%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM518+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:15 AM UTC 2025
% Result : Theorem 0.54s 0.73s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM518+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:23:31 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.54/0.73 % SZS status Theorem
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 tff(sz00_type, type, (
% 0.54/0.73 sz00: $i)).
% 0.54/0.73 tff(sdtasdt0_type, type, (
% 0.54/0.73 sdtasdt0: ( $i * $i ) > $i)).
% 0.54/0.73 tff(tptp_fun_W0_15_type, type, (
% 0.54/0.73 tptp_fun_W0_15: $i)).
% 0.54/0.73 tff(xr_type, type, (
% 0.54/0.73 xr: $i)).
% 0.54/0.73 tff(aNaturalNumber0_type, type, (
% 0.54/0.73 aNaturalNumber0: $i > $o)).
% 0.54/0.73 tff(xk_type, type, (
% 0.54/0.73 xk: $i)).
% 0.54/0.73 tff(doDivides0_type, type, (
% 0.54/0.73 doDivides0: ( $i * $i ) > $o)).
% 0.54/0.73 tff(sz10_type, type, (
% 0.54/0.73 sz10: $i)).
% 0.54/0.73 tff(isPrime0_type, type, (
% 0.54/0.73 isPrime0: $i > $o)).
% 0.54/0.73 tff(sdtsldt0_type, type, (
% 0.54/0.73 sdtsldt0: ( $i * $i ) > $i)).
% 0.54/0.73 tff(xn_type, type, (
% 0.54/0.73 xn: $i)).
% 0.54/0.73 tff(tptp_fun_W0_20_type, type, (
% 0.54/0.73 tptp_fun_W0_20: $i)).
% 0.54/0.73 tff(xp_type, type, (
% 0.54/0.73 xp: $i)).
% 0.54/0.73 tff(sdtlseqdt0_type, type, (
% 0.54/0.73 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.54/0.73 tff(sdtpldt0_type, type, (
% 0.54/0.73 sdtpldt0: ( $i * $i ) > $i)).
% 0.54/0.73 tff(tptp_fun_W0_19_type, type, (
% 0.54/0.73 tptp_fun_W0_19: $i)).
% 0.54/0.73 tff(xm_type, type, (
% 0.54/0.73 xm: $i)).
% 0.54/0.73 tff(1,plain,
% 0.54/0.73 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(2,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2342')).
% 0.54/0.73 tff(3,plain,
% 0.54/0.73 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 0.54/0.73 inference(and_elim,[status(thm)],[2])).
% 0.54/0.73 tff(4,plain,
% 0.54/0.73 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 0.54/0.73 inference(and_elim,[status(thm)],[3])).
% 0.54/0.73 tff(5,plain,
% 0.54/0.73 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 0.54/0.73 inference(and_elim,[status(thm)],[4])).
% 0.54/0.73 tff(6,plain,
% 0.54/0.73 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 0.54/0.73 inference(and_elim,[status(thm)],[5])).
% 0.54/0.73 tff(7,plain,
% 0.54/0.73 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.54/0.73 inference(and_elim,[status(thm)],[6])).
% 0.54/0.73 tff(8,plain,
% 0.54/0.73 (aNaturalNumber0(xr)),
% 0.54/0.73 inference(and_elim,[status(thm)],[7])).
% 0.54/0.73 tff(9,plain,
% 0.54/0.73 (aNaturalNumber0(xr)),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.54/0.73 tff(10,plain,
% 0.54/0.73 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(11,plain,
% 0.54/0.73 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[10])).
% 0.54/0.73 tff(12,plain,
% 0.54/0.73 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(13,plain,
% 0.54/0.73 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[12])).
% 0.54/0.73 tff(14,plain,
% 0.54/0.73 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(15,plain,
% 0.54/0.73 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(16,plain,
% 0.54/0.74 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[15])).
% 0.54/0.74 tff(17,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m_MulZero')).
% 0.54/0.74 tff(18,plain,
% 0.54/0.74 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.54/0.74 tff(19,plain,
% 0.54/0.74 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.54/0.74 tff(20,plain,(
% 0.54/0.74 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 0.54/0.74 inference(skolemize,[status(sab)],[19])).
% 0.54/0.74 tff(21,plain,
% 0.54/0.74 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.54/0.74 tff(22,plain,
% 0.54/0.74 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.54/0.74 tff(23,plain,
% 0.54/0.74 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(24,plain,
% 0.54/0.74 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(25,plain,
% 0.54/0.74 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr)))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.54/0.74 tff(26,plain,
% 0.54/0.74 (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.54/0.74 tff(27,plain,
% 0.54/0.74 (((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr)))) | (sdtasdt0(xr, sz00) = sz00)),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(28,plain,
% 0.54/0.74 (sdtasdt0(xr, sz00) = sz00),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.54/0.74 tff(29,plain,
% 0.54/0.74 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(30,axiom,(?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0))) & doDivides0(xr, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2487')).
% 0.54/0.74 tff(31,plain,
% 0.54/0.74 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 0.54/0.74 inference(and_elim,[status(thm)],[30])).
% 0.54/0.74 tff(32,plain,
% 0.54/0.74 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.54/0.74 tff(33,plain,(
% 0.54/0.74 aNaturalNumber0(W0!15) & (xn = sdtasdt0(xr, W0!15))),
% 0.54/0.74 inference(skolemize,[status(sab)],[32])).
% 0.54/0.74 tff(34,plain,
% 0.54/0.74 (xn = sdtasdt0(xr, W0!15)),
% 0.54/0.74 inference(and_elim,[status(thm)],[33])).
% 0.54/0.74 tff(35,plain,
% 0.54/0.74 (sdtasdt0(xr, W0!15) = xn),
% 0.54/0.74 inference(symmetry,[status(thm)],[34])).
% 0.54/0.74 tff(36,plain,
% 0.54/0.74 (sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) <=> sdtlseqdt0(xp, xn)),
% 0.54/0.74 inference(monotonicity,[status(thm)],[35])).
% 0.54/0.74 tff(37,plain,
% 0.54/0.74 (sdtlseqdt0(xp, xn) <=> sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 0.54/0.74 inference(symmetry,[status(thm)],[36])).
% 0.54/0.74 tff(38,plain,
% 0.54/0.74 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[37])).
% 0.54/0.74 tff(39,plain,
% 0.54/0.74 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, xn))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(40,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) | sdtlseqdt0(xp, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1870')).
% 0.54/0.74 tff(41,plain,
% 0.54/0.74 (~sdtlseqdt0(xp, xn)),
% 0.54/0.74 inference(or_elim,[status(thm)],[40])).
% 0.54/0.74 tff(42,plain,
% 0.54/0.74 (~sdtlseqdt0(xp, xn)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[41, 39])).
% 0.54/0.74 tff(43,plain,
% 0.54/0.74 (~sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.54/0.74 tff(44,plain,
% 0.54/0.74 ((~doDivides0(xp, xm)) <=> (~doDivides0(xp, xm))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(45,axiom,(~(((?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))) | doDivides0(xp, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.54/0.74 tff(46,plain,
% 0.54/0.74 (~doDivides0(xp, xm)),
% 0.54/0.74 inference(or_elim,[status(thm)],[45])).
% 0.54/0.74 tff(47,plain,
% 0.54/0.74 (~doDivides0(xp, xm)),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[46, 44])).
% 0.54/0.74 tff(48,plain,
% 0.54/0.74 (((~doDivides0(xp, xm)) | (~(xm = sdtasdt0(xp, W0!19))) | (~aNaturalNumber0(W0!19))) | doDivides0(xp, xm)),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(49,plain,
% 0.54/0.74 ((~doDivides0(xp, xm)) | (~(xm = sdtasdt0(xp, W0!19))) | (~aNaturalNumber0(W0!19))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.54/0.74 tff(50,plain,
% 0.54/0.74 (((aNaturalNumber0(W0!19) & (xm = sdtasdt0(xp, W0!19)) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & aNaturalNumber0(W0!20) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0!20)) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> ((~((~doDivides0(xp, xm)) | (~(xm = sdtasdt0(xp, W0!19))) | (~aNaturalNumber0(W0!19)))) | (~((~aNaturalNumber0(sdtsldt0(xn, xr))) | (~(xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) | (~aNaturalNumber0(W0!20)) | (~(sdtsldt0(xn, xr) = sdtasdt0(xp, W0!20))) | (~doDivides0(xp, sdtsldt0(xn, xr))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(51,plain,
% 0.54/0.74 ((((aNaturalNumber0(W0!19) & (xm = sdtasdt0(xp, W0!19))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & (aNaturalNumber0(W0!20) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0!20))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> ((aNaturalNumber0(W0!19) & (xm = sdtasdt0(xp, W0!19)) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & aNaturalNumber0(W0!20) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0!20)) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(52,plain,
% 0.54/0.74 ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))) <=> (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(53,plain,
% 0.54/0.74 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(54,plain,
% 0.54/0.74 (((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[53, 52])).
% 0.54/0.74 tff(55,plain,
% 0.54/0.74 (((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(56,plain,
% 0.54/0.74 (((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(57,plain,
% 0.54/0.74 (((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) <=> (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(58,plain,
% 0.54/0.74 (((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) <=> (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(59,plain,
% 0.54/0.74 ((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) <=> ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[58])).
% 0.54/0.74 tff(60,plain,
% 0.54/0.74 ((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) <=> (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(transitivity,[status(thm)],[59, 57])).
% 0.54/0.74 tff(61,plain,
% 0.54/0.74 (((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[60, 53])).
% 0.54/0.74 tff(62,plain,
% 0.54/0.74 (((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))) <=> ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[61, 56])).
% 0.54/0.74 tff(63,axiom,((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))) & doDivides0(xp, sdtsldt0(xn, xr))) | (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2645')).
% 0.54/0.74 tff(64,plain,
% 0.54/0.74 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.54/0.74 tff(65,plain,
% 0.54/0.74 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.54/0.74 tff(66,plain,
% 0.54/0.74 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.54/0.74 tff(67,plain,
% 0.54/0.74 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[66, 54])).
% 0.54/0.74 Proof display could not be completed: monotonicity rule is not handled
% 0.54/0.75 % E exiting
%------------------------------------------------------------------------------