%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM477+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:21:07 AM UTC 2025
% Result : Theorem 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM477+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 01:15:20 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(sz00_type, type, (
% 0.22/0.40 sz00: $i)).
% 0.22/0.40 tff(xn_type, type, (
% 0.22/0.40 xn: $i)).
% 0.22/0.40 tff(sdtasdt0_type, type, (
% 0.22/0.40 sdtasdt0: ( $i * $i ) > $i)).
% 0.22/0.40 tff(xm_type, type, (
% 0.22/0.40 xm: $i)).
% 0.22/0.40 tff(aNaturalNumber0_type, type, (
% 0.22/0.40 aNaturalNumber0: $i > $o)).
% 0.22/0.40 tff(tptp_fun_W0_2_type, type, (
% 0.22/0.40 tptp_fun_W0_2: $i)).
% 0.22/0.40 tff(sdtlseqdt0_type, type, (
% 0.22/0.40 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.22/0.40 tff(doDivides0_type, type, (
% 0.22/0.40 doDivides0: ( $i * $i ) > $o)).
% 0.22/0.40 tff(sdtpldt0_type, type, (
% 0.22/0.40 sdtpldt0: ( $i * $i ) > $i)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(2,axiom,(aNaturalNumber0(xm) & aNaturalNumber0(xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1494')).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (aNaturalNumber0(xm)),
% 0.22/0.40 inference(and_elim,[status(thm)],[2])).
% 0.22/0.40 tff(4,plain,
% 0.22/0.40 (aNaturalNumber0(xm)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(6,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[5])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[7])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.22/0.40 tff(12,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_MulZero')).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.22/0.40 tff(15,plain,(
% 0.22/0.40 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[14])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xm)) | (~((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xm)) | (~((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xm)) | (~((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm))))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xm)) | (~((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (~((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[20, 17, 4])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (((~(sdtasdt0(xm, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xm)))) | (sdtasdt0(xm, sz00) = sz00)),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 (sdtasdt0(xm, sz00) = sz00),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(25,axiom,((?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) & doDivides0(xm, xn)) & (~(xn = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1494_04')).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0))) & doDivides0(xm, xn)),
% 0.22/0.40 inference(and_elim,[status(thm)],[25])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.22/0.40 inference(and_elim,[status(thm)],[26])).
% 0.22/0.40 tff(28,plain,
% 0.22/0.40 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xm, W0)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.22/0.40 tff(29,plain,(
% 0.22/0.40 aNaturalNumber0(W0!2) & (xn = sdtasdt0(xm, W0!2))),
% 0.22/0.40 inference(skolemize,[status(sab)],[28])).
% 0.22/0.40 tff(30,plain,
% 0.22/0.40 (xn = sdtasdt0(xm, W0!2)),
% 0.22/0.40 inference(and_elim,[status(thm)],[29])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (sdtasdt0(xm, W0!2) = xn),
% 0.22/0.40 inference(symmetry,[status(thm)],[30])).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (sdtlseqdt0(xm, sdtasdt0(xm, W0!2)) <=> sdtlseqdt0(xm, xn)),
% 0.22/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 (sdtlseqdt0(xm, xn) <=> sdtlseqdt0(xm, sdtasdt0(xm, W0!2))),
% 0.22/0.40 inference(symmetry,[status(thm)],[32])).
% 0.22/0.40 tff(34,plain,
% 0.22/0.40 ((~sdtlseqdt0(xm, xn)) <=> (~sdtlseqdt0(xm, sdtasdt0(xm, W0!2)))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.22/0.40 tff(35,plain,
% 0.22/0.40 ((~sdtlseqdt0(xm, xn)) <=> (~sdtlseqdt0(xm, xn))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(36,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xn)) | sdtlseqdt0(xm, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.22/0.40 tff(37,plain,
% 0.22/0.40 (~sdtlseqdt0(xm, xn)),
% 0.22/0.40 inference(or_elim,[status(thm)],[36])).
% 0.22/0.40 tff(38,plain,
% 0.22/0.40 (~sdtlseqdt0(xm, xn)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.22/0.40 tff(39,plain,
% 0.22/0.40 (~sdtlseqdt0(xm, sdtasdt0(xm, W0!2))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.22/0.40 tff(40,plain,
% 0.22/0.40 (aNaturalNumber0(W0!2)),
% 0.22/0.40 inference(and_elim,[status(thm)],[29])).
% 0.22/0.40 tff(41,plain,
% 0.22/0.40 (^[W0: $i, W1: $i] : refl(((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(42,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.22/0.40 tff(43,plain,
% 0.22/0.40 (^[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))))), (((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite(((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(44,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.40 tff(45,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(46,plain,
% 0.22/0.40 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((~(W0 = sz00)) => sdtlseqdt0(W1, sdtasdt0(W1, W0))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(W0 = sz00)) => sdtlseqdt0(W1, sdtasdt0(W1, W0)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(W0 = sz00)) => sdtlseqdt0(W1, sdtasdt0(W1, W0)))) <=> ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(47,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(W0 = sz00)) => sdtlseqdt0(W1, sdtasdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.22/0.40 tff(48,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(W0 = sz00)) => sdtlseqdt0(W1, sdtasdt0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMonMul2')).
% 0.22/0.40 tff(49,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.22/0.40 tff(50,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.22/0.40 tff(51,plain,(
% 0.22/0.40 ![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.22/0.40 inference(skolemize,[status(sab)],[50])).
% 0.22/0.40 tff(52,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.22/0.40 tff(53,plain,
% 0.22/0.40 (![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.22/0.40 tff(54,plain,
% 0.22/0.40 (((~![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((W0!2 = sz00) | sdtlseqdt0(xm, sdtasdt0(xm, W0!2)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!2)))) <=> ((~![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (W0!2 = sz00) | sdtlseqdt0(xm, sdtasdt0(xm, W0!2)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!2)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(55,plain,
% 0.22/0.41 ((~![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((W0!2 = sz00) | sdtlseqdt0(xm, sdtasdt0(xm, W0!2)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!2)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(56,plain,
% 0.22/0.41 ((~![W0: $i, W1: $i] : ((W0 = sz00) | sdtlseqdt0(W1, sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (W0!2 = sz00) | sdtlseqdt0(xm, sdtasdt0(xm, W0!2)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(W0!2))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.41 tff(57,plain,
% 0.22/0.41 ((W0!2 = sz00) | sdtlseqdt0(xm, sdtasdt0(xm, W0!2))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[56, 53, 4, 40])).
% 0.22/0.41 tff(58,plain,
% 0.22/0.41 (W0!2 = sz00),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[57, 39])).
% 0.22/0.41 tff(59,plain,
% 0.22/0.41 (sdtasdt0(xm, W0!2) = sdtasdt0(xm, sz00)),
% 0.22/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 (xn = sz00),
% 0.22/0.41 inference(transitivity,[status(thm)],[30, 59, 23])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~(xn = sz00)) <=> (~(xn = sz00))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 (~(xn = sz00)),
% 0.22/0.41 inference(and_elim,[status(thm)],[25])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (~(xn = sz00)),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[63, 60])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.41 % E exiting
%------------------------------------------------------------------------------