%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM504+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:21:12 AM UTC 2025
% Result : Theorem 0.42s 0.59s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM504+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.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 01:19:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.42/0.59 % SZS status Theorem
% 0.42/0.59 % SZS output start Proof
% 0.42/0.59 tff(sdtlseqdt0_type, type, (
% 0.42/0.59 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.42/0.59 tff(sdtasdt0_type, type, (
% 0.42/0.59 sdtasdt0: ( $i * $i ) > $i)).
% 0.42/0.59 tff(tptp_fun_W0_8_type, type, (
% 0.42/0.59 tptp_fun_W0_8: $i)).
% 0.42/0.59 tff(xp_type, type, (
% 0.42/0.59 xp: $i)).
% 0.42/0.59 tff(xm_type, type, (
% 0.42/0.59 xm: $i)).
% 0.42/0.59 tff(xk_type, type, (
% 0.42/0.59 xk: $i)).
% 0.42/0.59 tff(xn_type, type, (
% 0.42/0.59 xn: $i)).
% 0.42/0.59 tff(aNaturalNumber0_type, type, (
% 0.42/0.59 aNaturalNumber0: $i > $o)).
% 0.42/0.59 tff(sdtsldt0_type, type, (
% 0.42/0.59 sdtsldt0: ( $i * $i ) > $i)).
% 0.42/0.59 tff(isPrime0_type, type, (
% 0.42/0.59 isPrime0: $i > $o)).
% 0.42/0.59 tff(sz10_type, type, (
% 0.42/0.59 sz10: $i)).
% 0.42/0.59 tff(doDivides0_type, type, (
% 0.42/0.59 doDivides0: ( $i * $i ) > $o)).
% 0.42/0.59 tff(sz00_type, type, (
% 0.42/0.59 sz00: $i)).
% 0.42/0.59 tff(sdtpldt0_type, type, (
% 0.42/0.59 sdtpldt0: ( $i * $i ) > $i)).
% 0.42/0.59 tff(1,plain,
% 0.42/0.59 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(2,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2306')).
% 0.42/0.59 tff(3,plain,
% 0.42/0.59 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.42/0.59 inference(and_elim,[status(thm)],[2])).
% 0.42/0.59 tff(4,plain,
% 0.42/0.59 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.42/0.59 inference(and_elim,[status(thm)],[3])).
% 0.42/0.59 tff(5,plain,
% 0.42/0.59 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.42/0.59 tff(6,plain,
% 0.42/0.59 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(7,axiom,((((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtasdt0(xn, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1860')).
% 0.42/0.59 tff(8,plain,
% 0.42/0.59 (((((~(xp = sz00)) & (~(xp = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xp = sdtasdt0(W0, W1))) | doDivides0(W0, xp))) => ((W0 = sz10) | (W0 = xp)))) & isPrime0(xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[7])).
% 0.42/0.59 tff(9,plain,
% 0.42/0.59 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[8])).
% 0.42/0.59 tff(10,plain,
% 0.42/0.59 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.42/0.59 tff(11,plain,(
% 0.42/0.59 aNaturalNumber0(W0!8) & (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8))),
% 0.42/0.59 inference(skolemize,[status(sab)],[10])).
% 0.42/0.59 tff(12,plain,
% 0.42/0.59 (sdtasdt0(xn, xm) = sdtasdt0(xp, W0!8)),
% 0.42/0.59 inference(and_elim,[status(thm)],[11])).
% 0.42/0.59 tff(13,plain,
% 0.42/0.59 (sdtasdt0(xp, W0!8) = sdtasdt0(xn, xm)),
% 0.42/0.59 inference(symmetry,[status(thm)],[12])).
% 0.42/0.59 tff(14,plain,
% 0.42/0.59 (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xk)),
% 0.42/0.59 inference(transitivity,[status(thm)],[13, 5])).
% 0.42/0.59 tff(15,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[14])).
% 0.42/0.59 tff(16,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))),
% 0.42/0.59 inference(symmetry,[status(thm)],[15])).
% 0.42/0.59 tff(17,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk)) <=> sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(18,axiom,((((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xp, xm), W0) = sdtasdt0(xp, xk)))) & sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2414')).
% 0.42/0.59 tff(19,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.42/0.59 inference(and_elim,[status(thm)],[18])).
% 0.42/0.59 tff(20,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, xk))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.42/0.59 tff(21,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.42/0.59 tff(22,plain,
% 0.42/0.59 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[13])).
% 0.42/0.59 tff(23,plain,
% 0.42/0.59 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xm)) <=> (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm))),
% 0.42/0.59 inference(symmetry,[status(thm)],[22])).
% 0.42/0.59 tff(24,plain,
% 0.42/0.59 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) <=> (~(sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[23])).
% 0.42/0.59 tff(25,plain,
% 0.42/0.59 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) <=> (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(26,plain,
% 0.42/0.59 (((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xp, xm), W0) = sdtasdt0(xp, xk)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[18])).
% 0.42/0.59 tff(27,plain,
% 0.42/0.59 ((((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))) & (~(sdtasdt0(xp, xm) = sdtasdt0(xp, xk)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[26])).
% 0.42/0.59 tff(28,plain,
% 0.42/0.59 (((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))) & sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(and_elim,[status(thm)],[27])).
% 0.42/0.59 tff(29,plain,
% 0.42/0.59 ((~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtasdt0(xn, xm), W0) = sdtasdt0(xp, xm)))),
% 0.42/0.59 inference(and_elim,[status(thm)],[28])).
% 0.42/0.59 tff(30,plain,
% 0.42/0.59 (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.42/0.59 inference(and_elim,[status(thm)],[29])).
% 0.42/0.59 tff(31,plain,
% 0.42/0.59 (~(sdtasdt0(xn, xm) = sdtasdt0(xp, xm))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.42/0.59 tff(32,plain,
% 0.42/0.59 (~(sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.42/0.59 tff(33,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[13])).
% 0.42/0.59 tff(34,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(symmetry,[status(thm)],[33])).
% 0.42/0.59 tff(35,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm)) <=> sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(36,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(and_elim,[status(thm)],[28])).
% 0.42/0.59 tff(37,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xn, xm), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.42/0.59 tff(38,plain,
% 0.42/0.59 (sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.42/0.59 tff(39,plain,
% 0.42/0.59 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(40,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1837')).
% 0.42/0.59 tff(41,plain,
% 0.42/0.59 (aNaturalNumber0(xp)),
% 0.42/0.59 inference(and_elim,[status(thm)],[40])).
% 0.42/0.59 tff(42,plain,
% 0.42/0.59 (aNaturalNumber0(xp)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.42/0.59 tff(43,plain,
% 0.42/0.59 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(44,plain,
% 0.42/0.59 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.42/0.59 inference(and_elim,[status(thm)],[40])).
% 0.42/0.59 tff(45,plain,
% 0.42/0.59 (aNaturalNumber0(xm)),
% 0.42/0.59 inference(and_elim,[status(thm)],[44])).
% 0.42/0.59 tff(46,plain,
% 0.42/0.59 (aNaturalNumber0(xm)),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[45, 43])).
% 0.42/0.59 tff(47,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(48,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[47])).
% 0.42/0.59 tff(49,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(50,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[49])).
% 0.42/0.59 tff(51,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(52,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(53,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[52])).
% 0.42/0.59 tff(54,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.42/0.59 tff(55,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.42/0.59 tff(56,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.42/0.59 tff(57,plain,(
% 0.42/0.59 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.42/0.59 inference(skolemize,[status(sab)],[56])).
% 0.42/0.59 tff(58,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.42/0.59 tff(59,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.42/0.59 tff(60,plain,
% 0.42/0.59 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(61,plain,
% 0.42/0.59 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(62,plain,
% 0.42/0.59 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.42/0.59 tff(63,plain,
% 0.42/0.59 (aNaturalNumber0(sdtasdt0(xp, xm))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[62, 59, 46, 42])).
% 0.42/0.59 tff(64,plain,
% 0.42/0.59 (aNaturalNumber0(W0!8)),
% 0.42/0.59 inference(and_elim,[status(thm)],[11])).
% 0.42/0.59 tff(65,plain,
% 0.42/0.59 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(66,plain,
% 0.42/0.59 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp)))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(67,plain,
% 0.42/0.59 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtasdt0(xp, W0!8)) | (~aNaturalNumber0(W0!8)) | (~aNaturalNumber0(xp))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.42/0.59 tff(68,plain,
% 0.42/0.59 (aNaturalNumber0(sdtasdt0(xp, W0!8))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[67, 59, 42, 64])).
% 0.42/0.59 tff(69,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(70,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[69])).
% 0.42/0.59 tff(71,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))))), rewrite(((W0 = W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))), (((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(72,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[71])).
% 0.42/0.59 tff(73,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(74,plain,
% 0.42/0.59 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))))),
% 0.42/0.59 inference(bind,[status(th)],[])).
% 0.42/0.59 tff(75,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(quant_intro,[status(thm)],[74])).
% 0.42/0.59 tff(76,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mLEAsym')).
% 0.42/0.59 tff(77,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.42/0.59 tff(78,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.42/0.59 tff(79,plain,(
% 0.42/0.59 ![W0: $i, W1: $i] : ((W0 = W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))))),
% 0.42/0.59 inference(skolemize,[status(sab)],[78])).
% 0.42/0.59 tff(80,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.42/0.59 tff(81,plain,
% 0.42/0.59 (![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.42/0.59 tff(82,plain,
% 0.42/0.59 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(83,plain,
% 0.44/0.60 (((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))) <=> ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(84,plain,
% 0.44/0.60 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[83])).
% 0.44/0.60 tff(85,plain,
% 0.44/0.60 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))),
% 0.44/0.60 inference(transitivity,[status(thm)],[84, 82])).
% 0.44/0.60 tff(86,plain,
% 0.44/0.60 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8))))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(87,plain,
% 0.44/0.60 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W1, W0)))) | (~aNaturalNumber0(sdtasdt0(xp, W0!8))) | (~aNaturalNumber0(sdtasdt0(xp, xm))) | (sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.44/0.60 tff(88,plain,
% 0.44/0.60 ((sdtasdt0(xp, W0!8) = sdtasdt0(xp, xm)) | (~sdtlseqdt0(sdtasdt0(xp, W0!8), sdtasdt0(xp, xm))) | (~sdtlseqdt0(sdtasdt0(xp, xm), sdtasdt0(xp, W0!8)))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[87, 81, 68, 63])).
% 0.44/0.60 tff(89,plain,
% 0.44/0.60 ($false),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[88, 38, 32, 21])).
% 0.44/0.60 % SZS output end Proof
% 0.44/0.60 % E exiting
%------------------------------------------------------------------------------