TSTP Solution File: SET195-6 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET195-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 05:06:06 EDT 2022
% Result : Unsatisfiable 169.41s 107.40s
% Output : Proof 169.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET195-6 : 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 : n017.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 02:43:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 169.41/107.40 % SZS status Unsatisfiable
% 169.41/107.40 % SZS output start Proof
% 169.41/107.40 tff(member_type, type, (
% 169.41/107.40 member: ( $i * $i ) > $o)).
% 169.41/107.40 tff(complement_type, type, (
% 169.41/107.40 complement: $i > $i)).
% 169.41/107.40 tff(y_type, type, (
% 169.41/107.40 y: $i)).
% 169.41/107.40 tff(not_subclass_element_type, type, (
% 169.41/107.40 not_subclass_element: ( $i * $i ) > $i)).
% 169.41/107.40 tff(union_type, type, (
% 169.41/107.40 union: ( $i * $i ) > $i)).
% 169.41/107.40 tff(x_type, type, (
% 169.41/107.40 x: $i)).
% 169.41/107.40 tff(intersection_type, type, (
% 169.41/107.40 intersection: ( $i * $i ) > $i)).
% 169.41/107.40 tff(universal_class_type, type, (
% 169.41/107.40 universal_class: $i)).
% 169.41/107.40 tff(subclass_type, type, (
% 169.41/107.40 subclass: ( $i * $i ) > $o)).
% 169.41/107.40 tff(1,assumption,(~subclass(y, universal_class)), introduced(assumption)).
% 169.41/107.40 tff(2,plain,
% 169.41/107.40 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(3,plain,
% 169.41/107.40 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 169.41/107.40 inference(quant_intro,[status(thm)],[2])).
% 169.41/107.40 tff(4,plain,
% 169.41/107.40 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 169.41/107.40 tff(6,plain,
% 169.41/107.40 (![X: $i] : subclass(X, universal_class)),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 169.41/107.40 tff(7,plain,(
% 169.41/107.40 ![X: $i] : subclass(X, universal_class)),
% 169.41/107.40 inference(skolemize,[status(sab)],[6])).
% 169.41/107.40 tff(8,plain,
% 169.41/107.40 (![X: $i] : subclass(X, universal_class)),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 169.41/107.40 tff(9,plain,
% 169.41/107.40 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(10,plain,
% 169.41/107.40 ($false),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 169.41/107.40 tff(11,plain,(subclass(y, universal_class)), inference(lemma,lemma(discharge,[]))).
% 169.41/107.40 tff(12,assumption,(~member(not_subclass_element(y, union(x, y)), universal_class)), introduced(assumption)).
% 169.41/107.40 tff(13,plain,
% 169.41/107.40 ((~subclass(y, union(x, y))) <=> (~subclass(y, union(x, y)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(14,axiom,(~subclass(y, union(x, y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_lattice_upper_bound2_1')).
% 169.41/107.40 tff(15,plain,
% 169.41/107.40 (~subclass(y, union(x, y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 169.41/107.40 tff(16,plain,
% 169.41/107.40 (^[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)))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(17,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[16])).
% 169.41/107.40 tff(18,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(19,plain,
% 169.41/107.40 (^[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)))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(20,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[19])).
% 169.41/107.40 tff(21,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 169.41/107.40 tff(22,plain,
% 169.41/107.40 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 169.41/107.40 tff(23,plain,
% 169.41/107.40 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 169.41/107.40 tff(24,plain,(
% 169.41/107.40 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 169.41/107.40 inference(skolemize,[status(sab)],[23])).
% 169.41/107.40 tff(25,plain,
% 169.41/107.40 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[24, 17])).
% 169.41/107.40 tff(26,plain,
% 169.41/107.40 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(y, union(x, y)) | member(not_subclass_element(y, union(x, y)), y))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(y, union(x, y)) | member(not_subclass_element(y, union(x, y)), y))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(27,plain,
% 169.41/107.40 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(y, union(x, y)) | member(not_subclass_element(y, union(x, y)), y))),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(28,plain,
% 169.41/107.40 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(y, union(x, y)) | member(not_subclass_element(y, union(x, y)), y)),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 169.41/107.40 tff(29,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), y)),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 169.41/107.40 tff(30,plain,
% 169.41/107.40 (^[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))))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(31,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[30])).
% 169.41/107.40 tff(32,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(33,plain,
% 169.41/107.40 (^[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)))))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(34,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[33])).
% 169.41/107.40 tff(35,axiom,(![Y: $i, U: $i, X: $i] : (((~subclass(X, Y)) | (~member(U, X))) | member(U, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','subclass_members')).
% 169.41/107.40 tff(36,plain,
% 169.41/107.40 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 169.41/107.40 tff(37,plain,
% 169.41/107.40 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 169.41/107.40 tff(38,plain,(
% 169.41/107.40 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 169.41/107.40 inference(skolemize,[status(sab)],[37])).
% 169.41/107.40 tff(39,plain,
% 169.41/107.40 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 169.41/107.40 tff(40,plain,
% 169.41/107.40 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(y, union(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(41,plain,
% 169.41/107.40 ((member(not_subclass_element(y, union(x, y)), universal_class) | (~member(not_subclass_element(y, union(x, y)), y)) | (~subclass(y, universal_class))) <=> (member(not_subclass_element(y, union(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(42,plain,
% 169.41/107.40 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(x, y)), universal_class) | (~member(not_subclass_element(y, union(x, y)), 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(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y))))),
% 169.41/107.40 inference(monotonicity,[status(thm)],[41])).
% 169.41/107.40 tff(43,plain,
% 169.41/107.40 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(x, y)), universal_class) | (~member(not_subclass_element(y, union(x, y)), 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(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y)))),
% 169.41/107.40 inference(transitivity,[status(thm)],[42, 40])).
% 169.41/107.40 tff(44,plain,
% 169.41/107.40 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(y, union(x, y)), universal_class) | (~member(not_subclass_element(y, union(x, y)), y)) | (~subclass(y, universal_class)))),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(45,plain,
% 169.41/107.40 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(y, union(x, y)), universal_class) | (~subclass(y, universal_class)) | (~member(not_subclass_element(y, union(x, y)), y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 169.41/107.40 tff(46,plain,
% 169.41/107.40 ($false),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[45, 39, 29, 12, 11])).
% 169.41/107.40 tff(47,plain,(member(not_subclass_element(y, union(x, y)), universal_class)), inference(lemma,lemma(discharge,[]))).
% 169.41/107.40 tff(48,plain,
% 169.41/107.40 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(49,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[48])).
% 169.41/107.40 tff(50,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(51,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','union')).
% 169.41/107.40 tff(52,plain,
% 169.41/107.40 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 169.41/107.40 tff(53,plain,(
% 169.41/107.40 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 169.41/107.40 inference(skolemize,[status(sab)],[52])).
% 169.41/107.40 tff(54,plain,
% 169.41/107.40 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 169.41/107.40 tff(55,plain,
% 169.41/107.40 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(x), complement(y))) = union(x, y))),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(56,plain,
% 169.41/107.40 (complement(intersection(complement(x), complement(y))) = union(x, y)),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[55, 54])).
% 169.41/107.40 tff(57,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y)))) <=> member(not_subclass_element(y, union(x, y)), union(x, y))),
% 169.41/107.40 inference(monotonicity,[status(thm)],[56])).
% 169.41/107.40 tff(58,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), union(x, y)) <=> member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y))))),
% 169.41/107.40 inference(symmetry,[status(thm)],[57])).
% 169.41/107.40 tff(59,plain,
% 169.41/107.40 ((~member(not_subclass_element(y, union(x, y)), union(x, y))) <=> (~member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y)))))),
% 169.41/107.40 inference(monotonicity,[status(thm)],[58])).
% 169.41/107.40 tff(60,plain,
% 169.41/107.40 (^[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)))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(61,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[60])).
% 169.41/107.40 tff(62,plain,
% 169.41/107.40 (![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))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(63,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 169.41/107.40 tff(64,plain,
% 169.41/107.40 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 169.41/107.40 tff(65,plain,(
% 169.41/107.40 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 169.41/107.40 inference(skolemize,[status(sab)],[64])).
% 169.41/107.40 tff(66,plain,
% 169.41/107.40 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 169.41/107.40 tff(67,plain,
% 169.41/107.40 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(y, union(x, y)), union(x, y))) | subclass(y, union(x, y)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(y, union(x, y)), union(x, y))) | subclass(y, union(x, y)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(68,plain,
% 169.41/107.40 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(y, union(x, y)), union(x, y))) | subclass(y, union(x, y)))),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(69,plain,
% 169.41/107.40 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(y, union(x, y)), union(x, y))) | subclass(y, union(x, y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[68, 67])).
% 169.41/107.40 tff(70,plain,
% 169.41/107.40 (~member(not_subclass_element(y, union(x, y)), union(x, y))),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[69, 66, 15])).
% 169.41/107.40 tff(71,plain,
% 169.41/107.40 (~member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y))))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[70, 59])).
% 169.41/107.40 tff(72,plain,
% 169.41/107.40 (^[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))))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(73,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[72])).
% 169.41/107.40 tff(74,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(75,plain,
% 169.41/107.40 (^[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))))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(76,plain,
% 169.41/107.40 (![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)))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[75])).
% 169.41/107.40 tff(77,axiom,(![Z: $i, X: $i] : (((~member(Z, universal_class)) | member(Z, complement(X))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','complement2')).
% 169.41/107.40 tff(78,plain,
% 169.41/107.40 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 169.41/107.40 tff(79,plain,
% 169.41/107.40 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 169.41/107.40 tff(80,plain,(
% 169.41/107.40 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 169.41/107.40 inference(skolemize,[status(sab)],[79])).
% 169.41/107.40 tff(81,plain,
% 169.41/107.40 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 169.41/107.40 tff(82,plain,
% 169.41/107.40 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class)) | member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y)))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class)) | member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y)))))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(83,plain,
% 169.41/107.40 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class)) | member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y)))))),
% 169.41/107.40 inference(quant_inst,[status(thm)],[])).
% 169.41/107.40 tff(84,plain,
% 169.41/107.40 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class)) | member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y))))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 169.41/107.40 tff(85,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class)) | member(not_subclass_element(y, union(x, y)), complement(intersection(complement(x), complement(y))))),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[84, 81])).
% 169.41/107.40 tff(86,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y))) | (~member(not_subclass_element(y, union(x, y)), universal_class))),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[85, 71])).
% 169.41/107.40 tff(87,plain,
% 169.41/107.40 (member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y)))),
% 169.41/107.40 inference(unit_resolution,[status(thm)],[86, 47])).
% 169.41/107.40 tff(88,plain,
% 169.41/107.40 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ((~member(Z, intersection(X, Y))) | member(Z, Y)))),
% 169.41/107.40 inference(bind,[status(th)],[])).
% 169.41/107.40 tff(89,plain,
% 169.41/107.40 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 169.41/107.40 inference(quant_intro,[status(thm)],[88])).
% 169.41/107.40 tff(90,plain,
% 169.41/107.40 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 169.41/107.40 inference(rewrite,[status(thm)],[])).
% 169.41/107.40 tff(91,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection2')).
% 169.41/107.40 tff(92,plain,
% 169.41/107.40 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 169.41/107.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 169.41/107.41 tff(93,plain,(
% 169.41/107.41 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 169.41/107.41 inference(skolemize,[status(sab)],[92])).
% 169.41/107.41 tff(94,plain,
% 169.41/107.41 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[93, 89])).
% 169.41/107.41 tff(95,plain,
% 169.41/107.41 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y)))) | member(not_subclass_element(y, union(x, y)), complement(y)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y)))) | member(not_subclass_element(y, union(x, y)), complement(y)))),
% 169.41/107.41 inference(rewrite,[status(thm)],[])).
% 169.41/107.41 tff(96,plain,
% 169.41/107.41 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y)))) | member(not_subclass_element(y, union(x, y)), complement(y)))),
% 169.41/107.41 inference(quant_inst,[status(thm)],[])).
% 169.41/107.41 tff(97,plain,
% 169.41/107.41 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(y, union(x, y)), intersection(complement(x), complement(y)))) | member(not_subclass_element(y, union(x, y)), complement(y))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 169.41/107.41 tff(98,plain,
% 169.41/107.41 (member(not_subclass_element(y, union(x, y)), complement(y))),
% 169.41/107.41 inference(unit_resolution,[status(thm)],[97, 94, 87])).
% 169.41/107.41 tff(99,plain,
% 169.41/107.41 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 169.41/107.41 inference(bind,[status(th)],[])).
% 169.41/107.41 tff(100,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(quant_intro,[status(thm)],[99])).
% 169.41/107.41 tff(101,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(rewrite,[status(thm)],[])).
% 169.41/107.41 tff(102,plain,
% 169.41/107.41 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 169.41/107.41 inference(bind,[status(th)],[])).
% 169.41/107.41 tff(103,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(quant_intro,[status(thm)],[102])).
% 169.41/107.41 tff(104,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','complement1')).
% 169.41/107.41 tff(105,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 169.41/107.41 tff(106,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[105, 101])).
% 169.41/107.41 tff(107,plain,(
% 169.41/107.41 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(skolemize,[status(sab)],[106])).
% 169.41/107.41 tff(108,plain,
% 169.41/107.41 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[107, 100])).
% 169.41/107.41 tff(109,plain,
% 169.41/107.41 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(y, union(x, y)), y)) | (~member(not_subclass_element(y, union(x, y)), complement(y))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(y, union(x, y)), y)) | (~member(not_subclass_element(y, union(x, y)), complement(y))))),
% 169.41/107.41 inference(rewrite,[status(thm)],[])).
% 169.41/107.41 tff(110,plain,
% 169.41/107.41 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(y, union(x, y)), y)) | (~member(not_subclass_element(y, union(x, y)), complement(y))))),
% 169.41/107.41 inference(quant_inst,[status(thm)],[])).
% 169.41/107.41 tff(111,plain,
% 169.41/107.41 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(y, union(x, y)), y)) | (~member(not_subclass_element(y, union(x, y)), complement(y)))),
% 169.41/107.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 169.41/107.41 tff(112,plain,
% 169.41/107.41 ($false),
% 169.41/107.41 inference(unit_resolution,[status(thm)],[111, 108, 29, 98])).
% 169.41/107.41 % SZS output end Proof
%------------------------------------------------------------------------------