%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET018-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:24:49 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET018-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:01:52 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(unordered_pair_type, type, (
% 0.21/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.21/0.38 tff(r2_type, type, (
% 0.21/0.38 r2: $i)).
% 0.21/0.38 tff(m2_type, type, (
% 0.21/0.38 m2: $i)).
% 0.21/0.38 tff(r1_type, type, (
% 0.21/0.38 r1: $i)).
% 0.21/0.38 tff(m1_type, type, (
% 0.21/0.38 m1: $i)).
% 0.21/0.38 tff(member_type, type, (
% 0.21/0.38 member: ( $i * $i ) > $o)).
% 0.21/0.38 tff(singleton_set_type, type, (
% 0.21/0.38 singleton_set: $i > $i)).
% 0.21/0.38 tff(ordered_pair_type, type, (
% 0.21/0.38 ordered_pair: ( $i * $i ) > $i)).
% 0.21/0.38 tff(1,plain,
% 0.21/0.38 ((unordered_pair(m2, r2) = unordered_pair(m1, r1)) <=> (unordered_pair(m1, r1) = unordered_pair(m2, r2))),
% 0.21/0.38 inference(commutativity,[status(thm)],[])).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 ((~(unordered_pair(m2, r2) = unordered_pair(m1, r1))) <=> (~(unordered_pair(m1, r1) = unordered_pair(m2, r2)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.38 tff(3,assumption,(unordered_pair(m2, r2) = unordered_pair(m1, r1)), introduced(assumption)).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (unordered_pair(m1, r1) = unordered_pair(m2, r2)),
% 0.21/0.38 inference(symmetry,[status(thm)],[3])).
% 0.21/0.38 tff(5,assumption,(~(singleton_set(m1) = singleton_set(m2))), introduced(assumption)).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (^[Y: $i, X: $i] : refl((ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y))) <=> (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y))) <=> ![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(9,axiom,(![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ordered_pair')).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.38 tff(11,plain,(
% 0.21/0.38 ![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[10])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))) | (ordered_pair(m1, r1) = unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (ordered_pair(m1, r1) = unordered_pair(singleton_set(m1), unordered_pair(m1, r1))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 ((ordered_pair(m1, r1) = ordered_pair(m2, r2)) <=> (ordered_pair(m1, r1) = ordered_pair(m2, r2))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(16,axiom,(ordered_pair(m1, r1) = ordered_pair(m2, r2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_ordered_pairs')).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (ordered_pair(m1, r1) = ordered_pair(m2, r2)),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (ordered_pair(m2, r2) = ordered_pair(m1, r1)),
% 0.21/0.38 inference(symmetry,[status(thm)],[17])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))) | (ordered_pair(m2, r2) = unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (ordered_pair(m2, r2) = unordered_pair(singleton_set(m2), unordered_pair(m2, r2))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[19, 12])).
% 0.21/0.38 tff(21,plain,
% 0.21/0.38 (unordered_pair(singleton_set(m2), unordered_pair(m2, r2)) = ordered_pair(m2, r2)),
% 0.21/0.38 inference(symmetry,[status(thm)],[20])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (unordered_pair(singleton_set(m2), unordered_pair(m2, r2)) = unordered_pair(singleton_set(m1), unordered_pair(m1, r1))),
% 0.21/0.38 inference(transitivity,[status(thm)],[21, 18, 14])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))) <=> member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1))) <=> member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.38 inference(symmetry,[status(thm)],[23])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 (^[Y: $i, X: $i] : refl(member(X, unordered_pair(X, Y)) <=> member(X, unordered_pair(X, Y)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(28,axiom,(![Y: $i, X: $i] : member(X, unordered_pair(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unordered_pair_1')).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.38 tff(30,plain,(
% 0.21/0.38 ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.21/0.38 inference(skolemize,[status(sab)],[29])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : member(X, unordered_pair(X, Y))) | member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[33, 24])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 (^[Z: $i, Y: $i, X: $i] : refl(((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z)))) <=> ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z)))) <=> ![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 (^[Z: $i, Y: $i, X: $i] : rewrite((((~member(X, unordered_pair(Y, Z))) | (X = Y)) | (X = Z)) <=> ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(39,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : (((~member(X, unordered_pair(Y, Z))) | (X = Y)) | (X = Z)) <=> ![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.38 tff(40,axiom,(![Z: $i, Y: $i, X: $i] : (((~member(X, unordered_pair(Y, Z))) | (X = Y)) | (X = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unordered_pair_3')).
% 0.21/0.38 tff(41,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.38 tff(42,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.38 tff(43,plain,(
% 0.21/0.38 ![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[42])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2)) | (~member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2)) | (~member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2)) | (~member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2)) | (~member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.38 tff(48,plain,
% 0.21/0.38 ((singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2)) | (~member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.21/0.38 tff(49,plain,
% 0.21/0.38 ((singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[48, 34])).
% 0.21/0.38 tff(50,plain,
% 0.21/0.38 (singleton_set(m1) = unordered_pair(m2, r2)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[49, 5])).
% 0.21/0.38 tff(51,plain,
% 0.21/0.38 (member(m2, singleton_set(m1)) <=> member(m2, unordered_pair(m2, r2))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[50])).
% 0.21/0.38 tff(52,plain,
% 0.21/0.38 (member(m2, unordered_pair(m2, r2)) <=> member(m2, singleton_set(m1))),
% 0.21/0.38 inference(symmetry,[status(thm)],[51])).
% 0.21/0.38 tff(53,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : member(X, unordered_pair(X, Y))) | member(m2, unordered_pair(m2, r2))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(54,plain,
% 0.21/0.38 (member(m2, unordered_pair(m2, r2))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[53, 31])).
% 0.21/0.38 tff(55,plain,
% 0.21/0.38 (member(m2, singleton_set(m1))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.21/0.38 tff(56,plain,
% 0.21/0.38 (^[Y: $i, X: $i] : refl(((~member(X, singleton_set(Y))) | (X = Y)) <=> ((~member(X, singleton_set(Y))) | (X = Y)))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(57,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.38 tff(58,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(59,axiom,(![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_2')).
% 0.21/0.38 tff(60,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.38 tff(61,plain,(
% 0.21/0.38 ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.21/0.38 inference(skolemize,[status(sab)],[60])).
% 0.21/0.38 tff(62,plain,
% 0.21/0.38 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.38 tff(63,plain,
% 0.21/0.38 (((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | ((~member(m2, singleton_set(m1))) | (m2 = m1))) <=> ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | (~member(m2, singleton_set(m1))) | (m2 = m1))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(64,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | ((~member(m2, singleton_set(m1))) | (m2 = m1))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(65,plain,
% 0.21/0.38 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | (~member(m2, singleton_set(m1))) | (m2 = m1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.39 tff(66,plain,
% 0.21/0.39 ((~member(m2, singleton_set(m1))) | (m2 = m1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.21/0.39 tff(67,plain,
% 0.21/0.39 (m2 = m1),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.21/0.39 tff(68,plain,
% 0.21/0.39 (singleton_set(m2) = singleton_set(m1)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.39 tff(69,plain,
% 0.21/0.39 (singleton_set(m1) = singleton_set(m2)),
% 0.21/0.39 inference(symmetry,[status(thm)],[68])).
% 0.21/0.39 tff(70,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[5, 69])).
% 0.21/0.39 tff(71,plain,(singleton_set(m1) = singleton_set(m2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(72,plain,
% 0.21/0.39 (singleton_set(m2) = singleton_set(m1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[71])).
% 0.21/0.39 tff(73,plain,
% 0.21/0.39 (member(m1, singleton_set(m2)) <=> member(m1, singleton_set(m1))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.39 tff(74,plain,
% 0.21/0.39 (member(m1, singleton_set(m1)) <=> member(m1, singleton_set(m2))),
% 0.21/0.39 inference(symmetry,[status(thm)],[73])).
% 0.21/0.39 tff(75,plain,
% 0.21/0.39 (^[X: $i] : refl(member(X, singleton_set(X)) <=> member(X, singleton_set(X)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(76,plain,
% 0.21/0.39 (![X: $i] : member(X, singleton_set(X)) <=> ![X: $i] : member(X, singleton_set(X))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.21/0.39 tff(77,plain,
% 0.21/0.39 (![X: $i] : member(X, singleton_set(X)) <=> ![X: $i] : member(X, singleton_set(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(78,axiom,(![X: $i] : member(X, singleton_set(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_1')).
% 0.21/0.39 tff(79,plain,
% 0.21/0.39 (![X: $i] : member(X, singleton_set(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.39 tff(80,plain,(
% 0.21/0.39 ![X: $i] : member(X, singleton_set(X))),
% 0.21/0.39 inference(skolemize,[status(sab)],[79])).
% 0.21/0.39 tff(81,plain,
% 0.21/0.39 (![X: $i] : member(X, singleton_set(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.21/0.39 tff(82,plain,
% 0.21/0.39 ((~![X: $i] : member(X, singleton_set(X))) | member(m1, singleton_set(m1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(83,plain,
% 0.21/0.39 (member(m1, singleton_set(m1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.39 tff(84,plain,
% 0.21/0.39 (member(m1, singleton_set(m2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[83, 74])).
% 0.21/0.39 tff(85,plain,
% 0.21/0.39 (((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | ((~member(m1, singleton_set(m2))) | (m1 = m2))) <=> ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | (~member(m1, singleton_set(m2))) | (m1 = m2))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(86,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | ((~member(m1, singleton_set(m2))) | (m1 = m2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(87,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | (~member(m1, singleton_set(m2))) | (m1 = m2)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.39 tff(88,plain,
% 0.21/0.39 ((~member(m1, singleton_set(m2))) | (m1 = m2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[87, 62])).
% 0.21/0.39 tff(89,plain,
% 0.21/0.39 (m1 = m2),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[88, 84])).
% 0.21/0.39 tff(90,plain,
% 0.21/0.39 (m2 = m1),
% 0.21/0.39 inference(symmetry,[status(thm)],[89])).
% 0.21/0.39 tff(91,plain,
% 0.21/0.39 (unordered_pair(m2, r1) = unordered_pair(m1, r1)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.39 tff(92,plain,
% 0.21/0.39 (unordered_pair(m2, r1) = unordered_pair(m2, r2)),
% 0.21/0.39 inference(transitivity,[status(thm)],[91, 4])).
% 0.21/0.39 tff(93,plain,
% 0.21/0.39 (member(r2, unordered_pair(m2, r1)) <=> member(r2, unordered_pair(m2, r2))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.39 tff(94,plain,
% 0.21/0.39 (member(r2, unordered_pair(m2, r2)) <=> member(r2, unordered_pair(m2, r1))),
% 0.21/0.39 inference(symmetry,[status(thm)],[93])).
% 0.21/0.39 tff(95,plain,
% 0.21/0.39 (^[Y: $i, X: $i] : refl(member(Y, unordered_pair(X, Y)) <=> member(Y, unordered_pair(X, Y)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(96,plain,
% 0.21/0.39 (![Y: $i, X: $i] : member(Y, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.39 tff(97,plain,
% 0.21/0.39 (![Y: $i, X: $i] : member(Y, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(98,axiom,(![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unordered_pair_2')).
% 0.21/0.39 tff(99,plain,
% 0.21/0.39 (![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.39 tff(100,plain,(
% 0.21/0.39 ![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))),
% 0.21/0.39 inference(skolemize,[status(sab)],[99])).
% 0.21/0.39 tff(101,plain,
% 0.21/0.39 (![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.21/0.39 tff(102,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))) | member(r2, unordered_pair(m2, r2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(103,plain,
% 0.21/0.39 (member(r2, unordered_pair(m2, r2))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.21/0.39 tff(104,plain,
% 0.21/0.39 (member(r2, unordered_pair(m2, r1))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[103, 94])).
% 0.21/0.39 tff(105,plain,
% 0.21/0.39 ((r2 = r1) <=> (r1 = r2)),
% 0.21/0.39 inference(commutativity,[status(thm)],[])).
% 0.21/0.39 tff(106,plain,
% 0.21/0.39 ((r1 = r2) <=> (r2 = r1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[105])).
% 0.21/0.39 tff(107,plain,
% 0.21/0.39 ((~(r1 = r2)) <=> (~(r2 = r1))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[106])).
% 0.21/0.39 tff(108,plain,
% 0.21/0.39 ((~(r1 = r2)) <=> (~(r1 = r2))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(109,axiom,(~(r1 = r2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_second_components_equal')).
% 0.21/0.39 tff(110,plain,
% 0.21/0.39 (~(r1 = r2)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.39 tff(111,plain,
% 0.21/0.39 (~(r2 = r1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[110, 107])).
% 0.21/0.39 tff(112,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r2 = m2) | (r2 = r1) | (~member(r2, unordered_pair(m2, r1))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (r2 = m2) | (r2 = r1) | (~member(r2, unordered_pair(m2, r1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(113,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r2 = m2) | (r2 = r1) | (~member(r2, unordered_pair(m2, r1))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(114,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (r2 = m2) | (r2 = r1) | (~member(r2, unordered_pair(m2, r1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.39 tff(115,plain,
% 0.21/0.39 ((r2 = m2) | (r2 = r1) | (~member(r2, unordered_pair(m2, r1)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[114, 44])).
% 0.21/0.39 tff(116,plain,
% 0.21/0.39 (r2 = m2),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[115, 111, 104])).
% 0.21/0.39 tff(117,plain,
% 0.21/0.39 (m2 = r2),
% 0.21/0.39 inference(symmetry,[status(thm)],[116])).
% 0.21/0.39 tff(118,plain,
% 0.21/0.39 ((r1 = m2) <=> (r1 = r2)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.39 tff(119,plain,
% 0.21/0.39 ((r1 = r2) <=> (r1 = m2)),
% 0.21/0.39 inference(symmetry,[status(thm)],[118])).
% 0.21/0.39 tff(120,plain,
% 0.21/0.39 ((~(r1 = r2)) <=> (~(r1 = m2))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[119])).
% 0.21/0.39 tff(121,plain,
% 0.21/0.39 (~(r1 = m2)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[110, 120])).
% 0.21/0.39 tff(122,plain,
% 0.21/0.39 (member(r1, unordered_pair(m2, r2)) <=> member(r1, unordered_pair(m1, r1))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.39 tff(123,plain,
% 0.21/0.39 (member(r1, unordered_pair(m1, r1)) <=> member(r1, unordered_pair(m2, r2))),
% 0.21/0.39 inference(symmetry,[status(thm)],[122])).
% 0.21/0.39 tff(124,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))) | member(r1, unordered_pair(m1, r1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(125,plain,
% 0.21/0.39 (member(r1, unordered_pair(m1, r1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[124, 101])).
% 0.21/0.39 tff(126,plain,
% 0.21/0.39 (member(r1, unordered_pair(m2, r2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[125, 123])).
% 0.21/0.39 tff(127,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(128,plain,
% 0.21/0.39 (((r1 = m2) | (r1 = r2) | (~member(r1, unordered_pair(m2, r2)))) <=> ((r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(129,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r1 = m2) | (r1 = r2) | (~member(r1, unordered_pair(m2, r2))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2)))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.39 tff(130,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r1 = m2) | (r1 = r2) | (~member(r1, unordered_pair(m2, r2))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.39 tff(131,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((r1 = m2) | (r1 = r2) | (~member(r1, unordered_pair(m2, r2))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(132,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (r1 = r2) | (r1 = m2) | (~member(r1, unordered_pair(m2, r2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.39 tff(133,plain,
% 0.21/0.39 ((r1 = m2) | (~member(r1, unordered_pair(m2, r2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[132, 44, 110])).
% 0.21/0.39 tff(134,plain,
% 0.21/0.39 (r1 = m2),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[133, 126])).
% 0.21/0.39 tff(135,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[134, 121])).
% 0.21/0.39 tff(136,plain,(~(unordered_pair(m2, r2) = unordered_pair(m1, r1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(137,plain,
% 0.21/0.39 (~(unordered_pair(m1, r1) = unordered_pair(m2, r2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[136, 2])).
% 0.21/0.39 tff(138,plain,
% 0.21/0.39 (unordered_pair(singleton_set(m1), unordered_pair(m1, r1)) = ordered_pair(m1, r1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[14])).
% 0.21/0.39 tff(139,plain,
% 0.21/0.39 (unordered_pair(singleton_set(m1), unordered_pair(m1, r1)) = unordered_pair(singleton_set(m2), unordered_pair(m2, r2))),
% 0.21/0.39 inference(transitivity,[status(thm)],[138, 17, 20])).
% 0.21/0.39 tff(140,plain,
% 0.21/0.39 (member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1))) <=> member(unordered_pair(m2, r2), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.39 tff(141,plain,
% 0.21/0.39 (member(unordered_pair(m2, r2), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))) <=> member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.39 inference(symmetry,[status(thm)],[140])).
% 0.21/0.39 tff(142,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))) | member(unordered_pair(m2, r2), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(143,plain,
% 0.21/0.39 (member(unordered_pair(m2, r2), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[142, 101])).
% 0.21/0.39 tff(144,plain,
% 0.21/0.39 (member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[143, 141])).
% 0.21/0.39 tff(145,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1)) | (~member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1)) | (~member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(146,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1)) | (~member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(147,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1)) | (~member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.39 tff(148,plain,
% 0.21/0.39 ((unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1)) | (~member(unordered_pair(m2, r2), unordered_pair(singleton_set(m1), unordered_pair(m1, r1))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[147, 44])).
% 0.21/0.39 tff(149,plain,
% 0.21/0.39 ((unordered_pair(m2, r2) = singleton_set(m1)) | (unordered_pair(m2, r2) = unordered_pair(m1, r1))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[148, 144])).
% 0.21/0.39 tff(150,plain,
% 0.21/0.39 (unordered_pair(m2, r2) = singleton_set(m1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[149, 136])).
% 0.21/0.39 tff(151,plain,
% 0.21/0.39 (unordered_pair(m2, r2) = singleton_set(m2)),
% 0.21/0.39 inference(transitivity,[status(thm)],[150, 71])).
% 0.21/0.39 tff(152,plain,
% 0.21/0.39 ((unordered_pair(m1, r1) = unordered_pair(m2, r2)) <=> (unordered_pair(m1, r1) = singleton_set(m2))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[151])).
% 0.21/0.39 tff(153,plain,
% 0.21/0.39 ((~(unordered_pair(m1, r1) = unordered_pair(m2, r2))) <=> (~(unordered_pair(m1, r1) = singleton_set(m2)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[152])).
% 0.21/0.39 tff(154,plain,
% 0.21/0.39 (~(unordered_pair(m1, r1) = singleton_set(m2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[137, 153])).
% 0.21/0.39 tff(155,plain,
% 0.21/0.39 (member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))) <=> member(unordered_pair(m1, r1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.39 tff(156,plain,
% 0.21/0.39 (member(unordered_pair(m1, r1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1))) <=> member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.39 inference(symmetry,[status(thm)],[155])).
% 0.21/0.39 tff(157,plain,
% 0.21/0.39 ((~![Y: $i, X: $i] : member(Y, unordered_pair(X, Y))) | member(unordered_pair(m1, r1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(158,plain,
% 0.21/0.39 (member(unordered_pair(m1, r1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[157, 101])).
% 0.21/0.39 tff(159,plain,
% 0.21/0.39 (member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[158, 156])).
% 0.21/0.39 tff(160,plain,
% 0.21/0.39 (((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2)) | (~member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))) <=> ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2)) | (~member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(161,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | ((unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2)) | (~member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(162,plain,
% 0.21/0.39 ((~![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))) | (unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2)) | (~member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.40 tff(163,plain,
% 0.21/0.40 ((unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2)) | (~member(unordered_pair(m1, r1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2))))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[162, 44])).
% 0.21/0.40 tff(164,plain,
% 0.21/0.40 ((unordered_pair(m1, r1) = singleton_set(m2)) | (unordered_pair(m1, r1) = unordered_pair(m2, r2))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[163, 159])).
% 0.21/0.40 tff(165,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[164, 154, 137])).
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------