%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET076-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:25:07 AM UTC 2025
% Result : Unsatisfiable 1.16s 1.32s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET076-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % 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 04:12:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.16/1.32 % SZS status Unsatisfiable
% 1.16/1.32 % SZS output start Proof
% 1.16/1.32 tff(member_type, type, (
% 1.16/1.32 member: ( $i * $i ) > $o)).
% 1.16/1.32 tff(z_type, type, (
% 1.16/1.32 z: $i)).
% 1.16/1.32 tff(not_subclass_element_type, type, (
% 1.16/1.32 not_subclass_element: ( $i * $i ) > $i)).
% 1.16/1.32 tff(unordered_pair_type, type, (
% 1.16/1.32 unordered_pair: ( $i * $i ) > $i)).
% 1.16/1.32 tff(y_type, type, (
% 1.16/1.32 y: $i)).
% 1.16/1.32 tff(x_type, type, (
% 1.16/1.32 x: $i)).
% 1.16/1.32 tff(subclass_type, type, (
% 1.16/1.32 subclass: ( $i * $i ) > $o)).
% 1.16/1.32 tff(1,assumption,(not_subclass_element(unordered_pair(x, y), z) = x), introduced(assumption)).
% 1.16/1.32 tff(2,plain,
% 1.16/1.32 (member(not_subclass_element(unordered_pair(x, y), z), z) <=> member(x, z)),
% 1.16/1.32 inference(monotonicity,[status(thm)],[1])).
% 1.16/1.32 tff(3,plain,
% 1.16/1.32 (member(x, z) <=> member(not_subclass_element(unordered_pair(x, y), z), z)),
% 1.16/1.32 inference(symmetry,[status(thm)],[2])).
% 1.16/1.32 tff(4,plain,
% 1.16/1.32 (member(x, z) <=> member(x, z)),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(5,axiom,(member(x, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_unordered_pair_is_subset_1')).
% 1.16/1.32 tff(6,plain,
% 1.16/1.32 (member(x, z)),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.16/1.32 tff(7,plain,
% 1.16/1.32 (member(not_subclass_element(unordered_pair(x, y), z), z)),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[6, 3])).
% 1.16/1.32 tff(8,plain,
% 1.16/1.32 ((~subclass(unordered_pair(x, y), z)) <=> (~subclass(unordered_pair(x, y), z))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(9,axiom,(~subclass(unordered_pair(x, y), z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_unordered_pair_is_subset_3')).
% 1.16/1.32 tff(10,plain,
% 1.16/1.32 (~subclass(unordered_pair(x, y), z)),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[9, 8])).
% 1.16/1.32 tff(11,plain,
% 1.16/1.32 (^[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)))),
% 1.16/1.32 inference(bind,[status(th)],[])).
% 1.16/1.32 tff(12,plain,
% 1.16/1.32 (![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))),
% 1.16/1.32 inference(quant_intro,[status(thm)],[11])).
% 1.16/1.32 tff(13,plain,
% 1.16/1.32 (![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))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(14,axiom,(![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members2')).
% 1.16/1.32 tff(15,plain,
% 1.16/1.32 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[14, 13])).
% 1.16/1.32 tff(16,plain,(
% 1.16/1.32 ![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 1.16/1.32 inference(skolemize,[status(sab)],[15])).
% 1.16/1.32 tff(17,plain,
% 1.16/1.32 (![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.16/1.32 tff(18,plain,
% 1.16/1.32 (((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(unordered_pair(x, y), z), z)) | subclass(unordered_pair(x, y), z))) <=> ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(unordered_pair(x, y), z), z)) | subclass(unordered_pair(x, y), z))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(19,plain,
% 1.16/1.32 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | ((~member(not_subclass_element(unordered_pair(x, y), z), z)) | subclass(unordered_pair(x, y), z))),
% 1.16/1.32 inference(quant_inst,[status(thm)],[])).
% 1.16/1.32 tff(20,plain,
% 1.16/1.32 ((~![Y: $i, X: $i] : ((~member(not_subclass_element(X, Y), Y)) | subclass(X, Y))) | (~member(not_subclass_element(unordered_pair(x, y), z), z)) | subclass(unordered_pair(x, y), z)),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.16/1.32 tff(21,plain,
% 1.16/1.32 (~member(not_subclass_element(unordered_pair(x, y), z), z)),
% 1.16/1.32 inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 1.16/1.32 tff(22,plain,
% 1.16/1.32 ($false),
% 1.16/1.32 inference(unit_resolution,[status(thm)],[21, 7])).
% 1.16/1.32 tff(23,plain,(~(not_subclass_element(unordered_pair(x, y), z) = x)), inference(lemma,lemma(discharge,[]))).
% 1.16/1.32 tff(24,plain,
% 1.16/1.32 (^[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)))),
% 1.16/1.32 inference(bind,[status(th)],[])).
% 1.16/1.32 tff(25,plain,
% 1.16/1.32 (![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))),
% 1.16/1.32 inference(quant_intro,[status(thm)],[24])).
% 1.16/1.32 tff(26,plain,
% 1.16/1.32 (![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))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(27,plain,
% 1.16/1.32 (^[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)))),
% 1.16/1.32 inference(bind,[status(th)],[])).
% 1.16/1.32 tff(28,plain,
% 1.16/1.32 (![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))),
% 1.16/1.32 inference(quant_intro,[status(thm)],[27])).
% 1.16/1.32 tff(29,axiom,(![Y: $i, X: $i] : (member(not_subclass_element(X, Y), X) | subclass(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','not_subclass_members1')).
% 1.16/1.32 tff(30,plain,
% 1.16/1.32 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.16/1.32 tff(31,plain,
% 1.16/1.32 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.16/1.32 tff(32,plain,(
% 1.16/1.32 ![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 1.16/1.32 inference(skolemize,[status(sab)],[31])).
% 1.16/1.32 tff(33,plain,
% 1.16/1.32 (![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.16/1.32 tff(34,plain,
% 1.16/1.32 (((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(unordered_pair(x, y), z) | member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y)))) <=> ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(unordered_pair(x, y), z) | member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y)))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(35,plain,
% 1.16/1.32 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | (subclass(unordered_pair(x, y), z) | member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y)))),
% 1.16/1.32 inference(quant_inst,[status(thm)],[])).
% 1.16/1.32 tff(36,plain,
% 1.16/1.32 ((~![Y: $i, X: $i] : (subclass(X, Y) | member(not_subclass_element(X, Y), X))) | subclass(unordered_pair(x, y), z) | member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y))),
% 1.16/1.32 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.16/1.32 tff(37,plain,
% 1.16/1.32 (member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y))),
% 1.16/1.32 inference(unit_resolution,[status(thm)],[36, 33, 10])).
% 1.16/1.32 tff(38,plain,
% 1.16/1.32 (^[Y: $i, U: $i, X: $i] : refl(((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 1.16/1.32 inference(bind,[status(th)],[])).
% 1.16/1.32 tff(39,plain,
% 1.16/1.32 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.32 inference(quant_intro,[status(thm)],[38])).
% 1.16/1.32 tff(40,plain,
% 1.16/1.32 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.32 inference(rewrite,[status(thm)],[])).
% 1.16/1.32 tff(41,plain,
% 1.16/1.32 (^[Y: $i, U: $i, X: $i] : rewrite((((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y)))))),
% 1.16/1.32 inference(bind,[status(th)],[])).
% 1.16/1.32 tff(42,plain,
% 1.16/1.32 (![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y)) <=> ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.33 inference(quant_intro,[status(thm)],[41])).
% 1.16/1.33 tff(43,axiom,(![Y: $i, U: $i, X: $i] : (((~member(U, unordered_pair(X, Y))) | (U = X)) | (U = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','unordered_pair_member')).
% 1.16/1.33 tff(44,plain,
% 1.16/1.33 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.16/1.33 tff(45,plain,
% 1.16/1.33 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.16/1.33 tff(46,plain,(
% 1.16/1.33 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.33 inference(skolemize,[status(sab)],[45])).
% 1.16/1.33 tff(47,plain,
% 1.16/1.33 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[46, 39])).
% 1.16/1.33 tff(48,plain,
% 1.16/1.33 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((not_subclass_element(unordered_pair(x, y), z) = y) | (not_subclass_element(unordered_pair(x, y), z) = x) | (~member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (not_subclass_element(unordered_pair(x, y), z) = y) | (not_subclass_element(unordered_pair(x, y), z) = x) | (~member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y))))),
% 1.16/1.33 inference(rewrite,[status(thm)],[])).
% 1.16/1.33 tff(49,plain,
% 1.16/1.33 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((not_subclass_element(unordered_pair(x, y), z) = y) | (not_subclass_element(unordered_pair(x, y), z) = x) | (~member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y))))),
% 1.16/1.33 inference(quant_inst,[status(thm)],[])).
% 1.16/1.33 tff(50,plain,
% 1.16/1.33 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (not_subclass_element(unordered_pair(x, y), z) = y) | (not_subclass_element(unordered_pair(x, y), z) = x) | (~member(not_subclass_element(unordered_pair(x, y), z), unordered_pair(x, y)))),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.16/1.33 tff(51,plain,
% 1.16/1.33 ((not_subclass_element(unordered_pair(x, y), z) = y) | (not_subclass_element(unordered_pair(x, y), z) = x)),
% 1.16/1.33 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 1.16/1.33 tff(52,plain,
% 1.16/1.33 (not_subclass_element(unordered_pair(x, y), z) = y),
% 1.16/1.33 inference(unit_resolution,[status(thm)],[51, 23])).
% 1.16/1.33 tff(53,plain,
% 1.16/1.33 (member(not_subclass_element(unordered_pair(x, y), z), z) <=> member(y, z)),
% 1.16/1.33 inference(monotonicity,[status(thm)],[52])).
% 1.16/1.33 tff(54,plain,
% 1.16/1.33 (member(y, z) <=> member(not_subclass_element(unordered_pair(x, y), z), z)),
% 1.16/1.33 inference(symmetry,[status(thm)],[53])).
% 1.16/1.33 tff(55,plain,
% 1.16/1.33 (member(y, z) <=> member(y, z)),
% 1.16/1.33 inference(rewrite,[status(thm)],[])).
% 1.16/1.33 tff(56,axiom,(member(y, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_unordered_pair_is_subset_2')).
% 1.16/1.33 tff(57,plain,
% 1.16/1.33 (member(y, z)),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.16/1.33 tff(58,plain,
% 1.16/1.33 (member(not_subclass_element(unordered_pair(x, y), z), z)),
% 1.16/1.33 inference(modus_ponens,[status(thm)],[57, 54])).
% 1.16/1.33 tff(59,plain,
% 1.16/1.33 ($false),
% 1.16/1.33 inference(unit_resolution,[status(thm)],[21, 58])).
% 1.16/1.33 % SZS output end Proof
% 1.16/1.33 % E exiting
%------------------------------------------------------------------------------