%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET123-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:25:18 AM UTC 2025
% Result : Unsatisfiable 17.84s 18.07s
% Output : Proof 17.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET123-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:20:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 17.84/18.07 % SZS status Unsatisfiable
% 17.84/18.07 % SZS output start Proof
% 17.84/18.07 tff(member_type, type, (
% 17.84/18.07 member: ( $i * $i ) > $o)).
% 17.84/18.07 tff(universal_class_type, type, (
% 17.84/18.07 universal_class: $i)).
% 17.84/18.07 tff(x_type, type, (
% 17.84/18.07 x: $i)).
% 17.84/18.07 tff(subclass_type, type, (
% 17.84/18.07 subclass: ( $i * $i ) > $o)).
% 17.84/18.07 tff(set_builder_type, type, (
% 17.84/18.07 set_builder: ( $i * $i ) > $i)).
% 17.84/18.07 tff(z_type, type, (
% 17.84/18.07 z: $i)).
% 17.84/18.07 tff(y_type, type, (
% 17.84/18.07 y: $i)).
% 17.84/18.07 tff(complement_type, type, (
% 17.84/18.07 complement: $i > $i)).
% 17.84/18.07 tff(singleton_type, type, (
% 17.84/18.07 singleton: $i > $i)).
% 17.84/18.07 tff(unordered_pair_type, type, (
% 17.84/18.07 unordered_pair: ( $i * $i ) > $i)).
% 17.84/18.07 tff(intersection_type, type, (
% 17.84/18.07 intersection: ( $i * $i ) > $i)).
% 17.84/18.07 tff(union_type, type, (
% 17.84/18.07 union: ( $i * $i ) > $i)).
% 17.84/18.07 tff(1,assumption,(~member(x, universal_class)), introduced(assumption)).
% 17.84/18.07 tff(2,assumption,(~subclass(set_builder(y, z), universal_class)), introduced(assumption)).
% 17.84/18.07 tff(3,plain,
% 17.84/18.07 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 17.84/18.07 inference(bind,[status(th)],[])).
% 17.84/18.07 tff(4,plain,
% 17.84/18.07 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 17.84/18.07 inference(quant_intro,[status(thm)],[3])).
% 17.84/18.07 tff(5,plain,
% 17.84/18.07 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 17.84/18.07 inference(rewrite,[status(thm)],[])).
% 17.84/18.07 tff(6,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 17.84/18.07 tff(7,plain,
% 17.84/18.07 (![X: $i] : subclass(X, universal_class)),
% 17.84/18.07 inference(modus_ponens,[status(thm)],[6, 5])).
% 17.84/18.07 tff(8,plain,(
% 17.84/18.07 ![X: $i] : subclass(X, universal_class)),
% 17.84/18.07 inference(skolemize,[status(sab)],[7])).
% 17.84/18.07 tff(9,plain,
% 17.84/18.07 (![X: $i] : subclass(X, universal_class)),
% 17.84/18.07 inference(modus_ponens,[status(thm)],[8, 4])).
% 17.84/18.07 tff(10,plain,
% 17.84/18.07 ((~![X: $i] : subclass(X, universal_class)) | subclass(set_builder(y, z), universal_class)),
% 17.84/18.07 inference(quant_inst,[status(thm)],[])).
% 17.84/18.07 tff(11,plain,
% 17.84/18.07 ($false),
% 17.84/18.07 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 17.84/18.07 tff(12,plain,(subclass(set_builder(y, z), universal_class)), inference(lemma,lemma(discharge,[]))).
% 17.84/18.07 tff(13,plain,
% 17.84/18.07 (member(x, set_builder(y, z)) <=> member(x, set_builder(y, z))),
% 17.84/18.07 inference(rewrite,[status(thm)],[])).
% 17.84/18.07 tff(14,axiom,(member(x, set_builder(y, z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_set_builder_alternate_defn1_1')).
% 17.84/18.07 tff(15,plain,
% 17.84/18.07 (member(x, set_builder(y, z))),
% 17.84/18.07 inference(modus_ponens,[status(thm)],[14, 13])).
% 17.84/18.07 tff(16,plain,
% 17.84/18.07 (^[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))))),
% 17.84/18.07 inference(bind,[status(th)],[])).
% 17.84/18.07 tff(17,plain,
% 17.84/18.07 (![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)))),
% 17.84/18.07 inference(quant_intro,[status(thm)],[16])).
% 17.84/18.07 tff(18,plain,
% 17.84/18.07 (![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)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(19,plain,
% 17.84/18.08 (^[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)))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(20,plain,
% 17.84/18.08 (![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)))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[19])).
% 17.84/18.08 tff(21,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 17.84/18.08 tff(22,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[21, 20])).
% 17.84/18.08 tff(23,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[22, 18])).
% 17.84/18.08 tff(24,plain,(
% 17.84/18.08 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 17.84/18.08 inference(skolemize,[status(sab)],[23])).
% 17.84/18.08 tff(25,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[24, 17])).
% 17.84/18.08 tff(26,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(27,plain,
% 17.84/18.08 ((member(x, universal_class) | (~member(x, set_builder(y, z))) | (~subclass(set_builder(y, z), universal_class))) <=> ((~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(28,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, set_builder(y, z))) | (~subclass(set_builder(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class))))),
% 17.84/18.08 inference(monotonicity,[status(thm)],[27])).
% 17.84/18.08 tff(29,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, set_builder(y, z))) | (~subclass(set_builder(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class)))),
% 17.84/18.08 inference(transitivity,[status(thm)],[28, 26])).
% 17.84/18.08 tff(30,plain,
% 17.84/18.08 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, set_builder(y, z))) | (~subclass(set_builder(y, z), universal_class)))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(31,plain,
% 17.84/18.08 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, set_builder(y, z))) | member(x, universal_class) | (~subclass(set_builder(y, z), universal_class))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[30, 29])).
% 17.84/18.08 tff(32,plain,
% 17.84/18.08 ($false),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[31, 25, 15, 12, 1])).
% 17.84/18.08 tff(33,plain,(member(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 17.84/18.08 tff(34,plain,
% 17.84/18.08 (^[X: $i] : refl((unordered_pair(X, X) = singleton(X)) <=> (unordered_pair(X, X) = singleton(X)))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(35,plain,
% 17.84/18.08 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[34])).
% 17.84/18.08 tff(36,plain,
% 17.84/18.08 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(37,axiom,(![X: $i] : (unordered_pair(X, X) = singleton(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','singleton_set')).
% 17.84/18.08 tff(38,plain,
% 17.84/18.08 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[37, 36])).
% 17.84/18.08 tff(39,plain,(
% 17.84/18.08 ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 17.84/18.08 inference(skolemize,[status(sab)],[38])).
% 17.84/18.08 tff(40,plain,
% 17.84/18.08 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[39, 35])).
% 17.84/18.08 tff(41,plain,
% 17.84/18.08 ((~![X: $i] : (unordered_pair(X, X) = singleton(X))) | (unordered_pair(y, y) = singleton(y))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(42,plain,
% 17.84/18.08 (unordered_pair(y, y) = singleton(y)),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[41, 40])).
% 17.84/18.08 tff(43,plain,
% 17.84/18.08 (member(x, unordered_pair(y, y)) <=> member(x, singleton(y))),
% 17.84/18.08 inference(monotonicity,[status(thm)],[42])).
% 17.84/18.08 tff(44,plain,
% 17.84/18.08 (member(x, singleton(y)) <=> member(x, unordered_pair(y, y))),
% 17.84/18.08 inference(symmetry,[status(thm)],[43])).
% 17.84/18.08 tff(45,assumption,(member(x, singleton(y))), introduced(assumption)).
% 17.84/18.08 tff(46,plain,
% 17.84/18.08 (member(x, unordered_pair(y, y))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[45, 44])).
% 17.84/18.08 tff(47,plain,
% 17.84/18.08 ((~(x = y)) <=> (~(x = y))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(48,axiom,(~(x = y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_set_builder_alternate_defn1_2')).
% 17.84/18.08 tff(49,plain,
% 17.84/18.08 (~(x = y)),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[48, 47])).
% 17.84/18.08 tff(50,plain,
% 17.84/18.08 (^[Y: $i, U: $i, X: $i] : refl(((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(51,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[50])).
% 17.84/18.08 tff(52,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(53,plain,
% 17.84/18.08 (^[Y: $i, U: $i, X: $i] : rewrite((((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(54,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[53])).
% 17.84/18.08 tff(55,axiom,(![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','unordered_pair_member')).
% 17.84/18.08 tff(56,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[55, 54])).
% 17.84/18.08 tff(57,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[56, 52])).
% 17.84/18.08 tff(58,plain,(
% 17.84/18.08 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(skolemize,[status(sab)],[57])).
% 17.84/18.08 tff(59,plain,
% 17.84/18.08 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[58, 51])).
% 17.84/18.08 tff(60,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((x = y) | (~member(x, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (x = y) | (~member(x, unordered_pair(y, y))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(61,plain,
% 17.84/18.08 (((x = y) | (x = y) | (~member(x, unordered_pair(y, y)))) <=> ((x = y) | (~member(x, unordered_pair(y, y))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(62,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((x = y) | (x = y) | (~member(x, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((x = y) | (~member(x, unordered_pair(y, y)))))),
% 17.84/18.08 inference(monotonicity,[status(thm)],[61])).
% 17.84/18.08 tff(63,plain,
% 17.84/18.08 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((x = y) | (x = y) | (~member(x, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (x = y) | (~member(x, unordered_pair(y, y))))),
% 17.84/18.08 inference(transitivity,[status(thm)],[62, 60])).
% 17.84/18.08 tff(64,plain,
% 17.84/18.08 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((x = y) | (x = y) | (~member(x, unordered_pair(y, y))))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(65,plain,
% 17.84/18.08 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (x = y) | (~member(x, unordered_pair(y, y)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[64, 63])).
% 17.84/18.08 tff(66,plain,
% 17.84/18.08 (~member(x, unordered_pair(y, y))),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 17.84/18.08 tff(67,plain,
% 17.84/18.08 ($false),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[66, 46])).
% 17.84/18.08 tff(68,plain,(~member(x, singleton(y))), inference(lemma,lemma(discharge,[]))).
% 17.84/18.08 tff(69,assumption,(~member(x, complement(singleton(y)))), introduced(assumption)).
% 17.84/18.08 tff(70,plain,
% 17.84/18.08 (^[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))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(71,plain,
% 17.84/18.08 (![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)))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[70])).
% 17.84/18.08 tff(72,plain,
% 17.84/18.08 (![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)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(73,plain,
% 17.84/18.08 (^[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))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(74,plain,
% 17.84/18.08 (![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)))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[73])).
% 17.84/18.08 tff(75,axiom,(![Z: $i, X: $i] : (((~member(Z, universal_class)) | member(Z, complement(X))) | member(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','complement2')).
% 17.84/18.08 tff(76,plain,
% 17.84/18.08 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[75, 74])).
% 17.84/18.08 tff(77,plain,
% 17.84/18.08 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[76, 72])).
% 17.84/18.08 tff(78,plain,(
% 17.84/18.08 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 17.84/18.08 inference(skolemize,[status(sab)],[77])).
% 17.84/18.08 tff(79,plain,
% 17.84/18.08 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[78, 71])).
% 17.84/18.08 tff(80,plain,
% 17.84/18.08 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(81,plain,
% 17.84/18.08 ((member(x, singleton(y)) | (~member(x, universal_class)) | member(x, complement(singleton(y)))) <=> (member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(82,plain,
% 17.84/18.08 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, singleton(y)) | (~member(x, universal_class)) | member(x, complement(singleton(y))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class))))),
% 17.84/18.08 inference(monotonicity,[status(thm)],[81])).
% 17.84/18.08 tff(83,plain,
% 17.84/18.08 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, singleton(y)) | (~member(x, universal_class)) | member(x, complement(singleton(y))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class)))),
% 17.84/18.08 inference(transitivity,[status(thm)],[82, 80])).
% 17.84/18.08 tff(84,plain,
% 17.84/18.08 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, singleton(y)) | (~member(x, universal_class)) | member(x, complement(singleton(y))))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(85,plain,
% 17.84/18.08 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, complement(singleton(y))) | member(x, singleton(y)) | (~member(x, universal_class))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[84, 83])).
% 17.84/18.08 tff(86,plain,
% 17.84/18.08 ($false),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[85, 79, 69, 33, 68])).
% 17.84/18.08 tff(87,plain,(member(x, complement(singleton(y)))), inference(lemma,lemma(discharge,[]))).
% 17.84/18.08 tff(88,plain,
% 17.84/18.08 (^[Y: $i, X: $i] : refl((union(singleton(X), Y) = set_builder(X, Y)) <=> (union(singleton(X), Y) = set_builder(X, Y)))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(89,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y)) <=> ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[88])).
% 17.84/18.08 tff(90,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y)) <=> ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(91,axiom,(![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','definition_of_set_builder')).
% 17.84/18.08 tff(92,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[91, 90])).
% 17.84/18.08 tff(93,plain,(
% 17.84/18.08 ![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 17.84/18.08 inference(skolemize,[status(sab)],[92])).
% 17.84/18.08 tff(94,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[93, 89])).
% 17.84/18.08 tff(95,plain,
% 17.84/18.08 ((~![Y: $i, X: $i] : (union(singleton(X), Y) = set_builder(X, Y))) | (union(singleton(y), z) = set_builder(y, z))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(96,plain,
% 17.84/18.08 (union(singleton(y), z) = set_builder(y, z)),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[95, 94])).
% 17.84/18.08 tff(97,plain,
% 17.84/18.08 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(98,plain,
% 17.84/18.08 (![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))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[97])).
% 17.84/18.08 tff(99,plain,
% 17.84/18.08 (![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))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(100,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','union')).
% 17.84/18.08 tff(101,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[100, 99])).
% 17.84/18.08 tff(102,plain,(
% 17.84/18.08 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 17.84/18.08 inference(skolemize,[status(sab)],[101])).
% 17.84/18.08 tff(103,plain,
% 17.84/18.08 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[102, 98])).
% 17.84/18.08 tff(104,plain,
% 17.84/18.08 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(singleton(y)), complement(z))) = union(singleton(y), z))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(105,plain,
% 17.84/18.08 (complement(intersection(complement(singleton(y)), complement(z))) = union(singleton(y), z)),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[104, 103])).
% 17.84/18.08 tff(106,plain,
% 17.84/18.08 (complement(intersection(complement(singleton(y)), complement(z))) = set_builder(y, z)),
% 17.84/18.08 inference(transitivity,[status(thm)],[105, 96])).
% 17.84/18.08 tff(107,plain,
% 17.84/18.08 (member(x, complement(intersection(complement(singleton(y)), complement(z)))) <=> member(x, set_builder(y, z))),
% 17.84/18.08 inference(monotonicity,[status(thm)],[106])).
% 17.84/18.08 tff(108,plain,
% 17.84/18.08 (member(x, set_builder(y, z)) <=> member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 17.84/18.08 inference(symmetry,[status(thm)],[107])).
% 17.84/18.08 tff(109,plain,
% 17.84/18.08 (member(x, complement(intersection(complement(singleton(y)), complement(z))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[15, 108])).
% 17.84/18.08 tff(110,plain,
% 17.84/18.08 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(111,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[110])).
% 17.84/18.08 tff(112,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(113,plain,
% 17.84/18.08 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(114,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[113])).
% 17.84/18.08 tff(115,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','complement1')).
% 17.84/18.08 tff(116,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[115, 114])).
% 17.84/18.08 tff(117,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[116, 112])).
% 17.84/18.08 tff(118,plain,(
% 17.84/18.08 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(skolemize,[status(sab)],[117])).
% 17.84/18.08 tff(119,plain,
% 17.84/18.08 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[118, 111])).
% 17.84/18.08 tff(120,plain,
% 17.84/18.08 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, intersection(complement(singleton(y)), complement(z)))) | (~member(x, complement(intersection(complement(singleton(y)), complement(z))))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, intersection(complement(singleton(y)), complement(z)))) | (~member(x, complement(intersection(complement(singleton(y)), complement(z))))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(121,plain,
% 17.84/18.08 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, intersection(complement(singleton(y)), complement(z)))) | (~member(x, complement(intersection(complement(singleton(y)), complement(z))))))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(122,plain,
% 17.84/18.08 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, intersection(complement(singleton(y)), complement(z)))) | (~member(x, complement(intersection(complement(singleton(y)), complement(z)))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[121, 120])).
% 17.84/18.08 tff(123,plain,
% 17.84/18.08 ((~member(x, intersection(complement(singleton(y)), complement(z)))) | (~member(x, complement(intersection(complement(singleton(y)), complement(z)))))),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[122, 119])).
% 17.84/18.08 tff(124,plain,
% 17.84/18.08 (~member(x, intersection(complement(singleton(y)), complement(z)))),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[123, 109])).
% 17.84/18.08 tff(125,plain,
% 17.84/18.08 (^[Z: $i, Y: $i, X: $i] : refl((member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(126,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[125])).
% 17.84/18.08 tff(127,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(128,plain,
% 17.84/18.08 (^[Z: $i, Y: $i, X: $i] : rewrite((((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y))) <=> (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X))))),
% 17.84/18.08 inference(bind,[status(th)],[])).
% 17.84/18.08 tff(129,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y))) <=> ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(quant_intro,[status(thm)],[128])).
% 17.84/18.08 tff(130,axiom,(![Z: $i, Y: $i, X: $i] : (((~member(Z, X)) | (~member(Z, Y))) | member(Z, intersection(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','intersection3')).
% 17.84/18.08 tff(131,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[130, 129])).
% 17.84/18.08 tff(132,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[131, 127])).
% 17.84/18.08 tff(133,plain,(
% 17.84/18.08 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(skolemize,[status(sab)],[132])).
% 17.84/18.08 tff(134,plain,
% 17.84/18.08 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[133, 126])).
% 17.84/18.08 tff(135,plain,
% 17.84/18.08 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(singleton(y)))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(singleton(y)))))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(136,plain,
% 17.84/18.08 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(singleton(y)))))),
% 17.84/18.08 inference(quant_inst,[status(thm)],[])).
% 17.84/18.08 tff(137,plain,
% 17.84/18.08 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(x, intersection(complement(singleton(y)), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(singleton(y))))),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[136, 135])).
% 17.84/18.08 tff(138,plain,
% 17.84/18.08 ((~member(x, complement(z))) | (~member(x, complement(singleton(y))))),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[137, 134, 124])).
% 17.84/18.08 tff(139,plain,
% 17.84/18.08 (~member(x, complement(z))),
% 17.84/18.08 inference(unit_resolution,[status(thm)],[138, 87])).
% 17.84/18.08 tff(140,plain,
% 17.84/18.08 ((~member(x, z)) <=> (~member(x, z))),
% 17.84/18.08 inference(rewrite,[status(thm)],[])).
% 17.84/18.08 tff(141,axiom,(~member(x, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_set_builder_alternate_defn1_3')).
% 17.84/18.08 tff(142,plain,
% 17.84/18.08 (~member(x, z)),
% 17.84/18.08 inference(modus_ponens,[status(thm)],[141, 140])).
% 17.84/18.08 tff(143,plain,
% 17.84/18.08 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, z) | member(x, complement(z)) | (~member(x, universal_class)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, z) | member(x, complement(z)) | (~member(x, universal_class)))),
% 17.84/18.09 inference(rewrite,[status(thm)],[])).
% 17.84/18.09 tff(144,plain,
% 17.84/18.09 ((member(x, z) | (~member(x, universal_class)) | member(x, complement(z))) <=> (member(x, z) | member(x, complement(z)) | (~member(x, universal_class)))),
% 17.84/18.09 inference(rewrite,[status(thm)],[])).
% 17.84/18.09 tff(145,plain,
% 17.84/18.09 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, z) | (~member(x, universal_class)) | member(x, complement(z)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, z) | member(x, complement(z)) | (~member(x, universal_class))))),
% 17.84/18.09 inference(monotonicity,[status(thm)],[144])).
% 17.84/18.09 tff(146,plain,
% 17.84/18.09 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, z) | (~member(x, universal_class)) | member(x, complement(z)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, z) | member(x, complement(z)) | (~member(x, universal_class)))),
% 17.84/18.09 inference(transitivity,[status(thm)],[145, 143])).
% 17.84/18.09 tff(147,plain,
% 17.84/18.09 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, z) | (~member(x, universal_class)) | member(x, complement(z)))),
% 17.84/18.09 inference(quant_inst,[status(thm)],[])).
% 17.84/18.09 tff(148,plain,
% 17.84/18.09 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, z) | member(x, complement(z)) | (~member(x, universal_class))),
% 17.84/18.09 inference(modus_ponens,[status(thm)],[147, 146])).
% 17.84/18.09 tff(149,plain,
% 17.84/18.09 ($false),
% 17.84/18.09 inference(unit_resolution,[status(thm)],[148, 79, 142, 139, 33])).
% 17.84/18.09 % SZS output end Proof
% 17.94/18.09 % E exiting
%------------------------------------------------------------------------------