TSTP Solution File: SET380-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET380-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:06:37 EDT 2022
% Result : Unsatisfiable 5.08s 3.47s
% Output : Proof 5.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET380-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Sat Sep 3 05:08:45 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.36 Usage: tptp [options] [-file:]file
% 0.20/0.36 -h, -? prints this message.
% 0.20/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.36 -m, -model generate model.
% 0.20/0.36 -p, -proof generate proof.
% 0.20/0.36 -c, -core generate unsat core of named formulas.
% 0.20/0.36 -st, -statistics display statistics.
% 0.20/0.36 -t:timeout set timeout (in second).
% 0.20/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.36 -<param>:<value> configuration parameter and value.
% 0.20/0.36 -o:<output-file> file to place output in.
% 5.08/3.47 % SZS status Unsatisfiable
% 5.08/3.47 % SZS output start Proof
% 5.08/3.47 tff(subclass_type, type, (
% 5.08/3.47 subclass: ( $i * $i ) > $o)).
% 5.08/3.47 tff(universal_class_type, type, (
% 5.08/3.47 universal_class: $i)).
% 5.08/3.47 tff(y_type, type, (
% 5.08/3.47 y: $i)).
% 5.08/3.47 tff(member_type, type, (
% 5.08/3.47 member: ( $i * $i ) > $o)).
% 5.08/3.47 tff(second_type, type, (
% 5.08/3.47 second: $i > $i)).
% 5.08/3.47 tff(not_subclass_element_type, type, (
% 5.08/3.47 not_subclass_element: ( $i * $i ) > $i)).
% 5.08/3.47 tff(cross_product_type, type, (
% 5.08/3.47 cross_product: ( $i * $i ) > $i)).
% 5.08/3.47 tff(restrict_type, type, (
% 5.08/3.47 restrict: ( $i * $i * $i ) > $i)).
% 5.08/3.47 tff(x_type, type, (
% 5.08/3.47 x: $i)).
% 5.08/3.47 tff(xf_type, type, (
% 5.08/3.47 xf: $i)).
% 5.08/3.47 tff(ordered_pair_type, type, (
% 5.08/3.47 ordered_pair: ( $i * $i ) > $i)).
% 5.08/3.47 tff(first_type, type, (
% 5.08/3.47 first: $i > $i)).
% 5.08/3.47 tff(intersection_type, type, (
% 5.08/3.47 intersection: ( $i * $i ) > $i)).
% 5.08/3.47 tff(1,assumption,(~subclass(y, universal_class)), introduced(assumption)).
% 5.08/3.47 tff(2,plain,
% 5.08/3.47 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 5.08/3.47 inference(bind,[status(th)],[])).
% 5.08/3.47 tff(3,plain,
% 5.08/3.47 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 5.08/3.47 inference(quant_intro,[status(thm)],[2])).
% 5.08/3.47 tff(4,plain,
% 5.08/3.47 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 5.08/3.47 inference(rewrite,[status(thm)],[])).
% 5.08/3.47 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 5.08/3.47 tff(6,plain,
% 5.08/3.47 (![X: $i] : subclass(X, universal_class)),
% 5.08/3.47 inference(modus_ponens,[status(thm)],[5, 4])).
% 5.08/3.47 tff(7,plain,(
% 5.08/3.47 ![X: $i] : subclass(X, universal_class)),
% 5.08/3.47 inference(skolemize,[status(sab)],[6])).
% 5.08/3.47 tff(8,plain,
% 5.08/3.47 (![X: $i] : subclass(X, universal_class)),
% 5.08/3.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 5.08/3.47 tff(9,plain,
% 5.08/3.47 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 5.08/3.47 inference(quant_inst,[status(thm)],[])).
% 5.08/3.47 tff(10,plain,
% 5.08/3.47 ($false),
% 5.08/3.47 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 5.08/3.47 tff(11,plain,(subclass(y, universal_class)), inference(lemma,lemma(discharge,[]))).
% 5.08/3.47 tff(12,plain,
% 5.08/3.47 (^[Y: $i, Xr: $i, X: $i] : refl((intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y)) <=> (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y)))),
% 5.08/3.47 inference(bind,[status(th)],[])).
% 5.08/3.47 tff(13,plain,
% 5.08/3.47 (![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y)) <=> ![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))),
% 5.08/3.47 inference(quant_intro,[status(thm)],[12])).
% 5.08/3.47 tff(14,plain,
% 5.08/3.47 (![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y)) <=> ![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))),
% 5.08/3.47 inference(rewrite,[status(thm)],[])).
% 5.08/3.47 tff(15,axiom,(![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','restriction2')).
% 5.08/3.47 tff(16,plain,
% 5.08/3.47 (![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))),
% 5.08/3.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 5.08/3.47 tff(17,plain,(
% 5.08/3.47 ![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))),
% 5.08/3.47 inference(skolemize,[status(sab)],[16])).
% 5.08/3.47 tff(18,plain,
% 5.08/3.47 (![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))),
% 5.08/3.47 inference(modus_ponens,[status(thm)],[17, 13])).
% 5.08/3.47 tff(19,plain,
% 5.08/3.47 ((~![Y: $i, Xr: $i, X: $i] : (intersection(cross_product(X, Y), Xr) = restrict(Xr, X, Y))) | (intersection(cross_product(x, y), xf) = restrict(xf, x, y))),
% 5.08/3.47 inference(quant_inst,[status(thm)],[])).
% 5.08/3.47 tff(20,plain,
% 5.08/3.47 (intersection(cross_product(x, y), xf) = restrict(xf, x, y)),
% 5.08/3.47 inference(unit_resolution,[status(thm)],[19, 18])).
% 5.08/3.47 tff(21,plain,
% 5.08/3.47 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf)) <=> member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y))),
% 5.08/3.47 inference(monotonicity,[status(thm)],[20])).
% 5.08/3.48 tff(22,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y)) <=> member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))),
% 5.08/3.48 inference(symmetry,[status(thm)],[21])).
% 5.08/3.48 tff(23,plain,
% 5.08/3.48 ((~subclass(restrict(xf, x, y), cross_product(universal_class, universal_class))) <=> (~subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(24,axiom,(~subclass(restrict(xf, x, y), cross_product(universal_class, universal_class))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_relation_property1_1')).
% 5.08/3.48 tff(25,plain,
% 5.08/3.48 (~subclass(restrict(xf, x, y), cross_product(universal_class, universal_class))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 5.08/3.48 tff(26,plain,
% 5.08/3.48 (^[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)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(27,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[26])).
% 5.08/3.48 tff(28,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(29,plain,
% 5.08/3.48 (^[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)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(30,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[29])).
% 5.08/3.48 tff(31,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')).
% 5.08/3.48 tff(32,plain,
% 5.08/3.48 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[31, 30])).
% 5.08/3.48 tff(33,plain,
% 5.08/3.48 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 5.08/3.48 tff(34,plain,(
% 5.08/3.48 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 5.08/3.48 inference(skolemize,[status(sab)],[33])).
% 5.08/3.48 tff(35,plain,
% 5.08/3.48 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[34, 27])).
% 5.08/3.48 tff(36,plain,
% 5.08/3.48 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y)))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y)))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(37,plain,
% 5.08/3.48 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y)))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(38,plain,
% 5.08/3.48 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[37, 36])).
% 5.08/3.48 tff(39,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), restrict(xf, x, y))),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[38, 35, 25])).
% 5.08/3.48 tff(40,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[39, 22])).
% 5.08/3.48 tff(41,plain,
% 5.08/3.48 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, intersection(X, Y))) | member(Z, X)) <=> ((~member(Z, intersection(X, Y))) | member(Z, X)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(42,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[41])).
% 5.08/3.48 tff(43,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(44,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','intersection1')).
% 5.08/3.48 tff(45,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[44, 43])).
% 5.08/3.48 tff(46,plain,(
% 5.08/3.48 ![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 5.08/3.48 inference(skolemize,[status(sab)],[45])).
% 5.08/3.48 tff(47,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[46, 42])).
% 5.08/3.48 tff(48,plain,
% 5.08/3.48 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(49,plain,
% 5.08/3.48 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(50,plain,
% 5.08/3.48 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, intersection(X, Y))) | member(Z, X))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 5.08/3.48 tff(51,plain,
% 5.08/3.48 ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), intersection(cross_product(x, y), xf))) | member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[50, 47])).
% 5.08/3.48 tff(52,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[51, 40])).
% 5.08/3.48 tff(53,plain,
% 5.08/3.48 (^[Z: $i, Y: $i, X: $i] : refl(((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(54,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[53])).
% 5.08/3.48 tff(55,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(56,axiom,(![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product4')).
% 5.08/3.48 tff(57,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[56, 55])).
% 5.08/3.48 tff(58,plain,(
% 5.08/3.48 ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 5.08/3.48 inference(skolemize,[status(sab)],[57])).
% 5.08/3.48 tff(59,plain,
% 5.08/3.48 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[58, 54])).
% 5.08/3.48 tff(60,plain,
% 5.08/3.48 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(61,plain,
% 5.08/3.48 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(62,plain,
% 5.08/3.48 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[61, 60])).
% 5.08/3.48 tff(63,plain,
% 5.08/3.48 (ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 5.08/3.48 tff(64,plain,
% 5.08/3.48 (member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y)) <=> member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 5.08/3.48 inference(monotonicity,[status(thm)],[63])).
% 5.08/3.48 tff(65,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(x, y)) <=> member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))),
% 5.08/3.48 inference(symmetry,[status(thm)],[64])).
% 5.08/3.48 tff(66,plain,
% 5.08/3.48 (member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[52, 65])).
% 5.08/3.48 tff(67,plain,
% 5.08/3.48 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(68,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[67])).
% 5.08/3.48 tff(69,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(70,axiom,(![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product2')).
% 5.08/3.48 tff(71,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[70, 69])).
% 5.08/3.48 tff(72,plain,(
% 5.08/3.48 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 5.08/3.48 inference(skolemize,[status(sab)],[71])).
% 5.08/3.48 tff(73,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[72, 68])).
% 5.08/3.48 tff(74,plain,
% 5.08/3.48 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(75,plain,
% 5.08/3.48 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(76,plain,
% 5.08/3.48 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))) | (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 5.08/3.48 tff(77,plain,
% 5.08/3.48 ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[76, 73])).
% 5.08/3.48 tff(78,plain,
% 5.08/3.48 (member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[77, 66])).
% 5.08/3.48 tff(79,assumption,(~subclass(x, universal_class)), introduced(assumption)).
% 5.08/3.48 tff(80,plain,
% 5.08/3.48 ((~![X: $i] : subclass(X, universal_class)) | subclass(x, universal_class)),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(81,plain,
% 5.08/3.48 ($false),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[80, 8, 79])).
% 5.08/3.48 tff(82,plain,(subclass(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 5.08/3.48 tff(83,plain,
% 5.08/3.48 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(84,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[83])).
% 5.08/3.48 tff(85,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X)) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(86,axiom,(![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product1')).
% 5.08/3.48 tff(87,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 5.08/3.48 tff(88,plain,(
% 5.08/3.48 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 5.08/3.48 inference(skolemize,[status(sab)],[87])).
% 5.08/3.48 tff(89,plain,
% 5.08/3.48 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[88, 84])).
% 5.08/3.48 tff(90,plain,
% 5.08/3.48 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(91,plain,
% 5.08/3.48 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(92,plain,
% 5.08/3.48 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))) | (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[91, 90])).
% 5.08/3.48 tff(93,plain,
% 5.08/3.48 ((~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[92, 89])).
% 5.08/3.48 tff(94,plain,
% 5.08/3.48 (member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[93, 66])).
% 5.08/3.48 tff(95,assumption,(~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)), introduced(assumption)).
% 5.08/3.48 tff(96,plain,
% 5.08/3.48 (^[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))))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(97,plain,
% 5.08/3.48 (![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)))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[96])).
% 5.08/3.48 tff(98,plain,
% 5.08/3.48 (![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)))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(99,plain,
% 5.08/3.48 (^[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)))))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(100,plain,
% 5.08/3.48 (![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)))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[99])).
% 5.08/3.48 tff(101,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')).
% 5.08/3.48 tff(102,plain,
% 5.08/3.48 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 5.08/3.48 tff(103,plain,
% 5.08/3.48 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[102, 98])).
% 5.08/3.48 tff(104,plain,(
% 5.08/3.48 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 5.08/3.48 inference(skolemize,[status(sab)],[103])).
% 5.08/3.48 tff(105,plain,
% 5.08/3.48 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[104, 97])).
% 5.08/3.48 tff(106,plain,
% 5.08/3.48 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class)))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(107,plain,
% 5.08/3.48 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class)))),
% 5.08/3.48 inference(quant_inst,[status(thm)],[])).
% 5.08/3.48 tff(108,plain,
% 5.08/3.48 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class))),
% 5.08/3.48 inference(modus_ponens,[status(thm)],[107, 106])).
% 5.08/3.48 tff(109,plain,
% 5.08/3.48 ($false),
% 5.08/3.48 inference(unit_resolution,[status(thm)],[108, 105, 95, 94, 82])).
% 5.08/3.48 tff(110,plain,(member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)), inference(lemma,lemma(discharge,[]))).
% 5.08/3.48 tff(111,plain,
% 5.08/3.48 (member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) <=> member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))),
% 5.08/3.48 inference(monotonicity,[status(thm)],[63])).
% 5.08/3.48 tff(112,plain,
% 5.08/3.48 (member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class)) <=> member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class))),
% 5.08/3.48 inference(symmetry,[status(thm)],[111])).
% 5.08/3.48 tff(113,plain,
% 5.08/3.48 ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) <=> (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)))),
% 5.08/3.48 inference(monotonicity,[status(thm)],[112])).
% 5.08/3.48 tff(114,plain,
% 5.08/3.48 (^[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)))),
% 5.08/3.48 inference(bind,[status(th)],[])).
% 5.08/3.48 tff(115,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(quant_intro,[status(thm)],[114])).
% 5.08/3.48 tff(116,plain,
% 5.08/3.48 (![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))),
% 5.08/3.48 inference(rewrite,[status(thm)],[])).
% 5.08/3.48 tff(117,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')).
% 5.08/3.48 tff(118,plain,
% 5.08/3.48 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 5.08/3.49 tff(119,plain,(
% 5.08/3.49 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 5.08/3.49 inference(skolemize,[status(sab)],[118])).
% 5.08/3.49 tff(120,plain,
% 5.08/3.49 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[119, 115])).
% 5.08/3.49 tff(121,plain,
% 5.08/3.49 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)))),
% 5.08/3.49 inference(rewrite,[status(thm)],[])).
% 5.08/3.49 tff(122,plain,
% 5.08/3.49 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class)))),
% 5.08/3.49 inference(quant_inst,[status(thm)],[])).
% 5.08/3.49 tff(123,plain,
% 5.08/3.49 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(restrict(xf, x, y), cross_product(universal_class, universal_class))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[122, 121])).
% 5.08/3.49 tff(124,plain,
% 5.08/3.49 (~member(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))),
% 5.08/3.49 inference(unit_resolution,[status(thm)],[123, 120, 25])).
% 5.08/3.49 tff(125,plain,
% 5.08/3.49 (~member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[124, 113])).
% 5.08/3.49 tff(126,plain,
% 5.08/3.49 (^[V: $i, Y: $i, U: $i, X: $i] : refl(((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 5.08/3.49 inference(bind,[status(th)],[])).
% 5.08/3.49 tff(127,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(quant_intro,[status(thm)],[126])).
% 5.08/3.49 tff(128,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(rewrite,[status(thm)],[])).
% 5.08/3.49 tff(129,plain,
% 5.08/3.49 (^[V: $i, Y: $i, U: $i, X: $i] : rewrite((((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y))))),
% 5.08/3.49 inference(bind,[status(th)],[])).
% 5.08/3.49 tff(130,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y))) <=> ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(quant_intro,[status(thm)],[129])).
% 5.08/3.49 tff(131,axiom,(![V: $i, Y: $i, U: $i, X: $i] : (((~member(U, X)) | (~member(V, Y))) | member(ordered_pair(U, V), cross_product(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','cartesian_product3')).
% 5.08/3.49 tff(132,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 5.08/3.49 tff(133,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[132, 128])).
% 5.08/3.49 tff(134,plain,(
% 5.08/3.49 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(skolemize,[status(sab)],[133])).
% 5.08/3.49 tff(135,plain,
% 5.08/3.49 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[134, 127])).
% 5.08/3.49 tff(136,plain,
% 5.08/3.49 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)))) <=> ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)))),
% 5.08/3.49 inference(rewrite,[status(thm)],[])).
% 5.08/3.49 tff(137,plain,
% 5.08/3.49 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)))),
% 5.08/3.49 inference(quant_inst,[status(thm)],[])).
% 5.08/3.49 tff(138,plain,
% 5.08/3.49 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class))),
% 5.08/3.49 inference(modus_ponens,[status(thm)],[137, 136])).
% 5.08/3.49 tff(139,plain,
% 5.08/3.49 ((~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class))),
% 5.08/3.50 inference(unit_resolution,[status(thm)],[138, 135])).
% 5.08/3.50 tff(140,plain,
% 5.08/3.50 ((~member(first(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class))),
% 5.08/3.50 inference(unit_resolution,[status(thm)],[139, 125])).
% 5.08/3.50 tff(141,plain,
% 5.08/3.50 (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class)),
% 5.08/3.50 inference(unit_resolution,[status(thm)],[140, 110])).
% 5.08/3.50 tff(142,plain,
% 5.08/3.50 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class)))),
% 5.08/3.50 inference(rewrite,[status(thm)],[])).
% 5.08/3.50 tff(143,plain,
% 5.08/3.50 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class)))),
% 5.08/3.50 inference(quant_inst,[status(thm)],[])).
% 5.08/3.50 tff(144,plain,
% 5.08/3.50 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(restrict(xf, x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class))),
% 5.08/3.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 5.08/3.50 tff(145,plain,
% 5.08/3.50 ($false),
% 5.08/3.50 inference(unit_resolution,[status(thm)],[144, 105, 141, 78, 11])).
% 5.08/3.50 % SZS output end Proof
%------------------------------------------------------------------------------