%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET125-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:19 AM UTC 2025
% Result : Unsatisfiable 0.62s 0.83s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET125-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:21:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.62/0.83 % SZS status Unsatisfiable
% 0.62/0.83 % SZS output start Proof
% 0.62/0.83 tff(member_type, type, (
% 0.62/0.83 member: ( $i * $i ) > $o)).
% 0.62/0.83 tff(complement_type, type, (
% 0.62/0.83 complement: $i > $i)).
% 0.62/0.83 tff(z_type, type, (
% 0.62/0.83 z: $i)).
% 0.62/0.83 tff(x_type, type, (
% 0.62/0.83 x: $i)).
% 0.62/0.83 tff(intersection_type, type, (
% 0.62/0.83 intersection: ( $i * $i ) > $i)).
% 0.62/0.83 tff(singleton_type, type, (
% 0.62/0.83 singleton: $i > $i)).
% 0.62/0.83 tff(y_type, type, (
% 0.62/0.83 y: $i)).
% 0.62/0.83 tff(universal_class_type, type, (
% 0.62/0.83 universal_class: $i)).
% 0.62/0.83 tff(subclass_type, type, (
% 0.62/0.83 subclass: ( $i * $i ) > $o)).
% 0.62/0.83 tff(set_builder_type, type, (
% 0.62/0.83 set_builder: ( $i * $i ) > $i)).
% 0.62/0.83 tff(union_type, type, (
% 0.62/0.83 union: ( $i * $i ) > $i)).
% 0.62/0.83 tff(1,assumption,(~subclass(z, universal_class)), introduced(assumption)).
% 0.62/0.83 tff(2,plain,
% 0.62/0.83 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(3,plain,
% 0.62/0.83 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 0.62/0.83 inference(quant_intro,[status(thm)],[2])).
% 0.62/0.83 tff(4,plain,
% 0.62/0.83 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 0.62/0.83 tff(6,plain,
% 0.62/0.83 (![X: $i] : subclass(X, universal_class)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.62/0.83 tff(7,plain,(
% 0.62/0.83 ![X: $i] : subclass(X, universal_class)),
% 0.62/0.83 inference(skolemize,[status(sab)],[6])).
% 0.62/0.83 tff(8,plain,
% 0.62/0.83 (![X: $i] : subclass(X, universal_class)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.62/0.83 tff(9,plain,
% 0.62/0.83 ((~![X: $i] : subclass(X, universal_class)) | subclass(z, universal_class)),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(10,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.62/0.83 tff(11,plain,(subclass(z, universal_class)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(12,assumption,(~member(x, universal_class)), introduced(assumption)).
% 0.62/0.83 tff(13,plain,
% 0.62/0.83 (member(x, z) <=> member(x, z)),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(14,axiom,(member(x, z)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_set_builder_alternate_defn3_1')).
% 0.62/0.83 tff(15,plain,
% 0.62/0.83 (member(x, z)),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.62/0.83 tff(16,plain,
% 0.62/0.83 (^[Y: $i, U: $i, X: $i] : refl((member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(17,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[16])).
% 0.62/0.83 tff(18,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y))) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(19,plain,
% 0.62/0.83 (^[Y: $i, U: $i, X: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | (~member(U, X))) <=> ((~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)))), rewrite((((~member(U, X)) | (~subclass(X, Y))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))), ((((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(20,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y)) <=> ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[19])).
% 0.62/0.83 tff(21,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 0.62/0.83 tff(22,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.62/0.83 tff(23,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.62/0.83 tff(24,plain,(
% 0.62/0.83 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[23])).
% 0.62/0.83 tff(25,plain,
% 0.62/0.83 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.62/0.83 tff(26,plain,
% 0.62/0.83 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(27,plain,
% 0.62/0.83 ((member(x, universal_class) | (~member(x, z)) | (~subclass(z, universal_class))) <=> ((~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(28,plain,
% 0.62/0.83 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, z)) | (~subclass(z, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[27])).
% 0.62/0.83 tff(29,plain,
% 0.62/0.83 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, z)) | (~subclass(z, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class)))),
% 0.62/0.83 inference(transitivity,[status(thm)],[28, 26])).
% 0.62/0.83 tff(30,plain,
% 0.62/0.83 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, z)) | (~subclass(z, universal_class)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(31,plain,
% 0.62/0.83 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, z)) | member(x, universal_class) | (~subclass(z, universal_class))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.62/0.83 tff(32,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[31, 25, 15, 12, 11])).
% 0.62/0.83 tff(33,plain,(member(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.83 tff(34,plain,
% 0.62/0.83 (^[Y: $i, X: $i] : refl((union(singleton(X), Y) = set_builder(X, Y)) <=> (union(singleton(X), Y) = set_builder(X, Y)))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(35,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y)) <=> ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[34])).
% 0.62/0.83 tff(36,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y)) <=> ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(37,axiom,(![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_of_set_builder')).
% 0.62/0.83 tff(38,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.62/0.83 tff(39,plain,(
% 0.62/0.83 ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 0.62/0.83 inference(skolemize,[status(sab)],[38])).
% 0.62/0.83 tff(40,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.62/0.83 tff(41,plain,
% 0.62/0.83 ((~![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))) | (union(singleton(y), z) = set_builder(y, z))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(42,plain,
% 0.62/0.83 (union(singleton(y), z) = set_builder(y, z)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.62/0.83 tff(43,plain,
% 0.62/0.83 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(44,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[43])).
% 0.62/0.83 tff(45,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(46,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','union')).
% 0.62/0.83 tff(47,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.62/0.83 tff(48,plain,(
% 0.62/0.83 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 0.62/0.83 inference(skolemize,[status(sab)],[47])).
% 0.62/0.83 tff(49,plain,
% 0.62/0.83 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.62/0.83 tff(50,plain,
% 0.62/0.83 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(singleton(y)), complement(z))) = union(singleton(y), z))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(51,plain,
% 0.62/0.83 (complement(intersection(complement(singleton(y)), complement(z))) = union(singleton(y), z)),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.62/0.83 tff(52,plain,
% 0.62/0.83 (complement(intersection(complement(singleton(y)), complement(z))) = set_builder(y, z)),
% 0.62/0.83 inference(transitivity,[status(thm)],[51, 42])).
% 0.62/0.83 tff(53,plain,
% 0.62/0.83 (member(x, complement(intersection(complement(singleton(y)), complement(z)))) <=> member(x, set_builder(y, z))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[52])).
% 0.62/0.83 tff(54,plain,
% 0.62/0.83 (member(x, set_builder(y, z)) <=> member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 0.62/0.83 inference(symmetry,[status(thm)],[53])).
% 0.62/0.83 tff(55,plain,
% 0.62/0.83 ((~member(x, set_builder(y, z))) <=> (~member(x, complement(intersection(complement(singleton(y)), complement(z)))))),
% 0.62/0.83 inference(monotonicity,[status(thm)],[54])).
% 0.62/0.83 tff(56,plain,
% 0.62/0.83 ((~member(x, set_builder(y, z))) <=> (~member(x, set_builder(y, z)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(57,axiom,(~member(x, set_builder(y, z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_set_builder_alternate_defn3_2')).
% 0.62/0.83 tff(58,plain,
% 0.62/0.83 (~member(x, set_builder(y, z))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.62/0.83 tff(59,plain,
% 0.62/0.83 (~member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.62/0.83 tff(60,plain,
% 0.62/0.83 (^[Z: $i, X: $i] : refl((member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X))) <=> (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(61,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X))) <=> ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[60])).
% 0.62/0.83 tff(62,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X))) <=> ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(63,plain,
% 0.62/0.83 (^[Z: $i, X: $i] : rewrite((((~member(Z, universal_class)) | member(Z, complement(X))) | member(Z, X)) <=> (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(64,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (((~member(Z, universal_class)) | member(Z, complement(X))) | member(Z, X)) <=> ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[63])).
% 0.62/0.83 tff(65,axiom,(![Z: $i, X: $i] : (((~member(Z, universal_class)) | member(Z, complement(X))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','complement2')).
% 0.62/0.83 tff(66,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.62/0.83 tff(67,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.62/0.83 tff(68,plain,(
% 0.62/0.83 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(skolemize,[status(sab)],[67])).
% 0.62/0.83 tff(69,plain,
% 0.62/0.83 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.62/0.83 tff(70,plain,
% 0.62/0.83 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class)) | member(x, complement(intersection(complement(singleton(y)), complement(z)))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class)) | member(x, complement(intersection(complement(singleton(y)), complement(z)))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(71,plain,
% 0.62/0.83 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class)) | member(x, complement(intersection(complement(singleton(y)), complement(z)))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(72,plain,
% 0.62/0.83 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class)) | member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.62/0.83 tff(73,plain,
% 0.62/0.83 (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class)) | member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.62/0.83 tff(74,plain,
% 0.62/0.83 (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, universal_class))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[73, 59])).
% 0.62/0.83 tff(75,plain,
% 0.62/0.83 (member(x, intersection(complement(singleton(y)), complement(z)))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[74, 33])).
% 0.62/0.83 tff(76,plain,
% 0.62/0.83 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ((~member(Z, intersection(X, Y))) | member(Z, Y)))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(77,plain,
% 0.62/0.83 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[76])).
% 0.62/0.83 tff(78,plain,
% 0.62/0.83 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(79,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection2')).
% 0.62/0.83 tff(80,plain,
% 0.62/0.83 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.62/0.83 tff(81,plain,(
% 0.62/0.83 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 0.62/0.83 inference(skolemize,[status(sab)],[80])).
% 0.62/0.83 tff(82,plain,
% 0.62/0.83 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.62/0.83 tff(83,plain,
% 0.62/0.83 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(x, intersection(complement(singleton(y)), complement(z)))) | member(x, complement(z)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(x, intersection(complement(singleton(y)), complement(z)))) | member(x, complement(z)))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(84,plain,
% 0.62/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(x, intersection(complement(singleton(y)), complement(z)))) | member(x, complement(z)))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(85,plain,
% 0.62/0.83 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(x, intersection(complement(singleton(y)), complement(z)))) | member(x, complement(z))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.62/0.83 tff(86,plain,
% 0.62/0.83 (member(x, complement(z))),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[85, 82, 75])).
% 0.62/0.83 tff(87,plain,
% 0.62/0.83 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(88,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[87])).
% 0.62/0.83 tff(89,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(90,plain,
% 0.62/0.83 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.62/0.83 inference(bind,[status(th)],[])).
% 0.62/0.83 tff(91,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(quant_intro,[status(thm)],[90])).
% 0.62/0.83 tff(92,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','complement1')).
% 0.62/0.83 tff(93,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.62/0.83 tff(94,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.62/0.83 tff(95,plain,(
% 0.62/0.83 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(skolemize,[status(sab)],[94])).
% 0.62/0.83 tff(96,plain,
% 0.62/0.83 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.62/0.83 tff(97,plain,
% 0.62/0.83 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, z)) | (~member(x, complement(z))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, z)) | (~member(x, complement(z))))),
% 0.62/0.83 inference(rewrite,[status(thm)],[])).
% 0.62/0.83 tff(98,plain,
% 0.62/0.83 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, z)) | (~member(x, complement(z))))),
% 0.62/0.83 inference(quant_inst,[status(thm)],[])).
% 0.62/0.83 tff(99,plain,
% 0.62/0.83 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, z)) | (~member(x, complement(z)))),
% 0.62/0.83 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.62/0.83 tff(100,plain,
% 0.62/0.83 ($false),
% 0.62/0.83 inference(unit_resolution,[status(thm)],[99, 96, 15, 86])).
% 0.62/0.83 % SZS output end Proof
% 0.62/0.84 % E exiting
%------------------------------------------------------------------------------