", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "intro c", "goal": "\u2200 (c : G), a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "success" }, { "tactic": "simp only [mul_div_mul_left, mul_div_cancel_left _ (div_ne_zero (div_ne_zero (div_ne_zero rfl) rfl) rfl)]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [div_eq_mul_inv]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp [mul_assoc]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [div_eq_mul_inv, mul_div_cancel' _ (inv_ne_zero (mul_ne_zero c.inv_ne_zero b.inv_ne_zero))]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "simp only [mul_div, div_div_cancel_left]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "blocked" }, { "tactic": "apply mul_right_cancel\u2080", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "failure" }, { "tactic": "rw [div_eq_mul_inv, div_eq_mul_inv, div_eq_mul_inv]", "goal": "a\u271d / c / (b\u271d / c) = a\u271d / b\u271d", "outcome": "success" } ], "mcts_tree": { "root_mvar_id": "cp1:_uniq.28376", "expansion_count": 5, "nodes": { "cp1:_uniq.28376": { "mvar_id": 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