%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET203-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 32.55s 32.73s
% Output : Proof 32.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET203-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 04:35:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 32.55/32.73 % SZS status Unsatisfiable
% 32.55/32.73 % SZS output start Proof
% 32.55/32.73 tff(subclass_type, type, (
% 32.55/32.73 subclass: ( $i * $i ) > $o)).
% 32.55/32.73 tff(universal_class_type, type, (
% 32.55/32.73 universal_class: $i)).
% 32.55/32.73 tff(y_type, type, (
% 32.55/32.73 y: $i)).
% 32.55/32.73 tff(member_type, type, (
% 32.55/32.73 member: ( $i * $i ) > $o)).
% 32.55/32.73 tff(v_type, type, (
% 32.55/32.73 v: $i)).
% 32.55/32.73 tff(u_type, type, (
% 32.55/32.73 u: $i)).
% 32.55/32.73 tff(x_type, type, (
% 32.55/32.73 x: $i)).
% 32.55/32.73 tff(cross_product_type, type, (
% 32.55/32.73 cross_product: ( $i * $i ) > $i)).
% 32.55/32.73 tff(ordered_pair_type, type, (
% 32.55/32.73 ordered_pair: ( $i * $i ) > $i)).
% 32.55/32.73 tff(1,assumption,(~subclass(x, universal_class)), introduced(assumption)).
% 32.55/32.73 tff(2,plain,
% 32.55/32.73 (^[X: $i] : refl(subclass(X, universal_class) <=> subclass(X, universal_class))),
% 32.55/32.73 inference(bind,[status(th)],[])).
% 32.55/32.73 tff(3,plain,
% 32.55/32.73 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 32.55/32.73 inference(quant_intro,[status(thm)],[2])).
% 32.55/32.73 tff(4,plain,
% 32.55/32.73 (![X: $i] : subclass(X, universal_class) <=> ![X: $i] : subclass(X, universal_class)),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(5,axiom,(![X: $i] : subclass(X, universal_class)), file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax','class_elements_are_sets')).
% 32.55/32.73 tff(6,plain,
% 32.55/32.73 (![X: $i] : subclass(X, universal_class)),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[5, 4])).
% 32.55/32.73 tff(7,plain,(
% 32.55/32.73 ![X: $i] : subclass(X, universal_class)),
% 32.55/32.73 inference(skolemize,[status(sab)],[6])).
% 32.55/32.73 tff(8,plain,
% 32.55/32.73 (![X: $i] : subclass(X, universal_class)),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[7, 3])).
% 32.55/32.73 tff(9,plain,
% 32.55/32.73 ((~![X: $i] : subclass(X, universal_class)) | subclass(x, universal_class)),
% 32.55/32.73 inference(quant_inst,[status(thm)],[])).
% 32.55/32.73 tff(10,plain,
% 32.55/32.73 ($false),
% 32.55/32.73 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 32.55/32.73 tff(11,plain,(subclass(x, universal_class)), inference(lemma,lemma(discharge,[]))).
% 32.55/32.73 tff(12,assumption,(~member(u, universal_class)), introduced(assumption)).
% 32.55/32.73 tff(13,plain,
% 32.55/32.73 (member(u, x) <=> member(u, x)),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(14,axiom,(member(u, x)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_1')).
% 32.55/32.73 tff(15,plain,
% 32.55/32.73 (member(u, x)),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[14, 13])).
% 32.55/32.73 tff(16,plain,
% 32.55/32.73 (^[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))))),
% 32.55/32.73 inference(bind,[status(th)],[])).
% 32.55/32.73 tff(17,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(quant_intro,[status(thm)],[16])).
% 32.55/32.73 tff(18,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(19,plain,
% 32.55/32.73 (^[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)))))),
% 32.55/32.73 inference(bind,[status(th)],[])).
% 32.55/32.73 tff(20,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(quant_intro,[status(thm)],[19])).
% 32.55/32.73 tff(21,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')).
% 32.55/32.73 tff(22,plain,
% 32.55/32.73 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[21, 20])).
% 32.55/32.73 tff(23,plain,
% 32.55/32.73 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[22, 18])).
% 32.55/32.73 tff(24,plain,(
% 32.55/32.73 ![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 32.55/32.73 inference(skolemize,[status(sab)],[23])).
% 32.55/32.73 tff(25,plain,
% 32.55/32.73 (![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[24, 17])).
% 32.55/32.73 tff(26,plain,
% 32.55/32.73 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(27,plain,
% 32.55/32.73 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class)))),
% 32.55/32.73 inference(quant_inst,[status(thm)],[])).
% 32.55/32.73 tff(28,plain,
% 32.55/32.73 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(u, universal_class) | (~member(u, x)) | (~subclass(x, universal_class))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[27, 26])).
% 32.55/32.73 tff(29,plain,
% 32.55/32.73 ($false),
% 32.55/32.73 inference(unit_resolution,[status(thm)],[28, 25, 15, 12, 11])).
% 32.55/32.73 tff(30,plain,(member(u, universal_class)), inference(lemma,lemma(discharge,[]))).
% 32.55/32.73 tff(31,plain,
% 32.55/32.73 ((~member(ordered_pair(u, v), cross_product(universal_class, universal_class))) <=> (~member(ordered_pair(u, v), cross_product(universal_class, universal_class)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(32,axiom,(~member(ordered_pair(u, v), cross_product(universal_class, universal_class))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_3')).
% 32.55/32.73 tff(33,plain,
% 32.55/32.73 (~member(ordered_pair(u, v), cross_product(universal_class, universal_class))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[32, 31])).
% 32.55/32.73 tff(34,plain,
% 32.55/32.73 (^[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))))),
% 32.55/32.73 inference(bind,[status(th)],[])).
% 32.55/32.73 tff(35,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(quant_intro,[status(thm)],[34])).
% 32.55/32.73 tff(36,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(37,plain,
% 32.55/32.73 (^[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))))),
% 32.55/32.73 inference(bind,[status(th)],[])).
% 32.55/32.73 tff(38,plain,
% 32.55/32.73 (![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)))),
% 32.55/32.73 inference(quant_intro,[status(thm)],[37])).
% 32.55/32.73 tff(39,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')).
% 32.55/32.73 tff(40,plain,
% 32.55/32.73 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[39, 38])).
% 32.55/32.73 tff(41,plain,
% 32.55/32.73 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[40, 36])).
% 32.55/32.73 tff(42,plain,(
% 32.55/32.73 ![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 32.55/32.73 inference(skolemize,[status(sab)],[41])).
% 32.55/32.73 tff(43,plain,
% 32.55/32.73 (![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[42, 35])).
% 32.55/32.73 tff(44,plain,
% 32.55/32.73 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, 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(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(45,plain,
% 32.55/32.73 (((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class))) <=> (member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(46,plain,
% 32.55/32.73 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, 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(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class))))),
% 32.55/32.73 inference(monotonicity,[status(thm)],[45])).
% 32.55/32.73 tff(47,plain,
% 32.55/32.73 (((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, 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(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class)))),
% 32.55/32.73 inference(transitivity,[status(thm)],[46, 44])).
% 32.55/32.73 tff(48,plain,
% 32.55/32.73 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | ((~member(u, universal_class)) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(v, universal_class)))),
% 32.55/32.73 inference(quant_inst,[status(thm)],[])).
% 32.55/32.73 tff(49,plain,
% 32.55/32.73 ((~![V: $i, Y: $i, U: $i, X: $i] : ((~member(U, X)) | member(ordered_pair(U, V), cross_product(X, Y)) | (~member(V, Y)))) | member(ordered_pair(u, v), cross_product(universal_class, universal_class)) | (~member(u, universal_class)) | (~member(v, universal_class))),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[48, 47])).
% 32.55/32.73 tff(50,plain,
% 32.55/32.73 ((~member(u, universal_class)) | (~member(v, universal_class))),
% 32.55/32.73 inference(unit_resolution,[status(thm)],[49, 43, 33])).
% 32.55/32.73 tff(51,plain,
% 32.55/32.73 (~member(v, universal_class)),
% 32.55/32.73 inference(unit_resolution,[status(thm)],[50, 30])).
% 32.55/32.73 tff(52,plain,
% 32.55/32.73 (member(v, y) <=> member(v, y)),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(53,axiom,(member(v, y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_corollary_to_X_product_property1_2')).
% 32.55/32.73 tff(54,plain,
% 32.55/32.73 (member(v, y)),
% 32.55/32.73 inference(modus_ponens,[status(thm)],[53, 52])).
% 32.55/32.73 tff(55,plain,
% 32.55/32.73 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y)))),
% 32.55/32.73 inference(rewrite,[status(thm)],[])).
% 32.55/32.73 tff(56,plain,
% 32.55/32.73 ((member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class))) <=> (member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y)))),
% 32.64/32.83 inference(rewrite,[status(thm)],[])).
% 32.64/32.83 tff(57,plain,
% 32.64/32.83 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y))))),
% 32.64/32.83 inference(monotonicity,[status(thm)],[56])).
% 32.64/32.83 tff(58,plain,
% 32.64/32.83 (((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))) <=> ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y)))),
% 32.64/32.83 inference(transitivity,[status(thm)],[57, 55])).
% 32.64/32.83 tff(59,plain,
% 32.64/32.83 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | (member(v, universal_class) | (~member(v, y)) | (~subclass(y, universal_class)))),
% 32.64/32.83 inference(quant_inst,[status(thm)],[])).
% 32.64/32.83 tff(60,plain,
% 32.64/32.83 ((~![Y: $i, U: $i, X: $i] : (member(U, Y) | (~member(U, X)) | (~subclass(X, Y)))) | member(v, universal_class) | (~subclass(y, universal_class)) | (~member(v, y))),
% 32.64/32.83 inference(modus_ponens,[status(thm)],[59, 58])).
% 32.64/32.83 tff(61,plain,
% 32.64/32.83 (~subclass(y, universal_class)),
% 32.64/32.83 inference(unit_resolution,[status(thm)],[60, 25, 54, 51])).
% 32.64/32.83 tff(62,plain,
% 32.64/32.83 ((~![X: $i] : subclass(X, universal_class)) | subclass(y, universal_class)),
% 32.64/32.83 inference(quant_inst,[status(thm)],[])).
% 32.64/32.83 tff(63,plain,
% 32.64/32.83 ($false),
% 32.64/32.83 inference(unit_resolution,[status(thm)],[62, 8, 61])).
% 32.64/32.83 % SZS output end Proof
% 32.64/32.83 % E exiting
%------------------------------------------------------------------------------