TSTP Solution File: NUM030-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM030-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Sun Sep 18 13:02:43 EDT 2022
% Result : Unsatisfiable 2.42s 1.78s
% Output : Proof 2.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM030-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 06:35:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.42/1.78 % SZS status Unsatisfiable
% 2.42/1.78 % SZS output start Proof
% 2.42/1.78 tff(member_type, type, (
% 2.42/1.78 member: ( $i * $i ) > $o)).
% 2.42/1.78 tff(complement_type, type, (
% 2.42/1.78 complement: $i > $i)).
% 2.42/1.78 tff(inverse_type, type, (
% 2.42/1.78 inverse: $i > $i)).
% 2.42/1.78 tff(x_type, type, (
% 2.42/1.78 x: $i)).
% 2.42/1.78 tff(not_subclass_element_type, type, (
% 2.42/1.78 not_subclass_element: ( $i * $i ) > $i)).
% 2.42/1.78 tff(intersection_type, type, (
% 2.42/1.78 intersection: ( $i * $i ) > $i)).
% 2.42/1.78 tff(universal_class_type, type, (
% 2.42/1.78 universal_class: $i)).
% 2.42/1.78 tff(subclass_type, type, (
% 2.42/1.78 subclass: ( $i * $i ) > $o)).
% 2.42/1.78 tff(symmetrization_of_type, type, (
% 2.42/1.78 symmetrization_of: $i > $i)).
% 2.42/1.78 tff(union_type, type, (
% 2.42/1.78 union: ( $i * $i ) > $i)).
% 2.42/1.78 tff(1,assumption,(~subclass(inverse(x), universal_class)), introduced(assumption)).
% 2.42/1.78 tff(2,plain,
% 2.42/1.78 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(3,plain,
% 2.42/1.78 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 2.42/1.78 inference(quant_intro,[status(thm)],[2])).
% 2.42/1.78 tff(4,plain,
% 2.42/1.78 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 2.42/1.78 tff(6,plain,
% 2.42/1.78 (![X: $i] : subclass(X, universal_class)),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.42/1.78 tff(7,plain,(
% 2.42/1.78 ![X: $i] : subclass(X, universal_class)),
% 2.42/1.78 inference(skolemize,[status(sab)],[6])).
% 2.42/1.78 tff(8,plain,
% 2.42/1.78 (![X: $i] : subclass(X, universal_class)),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.42/1.78 tff(9,plain,
% 2.42/1.78 ((~![X: $i] : subclass(X, universal_class)) | subclass(inverse(x), universal_class)),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(10,plain,
% 2.42/1.78 ($false),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 2.42/1.78 tff(11,plain,(subclass(inverse(x), universal_class)), inference(lemma,lemma(discharge,[]))).
% 2.42/1.78 tff(12,assumption,(~member(not_subclass_element(inverse(x), x), universal_class)), introduced(assumption)).
% 2.42/1.78 tff(13,plain,
% 2.42/1.78 ((~subclass(inverse(x), x)) <=> (~subclass(inverse(x), x))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(14,axiom,(~subclass(inverse(x), x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_symmetrization_property3_2')).
% 2.42/1.78 tff(15,plain,
% 2.42/1.78 (~subclass(inverse(x), x)),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[14, 13])).
% 2.42/1.78 tff(16,plain,
% 2.42/1.78 (^[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)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(17,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[16])).
% 2.42/1.78 tff(18,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(19,plain,
% 2.42/1.78 (^[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)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(20,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[19])).
% 2.42/1.78 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')).
% 2.42/1.78 tff(22,plain,
% 2.42/1.78 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[21, 20])).
% 2.42/1.78 tff(23,plain,
% 2.42/1.78 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[22, 18])).
% 2.42/1.78 tff(24,plain,(
% 2.42/1.78 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 2.42/1.78 inference(skolemize,[status(sab)],[23])).
% 2.42/1.78 tff(25,plain,
% 2.42/1.78 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[24, 17])).
% 2.42/1.78 tff(26,plain,
% 2.42/1.78 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(inverse(x), x) | member(not_subclass_element(inverse(x), x), inverse(x)))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(inverse(x), x) | member(not_subclass_element(inverse(x), x), inverse(x)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(27,plain,
% 2.42/1.78 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(inverse(x), x) | member(not_subclass_element(inverse(x), x), inverse(x)))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(28,plain,
% 2.42/1.78 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(inverse(x), x) | member(not_subclass_element(inverse(x), x), inverse(x))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.42/1.78 tff(29,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), inverse(x))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 2.42/1.78 tff(30,plain,
% 2.42/1.78 (^[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))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(31,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[30])).
% 2.42/1.78 tff(32,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(33,plain,
% 2.42/1.78 (^[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)))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(34,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[33])).
% 2.42/1.78 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')).
% 2.42/1.78 tff(36,plain,
% 2.42/1.78 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.42/1.78 tff(37,plain,
% 2.42/1.78 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[36, 32])).
% 2.42/1.78 tff(38,plain,(
% 2.42/1.78 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 2.42/1.78 inference(skolemize,[status(sab)],[37])).
% 2.42/1.78 tff(39,plain,
% 2.42/1.78 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[38, 31])).
% 2.42/1.78 tff(40,plain,
% 2.42/1.78 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(inverse(x), x), universal_class) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~subclass(inverse(x), universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(inverse(x), x), universal_class) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~subclass(inverse(x), universal_class)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(41,plain,
% 2.42/1.78 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(not_subclass_element(inverse(x), x), universal_class) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~subclass(inverse(x), universal_class)))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(42,plain,
% 2.42/1.78 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(not_subclass_element(inverse(x), x), universal_class) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~subclass(inverse(x), universal_class))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[41, 40])).
% 2.42/1.78 tff(43,plain,
% 2.42/1.78 ($false),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[42, 39, 29, 12, 11])).
% 2.42/1.78 tff(44,plain,(member(not_subclass_element(inverse(x), x), universal_class)), inference(lemma,lemma(discharge,[]))).
% 2.42/1.78 tff(45,plain,
% 2.42/1.78 ((symmetrization_of(x) = x) <=> (symmetrization_of(x) = x)),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(46,axiom,(symmetrization_of(x) = x), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_symmetrization_property3_1')).
% 2.42/1.78 tff(47,plain,
% 2.42/1.78 (symmetrization_of(x) = x),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[46, 45])).
% 2.42/1.78 tff(48,plain,
% 2.42/1.78 (^[X: $i] : refl((union(X, inverse(X)) = symmetrization_of(X)) <=> (union(X, inverse(X)) = symmetrization_of(X)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(49,plain,
% 2.42/1.78 (![X: $i] : (union(X, inverse(X)) = symmetrization_of(X)) <=> ![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[48])).
% 2.42/1.78 tff(50,plain,
% 2.42/1.78 (![X: $i] : (union(X, inverse(X)) = symmetrization_of(X)) <=> ![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(51,axiom,(![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))), file('/export/starexec/sandbox/benchmark/Axioms/NUM004-0.ax','symmetrization')).
% 2.42/1.78 tff(52,plain,
% 2.42/1.78 (![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.42/1.78 tff(53,plain,(
% 2.42/1.78 ![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))),
% 2.42/1.78 inference(skolemize,[status(sab)],[52])).
% 2.42/1.78 tff(54,plain,
% 2.42/1.78 (![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.42/1.78 tff(55,plain,
% 2.42/1.78 ((~![X: $i] : (union(X, inverse(X)) = symmetrization_of(X))) | (union(x, inverse(x)) = symmetrization_of(x))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(56,plain,
% 2.42/1.78 (union(x, inverse(x)) = symmetrization_of(x)),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[55, 54])).
% 2.42/1.78 tff(57,plain,
% 2.42/1.78 (^[Y: $i, X: $i] : refl((complement(intersection(complement(X), complement(Y))) = union(X, Y)) <=> (complement(intersection(complement(X), complement(Y))) = union(X, Y)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(58,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[57])).
% 2.42/1.78 tff(59,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(60,axiom,(![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','union')).
% 2.42/1.78 tff(61,plain,
% 2.42/1.78 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[60, 59])).
% 2.42/1.78 tff(62,plain,(
% 2.42/1.78 ![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 2.42/1.78 inference(skolemize,[status(sab)],[61])).
% 2.42/1.78 tff(63,plain,
% 2.42/1.78 (![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[62, 58])).
% 2.42/1.78 tff(64,plain,
% 2.42/1.78 ((~![Y: $i, X: $i] : (complement(intersection(complement(X), complement(Y))) = union(X, Y))) | (complement(intersection(complement(x), complement(inverse(x)))) = union(x, inverse(x)))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(65,plain,
% 2.42/1.78 (complement(intersection(complement(x), complement(inverse(x)))) = union(x, inverse(x))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[64, 63])).
% 2.42/1.78 tff(66,plain,
% 2.42/1.78 (complement(intersection(complement(x), complement(inverse(x)))) = x),
% 2.42/1.78 inference(transitivity,[status(thm)],[65, 56, 47])).
% 2.42/1.78 tff(67,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x))))) <=> member(not_subclass_element(inverse(x), x), x)),
% 2.42/1.78 inference(monotonicity,[status(thm)],[66])).
% 2.42/1.78 tff(68,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), x) <=> member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x)))))),
% 2.42/1.78 inference(symmetry,[status(thm)],[67])).
% 2.42/1.78 tff(69,plain,
% 2.42/1.78 ((~member(not_subclass_element(inverse(x), x), x)) <=> (~member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x))))))),
% 2.42/1.78 inference(monotonicity,[status(thm)],[68])).
% 2.42/1.78 tff(70,plain,
% 2.42/1.78 (^[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)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(71,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[70])).
% 2.42/1.78 tff(72,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(73,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')).
% 2.42/1.78 tff(74,plain,
% 2.42/1.78 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[73, 72])).
% 2.42/1.78 tff(75,plain,(
% 2.42/1.78 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 2.42/1.78 inference(skolemize,[status(sab)],[74])).
% 2.42/1.78 tff(76,plain,
% 2.42/1.78 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[75, 71])).
% 2.42/1.78 tff(77,plain,
% 2.42/1.78 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(inverse(x), x), x)) | subclass(inverse(x), x))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(inverse(x), x), x)) | subclass(inverse(x), x))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(78,plain,
% 2.42/1.78 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(inverse(x), x), x)) | subclass(inverse(x), x))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(79,plain,
% 2.42/1.78 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(inverse(x), x), x)) | subclass(inverse(x), x)),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.42/1.78 tff(80,plain,
% 2.42/1.78 (~member(not_subclass_element(inverse(x), x), x)),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[79, 76, 15])).
% 2.42/1.78 tff(81,plain,
% 2.42/1.78 (~member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x)))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[80, 69])).
% 2.42/1.78 tff(82,plain,
% 2.42/1.78 (^[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))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(83,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[82])).
% 2.42/1.78 tff(84,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(85,plain,
% 2.42/1.78 (^[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))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(86,plain,
% 2.42/1.78 (![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)))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[85])).
% 2.42/1.78 tff(87,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')).
% 2.42/1.78 tff(88,plain,
% 2.42/1.78 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.42/1.78 tff(89,plain,
% 2.42/1.78 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[88, 84])).
% 2.42/1.78 tff(90,plain,(
% 2.42/1.78 ![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 2.42/1.78 inference(skolemize,[status(sab)],[89])).
% 2.42/1.78 tff(91,plain,
% 2.42/1.78 (![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[90, 83])).
% 2.42/1.78 tff(92,plain,
% 2.42/1.78 (((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class)) | member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x))))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class)) | member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x))))))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(93,plain,
% 2.42/1.78 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | (member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class)) | member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x))))))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(94,plain,
% 2.42/1.78 ((~![Z: $i, X: $i] : (member(Z, X) | (~member(Z, universal_class)) | member(Z, complement(X)))) | member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class)) | member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x)))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[93, 92])).
% 2.42/1.78 tff(95,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class)) | member(not_subclass_element(inverse(x), x), complement(intersection(complement(x), complement(inverse(x)))))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[94, 91])).
% 2.42/1.78 tff(96,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x)))) | (~member(not_subclass_element(inverse(x), x), universal_class))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[95, 81])).
% 2.42/1.78 tff(97,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x))))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[96, 44])).
% 2.42/1.78 tff(98,plain,
% 2.42/1.78 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, Y)) <=> ((~member(Z, intersection(X, Y))) | member(Z, Y)))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(99,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[98])).
% 2.42/1.78 tff(100,plain,
% 2.42/1.78 (![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))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(101,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')).
% 2.42/1.78 tff(102,plain,
% 2.42/1.78 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[101, 100])).
% 2.42/1.78 tff(103,plain,(
% 2.42/1.78 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 2.42/1.78 inference(skolemize,[status(sab)],[102])).
% 2.42/1.78 tff(104,plain,
% 2.42/1.78 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[103, 99])).
% 2.42/1.78 tff(105,plain,
% 2.42/1.78 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x))))) | member(not_subclass_element(inverse(x), x), complement(inverse(x))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x))))) | member(not_subclass_element(inverse(x), x), complement(inverse(x))))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(106,plain,
% 2.42/1.78 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | ((~member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x))))) | member(not_subclass_element(inverse(x), x), complement(inverse(x))))),
% 2.42/1.78 inference(quant_inst,[status(thm)],[])).
% 2.42/1.78 tff(107,plain,
% 2.42/1.78 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, Y))) | (~member(not_subclass_element(inverse(x), x), intersection(complement(x), complement(inverse(x))))) | member(not_subclass_element(inverse(x), x), complement(inverse(x)))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[106, 105])).
% 2.42/1.78 tff(108,plain,
% 2.42/1.78 (member(not_subclass_element(inverse(x), x), complement(inverse(x)))),
% 2.42/1.78 inference(unit_resolution,[status(thm)],[107, 104, 97])).
% 2.42/1.78 tff(109,plain,
% 2.42/1.78 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(110,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[109])).
% 2.42/1.78 tff(111,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(rewrite,[status(thm)],[])).
% 2.42/1.78 tff(112,plain,
% 2.42/1.78 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 2.42/1.78 inference(bind,[status(th)],[])).
% 2.42/1.78 tff(113,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(quant_intro,[status(thm)],[112])).
% 2.42/1.78 tff(114,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','complement1')).
% 2.42/1.78 tff(115,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[114, 113])).
% 2.42/1.78 tff(116,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[115, 111])).
% 2.42/1.78 tff(117,plain,(
% 2.42/1.78 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(skolemize,[status(sab)],[116])).
% 2.42/1.78 tff(118,plain,
% 2.42/1.78 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 2.42/1.78 inference(modus_ponens,[status(thm)],[117, 110])).
% 2.42/1.79 tff(119,plain,
% 2.42/1.79 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(inverse(x), x), inverse(x))) | (~member(not_subclass_element(inverse(x), x), complement(inverse(x)))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~member(not_subclass_element(inverse(x), x), complement(inverse(x)))))),
% 2.42/1.79 inference(rewrite,[status(thm)],[])).
% 2.42/1.79 tff(120,plain,
% 2.42/1.79 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(not_subclass_element(inverse(x), x), inverse(x))) | (~member(not_subclass_element(inverse(x), x), complement(inverse(x)))))),
% 2.42/1.79 inference(quant_inst,[status(thm)],[])).
% 2.42/1.79 tff(121,plain,
% 2.42/1.79 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(not_subclass_element(inverse(x), x), inverse(x))) | (~member(not_subclass_element(inverse(x), x), complement(inverse(x))))),
% 2.42/1.79 inference(modus_ponens,[status(thm)],[120, 119])).
% 2.42/1.79 tff(122,plain,
% 2.42/1.79 ($false),
% 2.42/1.79 inference(unit_resolution,[status(thm)],[121, 118, 29, 108])).
% 2.42/1.79 % SZS output end Proof
%------------------------------------------------------------------------------