%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET012-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 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 05:24:46 AM UTC 2025
% Result : Unsatisfiable 0.10s 0.38s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET012-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.09/0.10 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Jun 20 04:01:05 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.38 % SZS status Unsatisfiable
% 0.10/0.38 % SZS output start Proof
% 0.10/0.38 tff(member_type, type, (
% 0.10/0.38 member: ( $i * $i ) > $o)).
% 0.10/0.38 tff(complement_type, type, (
% 0.10/0.38 complement: $i > $i)).
% 0.10/0.38 tff(as_type, type, (
% 0.10/0.38 as: $i)).
% 0.10/0.38 tff(f1_type, type, (
% 0.10/0.38 f1: ( $i * $i ) > $i)).
% 0.10/0.38 tff(cs_type, type, (
% 0.10/0.38 cs: $i)).
% 0.10/0.38 tff(bs_type, type, (
% 0.10/0.38 bs: $i)).
% 0.10/0.38 tff(little_set_type, type, (
% 0.10/0.38 little_set: $i > $o)).
% 0.10/0.38 tff(1,plain,
% 0.10/0.38 ((complement(as) = bs) <=> (complement(as) = bs)),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(2,axiom,(complement(as) = bs), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement_of_a_is_b')).
% 0.10/0.38 tff(3,plain,
% 0.10/0.38 (complement(as) = bs),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.10/0.38 tff(4,plain,
% 0.10/0.38 (member(f1(cs, as), complement(as)) <=> member(f1(cs, as), bs)),
% 0.10/0.38 inference(monotonicity,[status(thm)],[3])).
% 0.10/0.38 tff(5,plain,
% 0.10/0.38 (member(f1(cs, as), bs) <=> member(f1(cs, as), complement(as))),
% 0.10/0.38 inference(symmetry,[status(thm)],[4])).
% 0.10/0.38 tff(6,plain,
% 0.10/0.38 ((complement(bs) = cs) <=> (complement(bs) = cs)),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(7,axiom,(complement(bs) = cs), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement_of_b_is_c')).
% 0.10/0.38 tff(8,plain,
% 0.10/0.38 (complement(bs) = cs),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.10/0.38 tff(9,plain,
% 0.10/0.38 (member(f1(cs, as), complement(bs)) <=> member(f1(cs, as), cs)),
% 0.10/0.38 inference(monotonicity,[status(thm)],[8])).
% 0.10/0.38 tff(10,plain,
% 0.10/0.38 (member(f1(cs, as), cs) <=> member(f1(cs, as), complement(bs))),
% 0.10/0.38 inference(symmetry,[status(thm)],[9])).
% 0.10/0.38 tff(11,plain,
% 0.10/0.38 ((~member(f1(cs, as), cs)) <=> (~member(f1(cs, as), complement(bs)))),
% 0.10/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.10/0.38 tff(12,plain,
% 0.10/0.38 ((~member(f1(cs, as), bs)) <=> (~member(f1(cs, as), complement(as)))),
% 0.10/0.38 inference(monotonicity,[status(thm)],[5])).
% 0.10/0.38 tff(13,plain,
% 0.10/0.38 ((cs = as) <=> (as = cs)),
% 0.10/0.38 inference(commutativity,[status(thm)],[])).
% 0.10/0.38 tff(14,plain,
% 0.10/0.38 ((as = cs) <=> (cs = as)),
% 0.10/0.38 inference(symmetry,[status(thm)],[13])).
% 0.10/0.38 tff(15,plain,
% 0.10/0.38 ((~(as = cs)) <=> (~(cs = as))),
% 0.10/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.10/0.38 tff(16,plain,
% 0.10/0.38 ((~(as = cs)) <=> (~(as = cs))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(17,axiom,(~(as = cs)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_a_equals_c')).
% 0.10/0.38 tff(18,plain,
% 0.10/0.38 (~(as = cs)),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.10/0.38 tff(19,plain,
% 0.10/0.38 (~(cs = as)),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.10/0.38 tff(20,assumption,(~member(f1(cs, as), as)), introduced(assumption)).
% 0.10/0.38 tff(21,plain,
% 0.10/0.38 (^[Y: $i, X: $i] : refl(((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(22,plain,
% 0.10/0.38 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.10/0.38 tff(23,plain,
% 0.10/0.38 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(24,plain,
% 0.10/0.38 (^[Y: $i, X: $i] : rewrite(((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X)))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(25,plain,
% 0.10/0.38 (![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.10/0.38 tff(26,axiom,(![Y: $i, X: $i] : ((member(f1(X, Y), X) | member(f1(X, Y), Y)) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality2')).
% 0.10/0.38 tff(27,plain,
% 0.10/0.38 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.10/0.38 tff(28,plain,
% 0.10/0.38 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.10/0.38 tff(29,plain,(
% 0.10/0.38 ![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.39 inference(skolemize,[status(sab)],[28])).
% 0.10/0.39 tff(30,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.10/0.39 tff(31,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((cs = as) | member(f1(cs, as), as) | member(f1(cs, as), cs))) <=> ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (cs = as) | member(f1(cs, as), as) | member(f1(cs, as), cs))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(32,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | ((cs = as) | member(f1(cs, as), as) | member(f1(cs, as), cs))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(33,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : ((X = Y) | member(f1(X, Y), Y) | member(f1(X, Y), X))) | (cs = as) | member(f1(cs, as), as) | member(f1(cs, as), cs)),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.10/0.39 tff(34,plain,
% 0.10/0.39 (member(f1(cs, as), cs)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[33, 30, 20, 19])).
% 0.10/0.39 tff(35,plain,
% 0.10/0.39 (member(f1(cs, as), complement(bs))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[34, 10])).
% 0.10/0.39 tff(36,plain,
% 0.10/0.39 (^[Z: $i, X: $i] : refl(((~member(Z, X)) | (~member(Z, complement(X)))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(37,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.10/0.39 tff(38,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X)))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(39,plain,
% 0.10/0.39 (^[Z: $i, X: $i] : rewrite(((~member(Z, complement(X))) | (~member(Z, X))) <=> ((~member(Z, X)) | (~member(Z, complement(X)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(40,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X))) <=> ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.10/0.39 tff(41,axiom,(![Z: $i, X: $i] : ((~member(Z, complement(X))) | (~member(Z, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement1')).
% 0.10/0.39 tff(42,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.10/0.39 tff(43,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.10/0.39 tff(44,plain,(
% 0.10/0.39 ![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(skolemize,[status(sab)],[43])).
% 0.10/0.39 tff(45,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.10/0.39 tff(46,plain,
% 0.10/0.39 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(cs, as), bs)) | (~member(f1(cs, as), complement(bs))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(cs, as), bs)) | (~member(f1(cs, as), complement(bs))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(47,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(cs, as), bs)) | (~member(f1(cs, as), complement(bs))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(48,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(cs, as), bs)) | (~member(f1(cs, as), complement(bs)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.10/0.39 tff(49,plain,
% 0.10/0.39 ((~member(f1(cs, as), bs)) | (~member(f1(cs, as), complement(bs)))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.10/0.39 tff(50,plain,
% 0.10/0.39 (~member(f1(cs, as), bs)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[49, 35])).
% 0.10/0.39 tff(51,plain,
% 0.10/0.39 (~member(f1(cs, as), complement(as))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[50, 12])).
% 0.10/0.39 tff(52,plain,
% 0.10/0.39 (^[Y: $i, X: $i] : refl((little_set(f1(X, Y)) | (X = Y)) <=> (little_set(f1(X, Y)) | (X = Y)))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(53,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.10/0.39 tff(54,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(55,axiom,(![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality1')).
% 0.10/0.39 tff(56,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.10/0.39 tff(57,plain,(
% 0.10/0.39 ![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.10/0.39 inference(skolemize,[status(sab)],[56])).
% 0.10/0.39 tff(58,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.10/0.39 tff(59,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | (little_set(f1(cs, as)) | (cs = as))) <=> ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | little_set(f1(cs, as)) | (cs = as))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(60,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | (little_set(f1(cs, as)) | (cs = as))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(61,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : (little_set(f1(X, Y)) | (X = Y))) | little_set(f1(cs, as)) | (cs = as)),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.10/0.39 tff(62,plain,
% 0.10/0.39 (little_set(f1(cs, as))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[61, 58, 19])).
% 0.10/0.39 tff(63,plain,
% 0.10/0.39 (^[Z: $i, X: $i] : refl((member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(64,plain,
% 0.10/0.39 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.10/0.39 tff(65,plain,
% 0.10/0.39 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z))) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(66,plain,
% 0.10/0.39 (^[Z: $i, X: $i] : trans(monotonicity(rewrite((member(Z, complement(X)) | (~little_set(Z))) <=> (member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)))), rewrite(((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))), (((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(67,plain,
% 0.10/0.39 (![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X)) <=> ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.10/0.39 tff(68,axiom,(![Z: $i, X: $i] : ((member(Z, complement(X)) | (~little_set(Z))) | member(Z, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','complement2')).
% 0.10/0.39 tff(69,plain,
% 0.10/0.39 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.10/0.39 tff(70,plain,
% 0.10/0.39 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.10/0.39 tff(71,plain,(
% 0.10/0.39 ![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[70])).
% 0.10/0.39 tff(72,plain,
% 0.10/0.39 (![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.10/0.39 tff(73,plain,
% 0.10/0.39 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(cs, as), as) | member(f1(cs, as), complement(as)) | (~little_set(f1(cs, as))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(cs, as), as) | member(f1(cs, as), complement(as)) | (~little_set(f1(cs, as))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(74,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(cs, as), as) | member(f1(cs, as), complement(as)) | (~little_set(f1(cs, as))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(75,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(cs, as), as) | member(f1(cs, as), complement(as)) | (~little_set(f1(cs, as)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.10/0.39 tff(76,plain,
% 0.10/0.39 (member(f1(cs, as), complement(as))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[75, 72, 20, 62])).
% 0.10/0.39 tff(77,plain,
% 0.10/0.39 ($false),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[76, 51])).
% 0.10/0.39 tff(78,plain,(member(f1(cs, as), as)), inference(lemma,lemma(discharge,[]))).
% 0.10/0.39 tff(79,plain,
% 0.10/0.39 (^[Y: $i, X: $i] : refl(((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(80,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.10/0.39 tff(81,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(82,plain,
% 0.10/0.39 (^[Y: $i, X: $i] : rewrite((((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(83,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[82])).
% 0.10/0.39 tff(84,axiom,(![Y: $i, X: $i] : (((~member(f1(X, Y), X)) | (~member(f1(X, Y), Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','extensionality3')).
% 0.10/0.39 tff(85,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.10/0.39 tff(86,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.10/0.39 tff(87,plain,(
% 0.10/0.39 ![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[86])).
% 0.10/0.39 tff(88,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.10/0.39 tff(89,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(90,plain,
% 0.10/0.39 (((cs = as) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs))) <=> ((~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(91,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((cs = as) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as)))),
% 0.10/0.39 inference(monotonicity,[status(thm)],[90])).
% 0.10/0.39 tff(92,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((cs = as) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as))),
% 0.10/0.39 inference(transitivity,[status(thm)],[91, 89])).
% 0.10/0.39 tff(93,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | ((cs = as) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(94,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : ((X = Y) | (~member(f1(X, Y), Y)) | (~member(f1(X, Y), X)))) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as)),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.10/0.39 tff(95,plain,
% 0.10/0.39 ((~member(f1(cs, as), as)) | (~member(f1(cs, as), cs)) | (cs = as)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.10/0.39 tff(96,plain,
% 0.10/0.39 ((~member(f1(cs, as), as)) | (~member(f1(cs, as), cs))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[95, 19])).
% 0.10/0.39 tff(97,plain,
% 0.10/0.39 (~member(f1(cs, as), cs)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[96, 78])).
% 0.10/0.39 tff(98,plain,
% 0.10/0.39 (~member(f1(cs, as), complement(bs))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[97, 11])).
% 0.10/0.39 tff(99,plain,
% 0.10/0.39 (^[Y: $i, X: $i] : refl((little_set(X) | (~member(X, Y))) <=> (little_set(X) | (~member(X, Y))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(100,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[99])).
% 0.10/0.39 tff(101,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y))) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(102,plain,
% 0.10/0.39 (^[Y: $i, X: $i] : rewrite(((~member(X, Y)) | little_set(X)) <=> (little_set(X) | (~member(X, Y))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(103,plain,
% 0.10/0.39 (![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X)) <=> ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[102])).
% 0.10/0.39 tff(104,axiom,(![Y: $i, X: $i] : ((~member(X, Y)) | little_set(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','a2')).
% 0.10/0.39 tff(105,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.10/0.39 tff(106,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.10/0.39 tff(107,plain,(
% 0.10/0.39 ![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(skolemize,[status(sab)],[106])).
% 0.10/0.39 tff(108,plain,
% 0.10/0.39 (![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.10/0.39 tff(109,plain,
% 0.10/0.39 (((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(cs, as)) | (~member(f1(cs, as), as)))) <=> ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(cs, as)) | (~member(f1(cs, as), as)))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(110,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | (little_set(f1(cs, as)) | (~member(f1(cs, as), as)))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(111,plain,
% 0.10/0.39 ((~![Y: $i, X: $i] : (little_set(X) | (~member(X, Y)))) | little_set(f1(cs, as)) | (~member(f1(cs, as), as))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.10/0.39 tff(112,plain,
% 0.10/0.39 (little_set(f1(cs, as))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[111, 108, 78])).
% 0.10/0.39 tff(113,plain,
% 0.10/0.39 (((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(cs, as), bs) | member(f1(cs, as), complement(bs)) | (~little_set(f1(cs, as))))) <=> ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(cs, as), bs) | member(f1(cs, as), complement(bs)) | (~little_set(f1(cs, as))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(114,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | (member(f1(cs, as), bs) | member(f1(cs, as), complement(bs)) | (~little_set(f1(cs, as))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(115,plain,
% 0.10/0.39 ((~![Z: $i, X: $i] : (member(Z, X) | member(Z, complement(X)) | (~little_set(Z)))) | member(f1(cs, as), bs) | member(f1(cs, as), complement(bs)) | (~little_set(f1(cs, as)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.10/0.40 tff(116,plain,
% 0.10/0.40 (member(f1(cs, as), bs) | member(f1(cs, as), complement(bs))),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[115, 72, 112])).
% 0.10/0.40 tff(117,plain,
% 0.10/0.40 (member(f1(cs, as), bs)),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[116, 98])).
% 0.10/0.40 tff(118,plain,
% 0.10/0.40 (member(f1(cs, as), complement(as))),
% 0.10/0.40 inference(modus_ponens,[status(thm)],[117, 5])).
% 0.10/0.40 tff(119,plain,
% 0.10/0.40 (((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(cs, as), as)) | (~member(f1(cs, as), complement(as))))) <=> ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), complement(as))))),
% 0.10/0.40 inference(rewrite,[status(thm)],[])).
% 0.10/0.40 tff(120,plain,
% 0.10/0.40 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | ((~member(f1(cs, as), as)) | (~member(f1(cs, as), complement(as))))),
% 0.10/0.40 inference(quant_inst,[status(thm)],[])).
% 0.10/0.40 tff(121,plain,
% 0.10/0.40 ((~![Z: $i, X: $i] : ((~member(Z, X)) | (~member(Z, complement(X))))) | (~member(f1(cs, as), as)) | (~member(f1(cs, as), complement(as)))),
% 0.10/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.10/0.40 tff(122,plain,
% 0.10/0.40 (~member(f1(cs, as), complement(as))),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[121, 45, 78])).
% 0.10/0.40 tff(123,plain,
% 0.10/0.40 ($false),
% 0.10/0.40 inference(unit_resolution,[status(thm)],[122, 118])).
% 0.10/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------