%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET202-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:25:28 AM UTC 2025
% Result : Unsatisfiable 192.86s 193.08s
% Output : Proof 193.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET202-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:34:25 EDT 2025
% 0.13/0.35 % CPUTime :
% 192.86/193.08 % SZS status Unsatisfiable
% 192.86/193.08 % SZS output start Proof
% 192.86/193.08 tff(subclass_type, type, (
% 192.86/193.08 subclass: ( $i * $i ) > $o)).
% 192.86/193.08 tff(universal_class_type, type, (
% 192.86/193.08 universal_class: $i)).
% 192.86/193.08 tff(y_type, type, (
% 192.86/193.08 y: $i)).
% 192.86/193.08 tff(member_type, type, (
% 192.86/193.08 member: ( $i * $i ) > $o)).
% 192.86/193.08 tff(second_type, type, (
% 192.86/193.08 second: $i > $i)).
% 192.86/193.08 tff(not_subclass_element_type, type, (
% 192.86/193.08 not_subclass_element: ( $i * $i ) > $i)).
% 192.86/193.08 tff(cross_product_type, type, (
% 192.86/193.08 cross_product: ( $i * $i ) > $i)).
% 192.86/193.08 tff(x_type, type, (
% 192.86/193.08 x: $i)).
% 192.86/193.08 tff(ordered_pair_type, type, (
% 192.86/193.08 ordered_pair: ( $i * $i ) > $i)).
% 192.86/193.08 tff(first_type, type, (
% 192.86/193.08 first: $i > $i)).
% 192.86/193.08 tff(1,plain,
% 192.86/193.08 ((~subclass(cross_product(x, y), cross_product(universal_class, universal_class))) <=> (~subclass(cross_product(x, y), cross_product(universal_class, universal_class)))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(2,axiom,(~subclass(cross_product(x, y), cross_product(universal_class, universal_class))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_cross_product_property1_1')).
% 192.86/193.08 tff(3,plain,
% 192.86/193.08 (~subclass(cross_product(x, y), cross_product(universal_class, universal_class))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[2, 1])).
% 192.86/193.08 tff(4,plain,
% 192.86/193.08 (^[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)))),
% 192.86/193.08 inference(bind,[status(th)],[])).
% 192.86/193.08 tff(5,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(quant_intro,[status(thm)],[4])).
% 192.86/193.08 tff(6,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(7,plain,
% 192.86/193.08 (^[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)))),
% 192.86/193.08 inference(bind,[status(th)],[])).
% 192.86/193.08 tff(8,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(quant_intro,[status(thm)],[7])).
% 192.86/193.08 tff(9,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')).
% 192.86/193.08 tff(10,plain,
% 192.86/193.08 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[9, 8])).
% 192.86/193.08 tff(11,plain,
% 192.86/193.08 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[10, 6])).
% 192.86/193.08 tff(12,plain,(
% 192.86/193.08 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 192.86/193.08 inference(skolemize,[status(sab)],[11])).
% 192.86/193.08 tff(13,plain,
% 192.86/193.08 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[12, 5])).
% 192.86/193.08 tff(14,plain,
% 192.86/193.08 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(cross_product(x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(cross_product(x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(15,plain,
% 192.86/193.08 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(cross_product(x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y)))),
% 192.86/193.08 inference(quant_inst,[status(thm)],[])).
% 192.86/193.08 tff(16,plain,
% 192.86/193.08 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(cross_product(x, y), cross_product(universal_class, universal_class)) | member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[15, 14])).
% 192.86/193.08 tff(17,plain,
% 192.86/193.08 (member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 192.86/193.08 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 192.86/193.08 tff(18,plain,
% 192.86/193.08 (^[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)))),
% 192.86/193.08 inference(bind,[status(th)],[])).
% 192.86/193.08 tff(19,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(quant_intro,[status(thm)],[18])).
% 192.86/193.08 tff(20,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(21,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')).
% 192.86/193.08 tff(22,plain,
% 192.86/193.08 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[21, 20])).
% 192.86/193.08 tff(23,plain,(
% 192.86/193.08 ![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 192.86/193.08 inference(skolemize,[status(sab)],[22])).
% 192.86/193.08 tff(24,plain,
% 192.86/193.08 (![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[23, 19])).
% 192.86/193.08 tff(25,plain,
% 192.86/193.08 (((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(26,plain,
% 192.86/193.08 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | ((~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))))),
% 192.86/193.08 inference(quant_inst,[status(thm)],[])).
% 192.86/193.08 tff(27,plain,
% 192.86/193.08 ((~![Z: $i, Y: $i, X: $i] : ((~member(Z, cross_product(X, Y))) | (ordered_pair(first(Z), second(Z)) = Z))) | (~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))) | (ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[26, 25])).
% 192.86/193.08 tff(28,plain,
% 192.86/193.08 (ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))) = not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))),
% 192.86/193.08 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 192.86/193.08 tff(29,plain,
% 192.86/193.08 (member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y)) <=> member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y))),
% 192.86/193.08 inference(monotonicity,[status(thm)],[28])).
% 192.86/193.08 tff(30,plain,
% 192.86/193.08 (member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(x, y)) <=> member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))),
% 192.86/193.08 inference(symmetry,[status(thm)],[29])).
% 192.86/193.08 tff(31,plain,
% 192.86/193.08 (member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[17, 30])).
% 192.86/193.08 tff(32,plain,
% 192.86/193.08 (^[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)))),
% 192.86/193.08 inference(bind,[status(th)],[])).
% 192.86/193.08 tff(33,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(quant_intro,[status(thm)],[32])).
% 192.86/193.08 tff(34,plain,
% 192.86/193.08 (![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))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(35,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')).
% 192.86/193.08 tff(36,plain,
% 192.86/193.08 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[35, 34])).
% 192.86/193.08 tff(37,plain,(
% 192.86/193.08 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 192.86/193.08 inference(skolemize,[status(sab)],[36])).
% 192.86/193.08 tff(38,plain,
% 192.86/193.08 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(V, Y))),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[37, 33])).
% 192.86/193.08 tff(39,plain,
% 192.86/193.08 (((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y))),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(40,plain,
% 192.86/193.08 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y))),
% 192.86/193.08 inference(quant_inst,[status(thm)],[])).
% 192.86/193.08 tff(41,plain,
% 192.86/193.08 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[40, 39])).
% 192.86/193.08 tff(42,plain,
% 192.86/193.08 ((~member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)),
% 192.86/193.08 inference(unit_resolution,[status(thm)],[41, 38])).
% 192.86/193.08 tff(43,plain,
% 192.86/193.08 (member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)),
% 192.86/193.08 inference(unit_resolution,[status(thm)],[42, 31])).
% 192.86/193.08 tff(44,assumption,(~subclass(x, universal_class)), introduced(assumption)).
% 192.86/193.08 tff(45,plain,
% 192.86/193.08 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 192.86/193.08 inference(bind,[status(th)],[])).
% 192.86/193.08 tff(46,plain,
% 192.86/193.08 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 192.86/193.08 inference(quant_intro,[status(thm)],[45])).
% 192.86/193.08 tff(47,plain,
% 192.86/193.08 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 192.86/193.08 inference(rewrite,[status(thm)],[])).
% 192.86/193.08 tff(48,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 192.86/193.08 tff(49,plain,
% 192.86/193.08 (![X: $i] : subclass(X, universal_class)),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[48, 47])).
% 192.86/193.08 tff(50,plain,(
% 192.86/193.08 ![X: $i] : subclass(X, universal_class)),
% 192.86/193.08 inference(skolemize,[status(sab)],[49])).
% 192.86/193.08 tff(51,plain,
% 192.86/193.08 (![X: $i] : subclass(X, universal_class)),
% 192.86/193.08 inference(modus_ponens,[status(thm)],[50, 46])).
% 192.86/193.08 tff(52,plain,
% 192.86/193.08 ((~![X: $i] : subclass(X, universal_class)) | subclass(x, universal_class)),
% 192.86/193.08 inference(quant_inst,[status(thm)],[])).
% 192.86/193.08 tff(53,plain,
% 192.86/193.08 ($false),
% 192.86/193.08 inference(unit_resolution,[status(thm)],[52, 51, 44])).
% 192.86/193.09 tff(54,plain,(subclass(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 192.86/193.09 tff(55,plain,
% 192.86/193.09 (^[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)))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(56,plain,
% 192.86/193.09 (![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))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[55])).
% 192.86/193.09 tff(57,plain,
% 192.86/193.09 (![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))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(58,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')).
% 192.86/193.09 tff(59,plain,
% 192.86/193.09 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[58, 57])).
% 192.86/193.09 tff(60,plain,(
% 192.86/193.09 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 192.86/193.09 inference(skolemize,[status(sab)],[59])).
% 192.86/193.09 tff(61,plain,
% 192.86/193.09 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(ordered_pair(U, V), cross_product(X, Y))) | member(U, X))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[60, 56])).
% 192.86/193.09 tff(62,plain,
% 192.86/193.09 (((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(63,plain,
% 192.86/193.09 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x))),
% 192.86/193.09 inference(quant_inst,[status(thm)],[])).
% 192.86/193.09 tff(64,plain,
% 192.86/193.09 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[63, 62])).
% 192.86/193.09 tff(65,plain,
% 192.86/193.09 ((~member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(x, y))) | member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[64, 61])).
% 192.86/193.09 tff(66,plain,
% 192.86/193.09 (member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[65, 31])).
% 192.86/193.09 tff(67,assumption,(~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)), introduced(assumption)).
% 192.86/193.09 tff(68,plain,
% 192.86/193.09 (^[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))))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(69,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[68])).
% 192.86/193.09 tff(70,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(71,plain,
% 192.86/193.09 (^[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)))))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(72,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[71])).
% 192.86/193.09 tff(73,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')).
% 192.86/193.09 tff(74,plain,
% 192.86/193.09 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[73, 72])).
% 192.86/193.09 tff(75,plain,
% 192.86/193.09 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[74, 70])).
% 192.86/193.09 tff(76,plain,(
% 192.86/193.09 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 192.86/193.09 inference(skolemize,[status(sab)],[75])).
% 192.86/193.09 tff(77,plain,
% 192.86/193.09 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[76, 69])).
% 192.86/193.09 tff(78,plain,
% 192.86/193.09 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(79,plain,
% 192.86/193.09 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class)))),
% 192.86/193.09 inference(quant_inst,[status(thm)],[])).
% 192.86/193.09 tff(80,plain,
% 192.86/193.09 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), x)) | (~subclass(x, universal_class))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[79, 78])).
% 192.86/193.09 tff(81,plain,
% 192.86/193.09 ($false),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[80, 77, 67, 66, 54])).
% 192.86/193.09 tff(82,plain,(member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)), inference(lemma,lemma(discharge,[]))).
% 192.86/193.09 tff(83,plain,
% 192.86/193.09 (member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) <=> member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))),
% 192.86/193.09 inference(monotonicity,[status(thm)],[28])).
% 192.86/193.09 tff(84,plain,
% 192.86/193.09 (member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class)) <=> member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class))),
% 192.86/193.09 inference(symmetry,[status(thm)],[83])).
% 192.86/193.09 tff(85,plain,
% 192.86/193.09 ((~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) <=> (~member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)))),
% 192.86/193.09 inference(monotonicity,[status(thm)],[84])).
% 192.86/193.09 tff(86,plain,
% 192.86/193.09 (^[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)))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(87,plain,
% 192.86/193.09 (![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))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[86])).
% 192.86/193.09 tff(88,plain,
% 192.86/193.09 (![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))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(89,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')).
% 192.86/193.09 tff(90,plain,
% 192.86/193.09 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[89, 88])).
% 192.86/193.09 tff(91,plain,(
% 192.86/193.09 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 192.86/193.09 inference(skolemize,[status(sab)],[90])).
% 192.86/193.09 tff(92,plain,
% 192.86/193.09 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[91, 87])).
% 192.86/193.09 tff(93,plain,
% 192.86/193.09 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(cross_product(x, y), cross_product(universal_class, universal_class)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(94,plain,
% 192.86/193.09 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(cross_product(x, y), cross_product(universal_class, universal_class)))),
% 192.86/193.09 inference(quant_inst,[status(thm)],[])).
% 192.86/193.09 tff(95,plain,
% 192.86/193.09 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))) | subclass(cross_product(x, y), cross_product(universal_class, universal_class))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[94, 93])).
% 192.86/193.09 tff(96,plain,
% 192.86/193.09 (~member(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)), cross_product(universal_class, universal_class))),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[95, 92, 3])).
% 192.86/193.09 tff(97,plain,
% 192.86/193.09 (~member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[96, 85])).
% 192.86/193.09 tff(98,plain,
% 192.86/193.09 (^[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))))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(99,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[98])).
% 192.86/193.09 tff(100,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(101,plain,
% 192.86/193.09 (^[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))))),
% 192.86/193.09 inference(bind,[status(th)],[])).
% 192.86/193.09 tff(102,plain,
% 192.86/193.09 (![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)))),
% 192.86/193.09 inference(quant_intro,[status(thm)],[101])).
% 192.86/193.09 tff(103,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')).
% 192.86/193.09 tff(104,plain,
% 192.86/193.09 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[103, 102])).
% 192.86/193.09 tff(105,plain,
% 192.86/193.09 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[104, 100])).
% 192.86/193.09 tff(106,plain,(
% 192.86/193.09 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 192.86/193.09 inference(skolemize,[status(sab)],[105])).
% 192.86/193.09 tff(107,plain,
% 192.86/193.09 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[106, 99])).
% 192.86/193.09 tff(108,plain,
% 192.86/193.09 (((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(109,plain,
% 192.86/193.09 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)))),
% 192.86/193.09 inference(quant_inst,[status(thm)],[])).
% 192.86/193.09 tff(110,plain,
% 192.86/193.09 ((~![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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[109, 108])).
% 192.86/193.09 tff(111,plain,
% 192.86/193.09 ((~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | member(ordered_pair(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class)))), cross_product(universal_class, universal_class)) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class))),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[110, 107])).
% 192.86/193.09 tff(112,plain,
% 192.86/193.09 ((~member(first(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class))),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[111, 97])).
% 192.86/193.09 tff(113,plain,
% 192.86/193.09 (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class)),
% 192.86/193.09 inference(unit_resolution,[status(thm)],[112, 82])).
% 192.86/193.09 tff(114,plain,
% 192.86/193.09 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(cross_product(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(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class)))),
% 192.86/193.09 inference(rewrite,[status(thm)],[])).
% 192.86/193.09 tff(115,plain,
% 192.86/193.09 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class)))),
% 192.86/193.09 inference(quant_inst,[status(thm)],[])).
% 192.86/193.09 tff(116,plain,
% 192.86/193.09 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), universal_class) | (~member(second(not_subclass_element(cross_product(x, y), cross_product(universal_class, universal_class))), y)) | (~subclass(y, universal_class))),
% 192.86/193.09 inference(modus_ponens,[status(thm)],[115, 114])).
% 192.86/193.09 tff(117,plain,
% 192.86/193.09 (~subclass(y, universal_class)),
% 193.18/193.36 inference(unit_resolution,[status(thm)],[116, 77, 113, 43])).
% 193.18/193.36 tff(118,plain,
% 193.18/193.36 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 193.18/193.36 inference(quant_inst,[status(thm)],[])).
% 193.18/193.36 tff(119,plain,
% 193.18/193.36 ($false),
% 193.18/193.36 inference(unit_resolution,[status(thm)],[118, 51, 117])).
% 193.18/193.36 % SZS output end Proof
% 193.18/193.36 % E exiting
%------------------------------------------------------------------------------