%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT019-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:00:25 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT019-3 : TPTP v9.0.0. Released v1.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:53:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(there_exists_type, type, (
% 0.19/0.37 there_exists: $i > $o)).
% 0.19/0.37 tff(a_type, type, (
% 0.19/0.37 a: $i)).
% 0.19/0.37 tff(f1_type, type, (
% 0.19/0.37 f1: ( $i * $i ) > $i)).
% 0.19/0.37 tff(b_type, type, (
% 0.19/0.37 b: $i)).
% 0.19/0.37 tff(1,assumption,(b = f1(a, b)), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (there_exists(b) <=> there_exists(f1(a, b))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (there_exists(f1(a, b)) <=> there_exists(b)),
% 0.19/0.37 inference(symmetry,[status(thm)],[2])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 ((~(a = b)) <=> (~(a = b))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(5,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_a_equals_b')).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~(a = b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : refl((there_exists(f1(X, Y)) | (X = Y)) <=> (there_exists(f1(X, Y)) | (X = Y)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(10,axiom,(![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax','indiscernibles1')).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.19/0.37 tff(12,plain,(
% 0.19/0.37 ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.19/0.37 inference(skolemize,[status(sab)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | (there_exists(f1(a, b)) | (a = b))) <=> ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | there_exists(f1(a, b)) | (a = b))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | (there_exists(f1(a, b)) | (a = b))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | there_exists(f1(a, b)) | (a = b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (there_exists(f1(a, b))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[16, 13, 6])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (there_exists(b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 3])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (((~there_exists(b)) | (a = b)) <=> ((~there_exists(b)) | (a = b))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![Z: $i] : ((~there_exists(b)) | (a = b)) <=> ((~there_exists(b)) | (a = b))),
% 0.19/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z))) <=> ![Z: $i] : ((~there_exists(b)) | (a = b))),
% 0.19/0.37 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z))) <=> ((~there_exists(b)) | (a = b))),
% 0.19/0.37 inference(transitivity,[status(thm)],[21, 20])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[Z: $i] : rewrite((((~there_exists(Z)) | (a = Z)) | (~(b = Z))) <=> ((~there_exists(Z)) | (a = Z) | (~(b = Z))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![Z: $i] : (((~there_exists(Z)) | (a = Z)) | (~(b = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![Z: $i] : (((~there_exists(Z)) | (a = Z)) | (~(b = Z))) <=> ((~there_exists(b)) | (a = b))),
% 0.19/0.37 inference(transitivity,[status(thm)],[24, 22])).
% 0.19/0.37 tff(26,axiom,(![Z: $i] : (((~there_exists(Z)) | (a = Z)) | (~(b = Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equality_of_a_and_b2')).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~there_exists(b)) | (a = b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~there_exists(b)) | (a = b)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (~there_exists(b)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 6])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 18])).
% 0.19/0.37 tff(31,plain,(~(b = f1(a, b))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : refl(((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y))) <=> ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y))) <=> ![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y))) <=> ![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (^[Y: $i, X: $i] : rewrite((((X = f1(X, Y)) | (Y = f1(X, Y))) | (X = Y)) <=> ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![Y: $i, X: $i] : (((X = f1(X, Y)) | (Y = f1(X, Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.37 tff(37,axiom,(![Y: $i, X: $i] : (((X = f1(X, Y)) | (Y = f1(X, Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax','indiscernibles2')).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.37 tff(40,plain,(
% 0.19/0.37 ![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[39])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((a = b) | (a = f1(a, b)) | (b = f1(a, b)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | (a = b) | (a = f1(a, b)) | (b = f1(a, b)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (((a = b) | (b = f1(a, b)) | (a = f1(a, b))) <=> ((a = b) | (a = f1(a, b)) | (b = f1(a, b)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((a = b) | (b = f1(a, b)) | (a = f1(a, b)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((a = b) | (a = f1(a, b)) | (b = f1(a, b))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 (((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((a = b) | (b = f1(a, b)) | (a = f1(a, b)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | (a = b) | (a = f1(a, b)) | (b = f1(a, b)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((a = b) | (b = f1(a, b)) | (a = f1(a, b)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.37 ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | (a = b) | (a = f1(a, b)) | (b = f1(a, b))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.37 tff(48,plain,
% 0.19/0.37 ((a = f1(a, b)) | (b = f1(a, b))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[47, 41, 6])).
% 0.19/0.37 tff(49,plain,
% 0.19/0.37 (a = f1(a, b)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[48, 31])).
% 0.19/0.37 tff(50,plain,
% 0.19/0.37 (there_exists(a) <=> there_exists(f1(a, b))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.37 tff(51,plain,
% 0.19/0.37 (there_exists(f1(a, b)) <=> there_exists(a)),
% 0.19/0.37 inference(symmetry,[status(thm)],[50])).
% 0.19/0.37 tff(52,plain,
% 0.19/0.37 (there_exists(a)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 51])).
% 0.19/0.37 tff(53,plain,
% 0.19/0.37 ((a = b) <=> (b = a)),
% 0.19/0.37 inference(commutativity,[status(thm)],[])).
% 0.19/0.37 tff(54,plain,
% 0.19/0.37 ((~(a = b)) <=> (~(b = a))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.37 tff(55,plain,
% 0.19/0.37 (~(b = a)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 54])).
% 0.19/0.37 tff(56,plain,
% 0.19/0.37 (((~there_exists(a)) | (b = a)) <=> ((~there_exists(a)) | (b = a))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (![Z: $i] : ((~there_exists(a)) | (b = a)) <=> ((~there_exists(a)) | (b = a))),
% 0.19/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z))) <=> ![Z: $i] : ((~there_exists(a)) | (b = a))),
% 0.19/0.38 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z))) <=> ((~there_exists(a)) | (b = a))),
% 0.19/0.38 inference(transitivity,[status(thm)],[58, 57])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (^[Z: $i] : rewrite((((~there_exists(Z)) | (~(a = Z))) | (b = Z)) <=> ((~there_exists(Z)) | (b = Z) | (~(a = Z))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (![Z: $i] : (((~there_exists(Z)) | (~(a = Z))) | (b = Z)) <=> ![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 (![Z: $i] : (((~there_exists(Z)) | (~(a = Z))) | (b = Z)) <=> ((~there_exists(a)) | (b = a))),
% 0.19/0.38 inference(transitivity,[status(thm)],[61, 59])).
% 0.19/0.38 tff(63,axiom,(![Z: $i] : (((~there_exists(Z)) | (~(a = Z))) | (b = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equality_of_a_and_b1')).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 ((~there_exists(a)) | (b = a)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 ((~there_exists(a)) | (b = a)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[64, 56])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (~there_exists(a)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[65, 55])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[66, 52])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------