TSTP Solution File: LCL893+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 04:58:50 EDT 2022
% Result : Theorem 0.74s 0.72s
% Output : Proof 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL893+1 : TPTP v8.1.0. Released v5.5.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 01:18:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.74/0.72 % SZS status Theorem
% 0.74/0.72 % SZS output start Proof
% 0.74/0.72 tff(tptp_fun______type, type, (
% 0.74/0.72 tptp_fun_____: ( $i * $i ) > $o)).
% 0.74/0.72 tff(tptp_fun_X17_0_type, type, (
% 0.74/0.72 tptp_fun_X17_0: $i)).
% 0.74/0.72 tff(tptp_fun__0__type, type, (
% 0.74/0.72 tptp_fun__0_: $i)).
% 0.74/0.72 tff(tptp_fun_______type, type, (
% 0.74/0.72 tptp_fun______: ( $i * $i ) > $i)).
% 0.74/0.72 tff(h_type, type, (
% 0.74/0.72 h: $i > $i)).
% 0.74/0.72 tff(tptp_fun_____type, type, (
% 0.74/0.72 tptp_fun____: ( $i * $i ) > $i)).
% 0.74/0.72 tff(1,plain,
% 0.74/0.72 ((~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))) <=> (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(2,plain,
% 0.74/0.72 ((~![X17: $i] : ((h(X17) = X17) => (X17 = |'0'|))) <=> (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(3,axiom,(~![X17: $i] : ((h(X17) = X17) => (X17 = |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_15')).
% 0.74/0.72 tff(4,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.74/0.72 tff(5,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.74/0.72 tff(6,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.74/0.72 tff(7,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.74/0.72 tff(8,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.74/0.72 tff(9,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.74/0.72 tff(10,plain,
% 0.74/0.72 (~![X17: $i] : ((~(h(X17) = X17)) | (X17 = |'0'|))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.74/0.72 tff(11,plain,(
% 0.74/0.72 ~((~(h(X17!0) = X17!0)) | (X17!0 = |'0'|))),
% 0.74/0.72 inference(skolemize,[status(sab)],[10])).
% 0.74/0.72 tff(12,plain,
% 0.74/0.72 (h(X17!0) = X17!0),
% 0.74/0.72 inference(or_elim,[status(thm)],[11])).
% 0.74/0.72 tff(13,plain,
% 0.74/0.72 (X17!0 = h(X17!0)),
% 0.74/0.72 inference(symmetry,[status(thm)],[12])).
% 0.74/0.72 tff(14,plain,
% 0.74/0.72 (tptp_fun______(X17!0, X17!0) = tptp_fun______(h(X17!0), X17!0)),
% 0.74/0.72 inference(monotonicity,[status(thm)],[13])).
% 0.74/0.72 tff(15,plain,
% 0.74/0.72 (tptp_fun______(h(X17!0), X17!0) = tptp_fun______(X17!0, X17!0)),
% 0.74/0.72 inference(symmetry,[status(thm)],[14])).
% 0.74/0.72 tff(16,plain,
% 0.74/0.72 (^[A: $i] : refl((h(A) = tptp_fun______(h(A), A)) <=> (h(A) = tptp_fun______(h(A), A)))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(17,plain,
% 0.74/0.72 (![A: $i] : (h(A) = tptp_fun______(h(A), A)) <=> ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[16])).
% 0.74/0.72 tff(18,plain,
% 0.74/0.72 (![A: $i] : (h(A) = tptp_fun______(h(A), A)) <=> ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(19,axiom,(![A: $i] : (h(A) = tptp_fun______(h(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_14')).
% 0.74/0.72 tff(20,plain,
% 0.74/0.72 (![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.74/0.72 tff(21,plain,(
% 0.74/0.72 ![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 0.74/0.72 inference(skolemize,[status(sab)],[20])).
% 0.74/0.72 tff(22,plain,
% 0.74/0.72 (![A: $i] : (h(A) = tptp_fun______(h(A), A))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.74/0.72 tff(23,plain,
% 0.74/0.72 ((~![A: $i] : (h(A) = tptp_fun______(h(A), A))) | (h(X17!0) = tptp_fun______(h(X17!0), X17!0))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(24,plain,
% 0.74/0.72 (h(X17!0) = tptp_fun______(h(X17!0), X17!0)),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.74/0.72 tff(25,plain,
% 0.74/0.72 (X17!0 = tptp_fun______(X17!0, X17!0)),
% 0.74/0.72 inference(transitivity,[status(thm)],[13, 24, 15])).
% 0.74/0.72 tff(26,plain,
% 0.74/0.72 (tptp_fun_____(|'0'|, X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0))),
% 0.74/0.72 inference(monotonicity,[status(thm)],[25])).
% 0.74/0.72 tff(27,plain,
% 0.74/0.72 (tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0)) <=> tptp_fun_____(|'0'|, X17!0)),
% 0.74/0.72 inference(symmetry,[status(thm)],[26])).
% 0.74/0.72 tff(28,plain,
% 0.74/0.72 (^[X5: $i, X6: $i, X7: $i] : refl((tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(29,plain,
% 0.74/0.72 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[28])).
% 0.74/0.72 tff(30,plain,
% 0.74/0.72 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7))) <=> ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(31,axiom,(![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_08')).
% 0.74/0.72 tff(32,plain,
% 0.74/0.72 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.74/0.72 tff(33,plain,(
% 0.74/0.72 ![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 0.74/0.72 inference(skolemize,[status(sab)],[32])).
% 0.74/0.72 tff(34,plain,
% 0.74/0.72 (![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.74/0.72 tff(35,plain,
% 0.74/0.72 ((~![X5: $i, X6: $i, X7: $i] : (tptp_fun_____(tptp_fun____(X5, X6), X7) <=> tptp_fun_____(X6, tptp_fun______(X5, X7)))) | (tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0)))),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(36,plain,
% 0.74/0.72 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.74/0.72 tff(37,plain,
% 0.74/0.72 (^[A: $i] : refl((tptp_fun____(A, |'0'|) = A) <=> (tptp_fun____(A, |'0'|) = A))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(38,plain,
% 0.74/0.72 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 0.74/0.72 inference(quant_intro,[status(thm)],[37])).
% 0.74/0.72 tff(39,plain,
% 0.74/0.72 (![A: $i] : (tptp_fun____(A, |'0'|) = A) <=> ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(40,axiom,(![A: $i] : (tptp_fun____(A, |'0'|) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_03')).
% 0.74/0.72 tff(41,plain,
% 0.74/0.72 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.74/0.72 tff(42,plain,(
% 0.74/0.72 ![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 0.74/0.72 inference(skolemize,[status(sab)],[41])).
% 0.74/0.72 tff(43,plain,
% 0.74/0.72 (![A: $i] : (tptp_fun____(A, |'0'|) = A)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.74/0.72 tff(44,plain,
% 0.74/0.72 ((~![A: $i] : (tptp_fun____(A, |'0'|) = A)) | (tptp_fun____(X17!0, |'0'|) = X17!0)),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(45,plain,
% 0.74/0.72 (tptp_fun____(X17!0, |'0'|) = X17!0),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.74/0.72 tff(46,plain,
% 0.74/0.72 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0) <=> tptp_fun_____(X17!0, X17!0)),
% 0.74/0.72 inference(monotonicity,[status(thm)],[45])).
% 0.74/0.72 tff(47,plain,
% 0.74/0.72 (tptp_fun_____(X17!0, X17!0) <=> tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0)),
% 0.74/0.72 inference(symmetry,[status(thm)],[46])).
% 0.74/0.72 tff(48,plain,
% 0.74/0.72 (^[A: $i] : refl(tptp_fun_____(A, A) <=> tptp_fun_____(A, A))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(49,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 0.74/0.72 inference(quant_intro,[status(thm)],[48])).
% 0.74/0.72 tff(50,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, A) <=> ![A: $i] : tptp_fun_____(A, A)),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(51,axiom,(![A: $i] : tptp_fun_____(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_05')).
% 0.74/0.72 tff(52,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, A)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.74/0.72 tff(53,plain,(
% 0.74/0.72 ![A: $i] : tptp_fun_____(A, A)),
% 0.74/0.72 inference(skolemize,[status(sab)],[52])).
% 0.74/0.72 tff(54,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, A)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.74/0.72 tff(55,plain,
% 0.74/0.72 ((~![A: $i] : tptp_fun_____(A, A)) | tptp_fun_____(X17!0, X17!0)),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(56,plain,
% 0.74/0.72 (tptp_fun_____(X17!0, X17!0)),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.74/0.72 tff(57,plain,
% 0.74/0.72 (tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[56, 47])).
% 0.74/0.72 tff(58,plain,
% 0.74/0.72 ((~(tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0) <=> tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0)))) | (~tptp_fun_____(tptp_fun____(X17!0, |'0'|), X17!0)) | tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0))),
% 0.74/0.72 inference(tautology,[status(thm)],[])).
% 0.74/0.72 tff(59,plain,
% 0.74/0.72 (tptp_fun_____(|'0'|, tptp_fun______(X17!0, X17!0))),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[58, 57, 36])).
% 0.74/0.72 tff(60,plain,
% 0.74/0.72 (tptp_fun_____(|'0'|, X17!0)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[59, 27])).
% 0.74/0.72 tff(61,plain,
% 0.74/0.72 (^[A: $i] : refl(tptp_fun_____(A, |'0'|) <=> tptp_fun_____(A, |'0'|))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(62,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, |'0'|) <=> ![A: $i] : tptp_fun_____(A, |'0'|)),
% 0.74/0.72 inference(quant_intro,[status(thm)],[61])).
% 0.74/0.72 tff(63,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, |'0'|) <=> ![A: $i] : tptp_fun_____(A, |'0'|)),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(64,axiom,(![A: $i] : tptp_fun_____(A, |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_09')).
% 0.74/0.72 tff(65,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, |'0'|)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.74/0.72 tff(66,plain,(
% 0.74/0.72 ![A: $i] : tptp_fun_____(A, |'0'|)),
% 0.74/0.72 inference(skolemize,[status(sab)],[65])).
% 0.74/0.72 tff(67,plain,
% 0.74/0.72 (![A: $i] : tptp_fun_____(A, |'0'|)),
% 0.74/0.72 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.74/0.72 tff(68,plain,
% 0.74/0.72 ((~![A: $i] : tptp_fun_____(A, |'0'|)) | tptp_fun_____(X17!0, |'0'|)),
% 0.74/0.72 inference(quant_inst,[status(thm)],[])).
% 0.74/0.72 tff(69,plain,
% 0.74/0.72 (tptp_fun_____(X17!0, |'0'|)),
% 0.74/0.72 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.74/0.72 tff(70,plain,
% 0.74/0.72 (~(X17!0 = |'0'|)),
% 0.74/0.72 inference(or_elim,[status(thm)],[11])).
% 0.74/0.72 tff(71,plain,
% 0.74/0.72 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) <=> ![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(72,plain,
% 0.74/0.72 (^[X3: $i, X4: $i] : trans(monotonicity(trans(monotonicity(rewrite((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) <=> (~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))), ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) <=> (~(~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))))), rewrite((~(~((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))) <=> ((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))), ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) <=> ((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))))), (((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> (((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) | (X3 = X4)))), rewrite((((~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))), (((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(73,plain,
% 0.74/0.72 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 0.74/0.72 inference(quant_intro,[status(thm)],[72])).
% 0.74/0.72 tff(74,plain,
% 0.74/0.72 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)) <=> ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 0.74/0.72 inference(rewrite,[status(thm)],[])).
% 0.74/0.72 tff(75,plain,
% 0.74/0.72 (^[X3: $i, X4: $i] : rewrite(((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4)) <=> ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4)))),
% 0.74/0.72 inference(bind,[status(th)],[])).
% 0.74/0.72 tff(76,plain,
% 0.74/0.73 (![X3: $i, X4: $i] : ((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4)) <=> ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 0.74/0.73 inference(quant_intro,[status(thm)],[75])).
% 0.74/0.73 tff(77,axiom,(![X3: $i, X4: $i] : ((tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3)) => (X3 = X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_07')).
% 0.74/0.73 tff(78,plain,
% 0.74/0.73 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.74/0.73 tff(79,plain,
% 0.74/0.73 (![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.74/0.73 tff(80,plain,(
% 0.74/0.73 ![X3: $i, X4: $i] : ((~(tptp_fun_____(X3, X4) & tptp_fun_____(X4, X3))) | (X3 = X4))),
% 0.74/0.73 inference(skolemize,[status(sab)],[79])).
% 0.74/0.73 tff(81,plain,
% 0.74/0.73 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.74/0.73 tff(82,plain,
% 0.74/0.73 (![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.74/0.73 tff(83,plain,
% 0.74/0.73 (((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = |'0'|) | (~tptp_fun_____(X17!0, |'0'|)) | (~tptp_fun_____(|'0'|, X17!0)))) <=> ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (X17!0 = |'0'|) | (~tptp_fun_____(X17!0, |'0'|)) | (~tptp_fun_____(|'0'|, X17!0)))),
% 0.74/0.73 inference(rewrite,[status(thm)],[])).
% 0.74/0.73 tff(84,plain,
% 0.74/0.73 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | ((X17!0 = |'0'|) | (~tptp_fun_____(X17!0, |'0'|)) | (~tptp_fun_____(|'0'|, X17!0)))),
% 0.74/0.73 inference(quant_inst,[status(thm)],[])).
% 0.74/0.73 tff(85,plain,
% 0.74/0.73 ((~![X3: $i, X4: $i] : ((X3 = X4) | (~tptp_fun_____(X3, X4)) | (~tptp_fun_____(X4, X3)))) | (X17!0 = |'0'|) | (~tptp_fun_____(X17!0, |'0'|)) | (~tptp_fun_____(|'0'|, X17!0))),
% 0.74/0.73 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.74/0.73 tff(86,plain,
% 0.74/0.73 (~tptp_fun_____(|'0'|, X17!0)),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[85, 82, 70, 69])).
% 0.74/0.73 tff(87,plain,
% 0.74/0.73 ($false),
% 0.74/0.73 inference(unit_resolution,[status(thm)],[86, 60])).
% 0.74/0.73 % SZS output end Proof
%------------------------------------------------------------------------------