%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET016-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:48 AM UTC 2025
% Result : Unsatisfiable 5.44s 5.70s
% Output : Proof 5.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET016-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:01:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.44/5.70 % SZS status Unsatisfiable
% 5.44/5.70 % SZS output start Proof
% 5.44/5.70 tff(member_type, type, (
% 5.44/5.70 member: ( $i * $i ) > $o)).
% 5.44/5.70 tff(unordered_pair_type, type, (
% 5.44/5.70 unordered_pair: ( $i * $i ) > $i)).
% 5.44/5.70 tff(y_type, type, (
% 5.44/5.70 y: $i)).
% 5.44/5.70 tff(w_type, type, (
% 5.44/5.70 w: $i)).
% 5.44/5.70 tff(singleton_type, type, (
% 5.44/5.70 singleton: $i > $i)).
% 5.44/5.70 tff(x_type, type, (
% 5.44/5.70 x: $i)).
% 5.44/5.70 tff(universal_class_type, type, (
% 5.44/5.70 universal_class: $i)).
% 5.44/5.70 tff(z_type, type, (
% 5.44/5.70 z: $i)).
% 5.44/5.70 tff(ordered_pair_type, type, (
% 5.44/5.70 ordered_pair: ( $i * $i ) > $i)).
% 5.44/5.70 tff(1,plain,
% 5.44/5.70 (^[X: $i] : refl((unordered_pair(X, X) = singleton(X)) <=> (unordered_pair(X, X) = singleton(X)))),
% 5.44/5.70 inference(bind,[status(th)],[])).
% 5.44/5.70 tff(2,plain,
% 5.44/5.70 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 5.44/5.70 inference(quant_intro,[status(thm)],[1])).
% 5.44/5.70 tff(3,plain,
% 5.44/5.70 (![X: $i] : (unordered_pair(X, X) = singleton(X)) <=> ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(4,axiom,(![X: $i] : (unordered_pair(X, X) = singleton(X))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','singleton_set')).
% 5.44/5.70 tff(5,plain,
% 5.44/5.70 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[4, 3])).
% 5.44/5.70 tff(6,plain,(
% 5.44/5.70 ![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 5.44/5.70 inference(skolemize,[status(sab)],[5])).
% 5.44/5.70 tff(7,plain,
% 5.44/5.70 (![X: $i] : (unordered_pair(X, X) = singleton(X))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[6, 2])).
% 5.44/5.70 tff(8,plain,
% 5.44/5.70 ((~![X: $i] : (unordered_pair(X, X) = singleton(X))) | (unordered_pair(w, w) = singleton(w))),
% 5.44/5.70 inference(quant_inst,[status(thm)],[])).
% 5.44/5.70 tff(9,plain,
% 5.44/5.70 (unordered_pair(w, w) = singleton(w)),
% 5.44/5.70 inference(unit_resolution,[status(thm)],[8, 7])).
% 5.44/5.70 tff(10,plain,
% 5.44/5.70 (singleton(w) = unordered_pair(w, w)),
% 5.44/5.70 inference(symmetry,[status(thm)],[9])).
% 5.44/5.70 tff(11,assumption,(singleton(y) = unordered_pair(w, singleton(x))), introduced(assumption)).
% 5.44/5.70 tff(12,plain,
% 5.44/5.70 ((~![X: $i] : (unordered_pair(X, X) = singleton(X))) | (unordered_pair(y, y) = singleton(y))),
% 5.44/5.70 inference(quant_inst,[status(thm)],[])).
% 5.44/5.70 tff(13,plain,
% 5.44/5.70 (unordered_pair(y, y) = singleton(y)),
% 5.44/5.70 inference(unit_resolution,[status(thm)],[12, 7])).
% 5.44/5.70 tff(14,plain,
% 5.44/5.70 (unordered_pair(y, y) = unordered_pair(w, singleton(x))),
% 5.44/5.70 inference(transitivity,[status(thm)],[13, 11])).
% 5.44/5.70 tff(15,plain,
% 5.44/5.70 (member(w, unordered_pair(y, y)) <=> member(w, unordered_pair(w, singleton(x)))),
% 5.44/5.70 inference(monotonicity,[status(thm)],[14])).
% 5.44/5.70 tff(16,plain,
% 5.44/5.70 (member(w, unordered_pair(w, singleton(x))) <=> member(w, unordered_pair(y, y))),
% 5.44/5.70 inference(symmetry,[status(thm)],[15])).
% 5.44/5.70 tff(17,plain,
% 5.44/5.70 (member(w, universal_class) <=> member(w, universal_class)),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(18,axiom,(member(w, universal_class)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_ordered_pair_determines_components1_2')).
% 5.44/5.70 tff(19,plain,
% 5.44/5.70 (member(w, universal_class)),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[18, 17])).
% 5.44/5.70 tff(20,plain,
% 5.44/5.70 (^[Y: $i, X: $i] : refl(((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))))),
% 5.44/5.70 inference(bind,[status(th)],[])).
% 5.44/5.70 tff(21,plain,
% 5.44/5.70 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 5.44/5.70 inference(quant_intro,[status(thm)],[20])).
% 5.44/5.70 tff(22,plain,
% 5.44/5.70 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(23,axiom,(![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','unordered_pair2')).
% 5.44/5.70 tff(24,plain,
% 5.44/5.70 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[23, 22])).
% 5.44/5.70 tff(25,plain,(
% 5.44/5.70 ![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 5.44/5.70 inference(skolemize,[status(sab)],[24])).
% 5.44/5.70 tff(26,plain,
% 5.44/5.70 (![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[25, 21])).
% 5.44/5.70 tff(27,plain,
% 5.44/5.70 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(w, universal_class)) | member(w, unordered_pair(w, singleton(x))))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(w, universal_class)) | member(w, unordered_pair(w, singleton(x))))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(28,plain,
% 5.44/5.70 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(w, universal_class)) | member(w, unordered_pair(w, singleton(x))))),
% 5.44/5.70 inference(quant_inst,[status(thm)],[])).
% 5.44/5.70 tff(29,plain,
% 5.44/5.70 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(w, universal_class)) | member(w, unordered_pair(w, singleton(x)))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[28, 27])).
% 5.44/5.70 tff(30,plain,
% 5.44/5.70 (member(w, unordered_pair(w, singleton(x)))),
% 5.44/5.70 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 5.44/5.70 tff(31,plain,
% 5.44/5.70 (member(w, unordered_pair(y, y))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[30, 16])).
% 5.44/5.70 tff(32,plain,
% 5.44/5.70 ((~(w = y)) <=> (~(w = y))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(33,axiom,(~(w = y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_ordered_pair_determines_components1_3')).
% 5.44/5.70 tff(34,plain,
% 5.44/5.70 (~(w = y)),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[33, 32])).
% 5.44/5.70 tff(35,plain,
% 5.44/5.70 (^[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)))))),
% 5.44/5.70 inference(bind,[status(th)],[])).
% 5.44/5.70 tff(36,plain,
% 5.44/5.70 (![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))))),
% 5.44/5.70 inference(quant_intro,[status(thm)],[35])).
% 5.44/5.70 tff(37,plain,
% 5.44/5.70 (![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))))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(38,plain,
% 5.44/5.70 (^[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)))))),
% 5.44/5.70 inference(bind,[status(th)],[])).
% 5.44/5.70 tff(39,plain,
% 5.44/5.70 (![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))))),
% 5.44/5.70 inference(quant_intro,[status(thm)],[38])).
% 5.44/5.70 tff(40,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')).
% 5.44/5.70 tff(41,plain,
% 5.44/5.70 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[40, 39])).
% 5.44/5.70 tff(42,plain,
% 5.44/5.70 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[41, 37])).
% 5.44/5.70 tff(43,plain,(
% 5.44/5.70 ![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 5.44/5.70 inference(skolemize,[status(sab)],[42])).
% 5.44/5.70 tff(44,plain,
% 5.44/5.70 (![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))),
% 5.44/5.70 inference(modus_ponens,[status(thm)],[43, 36])).
% 5.44/5.70 tff(45,plain,
% 5.44/5.70 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((w = y) | (~member(w, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (w = y) | (~member(w, unordered_pair(y, y))))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.44/5.70 tff(46,plain,
% 5.44/5.70 (((w = y) | (w = y) | (~member(w, unordered_pair(y, y)))) <=> ((w = y) | (~member(w, unordered_pair(y, y))))),
% 5.44/5.70 inference(rewrite,[status(thm)],[])).
% 5.54/5.70 tff(47,plain,
% 5.54/5.70 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((w = y) | (w = y) | (~member(w, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((w = y) | (~member(w, unordered_pair(y, y)))))),
% 5.54/5.70 inference(monotonicity,[status(thm)],[46])).
% 5.54/5.70 tff(48,plain,
% 5.54/5.70 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((w = y) | (w = y) | (~member(w, unordered_pair(y, y))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (w = y) | (~member(w, unordered_pair(y, y))))),
% 5.54/5.70 inference(transitivity,[status(thm)],[47, 45])).
% 5.54/5.70 tff(49,plain,
% 5.54/5.70 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((w = y) | (w = y) | (~member(w, unordered_pair(y, y))))),
% 5.54/5.70 inference(quant_inst,[status(thm)],[])).
% 5.54/5.70 tff(50,plain,
% 5.54/5.70 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (w = y) | (~member(w, unordered_pair(y, y)))),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[49, 48])).
% 5.54/5.70 tff(51,plain,
% 5.54/5.70 (~member(w, unordered_pair(y, y))),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[50, 44, 34])).
% 5.54/5.70 tff(52,plain,
% 5.54/5.70 ($false),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[51, 31])).
% 5.54/5.70 tff(53,plain,(~(singleton(y) = unordered_pair(w, singleton(x)))), inference(lemma,lemma(discharge,[]))).
% 5.54/5.70 tff(54,plain,
% 5.54/5.70 (^[Y: $i, X: $i] : refl((unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)))),
% 5.54/5.70 inference(bind,[status(th)],[])).
% 5.54/5.70 tff(55,plain,
% 5.54/5.70 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 5.54/5.70 inference(quant_intro,[status(thm)],[54])).
% 5.54/5.70 tff(56,plain,
% 5.54/5.70 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y)) <=> ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 5.54/5.70 inference(rewrite,[status(thm)],[])).
% 5.54/5.70 tff(57,axiom,(![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','ordered_pair')).
% 5.54/5.70 tff(58,plain,
% 5.54/5.70 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[57, 56])).
% 5.54/5.70 tff(59,plain,(
% 5.54/5.70 ![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 5.54/5.70 inference(skolemize,[status(sab)],[58])).
% 5.54/5.70 tff(60,plain,
% 5.54/5.70 (![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[59, 55])).
% 5.54/5.70 tff(61,plain,
% 5.54/5.70 ((~![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))) | (unordered_pair(singleton(y), unordered_pair(y, singleton(z))) = ordered_pair(y, z))),
% 5.54/5.70 inference(quant_inst,[status(thm)],[])).
% 5.54/5.70 tff(62,plain,
% 5.54/5.70 (unordered_pair(singleton(y), unordered_pair(y, singleton(z))) = ordered_pair(y, z)),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[61, 60])).
% 5.54/5.70 tff(63,plain,
% 5.54/5.70 (ordered_pair(y, z) = unordered_pair(singleton(y), unordered_pair(y, singleton(z)))),
% 5.54/5.70 inference(symmetry,[status(thm)],[62])).
% 5.54/5.70 tff(64,plain,
% 5.54/5.70 ((ordered_pair(w, x) = ordered_pair(y, z)) <=> (ordered_pair(w, x) = ordered_pair(y, z))),
% 5.54/5.70 inference(rewrite,[status(thm)],[])).
% 5.54/5.70 tff(65,axiom,(ordered_pair(w, x) = ordered_pair(y, z)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_ordered_pair_determines_components1_1')).
% 5.54/5.70 tff(66,plain,
% 5.54/5.70 (ordered_pair(w, x) = ordered_pair(y, z)),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[65, 64])).
% 5.54/5.70 tff(67,plain,
% 5.54/5.70 ((~![Y: $i, X: $i] : (unordered_pair(singleton(X), unordered_pair(X, singleton(Y))) = ordered_pair(X, Y))) | (unordered_pair(singleton(w), unordered_pair(w, singleton(x))) = ordered_pair(w, x))),
% 5.54/5.70 inference(quant_inst,[status(thm)],[])).
% 5.54/5.70 tff(68,plain,
% 5.54/5.70 (unordered_pair(singleton(w), unordered_pair(w, singleton(x))) = ordered_pair(w, x)),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[67, 60])).
% 5.54/5.70 tff(69,plain,
% 5.54/5.70 (unordered_pair(singleton(w), unordered_pair(w, singleton(x))) = unordered_pair(singleton(y), unordered_pair(y, singleton(z)))),
% 5.54/5.70 inference(transitivity,[status(thm)],[68, 66, 63])).
% 5.54/5.70 tff(70,plain,
% 5.54/5.70 (member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x)))) <=> member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z))))),
% 5.54/5.70 inference(monotonicity,[status(thm)],[69])).
% 5.54/5.70 tff(71,plain,
% 5.54/5.70 (member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z)))) <=> member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x))))),
% 5.54/5.70 inference(symmetry,[status(thm)],[70])).
% 5.54/5.70 tff(72,plain,
% 5.54/5.70 (member(unordered_pair(y, y), universal_class) <=> member(singleton(y), universal_class)),
% 5.54/5.70 inference(monotonicity,[status(thm)],[13])).
% 5.54/5.70 tff(73,plain,
% 5.54/5.70 (^[Y: $i, X: $i] : refl(member(unordered_pair(X, Y), universal_class) <=> member(unordered_pair(X, Y), universal_class))),
% 5.54/5.70 inference(bind,[status(th)],[])).
% 5.54/5.70 tff(74,plain,
% 5.54/5.70 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class) <=> ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 5.54/5.70 inference(quant_intro,[status(thm)],[73])).
% 5.54/5.70 tff(75,plain,
% 5.54/5.70 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class) <=> ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 5.54/5.70 inference(rewrite,[status(thm)],[])).
% 5.54/5.70 tff(76,axiom,(![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)), file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax','unordered_pairs_in_universal')).
% 5.54/5.70 tff(77,plain,
% 5.54/5.70 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[76, 75])).
% 5.54/5.70 tff(78,plain,(
% 5.54/5.70 ![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 5.54/5.70 inference(skolemize,[status(sab)],[77])).
% 5.54/5.70 tff(79,plain,
% 5.54/5.70 (![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[78, 74])).
% 5.54/5.70 tff(80,plain,
% 5.54/5.70 ((~![Y: $i, X: $i] : member(unordered_pair(X, Y), universal_class)) | member(unordered_pair(y, y), universal_class)),
% 5.54/5.70 inference(quant_inst,[status(thm)],[])).
% 5.54/5.70 tff(81,plain,
% 5.54/5.70 (member(unordered_pair(y, y), universal_class)),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[80, 79])).
% 5.54/5.70 tff(82,plain,
% 5.54/5.70 (member(singleton(y), universal_class)),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[81, 72])).
% 5.54/5.70 tff(83,plain,
% 5.54/5.70 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(singleton(y), universal_class)) | member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z)))))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(singleton(y), universal_class)) | member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z)))))),
% 5.54/5.70 inference(rewrite,[status(thm)],[])).
% 5.54/5.70 tff(84,plain,
% 5.54/5.70 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(singleton(y), universal_class)) | member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z)))))),
% 5.54/5.70 inference(quant_inst,[status(thm)],[])).
% 5.54/5.70 tff(85,plain,
% 5.54/5.70 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(singleton(y), universal_class)) | member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z))))),
% 5.54/5.70 inference(modus_ponens,[status(thm)],[84, 83])).
% 5.54/5.70 tff(86,plain,
% 5.54/5.70 ((~member(singleton(y), universal_class)) | member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z))))),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[85, 26])).
% 5.54/5.70 tff(87,plain,
% 5.54/5.70 (member(singleton(y), unordered_pair(singleton(y), unordered_pair(y, singleton(z))))),
% 5.54/5.70 inference(unit_resolution,[status(thm)],[86, 82])).
% 5.54/5.71 tff(88,plain,
% 5.54/5.71 (member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x))))),
% 5.54/5.71 inference(modus_ponens,[status(thm)],[87, 71])).
% 5.54/5.71 tff(89,plain,
% 5.54/5.71 (((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w)) | (~member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x))))))) <=> ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w)) | (~member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x))))))),
% 5.54/5.71 inference(rewrite,[status(thm)],[])).
% 5.54/5.71 tff(90,plain,
% 5.54/5.71 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | ((singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w)) | (~member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x))))))),
% 5.54/5.71 inference(quant_inst,[status(thm)],[])).
% 5.54/5.71 tff(91,plain,
% 5.54/5.71 ((~![Y: $i, U: $i, X: $i] : ((U = Y) | (U = X) | (~member(U, unordered_pair(X, Y))))) | (singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w)) | (~member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x)))))),
% 5.54/5.71 inference(modus_ponens,[status(thm)],[90, 89])).
% 5.54/5.71 tff(92,plain,
% 5.54/5.71 ((singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w)) | (~member(singleton(y), unordered_pair(singleton(w), unordered_pair(w, singleton(x)))))),
% 5.54/5.71 inference(unit_resolution,[status(thm)],[91, 44])).
% 5.54/5.71 tff(93,plain,
% 5.54/5.71 ((singleton(y) = unordered_pair(w, singleton(x))) | (singleton(y) = singleton(w))),
% 5.54/5.71 inference(unit_resolution,[status(thm)],[92, 88])).
% 5.54/5.71 tff(94,plain,
% 5.54/5.71 (singleton(y) = singleton(w)),
% 5.54/5.71 inference(unit_resolution,[status(thm)],[93, 53])).
% 5.54/5.71 tff(95,plain,
% 5.54/5.71 (unordered_pair(y, y) = unordered_pair(w, w)),
% 5.54/5.71 inference(transitivity,[status(thm)],[13, 94, 10])).
% 5.54/5.71 tff(96,plain,
% 5.54/5.71 (member(w, unordered_pair(y, y)) <=> member(w, unordered_pair(w, w))),
% 5.54/5.71 inference(monotonicity,[status(thm)],[95])).
% 5.54/5.71 tff(97,plain,
% 5.54/5.71 (member(w, unordered_pair(w, w)) <=> member(w, unordered_pair(y, y))),
% 5.54/5.71 inference(symmetry,[status(thm)],[96])).
% 5.54/5.71 tff(98,plain,
% 5.54/5.71 (((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(w, universal_class)) | member(w, unordered_pair(w, w)))) <=> ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(w, universal_class)) | member(w, unordered_pair(w, w)))),
% 5.54/5.71 inference(rewrite,[status(thm)],[])).
% 5.54/5.71 tff(99,plain,
% 5.54/5.71 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | ((~member(w, universal_class)) | member(w, unordered_pair(w, w)))),
% 5.54/5.71 inference(quant_inst,[status(thm)],[])).
% 5.54/5.71 tff(100,plain,
% 5.54/5.71 ((~![Y: $i, X: $i] : ((~member(X, universal_class)) | member(X, unordered_pair(X, Y)))) | (~member(w, universal_class)) | member(w, unordered_pair(w, w))),
% 5.54/5.71 inference(modus_ponens,[status(thm)],[99, 98])).
% 5.54/5.71 tff(101,plain,
% 5.54/5.71 (member(w, unordered_pair(w, w))),
% 5.54/5.71 inference(unit_resolution,[status(thm)],[100, 26, 19])).
% 5.54/5.71 tff(102,plain,
% 5.54/5.71 (member(w, unordered_pair(y, y))),
% 5.54/5.71 inference(modus_ponens,[status(thm)],[101, 97])).
% 5.54/5.71 tff(103,plain,
% 5.54/5.71 ($false),
% 5.54/5.71 inference(unit_resolution,[status(thm)],[51, 102])).
% 5.54/5.71 % SZS output end Proof
% 5.54/5.71 % E exiting
%------------------------------------------------------------------------------