TSTP Solution File: CAT019-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 6 17:29:50 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : CAT019-3 : TPTP v8.1.0. Released v1.0.0.
% 0.14/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 30 06:29:50 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.37 Usage: tptp [options] [-file:]file
% 0.21/0.37 -h, -? prints this message.
% 0.21/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.37 -m, -model generate model.
% 0.21/0.37 -p, -proof generate proof.
% 0.21/0.37 -c, -core generate unsat core of named formulas.
% 0.21/0.37 -st, -statistics display statistics.
% 0.21/0.37 -t:timeout set timeout (in second).
% 0.21/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.37 -<param>:<value> configuration parameter and value.
% 0.21/0.37 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(f1_type, type, (
% 0.21/0.42 f1: ( $i * $i ) > $i)).
% 0.21/0.42 tff(a_type, type, (
% 0.21/0.42 a: $i)).
% 0.21/0.42 tff(b_type, type, (
% 0.21/0.42 b: $i)).
% 0.21/0.42 tff(there_exists_type, type, (
% 0.21/0.42 there_exists: $i > $o)).
% 0.21/0.42 tff(1,assumption,(~(b = f1(b, a))), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 ((b = a) <=> (a = b)),
% 0.21/0.42 inference(commutativity,[status(thm)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 ((a = b) <=> (b = a)),
% 0.21/0.42 inference(symmetry,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 ((~(a = b)) <=> (~(b = a))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 ((~(a = b)) <=> (~(a = b))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(6,axiom,(~(a = b)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_a_equals_b')).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (~(a = b)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (~(b = a)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (^[Y: $i, X: $i] : refl((there_exists(f1(X, Y)) | (X = Y)) <=> (there_exists(f1(X, Y)) | (X = Y)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y)) <=> ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(12,axiom,(![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax','indiscernibles1')).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.42 tff(14,plain,(
% 0.21/0.42 ![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.21/0.42 inference(skolemize,[status(sab)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | (there_exists(f1(b, a)) | (b = a))) <=> ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | there_exists(f1(b, a)) | (b = a))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | (there_exists(f1(b, a)) | (b = a))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : (there_exists(f1(X, Y)) | (X = Y))) | there_exists(f1(b, a)) | (b = a)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (there_exists(f1(b, a)) | (b = a)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[18, 15])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (there_exists(f1(b, a))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[19, 8])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (^[Z: $i] : refl(((~there_exists(Z)) | (b = Z) | (~(a = Z))) <=> ((~there_exists(Z)) | (b = Z) | (~(a = Z))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (^[Z: $i] : rewrite((((~there_exists(Z)) | (~(a = Z))) | (b = Z)) <=> ((~there_exists(Z)) | (b = Z) | (~(a = Z))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (![Z: $i] : (((~there_exists(Z)) | (~(a = Z))) | (b = Z)) <=> ![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.42 tff(26,axiom,(![Z: $i] : (((~there_exists(Z)) | (~(a = Z))) | (b = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equality_of_a_and_b1')).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.42 tff(29,plain,(
% 0.21/0.42 ![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[28])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | ((~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a)))) <=> ((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | (~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (((~there_exists(f1(b, a))) | (b = f1(b, a)) | (~(a = f1(b, a)))) <=> ((~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | ((~there_exists(f1(b, a))) | (b = f1(b, a)) | (~(a = f1(b, a))))) <=> ((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | ((~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[32])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | ((~there_exists(f1(b, a))) | (b = f1(b, a)) | (~(a = f1(b, a))))) <=> ((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | (~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | ((~there_exists(f1(b, a))) | (b = f1(b, a)) | (~(a = f1(b, a))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 ((~![Z: $i] : ((~there_exists(Z)) | (b = Z) | (~(a = Z)))) | (~there_exists(f1(b, a))) | (~(a = f1(b, a))) | (b = f1(b, a))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~(a = f1(b, a))) | (b = f1(b, a))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[36, 30, 20])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (~(a = f1(b, a))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.42 tff(44,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')).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.21/0.42 tff(47,plain,(
% 0.21/0.42 ![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[46])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((b = a) | (a = f1(b, a)) | (b = f1(b, a)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | (b = a) | (a = f1(b, a)) | (b = f1(b, a)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | ((b = a) | (a = f1(b, a)) | (b = f1(b, a)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((~![Y: $i, X: $i] : ((X = Y) | (Y = f1(X, Y)) | (X = f1(X, Y)))) | (b = a) | (a = f1(b, a)) | (b = f1(b, a))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 ((a = f1(b, a)) | (b = f1(b, a))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[51, 48, 8])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[52, 38, 1])).
% 0.21/0.43 tff(54,plain,(b = f1(b, a)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (^[Z: $i] : refl(((~there_exists(Z)) | (a = Z) | (~(b = Z))) <=> ((~there_exists(Z)) | (a = Z) | (~(b = Z))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[Z: $i] : rewrite((((~there_exists(Z)) | (a = Z)) | (~(b = Z))) <=> ((~there_exists(Z)) | (a = Z) | (~(b = Z))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![Z: $i] : (((~there_exists(Z)) | (a = Z)) | (~(b = Z))) <=> ![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,axiom,(![Z: $i] : (((~there_exists(Z)) | (a = Z)) | (~(b = Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','equality_of_a_and_b2')).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.21/0.43 tff(63,plain,(
% 0.21/0.43 ![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[62])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (((~![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))) | ((~there_exists(f1(b, a))) | (a = f1(b, a)) | (~(b = f1(b, a))))) <=> ((~![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))) | (~there_exists(f1(b, a))) | (a = f1(b, a)) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 ((~![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))) | ((~there_exists(f1(b, a))) | (a = f1(b, a)) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 ((~![Z: $i] : ((~there_exists(Z)) | (a = Z) | (~(b = Z)))) | (~there_exists(f1(b, a))) | (a = f1(b, a)) | (~(b = f1(b, a)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 ((a = f1(b, a)) | (~(b = f1(b, a)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[67, 64, 20])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (a = f1(b, a)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[68, 54])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.21/0.43 tff(75,axiom,(![Y: $i, X: $i] : (((~(X = f1(X, Y))) | (~(Y = f1(X, Y)))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax','indiscernibles3')).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.21/0.43 tff(78,plain,(
% 0.21/0.43 ![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[77])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | ((~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | (~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (((b = a) | (~(a = f1(b, a))) | (~(b = f1(b, a)))) <=> ((~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | ((b = a) | (~(a = f1(b, a))) | (~(b = f1(b, a))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | ((~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | ((b = a) | (~(a = f1(b, a))) | (~(b = f1(b, a))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | (~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[82, 80])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | ((b = a) | (~(a = f1(b, a))) | (~(b = f1(b, a))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 ((~![Y: $i, X: $i] : ((X = Y) | (~(Y = f1(X, Y))) | (~(X = f1(X, Y))))) | (~(a = f1(b, a))) | (b = a) | (~(b = f1(b, a)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 ((~(a = f1(b, a))) | (~(b = f1(b, a)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[85, 79, 8])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[86, 69, 54])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------