%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET016-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET016-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.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 04:02:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(member_type, type, (
% 0.12/0.37 member: ( $i * $i ) > $o)).
% 0.12/0.37 tff(singleton_set_type, type, (
% 0.12/0.37 singleton_set: $i > $i)).
% 0.12/0.37 tff(m1_type, type, (
% 0.12/0.37 m1: $i)).
% 0.12/0.37 tff(m2_type, type, (
% 0.12/0.37 m2: $i)).
% 0.12/0.37 tff(unordered_pair_type, type, (
% 0.12/0.37 unordered_pair: ( $i * $i ) > $i)).
% 0.12/0.37 tff(r2_type, type, (
% 0.12/0.37 r2: $i)).
% 0.12/0.37 tff(r1_type, type, (
% 0.12/0.37 r1: $i)).
% 0.12/0.37 tff(ordered_pair_type, type, (
% 0.12/0.37 ordered_pair: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,assumption,(singleton_set(m1) = unordered_pair(m2, r2)), introduced(assumption)).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (member(m2, singleton_set(m1)) <=> member(m2, unordered_pair(m2, r2))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (member(m2, unordered_pair(m2, r2)) <=> member(m2, singleton_set(m1))),
% 0.12/0.37 inference(symmetry,[status(thm)],[2])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (^[Y: $i, X: $i] : refl(member(X, unordered_pair(X, Y)) <=> member(X, unordered_pair(X, Y)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y)) <=> ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,axiom,(![Y: $i, X: $i] : member(X, unordered_pair(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unordered_pair_1')).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 ![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.12/0.37 inference(skolemize,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![Y: $i, X: $i] : member(X, unordered_pair(X, Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![Y: $i, X: $i] : member(X, unordered_pair(X, Y))) | member(m2, unordered_pair(m2, r2))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (member(m2, unordered_pair(m2, r2))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (member(m2, singleton_set(m1))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.12/0.37 tff(14,assumption,(member(m2, singleton_set(m1))), introduced(assumption)).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 ((m2 = m1) <=> (m1 = m2)),
% 0.12/0.37 inference(commutativity,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((m1 = m2) <=> (m2 = m1)),
% 0.12/0.37 inference(symmetry,[status(thm)],[15])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~(m1 = m2)) <=> (~(m2 = m1))),
% 0.12/0.37 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 ((~(m1 = m2)) <=> (~(m1 = m2))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(19,axiom,(~(m1 = m2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_first_components_equal')).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (~(m1 = m2)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 (~(m2 = m1)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (^[Y: $i, X: $i] : refl(((~member(X, singleton_set(Y))) | (X = Y)) <=> ((~member(X, singleton_set(Y))) | (X = Y)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(25,axiom,(![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_2')).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.12/0.37 tff(27,plain,(
% 0.12/0.37 ![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.12/0.37 inference(skolemize,[status(sab)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (((~![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))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | ((~member(m2, singleton_set(m1))) | (m2 = m1))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : ((~member(X, singleton_set(Y))) | (X = Y))) | (~member(m2, singleton_set(m1))) | (m2 = m1)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~member(m2, singleton_set(m1))) | (m2 = m1)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[32, 21, 14])).
% 0.12/0.38 tff(34,plain,(~member(m2, singleton_set(m1))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 13])).
% 0.12/0.38 tff(36,plain,(~(singleton_set(m1) = unordered_pair(m2, r2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,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')).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,(
% 0.12/0.38 ![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![Y: $i, X: $i] : (ordered_pair(X, Y) = unordered_pair(singleton_set(X), unordered_pair(X, Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~![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)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (ordered_pair(m1, r1) = unordered_pair(singleton_set(m1), unordered_pair(m1, r1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((ordered_pair(m1, r1) = ordered_pair(m2, r2)) <=> (ordered_pair(m1, r1) = ordered_pair(m2, r2))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(47,axiom,(ordered_pair(m1, r1) = ordered_pair(m2, r2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equal_ordered_pairs')).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (ordered_pair(m1, r1) = ordered_pair(m2, r2)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (ordered_pair(m2, r2) = ordered_pair(m1, r1)),
% 0.12/0.38 inference(symmetry,[status(thm)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![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)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (ordered_pair(m2, r2) = unordered_pair(singleton_set(m2), unordered_pair(m2, r2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 43])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (unordered_pair(singleton_set(m2), unordered_pair(m2, r2)) = ordered_pair(m2, r2)),
% 0.12/0.38 inference(symmetry,[status(thm)],[51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (unordered_pair(singleton_set(m2), unordered_pair(m2, r2)) = unordered_pair(singleton_set(m1), unordered_pair(m1, r1))),
% 0.12/0.38 inference(transitivity,[status(thm)],[52, 49, 45])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 (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)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (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)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[54])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 ((~![Y: $i, X: $i] : member(X, unordered_pair(X, Y))) | member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m1), unordered_pair(m1, r1)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[56, 10])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 (member(singleton_set(m1), unordered_pair(singleton_set(m2), unordered_pair(m2, r2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[59])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[62])).
% 0.12/0.38 tff(64,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')).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.12/0.38 tff(67,plain,(
% 0.12/0.38 ![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[66])).
% 0.12/0.38 tff(68,plain,
% 0.12/0.38 (![Z: $i, Y: $i, X: $i] : ((X = Y) | (X = Z) | (~member(X, unordered_pair(Y, Z))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.12/0.38 tff(69,plain,
% 0.12/0.38 (((~![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)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(70,plain,
% 0.12/0.38 ((~![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)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(71,plain,
% 0.12/0.38 ((~![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))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 ((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))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 ((singleton_set(m1) = singleton_set(m2)) | (singleton_set(m1) = unordered_pair(m2, r2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[72, 58])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (singleton_set(m1) = singleton_set(m2)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[73, 36])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 (member(m2, singleton_set(m1)) <=> member(m2, singleton_set(m2))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (member(m2, singleton_set(m2)) <=> member(m2, singleton_set(m1))),
% 0.20/0.38 inference(symmetry,[status(thm)],[75])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (^[X: $i] : refl(member(X, singleton_set(X)) <=> member(X, singleton_set(X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 (![X: $i] : member(X, singleton_set(X)) <=> ![X: $i] : member(X, singleton_set(X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 (![X: $i] : member(X, singleton_set(X)) <=> ![X: $i] : member(X, singleton_set(X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(80,axiom,(![X: $i] : member(X, singleton_set(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','singleton_1')).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 (![X: $i] : member(X, singleton_set(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.38 tff(82,plain,(
% 0.20/0.38 ![X: $i] : member(X, singleton_set(X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[81])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (![X: $i] : member(X, singleton_set(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 ((~![X: $i] : member(X, singleton_set(X))) | member(m2, singleton_set(m2))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (member(m2, singleton_set(m2))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.20/0.38 tff(86,plain,
% 0.20/0.38 (member(m2, singleton_set(m1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[85, 76])).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[34, 86])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------