TSTP Solution File: SET166-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET166-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Tue Sep 20 05:05:58 EDT 2022
% Result : Unsatisfiable 1.44s 1.15s
% Output : Proof 1.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET166-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 03:13:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.44/1.15 % SZS status Unsatisfiable
% 1.44/1.15 % SZS output start Proof
% 1.44/1.15 tff(member_type, type, (
% 1.44/1.15 member: ( $i * $i ) > $o)).
% 1.44/1.15 tff(universal_class_type, type, (
% 1.44/1.15 universal_class: $i)).
% 1.44/1.15 tff(x_type, type, (
% 1.44/1.15 x: $i)).
% 1.44/1.15 tff(subclass_type, type, (
% 1.44/1.15 subclass: ( $i * $i ) > $o)).
% 1.44/1.15 tff(union_type, type, (
% 1.44/1.15 union: ( $i * $i ) > $i)).
% 1.44/1.15 tff(z_type, type, (
% 1.44/1.15 z: $i)).
% 1.44/1.15 tff(y_type, type, (
% 1.44/1.15 y: $i)).
% 1.44/1.15 tff(complement_type, type, (
% 1.44/1.15 complement: $i > $i)).
% 1.44/1.15 tff(intersection_type, type, (
% 1.44/1.15 intersection: ( $i * $i ) > $i)).
% 1.44/1.15 tff(1,assumption,(~member(x, universal_class)), introduced(assumption)).
% 1.44/1.15 tff(2,assumption,(~subclass(union(y, z), universal_class)), introduced(assumption)).
% 1.44/1.15 tff(3,plain,
% 1.44/1.15 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(4,plain,
% 1.44/1.15 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 1.44/1.15 inference(quant_intro,[status(thm)],[3])).
% 1.44/1.15 tff(5,plain,
% 1.44/1.15 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(6,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 1.44/1.15 tff(7,plain,
% 1.44/1.15 (![X: $i] : subclass(X, universal_class)),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.44/1.15 tff(8,plain,(
% 1.44/1.15 ![X: $i] : subclass(X, universal_class)),
% 1.44/1.15 inference(skolemize,[status(sab)],[7])).
% 1.44/1.15 tff(9,plain,
% 1.44/1.15 (![X: $i] : subclass(X, universal_class)),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.44/1.15 tff(10,plain,
% 1.44/1.15 ((~![X: $i] : subclass(X, universal_class)) | subclass(union(y, z), universal_class)),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(11,plain,
% 1.44/1.15 ($false),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 1.44/1.15 tff(12,plain,(subclass(union(y, z), universal_class)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.15 tff(13,plain,
% 1.44/1.15 (member(x, union(y, z)) <=> member(x, union(y, z))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(14,axiom,(member(x, union(y, z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_members_of_union1_1')).
% 1.44/1.15 tff(15,plain,
% 1.44/1.15 (member(x, union(y, z))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.44/1.15 tff(16,plain,
% 1.44/1.15 (^[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))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(17,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[16])).
% 1.44/1.15 tff(18,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(19,plain,
% 1.44/1.15 (^[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)))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(20,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[19])).
% 1.44/1.15 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')).
% 1.44/1.15 tff(22,plain,
% 1.44/1.15 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.44/1.15 tff(23,plain,
% 1.44/1.15 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.44/1.15 tff(24,plain,(
% 1.44/1.15 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 1.44/1.15 inference(skolemize,[status(sab)],[23])).
% 1.44/1.15 tff(25,plain,
% 1.44/1.15 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.44/1.15 tff(26,plain,
% 1.44/1.15 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(27,plain,
% 1.44/1.15 ((member(x, universal_class) | (~member(x, union(y, z))) | (~subclass(union(y, z), universal_class))) <=> ((~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(28,plain,
% 1.44/1.15 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, union(y, z))) | (~subclass(union(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | ((~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class))))),
% 1.44/1.15 inference(monotonicity,[status(thm)],[27])).
% 1.44/1.15 tff(29,plain,
% 1.44/1.15 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, union(y, z))) | (~subclass(union(y, z), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class)))),
% 1.44/1.15 inference(transitivity,[status(thm)],[28, 26])).
% 1.44/1.15 tff(30,plain,
% 1.44/1.15 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, universal_class) | (~member(x, union(y, z))) | (~subclass(union(y, z), universal_class)))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(31,plain,
% 1.44/1.15 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (~member(x, union(y, z))) | member(x, universal_class) | (~subclass(union(y, z), universal_class))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.44/1.15 tff(32,plain,
% 1.44/1.15 ($false),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[31, 25, 15, 12, 1])).
% 1.44/1.15 tff(33,plain,(member(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.15 tff(34,assumption,(~member(x, complement(y))), introduced(assumption)).
% 1.44/1.15 tff(35,plain,
% 1.44/1.15 ((~member(x, y)) <=> (~member(x, y))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(36,axiom,(~member(x, y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_members_of_union1_2')).
% 1.44/1.15 tff(37,plain,
% 1.44/1.15 (~member(x, y)),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.44/1.15 tff(38,plain,
% 1.44/1.15 (^[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))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(39,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[38])).
% 1.44/1.15 tff(40,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(41,plain,
% 1.44/1.15 (^[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))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(42,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[41])).
% 1.44/1.15 tff(43,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')).
% 1.44/1.15 tff(44,plain,
% 1.44/1.15 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.44/1.15 tff(45,plain,
% 1.44/1.15 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.44/1.15 tff(46,plain,(
% 1.44/1.15 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 1.44/1.15 inference(skolemize,[status(sab)],[45])).
% 1.44/1.15 tff(47,plain,
% 1.44/1.15 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.44/1.15 tff(48,plain,
% 1.44/1.15 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, y) | member(x, complement(y)) | (~member(x, universal_class)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, y) | member(x, complement(y)) | (~member(x, universal_class)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(49,plain,
% 1.44/1.15 ((member(x, y) | (~member(x, universal_class)) | member(x, complement(y))) <=> (member(x, y) | member(x, complement(y)) | (~member(x, universal_class)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(50,plain,
% 1.44/1.15 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, y) | (~member(x, universal_class)) | member(x, complement(y)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, y) | member(x, complement(y)) | (~member(x, universal_class))))),
% 1.44/1.15 inference(monotonicity,[status(thm)],[49])).
% 1.44/1.15 tff(51,plain,
% 1.44/1.15 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, y) | (~member(x, universal_class)) | member(x, complement(y)))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, y) | member(x, complement(y)) | (~member(x, universal_class)))),
% 1.44/1.15 inference(transitivity,[status(thm)],[50, 48])).
% 1.44/1.15 tff(52,plain,
% 1.44/1.15 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(x, y) | (~member(x, universal_class)) | member(x, complement(y)))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(53,plain,
% 1.44/1.15 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, y) | member(x, complement(y)) | (~member(x, universal_class))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.44/1.15 tff(54,plain,
% 1.44/1.15 ($false),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[53, 47, 37, 34, 33])).
% 1.44/1.15 tff(55,plain,(member(x, complement(y))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.15 tff(56,plain,
% 1.44/1.15 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(57,plain,
% 1.44/1.15 (![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))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[56])).
% 1.44/1.15 tff(58,plain,
% 1.44/1.15 (![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))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(59,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','union')).
% 1.44/1.15 tff(60,plain,
% 1.44/1.15 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.44/1.15 tff(61,plain,(
% 1.44/1.15 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 1.44/1.15 inference(skolemize,[status(sab)],[60])).
% 1.44/1.15 tff(62,plain,
% 1.44/1.15 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.44/1.15 tff(63,plain,
% 1.44/1.15 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(y), complement(z))) = union(y, z))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(64,plain,
% 1.44/1.15 (complement(intersection(complement(y), complement(z))) = union(y, z)),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[63, 62])).
% 1.44/1.15 tff(65,plain,
% 1.44/1.15 (member(x, complement(intersection(complement(y), complement(z)))) <=> member(x, union(y, z))),
% 1.44/1.15 inference(monotonicity,[status(thm)],[64])).
% 1.44/1.15 tff(66,plain,
% 1.44/1.15 (member(x, union(y, z)) <=> member(x, complement(intersection(complement(y), complement(z))))),
% 1.44/1.15 inference(symmetry,[status(thm)],[65])).
% 1.44/1.15 tff(67,plain,
% 1.44/1.15 (member(x, complement(intersection(complement(y), complement(z))))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[15, 66])).
% 1.44/1.15 tff(68,plain,
% 1.44/1.15 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(69,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[68])).
% 1.44/1.15 tff(70,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(71,plain,
% 1.44/1.15 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(72,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[71])).
% 1.44/1.15 tff(73,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','complement1')).
% 1.44/1.15 tff(74,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.44/1.15 tff(75,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.44/1.15 tff(76,plain,(
% 1.44/1.15 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(skolemize,[status(sab)],[75])).
% 1.44/1.15 tff(77,plain,
% 1.44/1.15 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.44/1.15 tff(78,plain,
% 1.44/1.15 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, intersection(complement(y), complement(z)))) | (~member(x, complement(intersection(complement(y), complement(z))))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, intersection(complement(y), complement(z)))) | (~member(x, complement(intersection(complement(y), complement(z))))))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(79,plain,
% 1.44/1.15 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(x, intersection(complement(y), complement(z)))) | (~member(x, complement(intersection(complement(y), complement(z))))))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(80,plain,
% 1.44/1.15 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(x, intersection(complement(y), complement(z)))) | (~member(x, complement(intersection(complement(y), complement(z)))))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.44/1.15 tff(81,plain,
% 1.44/1.15 ((~member(x, intersection(complement(y), complement(z)))) | (~member(x, complement(intersection(complement(y), complement(z)))))),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[80, 77])).
% 1.44/1.15 tff(82,plain,
% 1.44/1.15 (~member(x, intersection(complement(y), complement(z)))),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[81, 67])).
% 1.44/1.15 tff(83,plain,
% 1.44/1.15 (^[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))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(84,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[83])).
% 1.44/1.15 tff(85,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(86,plain,
% 1.44/1.15 (^[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))))),
% 1.44/1.15 inference(bind,[status(th)],[])).
% 1.44/1.15 tff(87,plain,
% 1.44/1.15 (![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)))),
% 1.44/1.15 inference(quant_intro,[status(thm)],[86])).
% 1.44/1.15 tff(88,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')).
% 1.44/1.15 tff(89,plain,
% 1.44/1.15 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.44/1.15 tff(90,plain,
% 1.44/1.15 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[89, 85])).
% 1.44/1.15 tff(91,plain,(
% 1.44/1.15 ![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 1.44/1.15 inference(skolemize,[status(sab)],[90])).
% 1.44/1.15 tff(92,plain,
% 1.44/1.15 (![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[91, 84])).
% 1.44/1.15 tff(93,plain,
% 1.44/1.15 (((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(x, intersection(complement(y), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(y))))) <=> ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(x, intersection(complement(y), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(y))))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(94,plain,
% 1.44/1.15 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | (member(x, intersection(complement(y), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(y))))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(95,plain,
% 1.44/1.15 ((~![Z: $i, Y: $i, X: $i] : (member(Z, intersection(X, Y)) | (~member(Z, Y)) | (~member(Z, X)))) | member(x, intersection(complement(y), complement(z))) | (~member(x, complement(z))) | (~member(x, complement(y)))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.44/1.15 tff(96,plain,
% 1.44/1.15 ((~member(x, complement(z))) | (~member(x, complement(y)))),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[95, 92, 82])).
% 1.44/1.15 tff(97,plain,
% 1.44/1.15 (~member(x, complement(z))),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[96, 55])).
% 1.44/1.15 tff(98,plain,
% 1.44/1.15 ((~member(x, z)) <=> (~member(x, z))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(99,axiom,(~member(x, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_members_of_union1_3')).
% 1.44/1.15 tff(100,plain,
% 1.44/1.15 (~member(x, z)),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.44/1.15 tff(101,plain,
% 1.44/1.15 (((~![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)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(102,plain,
% 1.44/1.15 ((member(x, z) | (~member(x, universal_class)) | member(x, complement(z))) <=> (member(x, z) | member(x, complement(z)) | (~member(x, universal_class)))),
% 1.44/1.15 inference(rewrite,[status(thm)],[])).
% 1.44/1.15 tff(103,plain,
% 1.44/1.15 (((~![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))))),
% 1.44/1.15 inference(monotonicity,[status(thm)],[102])).
% 1.44/1.15 tff(104,plain,
% 1.44/1.15 (((~![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)))),
% 1.44/1.15 inference(transitivity,[status(thm)],[103, 101])).
% 1.44/1.15 tff(105,plain,
% 1.44/1.15 ((~![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)))),
% 1.44/1.15 inference(quant_inst,[status(thm)],[])).
% 1.44/1.15 tff(106,plain,
% 1.44/1.15 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(x, z) | member(x, complement(z)) | (~member(x, universal_class))),
% 1.44/1.15 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.44/1.15 tff(107,plain,
% 1.44/1.15 ($false),
% 1.44/1.15 inference(unit_resolution,[status(thm)],[106, 47, 100, 97, 33])).
% 1.44/1.15 % SZS output end Proof
%------------------------------------------------------------------------------