%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM495+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:21:10 AM UTC 2025
% Result : Theorem 1.03s 1.20s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM495+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:18:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.03/1.20 % SZS status Theorem
% 1.03/1.20 % SZS output start Proof
% 1.03/1.20 tff(iLess0_type, type, (
% 1.03/1.20 iLess0: ( $i * $i ) > $o)).
% 1.03/1.20 tff(sdtpldt0_type, type, (
% 1.03/1.20 sdtpldt0: ( $i * $i ) > $i)).
% 1.03/1.20 tff(xp_type, type, (
% 1.03/1.20 xp: $i)).
% 1.03/1.20 tff(xm_type, type, (
% 1.03/1.20 xm: $i)).
% 1.03/1.20 tff(xn_type, type, (
% 1.03/1.20 xn: $i)).
% 1.03/1.20 tff(xr_type, type, (
% 1.03/1.20 xr: $i)).
% 1.03/1.20 tff(sdtmndt0_type, type, (
% 1.03/1.20 sdtmndt0: ( $i * $i ) > $i)).
% 1.03/1.20 tff(aNaturalNumber0_type, type, (
% 1.03/1.20 aNaturalNumber0: $i > $o)).
% 1.03/1.20 tff(doDivides0_type, type, (
% 1.03/1.20 doDivides0: ( $i * $i ) > $o)).
% 1.03/1.20 tff(sdtasdt0_type, type, (
% 1.03/1.20 sdtasdt0: ( $i * $i ) > $i)).
% 1.03/1.20 tff(tptp_fun_W3_5_type, type, (
% 1.03/1.20 tptp_fun_W3_5: ( $i * $i ) > $i)).
% 1.03/1.20 tff(sz10_type, type, (
% 1.03/1.20 sz10: $i)).
% 1.03/1.20 tff(tptp_fun_W3_6_type, type, (
% 1.03/1.20 tptp_fun_W3_6: $i > $i)).
% 1.03/1.20 tff(tptp_fun_W4_7_type, type, (
% 1.03/1.20 tptp_fun_W4_7: $i > $i)).
% 1.03/1.20 tff(sz00_type, type, (
% 1.03/1.20 sz00: $i)).
% 1.03/1.20 tff(isPrime0_type, type, (
% 1.03/1.20 isPrime0: $i > $o)).
% 1.03/1.20 tff(tptp_fun_W3_4_type, type, (
% 1.03/1.20 tptp_fun_W3_4: ( $i * $i ) > $i)).
% 1.03/1.20 tff(tptp_fun_W0_9_type, type, (
% 1.03/1.20 tptp_fun_W0_9: $i)).
% 1.03/1.20 tff(sdtlseqdt0_type, type, (
% 1.03/1.20 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.03/1.20 tff(1,plain,
% 1.03/1.20 ((xr = sdtmndt0(xn, xp)) <=> (xr = sdtmndt0(xn, xp))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(2,axiom,((aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)) & (xr = sdtmndt0(xn, xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1883')).
% 1.03/1.20 tff(3,plain,
% 1.03/1.20 (xr = sdtmndt0(xn, xp)),
% 1.03/1.20 inference(and_elim,[status(thm)],[2])).
% 1.03/1.20 tff(4,plain,
% 1.03/1.20 (xr = sdtmndt0(xn, xp)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[3, 1])).
% 1.03/1.20 tff(5,plain,
% 1.03/1.20 (sdtmndt0(xn, xp) = xr),
% 1.03/1.20 inference(symmetry,[status(thm)],[4])).
% 1.03/1.20 tff(6,plain,
% 1.03/1.20 (sdtpldt0(sdtmndt0(xn, xp), xm) = sdtpldt0(xr, xm)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[5])).
% 1.03/1.20 tff(7,plain,
% 1.03/1.20 (sdtpldt0(xr, xm) = sdtpldt0(sdtmndt0(xn, xp), xm)),
% 1.03/1.20 inference(symmetry,[status(thm)],[6])).
% 1.03/1.20 tff(8,plain,
% 1.03/1.20 (sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[7])).
% 1.03/1.20 tff(9,plain,
% 1.03/1.20 (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtpldt0(xr, xm), xp)),
% 1.03/1.20 inference(symmetry,[status(thm)],[8])).
% 1.03/1.20 tff(10,plain,
% 1.03/1.20 (iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) <=> iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[9])).
% 1.03/1.20 tff(11,plain,
% 1.03/1.20 ((~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) <=> (~iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[10])).
% 1.03/1.20 tff(12,plain,
% 1.03/1.20 (sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xr, xm)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[5])).
% 1.03/1.20 tff(13,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) <=> doDivides0(xp, sdtasdt0(xr, xm))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[12])).
% 1.03/1.20 tff(14,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(xr, xm)) <=> doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))),
% 1.03/1.20 inference(symmetry,[status(thm)],[13])).
% 1.03/1.20 tff(15,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(xr, xm)) <=> doDivides0(xp, sdtasdt0(xr, xm))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(16,axiom,(?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xr, xm) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xr, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1913')).
% 1.03/1.20 tff(17,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(xr, xm))),
% 1.03/1.20 inference(and_elim,[status(thm)],[16])).
% 1.03/1.20 tff(18,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(xr, xm))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[17, 15])).
% 1.03/1.20 tff(19,plain,
% 1.03/1.20 (doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.03/1.20 tff(20,plain,
% 1.03/1.20 (((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))) | (~doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(21,plain,
% 1.03/1.20 ((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[20, 19])).
% 1.03/1.20 tff(22,plain,
% 1.03/1.20 (aNaturalNumber0(sdtmndt0(xn, xp)) <=> aNaturalNumber0(xr)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[5])).
% 1.03/1.20 tff(23,plain,
% 1.03/1.20 (aNaturalNumber0(xr) <=> aNaturalNumber0(sdtmndt0(xn, xp))),
% 1.03/1.20 inference(symmetry,[status(thm)],[22])).
% 1.03/1.20 tff(24,plain,
% 1.03/1.20 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(25,plain,
% 1.03/1.20 (aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xn)),
% 1.03/1.20 inference(and_elim,[status(thm)],[2])).
% 1.03/1.20 tff(26,plain,
% 1.03/1.20 (aNaturalNumber0(xr)),
% 1.03/1.20 inference(and_elim,[status(thm)],[25])).
% 1.03/1.20 tff(27,plain,
% 1.03/1.20 (aNaturalNumber0(xr)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[26, 24])).
% 1.03/1.20 tff(28,plain,
% 1.03/1.20 (aNaturalNumber0(sdtmndt0(xn, xp))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.03/1.20 tff(29,plain,
% 1.03/1.20 (doDivides0(xp, sdtmndt0(xn, xp)) <=> doDivides0(xp, xr)),
% 1.03/1.20 inference(monotonicity,[status(thm)],[5])).
% 1.03/1.20 tff(30,plain,
% 1.03/1.20 (doDivides0(xp, xr) <=> doDivides0(xp, sdtmndt0(xn, xp))),
% 1.03/1.20 inference(symmetry,[status(thm)],[29])).
% 1.03/1.20 tff(31,plain,
% 1.03/1.20 ((~doDivides0(xp, xr)) <=> (~doDivides0(xp, sdtmndt0(xn, xp)))),
% 1.03/1.20 inference(monotonicity,[status(thm)],[30])).
% 1.03/1.20 tff(32,plain,
% 1.03/1.20 ((~doDivides0(xp, xr)) <=> (~doDivides0(xp, xr))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(33,axiom,(~(((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) | doDivides0(xp, xr)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))) | doDivides0(xp, xm))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.03/1.20 tff(34,plain,
% 1.03/1.20 (~((?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) | doDivides0(xp, xr)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))))),
% 1.03/1.20 inference(or_elim,[status(thm)],[33])).
% 1.03/1.20 tff(35,plain,
% 1.03/1.20 (~(?[W0: $i] : (aNaturalNumber0(W0) & (xr = sdtasdt0(xp, W0))) | doDivides0(xp, xr))),
% 1.03/1.20 inference(or_elim,[status(thm)],[34])).
% 1.03/1.20 tff(36,plain,
% 1.03/1.20 (~doDivides0(xp, xr)),
% 1.03/1.20 inference(or_elim,[status(thm)],[35])).
% 1.03/1.20 tff(37,plain,
% 1.03/1.20 (~doDivides0(xp, xr)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[36, 32])).
% 1.03/1.20 tff(38,plain,
% 1.03/1.20 (~doDivides0(xp, sdtmndt0(xn, xp))),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[37, 31])).
% 1.03/1.20 tff(39,plain,
% 1.03/1.20 (((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | doDivides0(xp, sdtmndt0(xn, xp))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(40,plain,
% 1.03/1.20 ((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.03/1.20 tff(41,plain,
% 1.03/1.20 (isPrime0(xp) <=> isPrime0(xp)),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(42,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/sandbox2/benchmark/theBenchmark.p','m__1860')).
% 1.03/1.20 tff(43,plain,
% 1.03/1.20 (((((~(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)))),
% 1.03/1.20 inference(and_elim,[status(thm)],[42])).
% 1.03/1.20 tff(44,plain,
% 1.03/1.20 ((((~(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)),
% 1.03/1.20 inference(and_elim,[status(thm)],[43])).
% 1.03/1.20 tff(45,plain,
% 1.03/1.20 (isPrime0(xp)),
% 1.03/1.20 inference(and_elim,[status(thm)],[44])).
% 1.03/1.20 tff(46,plain,
% 1.03/1.20 (isPrime0(xp)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[45, 41])).
% 1.03/1.20 tff(47,plain,
% 1.03/1.20 ((isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))) | (~isPrime0(xp))),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(48,plain,
% 1.03/1.20 (isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[47, 46])).
% 1.03/1.20 tff(49,plain,
% 1.03/1.20 ((~doDivides0(xp, xm)) <=> (~doDivides0(xp, xm))),
% 1.03/1.20 inference(rewrite,[status(thm)],[])).
% 1.03/1.20 tff(50,plain,
% 1.03/1.20 (~doDivides0(xp, xm)),
% 1.03/1.20 inference(or_elim,[status(thm)],[33])).
% 1.03/1.20 tff(51,plain,
% 1.03/1.20 (~doDivides0(xp, xm)),
% 1.03/1.20 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.03/1.20 tff(52,plain,
% 1.03/1.20 (((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm))))) | doDivides0(xp, xm)),
% 1.03/1.20 inference(tautology,[status(thm)],[])).
% 1.03/1.20 tff(53,plain,
% 1.03/1.20 ((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm))))),
% 1.03/1.20 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.03/1.20 tff(54,plain,
% 1.03/1.20 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite((~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), rewrite((~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) <=> (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0))))), monotonicity(monotonicity(rewrite((~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))) <=> (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), ((isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))) <=> (isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))), ((~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))), rewrite(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), (((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(55,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[54])).
% 1.03/1.21 tff(56,plain,
% 1.03/1.21 (^[W0: $i, W1: $i, W2: $i] : refl(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(57,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[56])).
% 1.03/1.21 tff(58,plain,
% 1.03/1.21 (^[W0: $i, W1: $i, W2: $i] : rewrite(((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(59,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[58])).
% 1.03/1.21 tff(60,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(transitivity,[status(thm)],[59, 57])).
% 1.03/1.21 tff(61,plain,
% 1.03/1.21 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), trans(monotonicity(quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) <=> (~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), ((~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> (~(~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), rewrite((~(~((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))) <=> ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))), ((~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), (![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))) <=> ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), (((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), rewrite(((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), (((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) <=> (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), rewrite((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) <=> (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))))))), rewrite((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) <=> (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0))))), trans(monotonicity(trans(monotonicity(rewrite(((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)) <=> (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))), (((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), rewrite(((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))), (((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))) <=> ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))), (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) <=> ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))), rewrite(((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))), (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) <=> (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2))))))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(62,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[61])).
% 1.03/1.21 tff(63,plain,
% 1.03/1.21 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) <=> (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1))), rewrite(((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) <=> (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0))), rewrite((((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))) <=> (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))), ((((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), rewrite(((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))), ((((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(64,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[63])).
% 1.03/1.21 tff(65,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(66,plain,
% 1.03/1.21 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) <=> ((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))), trans(monotonicity(trans(monotonicity(rewrite((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) <=> (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0))), rewrite((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) <=> (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))), (((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))), rewrite(((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))), (((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0))))), ((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))) <=> (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))))), rewrite((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))), ((iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)))))), (((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))) <=> (((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))))), rewrite((((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), (((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))))),
% 1.03/1.21 inference(bind,[status(th)],[])).
% 1.03/1.21 tff(67,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)))))) <=> ![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 1.03/1.21 inference(quant_intro,[status(thm)],[66])).
% 1.03/1.21 tff(68,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((((((~(W2 = sz00)) & (~(W2 = sz10))) & ![W3: $i] : (((aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4)))) & doDivides0(W3, W2)) => ((W3 = sz10) | (W3 = W2)))) | isPrime0(W2)) & (?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))) | doDivides0(W2, sdtasdt0(W0, W1)))) => (iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1799')).
% 1.03/1.21 tff(69,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.03/1.21 tff(70,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((?[W3: $i] : (aNaturalNumber0(W3) & (W1 = sdtasdt0(W2, W3))) & doDivides0(W2, W1)) | (?[W3: $i] : (aNaturalNumber0(W3) & (W0 = sdtasdt0(W2, W3))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((isPrime0(W2) | ((~(W2 = sz00)) & (~(W2 = sz10)) & ![W3: $i] : ((W3 = W2) | (W3 = sz10) | (~(aNaturalNumber0(W3) & ?[W4: $i] : (aNaturalNumber0(W4) & (W2 = sdtasdt0(W3, W4))) & doDivides0(W3, W2)))))) & (doDivides0(W2, sdtasdt0(W0, W1)) | ?[W3: $i] : (aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[69, 65])).
% 1.03/1.21 tff(71,plain,(
% 1.03/1.21 ![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))) & doDivides0(W2, W1)) | ((aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) & doDivides0(W2, W0)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & (aNaturalNumber0(tptp_fun_W3_6(W2)) & (aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) & doDivides0(tptp_fun_W3_6(W2), W2))))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3)))))))),
% 1.03/1.21 inference(skolemize,[status(sab)],[70])).
% 1.03/1.21 tff(72,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | ((~doDivides0(W2, sdtasdt0(W0, W1))) & ![W3: $i] : (~(aNaturalNumber0(W3) & (sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))) | (aNaturalNumber0(tptp_fun_W3_4(W2, W1)) & (W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1))) & doDivides0(W2, W1)) | (aNaturalNumber0(tptp_fun_W3_5(W2, W0)) & (W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0))) & doDivides0(W2, W0)) | ((~isPrime0(W2)) & ((W2 = sz00) | (W2 = sz10) | ((~(tptp_fun_W3_6(W2) = W2)) & (~(tptp_fun_W3_6(W2) = sz10)) & aNaturalNumber0(tptp_fun_W3_6(W2)) & aNaturalNumber0(tptp_fun_W4_7(W2)) & (W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2))) & doDivides0(tptp_fun_W3_6(W2), W2)))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[71, 64])).
% 1.03/1.21 tff(73,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[72, 62])).
% 1.03/1.21 tff(74,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[73, 60])).
% 1.03/1.21 tff(75,plain,
% 1.03/1.21 (![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[74, 55])).
% 1.03/1.21 tff(76,plain,
% 1.03/1.21 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(77,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 1.03/1.21 tff(78,plain,
% 1.03/1.21 (aNaturalNumber0(xp)),
% 1.03/1.21 inference(and_elim,[status(thm)],[77])).
% 1.03/1.21 tff(79,plain,
% 1.03/1.21 (aNaturalNumber0(xp)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[78, 76])).
% 1.03/1.21 tff(80,plain,
% 1.03/1.21 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 1.03/1.21 inference(rewrite,[status(thm)],[])).
% 1.03/1.21 tff(81,plain,
% 1.03/1.21 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 1.03/1.21 inference(and_elim,[status(thm)],[77])).
% 1.03/1.21 tff(82,plain,
% 1.03/1.21 (aNaturalNumber0(xm)),
% 1.03/1.21 inference(and_elim,[status(thm)],[81])).
% 1.03/1.21 tff(83,plain,
% 1.03/1.21 (aNaturalNumber0(xm)),
% 1.03/1.21 inference(modus_ponens,[status(thm)],[82, 80])).
% 1.03/1.21 tff(84,plain,
% 1.03/1.22 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))),
% 1.03/1.22 inference(rewrite,[status(thm)],[])).
% 1.03/1.22 tff(85,plain,
% 1.03/1.22 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))))) <=> ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(86,plain,
% 1.06/1.22 ((~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))))) <=> (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(87,plain,
% 1.06/1.22 ((~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) <=> (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10)))))))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(88,plain,
% 1.06/1.22 ((~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) <=> (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(89,plain,
% 1.06/1.22 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3)))))))) <=> ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))),
% 1.06/1.22 inference(monotonicity,[status(thm)],[88, 87, 86])).
% 1.06/1.22 tff(90,plain,
% 1.06/1.22 (((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3)))))))) <=> ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))),
% 1.06/1.22 inference(transitivity,[status(thm)],[89, 85])).
% 1.06/1.22 tff(91,plain,
% 1.06/1.22 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))))))),
% 1.06/1.22 inference(monotonicity,[status(thm)],[90])).
% 1.06/1.22 tff(92,plain,
% 1.06/1.22 (((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)))))),
% 1.06/1.22 inference(transitivity,[status(thm)],[91, 84])).
% 1.06/1.22 tff(93,plain,
% 1.06/1.22 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | ((~aNaturalNumber0(xp)) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~doDivides0(xp, sdtmndt0(xn, xp))))) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((tptp_fun_W3_6(xp) = sz10) | (tptp_fun_W3_6(xp) = xp) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~doDivides0(tptp_fun_W3_6(xp), xp)))))))) | (~(doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))))))),
% 1.06/1.22 inference(quant_inst,[status(thm)],[])).
% 1.06/1.22 tff(94,plain,
% 1.06/1.22 ((~![W0: $i, W1: $i, W2: $i] : ((~aNaturalNumber0(W2)) | (~iLess0(sdtpldt0(sdtpldt0(W0, W1), W2), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~((~doDivides0(W2, W1)) | (~aNaturalNumber0(tptp_fun_W3_4(W2, W1))) | (~(W1 = sdtasdt0(W2, tptp_fun_W3_4(W2, W1)))))) | (~((~aNaturalNumber0(tptp_fun_W3_5(W2, W0))) | (~(W0 = sdtasdt0(W2, tptp_fun_W3_5(W2, W0)))) | (~doDivides0(W2, W0)))) | (~(isPrime0(W2) | (~((W2 = sz00) | (W2 = sz10) | (~((tptp_fun_W3_6(W2) = sz10) | (tptp_fun_W3_6(W2) = W2) | (~aNaturalNumber0(tptp_fun_W3_6(W2))) | (~aNaturalNumber0(tptp_fun_W4_7(W2))) | (~(W2 = sdtasdt0(tptp_fun_W3_6(W2), tptp_fun_W4_7(W2)))) | (~doDivides0(tptp_fun_W3_6(W2), W2)))))))) | (~(doDivides0(W2, sdtasdt0(W0, W1)) | (~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(W0, W1) = sdtasdt0(W2, W3))))))))) | (~((~doDivides0(xp, xm)) | (~aNaturalNumber0(tptp_fun_W3_4(xp, xm))) | (~(xm = sdtasdt0(xp, tptp_fun_W3_4(xp, xm)))))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~(isPrime0(xp) | (~((xp = sz00) | (xp = sz10) | (~((~doDivides0(tptp_fun_W3_6(xp), xp)) | (~(xp = sdtasdt0(tptp_fun_W3_6(xp), tptp_fun_W4_7(xp)))) | (~aNaturalNumber0(tptp_fun_W4_7(xp))) | (~aNaturalNumber0(tptp_fun_W3_6(xp))) | (tptp_fun_W3_6(xp) = xp) | (tptp_fun_W3_6(xp) = sz10))))))) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.06/1.22 tff(95,plain,
% 1.06/1.22 ((~aNaturalNumber0(sdtmndt0(xn, xp))) | (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~((~doDivides0(xp, sdtmndt0(xn, xp))) | (~(sdtmndt0(xn, xp) = sdtasdt0(xp, tptp_fun_W3_5(xp, sdtmndt0(xn, xp))))) | (~aNaturalNumber0(tptp_fun_W3_5(xp, sdtmndt0(xn, xp)))))) | (~((~![W3: $i] : ((~aNaturalNumber0(W3)) | (~(sdtasdt0(sdtmndt0(xn, xp), xm) = sdtasdt0(xp, W3))))) | doDivides0(xp, sdtasdt0(sdtmndt0(xn, xp), xm))))),
% 1.06/1.22 inference(unit_resolution,[status(thm)],[94, 83, 79, 75, 53, 48])).
% 1.06/1.22 tff(96,plain,
% 1.06/1.22 (~iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.06/1.22 inference(unit_resolution,[status(thm)],[95, 40, 28, 21])).
% 1.06/1.22 tff(97,plain,
% 1.06/1.22 (~iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[96, 11])).
% 1.06/1.22 tff(98,plain,
% 1.06/1.22 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(99,axiom,(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) & sdtlseqdt0(xp, xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1870')).
% 1.06/1.22 tff(100,plain,
% 1.06/1.22 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn))),
% 1.06/1.22 inference(and_elim,[status(thm)],[99])).
% 1.06/1.22 tff(101,plain,
% 1.06/1.22 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[100, 98])).
% 1.06/1.22 tff(102,plain,(
% 1.06/1.22 aNaturalNumber0(W0!9) & (sdtpldt0(xp, W0!9) = xn)),
% 1.06/1.22 inference(skolemize,[status(sab)],[101])).
% 1.06/1.22 tff(103,plain,
% 1.06/1.22 (sdtpldt0(xp, W0!9) = xn),
% 1.06/1.22 inference(and_elim,[status(thm)],[102])).
% 1.06/1.22 tff(104,plain,
% 1.06/1.22 (aNaturalNumber0(W0!9)),
% 1.06/1.22 inference(and_elim,[status(thm)],[102])).
% 1.06/1.22 tff(105,plain,
% 1.06/1.22 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.06/1.22 inference(bind,[status(th)],[])).
% 1.06/1.22 tff(106,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.22 inference(quant_intro,[status(thm)],[105])).
% 1.06/1.22 tff(107,plain,
% 1.06/1.22 (^[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(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.06/1.22 inference(bind,[status(th)],[])).
% 1.06/1.22 tff(108,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.22 inference(quant_intro,[status(thm)],[107])).
% 1.06/1.22 tff(109,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(110,plain,
% 1.06/1.22 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 1.06/1.22 inference(bind,[status(th)],[])).
% 1.06/1.22 tff(111,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.06/1.22 inference(quant_intro,[status(thm)],[110])).
% 1.06/1.22 tff(112,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddComm')).
% 1.06/1.22 tff(113,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.06/1.22 tff(114,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[113, 109])).
% 1.06/1.22 tff(115,plain,(
% 1.06/1.22 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 1.06/1.22 inference(skolemize,[status(sab)],[114])).
% 1.06/1.22 tff(116,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[115, 108])).
% 1.06/1.22 tff(117,plain,
% 1.06/1.22 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.22 inference(modus_ponens,[status(thm)],[116, 106])).
% 1.06/1.22 tff(118,plain,
% 1.06/1.22 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(119,plain,
% 1.06/1.22 (((sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)))),
% 1.06/1.22 inference(rewrite,[status(thm)],[])).
% 1.06/1.22 tff(120,plain,
% 1.06/1.22 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9))))),
% 1.06/1.22 inference(monotonicity,[status(thm)],[119])).
% 1.06/1.23 tff(121,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)))),
% 1.06/1.23 inference(transitivity,[status(thm)],[120, 118])).
% 1.06/1.23 tff(122,plain,
% 1.06/1.23 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(123,plain,
% 1.06/1.23 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.06/1.23 tff(124,plain,
% 1.06/1.23 (sdtpldt0(W0!9, xp) = sdtpldt0(xp, W0!9)),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[123, 117, 79, 104])).
% 1.06/1.23 tff(125,plain,
% 1.06/1.23 (sdtpldt0(W0!9, xp) = xn),
% 1.06/1.23 inference(transitivity,[status(thm)],[124, 103])).
% 1.06/1.23 tff(126,plain,
% 1.06/1.23 (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(xn, xm)),
% 1.06/1.23 inference(monotonicity,[status(thm)],[125])).
% 1.06/1.23 tff(127,plain,
% 1.06/1.23 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(128,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[127])).
% 1.06/1.23 tff(129,plain,
% 1.06/1.23 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(130,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[129])).
% 1.06/1.23 tff(131,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(132,plain,
% 1.06/1.23 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 1.06/1.23 inference(bind,[status(th)],[])).
% 1.06/1.23 tff(133,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.06/1.23 inference(quant_intro,[status(thm)],[132])).
% 1.06/1.23 tff(134,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mAddAsso')).
% 1.06/1.23 tff(135,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[134, 133])).
% 1.06/1.23 tff(136,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[135, 131])).
% 1.06/1.23 tff(137,plain,(
% 1.06/1.23 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 1.06/1.23 inference(skolemize,[status(sab)],[136])).
% 1.06/1.23 tff(138,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[137, 130])).
% 1.06/1.23 tff(139,plain,
% 1.06/1.23 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[138, 128])).
% 1.06/1.23 tff(140,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(141,plain,
% 1.06/1.23 (((sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(142,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm)))))),
% 1.06/1.23 inference(monotonicity,[status(thm)],[141])).
% 1.06/1.23 tff(143,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))))),
% 1.06/1.23 inference(transitivity,[status(thm)],[142, 140])).
% 1.06/1.23 tff(144,plain,
% 1.06/1.23 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)))),
% 1.06/1.23 inference(quant_inst,[status(thm)],[])).
% 1.06/1.23 tff(145,plain,
% 1.06/1.23 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!9)) | (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm)))),
% 1.06/1.23 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.06/1.23 tff(146,plain,
% 1.06/1.23 (sdtpldt0(sdtpldt0(W0!9, xp), xm) = sdtpldt0(W0!9, sdtpldt0(xp, xm))),
% 1.06/1.23 inference(unit_resolution,[status(thm)],[145, 139, 83, 79, 104])).
% 1.06/1.23 tff(147,plain,
% 1.06/1.23 (sdtpldt0(W0!9, sdtpldt0(xp, xm)) = sdtpldt0(sdtpldt0(W0!9, xp), xm)),
% 1.06/1.23 inference(symmetry,[status(thm)],[146])).
% 1.06/1.23 tff(148,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(149,plain,
% 1.06/1.23 (((sdtpldt0(xp, xm) = sdtpldt0(xm, xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp)))),
% 1.06/1.23 inference(rewrite,[status(thm)],[])).
% 1.06/1.23 tff(150,plain,
% 1.06/1.23 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xp, xm) = sdtpldt0(xm, xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[149])).
% 1.07/1.23 tff(151,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xp, xm) = sdtpldt0(xm, xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp)))),
% 1.07/1.23 inference(transitivity,[status(thm)],[150, 148])).
% 1.07/1.23 tff(152,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xp, xm) = sdtpldt0(xm, xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(153,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (sdtpldt0(xp, xm) = sdtpldt0(xm, xp))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.07/1.23 tff(154,plain,
% 1.07/1.23 (sdtpldt0(xp, xm) = sdtpldt0(xm, xp)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[153, 117, 83, 79])).
% 1.07/1.23 tff(155,plain,
% 1.07/1.23 (sdtpldt0(xm, xp) = sdtpldt0(xp, xm)),
% 1.07/1.23 inference(symmetry,[status(thm)],[154])).
% 1.07/1.23 tff(156,plain,
% 1.07/1.23 (sdtpldt0(W0!9, sdtpldt0(xm, xp)) = sdtpldt0(W0!9, sdtpldt0(xp, xm))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[155])).
% 1.07/1.23 tff(157,plain,
% 1.07/1.23 (sdtlseqdt0(xp, xn) <=> sdtlseqdt0(xp, xn)),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(158,plain,
% 1.07/1.23 (sdtlseqdt0(xp, xn)),
% 1.07/1.23 inference(and_elim,[status(thm)],[99])).
% 1.07/1.23 tff(159,plain,
% 1.07/1.23 (sdtlseqdt0(xp, xn)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.07/1.23 tff(160,plain,
% 1.07/1.23 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(161,plain,
% 1.07/1.23 (aNaturalNumber0(xn)),
% 1.07/1.23 inference(and_elim,[status(thm)],[81])).
% 1.07/1.23 tff(162,plain,
% 1.07/1.23 (aNaturalNumber0(xn)),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.07/1.23 tff(163,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : refl(((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(164,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[163])).
% 1.07/1.23 tff(165,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : rewrite(((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(166,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[165])).
% 1.07/1.23 tff(167,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[166, 164])).
% 1.07/1.23 tff(168,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(trans(monotonicity(rewrite((aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> ((W2 = sdtmndt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))))), rewrite(((W2 = sdtmndt0(W1, W0)) <=> (~((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))), rewrite((~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))), (((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0))))))), (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) <=> ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(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))))), ((![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~sdtlseqdt0(W0, W1))))), rewrite((![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~sdtlseqdt0(W0, W1))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))), ((![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(169,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[168])).
% 1.07/1.23 tff(170,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(171,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))) <=> ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~sdtlseqdt0(W0, W1)) | ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(172,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))))) <=> ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[171])).
% 1.07/1.23 tff(173,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtlseqdt0(W0, W1) => ![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefDiff')).
% 1.07/1.23 tff(174,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[173, 172])).
% 1.07/1.23 tff(175,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[174, 170])).
% 1.07/1.23 tff(176,plain,(
% 1.07/1.23 ![W0: $i, W1: $i] : (![W2: $i] : ((W2 = sdtmndt0(W1, W0)) <=> (aNaturalNumber0(W2) & (sdtpldt0(W0, W2) = W1))) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~sdtlseqdt0(W0, W1)))),
% 1.07/1.23 inference(skolemize,[status(sab)],[175])).
% 1.07/1.23 tff(177,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[176, 169])).
% 1.07/1.23 tff(178,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[177, 167])).
% 1.07/1.23 tff(179,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(180,plain,
% 1.07/1.23 (((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xp, xn)) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp))))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(181,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xp, xn)) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[180])).
% 1.07/1.23 tff(182,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xp, xn)) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))) <=> ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[181, 179])).
% 1.07/1.23 tff(183,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | ((~aNaturalNumber0(xn)) | (~sdtlseqdt0(xp, xn)) | (~aNaturalNumber0(xp)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp)))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(184,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : ((~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(W0, W2) = W1))) <=> (W2 = sdtmndt0(W1, W0)))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, xn)) | ![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[183, 182])).
% 1.07/1.23 tff(185,plain,
% 1.07/1.23 (![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[184, 178, 162, 79, 159])).
% 1.07/1.23 tff(186,plain,
% 1.07/1.23 ((~![W2: $i] : (~(((~aNaturalNumber0(W2)) | (~(sdtpldt0(xp, W2) = xn))) <=> (W2 = sdtmndt0(xn, xp))))) | (~(((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))) <=> (W0!9 = sdtmndt0(xn, xp))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(187,plain,
% 1.07/1.23 (~(((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))) <=> (W0!9 = sdtmndt0(xn, xp)))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[186, 185])).
% 1.07/1.23 tff(188,plain,
% 1.07/1.23 ((~((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn)))) | (~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))),
% 1.07/1.23 inference(tautology,[status(thm)],[])).
% 1.07/1.23 tff(189,plain,
% 1.07/1.23 (~((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn)))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[188, 104, 103])).
% 1.07/1.23 tff(190,plain,
% 1.07/1.23 ((((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))) <=> (W0!9 = sdtmndt0(xn, xp))) | ((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))) | (W0!9 = sdtmndt0(xn, xp))),
% 1.07/1.23 inference(tautology,[status(thm)],[])).
% 1.07/1.23 tff(191,plain,
% 1.07/1.23 ((((~aNaturalNumber0(W0!9)) | (~(sdtpldt0(xp, W0!9) = xn))) <=> (W0!9 = sdtmndt0(xn, xp))) | (W0!9 = sdtmndt0(xn, xp))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[190, 189])).
% 1.07/1.23 tff(192,plain,
% 1.07/1.23 (W0!9 = sdtmndt0(xn, xp)),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[191, 187])).
% 1.07/1.23 tff(193,plain,
% 1.07/1.23 (sdtmndt0(xn, xp) = W0!9),
% 1.07/1.23 inference(symmetry,[status(thm)],[192])).
% 1.07/1.23 tff(194,plain,
% 1.07/1.23 (sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp)) = sdtpldt0(W0!9, sdtpldt0(xm, xp))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[193])).
% 1.07/1.23 tff(195,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(196,plain,
% 1.07/1.23 (((sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp)))) <=> ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(197,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp)))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[196])).
% 1.07/1.23 tff(198,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[197, 195])).
% 1.07/1.23 tff(199,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtmndt0(xn, xp))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(200,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.07/1.23 tff(201,plain,
% 1.07/1.23 ((~aNaturalNumber0(sdtmndt0(xn, xp))) | (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp)))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[200, 139, 83, 79])).
% 1.07/1.23 tff(202,plain,
% 1.07/1.23 (sdtpldt0(sdtpldt0(sdtmndt0(xn, xp), xm), xp) = sdtpldt0(sdtmndt0(xn, xp), sdtpldt0(xm, xp))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[201, 28])).
% 1.07/1.23 tff(203,plain,
% 1.07/1.23 (sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(xn, xm)),
% 1.07/1.23 inference(transitivity,[status(thm)],[8, 202, 194, 156, 147, 126])).
% 1.07/1.23 tff(204,plain,
% 1.07/1.23 (aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp)) <=> aNaturalNumber0(sdtpldt0(xn, xm))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[203])).
% 1.07/1.23 tff(205,plain,
% 1.07/1.23 (aNaturalNumber0(sdtpldt0(xn, xm)) <=> aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))),
% 1.07/1.23 inference(symmetry,[status(thm)],[204])).
% 1.07/1.23 tff(206,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(207,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[206])).
% 1.07/1.23 tff(208,plain,
% 1.07/1.23 (^[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(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtpldt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(209,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[208])).
% 1.07/1.23 tff(210,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(211,plain,
% 1.07/1.23 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 1.07/1.23 inference(bind,[status(th)],[])).
% 1.07/1.23 tff(212,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.07/1.23 inference(quant_intro,[status(thm)],[211])).
% 1.07/1.23 tff(213,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB')).
% 1.07/1.23 tff(214,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.07/1.23 tff(215,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[214, 210])).
% 1.07/1.23 tff(216,plain,(
% 1.07/1.23 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 1.07/1.23 inference(skolemize,[status(sab)],[215])).
% 1.07/1.23 tff(217,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.07/1.23 tff(218,plain,
% 1.07/1.23 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[217, 207])).
% 1.07/1.23 tff(219,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtpldt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(220,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn)))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(221,plain,
% 1.07/1.23 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | aNaturalNumber0(sdtpldt0(xn, xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(xn))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.07/1.23 tff(222,plain,
% 1.07/1.23 (aNaturalNumber0(sdtpldt0(xn, xm))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[221, 218, 162, 83])).
% 1.07/1.23 tff(223,plain,
% 1.07/1.23 (aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[222, 205])).
% 1.07/1.23 tff(224,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(225,plain,
% 1.07/1.23 ((aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(226,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[225])).
% 1.07/1.23 tff(227,plain,
% 1.07/1.23 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[226, 224])).
% 1.07/1.24 tff(228,plain,
% 1.07/1.24 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(229,plain,
% 1.07/1.24 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtpldt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtpldt0(xn, xm))) | aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.07/1.24 tff(230,plain,
% 1.07/1.24 (aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[229, 218, 79, 222])).
% 1.07/1.24 tff(231,plain,
% 1.07/1.24 (sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) <=> sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(232,axiom,(((~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(xr, xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))) & sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2062')).
% 1.07/1.24 tff(233,plain,
% 1.07/1.24 (sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(and_elim,[status(thm)],[232])).
% 1.07/1.24 tff(234,plain,
% 1.07/1.24 (sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[233, 231])).
% 1.07/1.24 tff(235,plain,
% 1.07/1.24 ((~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))) <=> (~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(236,plain,
% 1.07/1.24 ((~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtpldt0(sdtpldt0(xr, xm), xp), W0) = sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.24 inference(and_elim,[status(thm)],[232])).
% 1.07/1.24 tff(237,plain,
% 1.07/1.24 (~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(and_elim,[status(thm)],[236])).
% 1.07/1.24 tff(238,plain,
% 1.07/1.24 (~(sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[237, 235])).
% 1.07/1.24 tff(239,plain,
% 1.07/1.24 (^[W0: $i, W1: $i] : refl(((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(240,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[239])).
% 1.07/1.24 tff(241,plain,
% 1.07/1.24 (^[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(((~(W0 = W1)) & sdtlseqdt0(W0, W1)) <=> (~((W0 = W1) | (~sdtlseqdt0(W0, W1))))), ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) <=> (~(~((W0 = W1) | (~sdtlseqdt0(W0, W1))))))), rewrite((~(~((W0 = W1) | (~sdtlseqdt0(W0, W1))))) <=> ((W0 = W1) | (~sdtlseqdt0(W0, W1)))), ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) <=> ((W0 = W1) | (~sdtlseqdt0(W0, W1))))), ((iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> (iLess0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = W1) | (~sdtlseqdt0(W0, W1)))))), rewrite((iLess0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((W0 = W1) | (~sdtlseqdt0(W0, W1)))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))), ((iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(242,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[241])).
% 1.07/1.24 tff(243,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1)))) <=> ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(244,plain,
% 1.07/1.24 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1)) <=> ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~((~(W0 = W1)) & sdtlseqdt0(W0, W1))) | iLess0(W0, W1))) <=> (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(245,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1))) <=> ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[244])).
% 1.07/1.24 tff(246,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (((~(W0 = W1)) & sdtlseqdt0(W0, W1)) => iLess0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mIH_03')).
% 1.07/1.24 tff(247,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.07/1.24 tff(248,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.07/1.24 tff(249,plain,(
% 1.07/1.24 ![W0: $i, W1: $i] : (iLess0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~((~(W0 = W1)) & sdtlseqdt0(W0, W1))))),
% 1.07/1.24 inference(skolemize,[status(sab)],[248])).
% 1.07/1.24 tff(250,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[249, 242])).
% 1.07/1.24 tff(251,plain,
% 1.07/1.24 (![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[250, 240])).
% 1.07/1.24 tff(252,plain,
% 1.07/1.24 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(253,plain,
% 1.07/1.24 (((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp)))) <=> ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(254,plain,
% 1.07/1.24 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[253])).
% 1.07/1.24 tff(255,plain,
% 1.07/1.24 (((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[254, 252])).
% 1.07/1.24 tff(256,plain,
% 1.07/1.24 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(257,plain,
% 1.07/1.24 ((~![W0: $i, W1: $i] : ((W0 = W1) | iLess0(W0, W1) | (~aNaturalNumber0(W1)) | (~sdtlseqdt0(W0, W1)) | (~aNaturalNumber0(W0)))) | (sdtpldt0(sdtpldt0(xr, xm), xp) = sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)) | (~aNaturalNumber0(sdtpldt0(sdtpldt0(xn, xm), xp))) | (~sdtlseqdt0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.07/1.24 tff(258,plain,
% 1.07/1.24 ((~aNaturalNumber0(sdtpldt0(sdtpldt0(xr, xm), xp))) | iLess0(sdtpldt0(sdtpldt0(xr, xm), xp), sdtpldt0(sdtpldt0(xn, xm), xp))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[257, 251, 238, 234, 230])).
% 1.07/1.24 tff(259,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[258, 223, 97])).
% 1.07/1.24 % SZS output end Proof
% 1.07/1.25 % E exiting
%------------------------------------------------------------------------------