%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM521+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:21:16 AM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM521+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.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 : Fri Jun 20 01:22:09 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(xp_type, type, (
% 0.23/0.42 xp: $i)).
% 0.23/0.42 tff(sdtpldt0_type, type, (
% 0.23/0.42 sdtpldt0: ( $i * $i ) > $i)).
% 0.23/0.42 tff(xm_type, type, (
% 0.23/0.42 xm: $i)).
% 0.23/0.42 tff(aNaturalNumber0_type, type, (
% 0.23/0.42 aNaturalNumber0: $i > $o)).
% 0.23/0.42 tff(sdtlseqdt0_type, type, (
% 0.23/0.42 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.23/0.42 tff(xn_type, type, (
% 0.23/0.42 xn: $i)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 ((~sdtlseqdt0(xp, xm)) <=> (~sdtlseqdt0(xp, xm))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(2,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xm)) | sdtlseqdt0(xp, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2075')).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (~sdtlseqdt0(xp, xm)),
% 0.23/0.42 inference(or_elim,[status(thm)],[2])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (~sdtlseqdt0(xp, xm)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (((~sdtlseqdt0(xp, xm)) | (xp = xm)) | sdtlseqdt0(xp, xm)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 ((~sdtlseqdt0(xp, xm)) | (xp = xm)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(8,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (aNaturalNumber0(xp)),
% 0.23/0.42 inference(and_elim,[status(thm)],[8])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (aNaturalNumber0(xp)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[9, 7])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.23/0.42 inference(and_elim,[status(thm)],[8])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (aNaturalNumber0(xm)),
% 0.23/0.42 inference(and_elim,[status(thm)],[12])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (aNaturalNumber0(xm)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 (^[W0: $i, W1: $i] : refl((sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((~(W1 = W0)) & sdtlseqdt0(W1, W0)) <=> (~((W1 = W0) | (~sdtlseqdt0(W1, W0))))), 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))))), ((sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (sdtlseqdt0(W0, W1) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((sdtlseqdt0(W0, W1) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))), ((sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)))) <=> (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.23/0.42 tff(22,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mLETotal')).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.23/0.42 tff(25,plain,(
% 0.23/0.42 ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | ((~(W1 = W0)) & sdtlseqdt0(W1, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[24])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 ((~((xp = xm) | (~sdtlseqdt0(xp, xm)))) <=> (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm))))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 ((sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm))))) <=> (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.23/0.42 inference(transitivity,[status(thm)],[31, 29])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.23/0.43 tff(34,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[33, 28])).
% 0.23/0.43 tff(35,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~((xp = xm) | (~sdtlseqdt0(xp, xm)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xm, xp) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xm)) | (xp = xm)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.23/0.43 tff(37,plain,
% 0.23/0.43 (sdtlseqdt0(xm, xp)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[36, 27, 14, 10, 6])).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 ((sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))) | (~sdtlseqdt0(xm, xp))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 (sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, xn))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(41,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) | sdtlseqdt0(xp, xn))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1870')).
% 0.23/0.43 tff(42,plain,
% 0.23/0.43 (~sdtlseqdt0(xp, xn)),
% 0.23/0.43 inference(or_elim,[status(thm)],[41])).
% 0.23/0.43 tff(43,plain,
% 0.23/0.43 (~sdtlseqdt0(xp, xn)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[42, 40])).
% 0.23/0.43 tff(44,plain,
% 0.23/0.43 (((~sdtlseqdt0(xp, xn)) | (xp = xn)) | sdtlseqdt0(xp, xn)),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(45,plain,
% 0.23/0.43 ((~sdtlseqdt0(xp, xn)) | (xp = xn)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.23/0.43 tff(46,plain,
% 0.23/0.43 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(47,plain,
% 0.23/0.43 (aNaturalNumber0(xn)),
% 0.23/0.43 inference(and_elim,[status(thm)],[12])).
% 0.23/0.43 tff(48,plain,
% 0.23/0.43 (aNaturalNumber0(xn)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.23/0.43 tff(49,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(50,plain,
% 0.23/0.43 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(51,plain,
% 0.23/0.43 ((~((xp = xn) | (~sdtlseqdt0(xp, xn)))) <=> (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(52,plain,
% 0.23/0.43 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn))))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[51])).
% 0.23/0.43 tff(53,plain,
% 0.23/0.43 ((sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn))))) <=> (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[52, 50])).
% 0.23/0.43 tff(54,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.23/0.43 tff(55,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[54, 49])).
% 0.23/0.43 tff(56,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xn)) | (~((xp = xn) | (~sdtlseqdt0(xp, xn)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(57,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xn, xp) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((~sdtlseqdt0(xp, xn)) | (xp = xn)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (sdtlseqdt0(xn, xp)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[57, 27, 48, 10, 45])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 ((sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))) | (~sdtlseqdt0(xn, xp))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(60,plain,
% 0.23/0.43 (sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xn) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~((xn = xp) | (~sdtlseqdt0(xn, xp))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.23/0.43 tff(64,plain,
% 0.23/0.43 (~((xn = xp) | (~sdtlseqdt0(xn, xp)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[63, 27, 48, 10, 43])).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 (((xn = xp) | (~sdtlseqdt0(xn, xp))) | (~(xn = xp))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 (~(xn = xp)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 (((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | (sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp)))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 ((~![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((W1 = W0) | (~sdtlseqdt0(W1, W0)))))) | sdtlseqdt0(xp, xm) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~((xm = xp) | (~sdtlseqdt0(xm, xp))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.23/0.43 tff(70,plain,
% 0.23/0.43 (~((xm = xp) | (~sdtlseqdt0(xm, xp)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[69, 27, 14, 10, 4])).
% 0.23/0.43 tff(71,plain,
% 0.23/0.43 (((xm = xp) | (~sdtlseqdt0(xm, xp))) | (~(xm = xp))),
% 0.23/0.43 inference(tautology,[status(thm)],[])).
% 0.23/0.43 tff(72,plain,
% 0.23/0.43 (~(xm = xp)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.23/0.43 tff(73,plain,
% 0.23/0.43 (((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(74,plain,
% 0.23/0.43 (((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(75,plain,
% 0.23/0.43 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))) <=> (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(76,plain,
% 0.23/0.43 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[76])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[77])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[78, 75])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))) <=> (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) <=> (~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> (~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))), ((~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[81])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[83, 80])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 (((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[84, 79])).
% 0.23/0.44 tff(86,plain,
% 0.23/0.44 (((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | (~(sdtlseqdt0(xn, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xn, W0) = xp)))))) | (~(sdtlseqdt0(xm, xp) | (~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(sdtpldt0(xm, W0) = xp)))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[85, 74])).
% 0.23/0.44 tff(87,plain,
% 0.23/0.44 (((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(88,plain,
% 0.23/0.44 (((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(89,plain,
% 0.23/0.44 (((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) <=> ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(90,plain,
% 0.23/0.44 (((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[89, 88])).
% 0.23/0.44 tff(91,plain,
% 0.23/0.44 (((xn = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | (xm = xp) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> ((xn = xp) | (xm = xp) | ((~sdtlseqdt0(xn, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))) | ((~sdtlseqdt0(xm, xp)) & ![W0: $i] : (~(aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[90, 87])).
% 0.23/0.44 tff(92,plain,
% 0.23/0.44 ((sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) <=> (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(93,plain,
% 0.23/0.44 ((sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) <=> (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(94,plain,
% 0.23/0.44 (((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))) <=> ((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[93, 92])).
% 0.23/0.44 tff(95,plain,
% 0.23/0.44 ((~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[94])).
% 0.23/0.44 tff(96,plain,
% 0.23/0.44 ((~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(97,plain,
% 0.23/0.44 ((~((((~(xn = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) | sdtlseqdt0(xn, xp))) & (~(xm = xp))) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) | sdtlseqdt0(xm, xp)))) <=> (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(98,axiom,(~((((~(xn = xp)) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp)) | sdtlseqdt0(xn, xp))) & (~(xm = xp))) & (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) | sdtlseqdt0(xm, xp)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2287')).
% 0.23/0.44 tff(99,plain,
% 0.23/0.44 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.23/0.44 tff(100,plain,
% 0.23/0.44 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.23/0.44 tff(101,plain,
% 0.23/0.44 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.23/0.44 tff(102,plain,
% 0.23/0.44 (~((~(xn = xp)) & (sdtlseqdt0(xn, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & (~(xm = xp)) & (sdtlseqdt0(xm, xp) | ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.23/0.45 unexpected number of arguments: (let ((a!1 (refl (~ (not (sdtlseqdt0 xn xp)) (not (sdtlseqdt0 xn xp)))))
% 0.23/0.45 (a!2 (proof-bind (lambda ((W0 $i))
% 0.23/0.45 (let ((a!1 (not (and (aNaturalNumber0 W0)
% 0.23/0.45 (= (sdtpldt0 xn W0) xp)))))
% 0.23/0.45 (refl (~ a!1 a!1))))))
% 0.23/0.45 (a!3 (exists ((W0 $i)) (and (aNaturalNumber0 W0) (= (sdtpldt0 xn W0) xp))))
% 0.23/0.45 (a!4 (forall ((W0 $i))
% 0.23/0.45 (not (and (aNaturalNumber0 W0) (= (sdtpldt0 xn W0) xp)))))
% 0.23/0.45 (a!7 (refl (~ (not (sdtlseqdt0 xm xp)) (not (sdtlseqdt0 xm xp)))))
% 0.23/0.45 (a!8 (proof-bind (lambda ((W0 $i))
% 0.23/0.45 (let ((a!1 (not (and (aNaturalNumber0 W0)
% 0.23/0.45 (= (sdtpldt0 xm W0) xp)))))
% 0.23/0.45 (refl (~ a!1 a!1))))))
% 0.23/0.45 (a!9 (exists ((W0 $i)) (and (aNaturalNumber0 W0) (= (sdtpldt0 xm W0) xp))))
% 0.23/0.45 (a!10 (forall ((W0 $i))
% 0.23/0.45 (not (and (aNaturalNumber0 W0) (= (sdtpldt0 xm W0) xp))))))
% 0.23/0.45 (let ((a!5 (~ (not (or (sdtlseqdt0 xn xp) a!3))
% 0.23/0.45 (and (not (sdtlseqdt0 xn xp)) a!4)))
% 0.23/0.45 (a!11 (~ (not (or (sdtlseqdt0 xm xp) a!9))
% 0.23/0.45 (and (not (sdtlseqdt0 xm xp)) a!10)))
% 0.23/0.45 (a!13 (not (and (not (= xn xp))
% 0.23/0.45 (or (sdtlseqdt0 xn xp) a!3)
% 0.23/0.45 (not (= xm xp))
% 0.23/0.45 (or (sdtlseqdt0 xm xp) a!9))))
% 0.23/0.45 (a!14 (or (= xn xp)
% 0.23/0.45 (and (not (sdtlseqdt0 xn xp)) a!4)
% 0.23/0.45 (= xm xp)
% 0.23/0.45 (and (not (sdtlseqdt0 xm xp)) a!10))))
% 0.23/0.45 (let ((a!6 (nnf-neg a!1 (nnf-neg a!2 (~ (not a!3) a!4)) a!5))
% 0.23/0.45 (a!12 (nnf-neg a!7 (nnf-neg a!8 (~ (not a!9) a!10)) a!11)))
% 0.23/0.45 (nnf-neg (refl (~ (= xn xp) (= xn xp)))
% 0.23/0.45 a!6
% 0.23/0.45 (refl (~ (= xm xp) (= xm xp)))
% 0.23/0.45 a!12
% 0.23/0.45 (~ a!13 a!14)))))
% 0.23/0.45 Proof display could not be completed: unexpected number of arguments
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------