TSTP Solution File: SET167-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET167-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 55.97s 35.90s
% Output : Proof 56.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET167-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 03:16:47 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.
% 55.97/35.90 % SZS status Unsatisfiable
% 55.97/35.90 % SZS output start Proof
% 55.97/35.90 tff(member_type, type, (
% 55.97/35.90 member: ( $i * $i ) > $o)).
% 55.97/35.90 tff(complement_type, type, (
% 55.97/35.90 complement: $i > $i)).
% 55.97/35.90 tff(y_type, type, (
% 55.97/35.90 y: $i)).
% 55.97/35.90 tff(not_subclass_element_type, type, (
% 55.97/35.90 not_subclass_element: ( $i * $i ) > $i)).
% 55.97/35.90 tff(union_type, type, (
% 55.97/35.90 union: ( $i * $i ) > $i)).
% 55.97/35.90 tff(z_type, type, (
% 55.97/35.90 z: $i)).
% 55.97/35.90 tff(intersection_type, type, (
% 55.97/35.90 intersection: ( $i * $i ) > $i)).
% 55.97/35.90 tff(universal_class_type, type, (
% 55.97/35.90 universal_class: $i)).
% 55.97/35.90 tff(subclass_type, type, (
% 55.97/35.90 subclass: ( $i * $i ) > $o)).
% 55.97/35.90 tff(x_type, type, (
% 55.97/35.90 x: $i)).
% 55.97/35.90 tff(1,assumption,(~subclass(y, universal_class)), introduced(assumption)).
% 55.97/35.90 tff(2,plain,
% 55.97/35.90 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 55.97/35.90 inference(bind,[status(th)],[])).
% 55.97/35.90 tff(3,plain,
% 55.97/35.90 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 55.97/35.90 inference(quant_intro,[status(thm)],[2])).
% 55.97/35.90 tff(4,plain,
% 55.97/35.90 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 55.97/35.90 inference(rewrite,[status(thm)],[])).
% 55.97/35.90 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 55.97/35.90 tff(6,plain,
% 55.97/35.90 (![X: $i] : subclass(X, universal_class)),
% 55.97/35.90 inference(modus_ponens,[status(thm)],[5, 4])).
% 55.97/35.90 tff(7,plain,(
% 55.97/35.90 ![X: $i] : subclass(X, universal_class)),
% 55.97/35.90 inference(skolemize,[status(sab)],[6])).
% 55.97/35.90 tff(8,plain,
% 55.97/35.90 (![X: $i] : subclass(X, universal_class)),
% 55.97/35.90 inference(modus_ponens,[status(thm)],[7, 3])).
% 55.97/35.90 tff(9,plain,
% 55.97/35.90 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 55.97/35.90 inference(quant_inst,[status(thm)],[])).
% 55.97/35.90 tff(10,plain,
% 55.97/35.90 ($false),
% 55.97/35.90 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 55.97/35.90 tff(11,plain,(subclass(y, universal_class)), inference(lemma,lemma(discharge,[]))).
% 55.97/35.90 tff(12,assumption,(~member(not_subclass_element(y, union(y, z)), universal_class)), introduced(assumption)).
% 55.97/35.90 tff(13,plain,
% 55.97/35.90 ((~member(x, union(y, z))) <=> (~member(x, union(y, z)))),
% 55.97/35.90 inference(rewrite,[status(thm)],[])).
% 55.97/35.90 tff(14,axiom,(~member(x, union(y, z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_members_of_union2_2')).
% 55.97/35.90 tff(15,plain,
% 55.97/35.90 (~member(x, union(y, z))),
% 55.97/35.90 inference(modus_ponens,[status(thm)],[14, 13])).
% 55.97/35.90 tff(16,plain,
% 55.97/35.90 (member(x, y) <=> member(x, y)),
% 55.97/35.90 inference(rewrite,[status(thm)],[])).
% 55.97/35.90 tff(17,axiom,(member(x, y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_members_of_union2_1')).
% 55.97/35.90 tff(18,plain,
% 55.97/35.90 (member(x, y)),
% 55.97/35.90 inference(modus_ponens,[status(thm)],[17, 16])).
% 55.97/35.90 tff(19,plain,
% 55.97/35.90 (^[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))))),
% 55.97/35.90 inference(bind,[status(th)],[])).
% 55.97/35.90 tff(20,plain,
% 55.97/35.90 (![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)))),
% 55.97/35.90 inference(quant_intro,[status(thm)],[19])).
% 55.97/35.90 tff(21,plain,
% 55.97/35.90 (![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)))),
% 55.97/35.90 inference(rewrite,[status(thm)],[])).
% 55.97/35.90 tff(22,plain,
% 55.97/35.90 (^[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)))))),
% 55.97/35.90 inference(bind,[status(th)],[])).
% 55.97/35.90 tff(23,plain,
% 55.97/35.90 (![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)))),
% 55.97/35.90 inference(quant_intro,[status(thm)],[22])).
% 55.97/35.90 tff(24,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')).
% 56.01/35.90 tff(25,plain,
% 56.01/35.90 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[24, 23])).
% 56.01/35.90 tff(26,plain,
% 56.01/35.90 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[25, 21])).
% 56.01/35.90 tff(27,plain,(
% 56.01/35.90 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 56.01/35.90 inference(skolemize,[status(sab)],[26])).
% 56.01/35.90 tff(28,plain,
% 56.01/35.90 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[27, 20])).
% 56.01/35.90 tff(29,plain,
% 56.01/35.90 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, union(y, z)) | (~member(x, y)) | (~subclass(y, union(y, z))))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(x, union(y, z)) | (~member(x, y)) | (~subclass(y, union(y, z))))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(30,plain,
% 56.01/35.90 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(x, union(y, z)) | (~member(x, y)) | (~subclass(y, union(y, z))))),
% 56.01/35.90 inference(quant_inst,[status(thm)],[])).
% 56.01/35.90 tff(31,plain,
% 56.01/35.90 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(x, union(y, z)) | (~member(x, y)) | (~subclass(y, union(y, z)))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[30, 29])).
% 56.01/35.90 tff(32,plain,
% 56.01/35.90 (~subclass(y, union(y, z))),
% 56.01/35.90 inference(unit_resolution,[status(thm)],[31, 28, 18, 15])).
% 56.01/35.90 tff(33,plain,
% 56.01/35.90 (^[Y: $i, X: $i] : refl((subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(34,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[33])).
% 56.01/35.90 tff(35,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(36,plain,
% 56.01/35.90 (^[Y: $i, X: $i] : rewrite((member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> (subclass(X, Y) | member(not_subclass_element(X, Y), X)))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(37,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y)) <=> ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[36])).
% 56.01/35.90 tff(38,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 56.01/35.90 tff(39,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[38, 37])).
% 56.01/35.90 tff(40,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[39, 35])).
% 56.01/35.90 tff(41,plain,(
% 56.01/35.90 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(skolemize,[status(sab)],[40])).
% 56.01/35.90 tff(42,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[41, 34])).
% 56.01/35.90 tff(43,plain,
% 56.01/35.90 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(y, union(y, z)) | member(not_subclass_element(y, union(y, z)), y))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(y, union(y, z)) | member(not_subclass_element(y, union(y, z)), y))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(44,plain,
% 56.01/35.90 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(y, union(y, z)) | member(not_subclass_element(y, union(y, z)), y))),
% 56.01/35.90 inference(quant_inst,[status(thm)],[])).
% 56.01/35.90 tff(45,plain,
% 56.01/35.90 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(y, union(y, z)) | member(not_subclass_element(y, union(y, z)), y)),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[44, 43])).
% 56.01/35.90 tff(46,plain,
% 56.01/35.90 (member(not_subclass_element(y, union(y, z)), y)),
% 56.01/35.90 inference(unit_resolution,[status(thm)],[45, 42, 32])).
% 56.01/35.90 tff(47,plain,
% 56.01/35.90 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(y, z)), universal_class) | (~member(not_subclass_element(y, union(y, z)), y)) | (~subclass(y, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(y, union(y, z)), universal_class) | (~member(not_subclass_element(y, union(y, z)), y)) | (~subclass(y, universal_class)))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(48,plain,
% 56.01/35.90 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(y, z)), universal_class) | (~member(not_subclass_element(y, union(y, z)), y)) | (~subclass(y, universal_class)))),
% 56.01/35.90 inference(quant_inst,[status(thm)],[])).
% 56.01/35.90 tff(49,plain,
% 56.01/35.90 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(y, union(y, z)), universal_class) | (~member(not_subclass_element(y, union(y, z)), y)) | (~subclass(y, universal_class))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[48, 47])).
% 56.01/35.90 tff(50,plain,
% 56.01/35.90 ($false),
% 56.01/35.90 inference(unit_resolution,[status(thm)],[49, 28, 46, 12, 11])).
% 56.01/35.90 tff(51,plain,(member(not_subclass_element(y, union(y, z)), universal_class)), inference(lemma,lemma(discharge,[]))).
% 56.01/35.90 tff(52,plain,
% 56.01/35.90 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(53,plain,
% 56.01/35.90 (![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))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[52])).
% 56.01/35.90 tff(54,plain,
% 56.01/35.90 (![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))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(55,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','union')).
% 56.01/35.90 tff(56,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[55, 54])).
% 56.01/35.90 tff(57,plain,(
% 56.01/35.90 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 56.01/35.90 inference(skolemize,[status(sab)],[56])).
% 56.01/35.90 tff(58,plain,
% 56.01/35.90 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[57, 53])).
% 56.01/35.90 tff(59,plain,
% 56.01/35.90 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(y), complement(z))) = union(y, z))),
% 56.01/35.90 inference(quant_inst,[status(thm)],[])).
% 56.01/35.90 tff(60,plain,
% 56.01/35.90 (complement(intersection(complement(y), complement(z))) = union(y, z)),
% 56.01/35.90 inference(unit_resolution,[status(thm)],[59, 58])).
% 56.01/35.90 tff(61,plain,
% 56.01/35.90 (member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z)))) <=> member(not_subclass_element(y, union(y, z)), union(y, z))),
% 56.01/35.90 inference(monotonicity,[status(thm)],[60])).
% 56.01/35.90 tff(62,plain,
% 56.01/35.90 (member(not_subclass_element(y, union(y, z)), union(y, z)) <=> member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z))))),
% 56.01/35.90 inference(symmetry,[status(thm)],[61])).
% 56.01/35.90 tff(63,plain,
% 56.01/35.90 ((~member(not_subclass_element(y, union(y, z)), union(y, z))) <=> (~member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z)))))),
% 56.01/35.90 inference(monotonicity,[status(thm)],[62])).
% 56.01/35.90 tff(64,plain,
% 56.01/35.90 (^[Y: $i, X: $i] : refl(((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(65,plain,
% 56.01/35.90 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[64])).
% 56.01/35.90 tff(66,plain,
% 56.01/35.90 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y)) <=> ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(67,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 56.01/35.90 tff(68,plain,
% 56.01/35.90 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[67, 66])).
% 56.01/35.90 tff(69,plain,(
% 56.01/35.90 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 56.01/35.90 inference(skolemize,[status(sab)],[68])).
% 56.01/35.90 tff(70,plain,
% 56.01/35.90 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[69, 65])).
% 56.01/35.90 tff(71,plain,
% 56.01/35.90 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(y, union(y, z)), union(y, z))) | subclass(y, union(y, z)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(y, union(y, z)), union(y, z))) | subclass(y, union(y, z)))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(72,plain,
% 56.01/35.90 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(y, union(y, z)), union(y, z))) | subclass(y, union(y, z)))),
% 56.01/35.90 inference(quant_inst,[status(thm)],[])).
% 56.01/35.90 tff(73,plain,
% 56.01/35.90 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(y, union(y, z)), union(y, z))) | subclass(y, union(y, z))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[72, 71])).
% 56.01/35.90 tff(74,plain,
% 56.01/35.90 (~member(not_subclass_element(y, union(y, z)), union(y, z))),
% 56.01/35.90 inference(unit_resolution,[status(thm)],[73, 70, 32])).
% 56.01/35.90 tff(75,plain,
% 56.01/35.90 (~member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z))))),
% 56.01/35.90 inference(modus_ponens,[status(thm)],[74, 63])).
% 56.01/35.90 tff(76,plain,
% 56.01/35.90 (^[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))))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(77,plain,
% 56.01/35.90 (![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)))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[76])).
% 56.01/35.90 tff(78,plain,
% 56.01/35.90 (![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)))),
% 56.01/35.90 inference(rewrite,[status(thm)],[])).
% 56.01/35.90 tff(79,plain,
% 56.01/35.90 (^[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))))),
% 56.01/35.90 inference(bind,[status(th)],[])).
% 56.01/35.90 tff(80,plain,
% 56.01/35.90 (![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)))),
% 56.01/35.90 inference(quant_intro,[status(thm)],[79])).
% 56.01/35.90 tff(81,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')).
% 56.01/35.90 tff(82,plain,
% 56.01/35.90 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[81, 80])).
% 56.01/35.91 tff(83,plain,
% 56.01/35.91 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[82, 78])).
% 56.01/35.91 tff(84,plain,(
% 56.01/35.91 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 56.01/35.91 inference(skolemize,[status(sab)],[83])).
% 56.01/35.91 tff(85,plain,
% 56.01/35.91 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[84, 77])).
% 56.01/35.91 tff(86,plain,
% 56.01/35.91 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class)) | member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z)))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class)) | member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z)))))),
% 56.01/35.91 inference(rewrite,[status(thm)],[])).
% 56.01/35.91 tff(87,plain,
% 56.01/35.91 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class)) | member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z)))))),
% 56.01/35.91 inference(quant_inst,[status(thm)],[])).
% 56.01/35.91 tff(88,plain,
% 56.01/35.91 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class)) | member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z))))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[87, 86])).
% 56.01/35.91 tff(89,plain,
% 56.01/35.91 (member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class)) | member(not_subclass_element(y, union(y, z)), complement(intersection(complement(y), complement(z))))),
% 56.01/35.91 inference(unit_resolution,[status(thm)],[88, 85])).
% 56.01/35.91 tff(90,plain,
% 56.01/35.91 (member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z))) | (~member(not_subclass_element(y, union(y, z)), universal_class))),
% 56.01/35.91 inference(unit_resolution,[status(thm)],[89, 75])).
% 56.01/35.91 tff(91,plain,
% 56.01/35.91 (member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z)))),
% 56.01/35.91 inference(unit_resolution,[status(thm)],[90, 51])).
% 56.01/35.91 tff(92,plain,
% 56.01/35.91 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ((~member(Z, intersection(X, Y))) | member(Z, X)))),
% 56.01/35.91 inference(bind,[status(th)],[])).
% 56.01/35.91 tff(93,plain,
% 56.01/35.91 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 56.01/35.91 inference(quant_intro,[status(thm)],[92])).
% 56.01/35.91 tff(94,plain,
% 56.01/35.91 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 56.01/35.91 inference(rewrite,[status(thm)],[])).
% 56.01/35.91 tff(95,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','intersection1')).
% 56.01/35.91 tff(96,plain,
% 56.01/35.91 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[95, 94])).
% 56.01/35.91 tff(97,plain,(
% 56.01/35.91 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 56.01/35.91 inference(skolemize,[status(sab)],[96])).
% 56.01/35.91 tff(98,plain,
% 56.01/35.91 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[97, 93])).
% 56.01/35.91 tff(99,plain,
% 56.01/35.91 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z)))) | member(not_subclass_element(y, union(y, z)), complement(y)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z)))) | member(not_subclass_element(y, union(y, z)), complement(y)))),
% 56.01/35.91 inference(rewrite,[status(thm)],[])).
% 56.01/35.91 tff(100,plain,
% 56.01/35.91 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z)))) | member(not_subclass_element(y, union(y, z)), complement(y)))),
% 56.01/35.91 inference(quant_inst,[status(thm)],[])).
% 56.01/35.91 tff(101,plain,
% 56.01/35.91 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(y, union(y, z)), intersection(complement(y), complement(z)))) | member(not_subclass_element(y, union(y, z)), complement(y))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[100, 99])).
% 56.01/35.91 tff(102,plain,
% 56.01/35.91 (member(not_subclass_element(y, union(y, z)), complement(y))),
% 56.01/35.91 inference(unit_resolution,[status(thm)],[101, 98, 91])).
% 56.01/35.91 tff(103,plain,
% 56.01/35.91 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 56.01/35.91 inference(bind,[status(th)],[])).
% 56.01/35.91 tff(104,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(quant_intro,[status(thm)],[103])).
% 56.01/35.91 tff(105,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(rewrite,[status(thm)],[])).
% 56.01/35.91 tff(106,plain,
% 56.01/35.91 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 56.01/35.91 inference(bind,[status(th)],[])).
% 56.01/35.91 tff(107,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(quant_intro,[status(thm)],[106])).
% 56.01/35.91 tff(108,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','complement1')).
% 56.01/35.91 tff(109,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[108, 107])).
% 56.01/35.91 tff(110,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[109, 105])).
% 56.01/35.91 tff(111,plain,(
% 56.01/35.91 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(skolemize,[status(sab)],[110])).
% 56.01/35.91 tff(112,plain,
% 56.01/35.91 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[111, 104])).
% 56.01/35.91 tff(113,plain,
% 56.01/35.91 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(y, union(y, z)), y)) | (~member(not_subclass_element(y, union(y, z)), complement(y))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(y, union(y, z)), y)) | (~member(not_subclass_element(y, union(y, z)), complement(y))))),
% 56.01/35.91 inference(rewrite,[status(thm)],[])).
% 56.01/35.91 tff(114,plain,
% 56.01/35.91 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(y, union(y, z)), y)) | (~member(not_subclass_element(y, union(y, z)), complement(y))))),
% 56.01/35.91 inference(quant_inst,[status(thm)],[])).
% 56.01/35.91 tff(115,plain,
% 56.01/35.91 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(y, union(y, z)), y)) | (~member(not_subclass_element(y, union(y, z)), complement(y)))),
% 56.01/35.91 inference(modus_ponens,[status(thm)],[114, 113])).
% 56.01/35.92 tff(116,plain,
% 56.01/35.92 ($false),
% 56.01/35.92 inference(unit_resolution,[status(thm)],[115, 112, 46, 102])).
% 56.01/35.92 % SZS output end Proof
%------------------------------------------------------------------------------