TSTP Solution File: NUM518+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM518+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Sun Sep 18 13:10:13 EDT 2022
% Result : Theorem 1.10s 0.94s
% Output : Proof 1.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM518+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 11:33:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.10/0.94 % SZS status Theorem
% 1.10/0.94 % SZS output start Proof
% 1.10/0.94 tff(sz00_type, type, (
% 1.10/0.94 sz00: $i)).
% 1.10/0.94 tff(sdtasdt0_type, type, (
% 1.10/0.94 sdtasdt0: ( $i * $i ) > $i)).
% 1.10/0.94 tff(tptp_fun_W0_15_type, type, (
% 1.10/0.94 tptp_fun_W0_15: $i)).
% 1.10/0.94 tff(xr_type, type, (
% 1.10/0.94 xr: $i)).
% 1.10/0.94 tff(aNaturalNumber0_type, type, (
% 1.10/0.94 aNaturalNumber0: $i > $o)).
% 1.10/0.94 tff(xk_type, type, (
% 1.10/0.94 xk: $i)).
% 1.10/0.94 tff(doDivides0_type, type, (
% 1.10/0.94 doDivides0: ( $i * $i ) > $o)).
% 1.10/0.94 tff(sz10_type, type, (
% 1.10/0.94 sz10: $i)).
% 1.10/0.94 tff(isPrime0_type, type, (
% 1.10/0.94 isPrime0: $i > $o)).
% 1.10/0.94 tff(sdtsldt0_type, type, (
% 1.10/0.94 sdtsldt0: ( $i * $i ) > $i)).
% 1.10/0.94 tff(xn_type, type, (
% 1.10/0.94 xn: $i)).
% 1.10/0.94 tff(tptp_fun_W0_18_type, type, (
% 1.10/0.94 tptp_fun_W0_18: $i)).
% 1.10/0.94 tff(xp_type, type, (
% 1.10/0.94 xp: $i)).
% 1.10/0.94 tff(sdtlseqdt0_type, type, (
% 1.10/0.94 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.10/0.94 tff(sdtpldt0_type, type, (
% 1.10/0.94 sdtpldt0: ( $i * $i ) > $i)).
% 1.10/0.94 tff(xm_type, type, (
% 1.10/0.94 xm: $i)).
% 1.10/0.94 tff(1,plain,
% 1.10/0.94 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 1.10/0.94 inference(rewrite,[status(thm)],[])).
% 1.10/0.94 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/sandbox2/benchmark/theBenchmark.p','m__2342')).
% 1.10/0.95 tff(3,plain,
% 1.10/0.95 (((((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)))),
% 1.10/0.95 inference(and_elim,[status(thm)],[2])).
% 1.10/0.95 tff(4,plain,
% 1.10/0.95 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 1.10/0.95 inference(and_elim,[status(thm)],[3])).
% 1.10/0.95 tff(5,plain,
% 1.10/0.95 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 1.10/0.95 inference(and_elim,[status(thm)],[4])).
% 1.10/0.95 tff(6,plain,
% 1.10/0.95 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 1.10/0.95 inference(and_elim,[status(thm)],[5])).
% 1.10/0.95 tff(7,plain,
% 1.10/0.95 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 1.10/0.95 inference(and_elim,[status(thm)],[6])).
% 1.10/0.95 tff(8,plain,
% 1.10/0.95 (aNaturalNumber0(xr)),
% 1.10/0.95 inference(and_elim,[status(thm)],[7])).
% 1.10/0.95 tff(9,plain,
% 1.10/0.95 (aNaturalNumber0(xr)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[8, 1])).
% 1.10/0.95 tff(10,plain,
% 1.10/0.95 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(11,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[10])).
% 1.10/0.95 tff(12,plain,
% 1.10/0.95 (^[W0: $i] : rewrite(((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0)))))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(13,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[12])).
% 1.10/0.95 tff(14,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(15,plain,
% 1.10/0.95 (^[W0: $i] : rewrite((aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(16,plain,
% 1.10/0.95 (![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[15])).
% 1.10/0.95 tff(17,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_MulZero')).
% 1.10/0.95 tff(18,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.10/0.95 tff(19,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.10/0.95 tff(20,plain,(
% 1.10/0.95 ![W0: $i] : ((~aNaturalNumber0(W0)) | ((sdtasdt0(W0, sz00) = sz00) & (sz00 = sdtasdt0(sz00, W0))))),
% 1.10/0.95 inference(skolemize,[status(sab)],[19])).
% 1.10/0.95 tff(21,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.10/0.95 tff(22,plain,
% 1.10/0.95 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[21, 11])).
% 1.10/0.95 tff(23,plain,
% 1.10/0.95 (((~![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))))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(24,plain,
% 1.10/0.95 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))))),
% 1.10/0.95 inference(quant_inst,[status(thm)],[])).
% 1.10/0.95 tff(25,plain,
% 1.10/0.95 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xr)) | (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr)))))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.10/0.95 tff(26,plain,
% 1.10/0.95 (~((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr))))),
% 1.10/0.95 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 1.10/0.95 tff(27,plain,
% 1.10/0.95 (((~(sdtasdt0(xr, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xr)))) | (sdtasdt0(xr, sz00) = sz00)),
% 1.10/0.95 inference(tautology,[status(thm)],[])).
% 1.10/0.95 tff(28,plain,
% 1.10/0.95 (sdtasdt0(xr, sz00) = sz00),
% 1.10/0.95 inference(unit_resolution,[status(thm)],[27, 26])).
% 1.10/0.95 tff(29,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(30,axiom,(?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0))) & doDivides0(xr, xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2487')).
% 1.10/0.95 tff(31,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 1.10/0.95 inference(and_elim,[status(thm)],[30])).
% 1.10/0.95 tff(32,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xr, W0)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[31, 29])).
% 1.10/0.95 tff(33,plain,(
% 1.10/0.95 aNaturalNumber0(W0!15) & (xn = sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(skolemize,[status(sab)],[32])).
% 1.10/0.95 tff(34,plain,
% 1.10/0.95 (xn = sdtasdt0(xr, W0!15)),
% 1.10/0.95 inference(and_elim,[status(thm)],[33])).
% 1.10/0.95 tff(35,plain,
% 1.10/0.95 (sdtasdt0(xr, W0!15) = xn),
% 1.10/0.95 inference(symmetry,[status(thm)],[34])).
% 1.10/0.95 tff(36,plain,
% 1.10/0.95 (sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) <=> sdtlseqdt0(xp, xn)),
% 1.10/0.95 inference(monotonicity,[status(thm)],[35])).
% 1.10/0.95 tff(37,plain,
% 1.10/0.95 (sdtlseqdt0(xp, xn) <=> sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(symmetry,[status(thm)],[36])).
% 1.10/0.95 tff(38,plain,
% 1.10/0.95 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[37])).
% 1.10/0.95 tff(39,plain,
% 1.10/0.95 ((~sdtlseqdt0(xp, xn)) <=> (~sdtlseqdt0(xp, xn))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(40,axiom,(~(?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xp, W0) = xn)) | sdtlseqdt0(xp, xn))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1870')).
% 1.10/0.95 tff(41,plain,
% 1.10/0.95 (~sdtlseqdt0(xp, xn)),
% 1.10/0.95 inference(or_elim,[status(thm)],[40])).
% 1.10/0.95 tff(42,plain,
% 1.10/0.95 (~sdtlseqdt0(xp, xn)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[41, 39])).
% 1.10/0.95 tff(43,plain,
% 1.10/0.95 (~sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.10/0.95 tff(44,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(45,plain,
% 1.10/0.95 (($false | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(46,plain,
% 1.10/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(47,plain,
% 1.10/0.95 (($false & $false) <=> $false),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(48,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/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.10/0.95 tff(49,plain,
% 1.10/0.95 (~doDivides0(xp, xm)),
% 1.10/0.95 inference(or_elim,[status(thm)],[48])).
% 1.10/0.95 tff(50,plain,
% 1.10/0.95 (doDivides0(xp, xm) <=> $false),
% 1.10/0.95 inference(iff_false,[status(thm)],[49])).
% 1.10/0.95 tff(51,plain,
% 1.10/0.95 ((~?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(52,plain,
% 1.10/0.95 (~((?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn)) | ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))))),
% 1.10/0.95 inference(or_elim,[status(thm)],[48])).
% 1.10/0.95 tff(53,plain,
% 1.10/0.95 (~?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))),
% 1.10/0.95 inference(or_elim,[status(thm)],[52])).
% 1.10/0.95 tff(54,plain,
% 1.10/0.95 (~?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[53, 51])).
% 1.10/0.95 tff(55,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) <=> $false),
% 1.10/0.95 inference(iff_false,[status(thm)],[54])).
% 1.10/0.95 tff(56,plain,
% 1.10/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) <=> ($false & $false)),
% 1.10/0.95 inference(monotonicity,[status(thm)],[55, 50])).
% 1.10/0.95 tff(57,plain,
% 1.10/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) <=> $false),
% 1.10/0.95 inference(transitivity,[status(thm)],[56, 47])).
% 1.10/0.95 tff(58,plain,
% 1.10/0.95 (((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> ($false | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[57, 46])).
% 1.10/0.95 tff(59,plain,
% 1.10/0.95 (((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(transitivity,[status(thm)],[58, 45])).
% 1.10/0.95 tff(60,plain,
% 1.10/0.95 (((?[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)) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(61,plain,
% 1.10/0.95 ((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)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(62,plain,
% 1.10/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) <=> (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(63,plain,
% 1.10/0.95 (((?[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))))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[62, 61])).
% 1.10/0.95 tff(64,plain,
% 1.10/0.95 (((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))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(65,plain,
% 1.10/0.95 (((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)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(66,plain,
% 1.10/0.95 (((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))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(67,plain,
% 1.10/0.95 ((((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)))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[66])).
% 1.10/0.95 tff(68,plain,
% 1.10/0.95 ((((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)))),
% 1.10/0.95 inference(transitivity,[status(thm)],[67, 65])).
% 1.10/0.95 tff(69,plain,
% 1.10/0.95 (((((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)))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[68, 62])).
% 1.10/0.95 tff(70,plain,
% 1.10/0.95 (((((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))))),
% 1.10/0.95 inference(transitivity,[status(thm)],[69, 64])).
% 1.10/0.95 tff(71,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/sandbox2/benchmark/theBenchmark.p','m__2645')).
% 1.10/0.95 tff(72,plain,
% 1.10/0.95 ((?[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)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.10/0.95 tff(73,plain,
% 1.10/0.95 ((?[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)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[72, 63])).
% 1.10/0.95 tff(74,plain,
% 1.10/0.95 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xp, W0))) & doDivides0(xp, xm)) | (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[73, 60])).
% 1.10/0.95 tff(75,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtsldt0(xn, xr))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[74, 59])).
% 1.10/0.95 tff(76,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))),
% 1.10/0.95 inference(and_elim,[status(thm)],[75])).
% 1.10/0.95 tff(77,plain,
% 1.10/0.95 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0)))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[76, 44])).
% 1.10/0.95 tff(78,plain,(
% 1.10/0.95 aNaturalNumber0(W0!18) & (sdtsldt0(xn, xr) = sdtasdt0(xp, W0!18))),
% 1.10/0.95 inference(skolemize,[status(sab)],[77])).
% 1.10/0.95 tff(79,plain,
% 1.10/0.95 (sdtsldt0(xn, xr) = sdtasdt0(xp, W0!18)),
% 1.10/0.95 inference(and_elim,[status(thm)],[78])).
% 1.10/0.95 tff(80,plain,
% 1.10/0.95 (sdtasdt0(xp, W0!18) = sdtsldt0(xn, xr)),
% 1.10/0.95 inference(symmetry,[status(thm)],[79])).
% 1.10/0.95 tff(81,plain,
% 1.10/0.95 (sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15)) <=> sdtlseqdt0(sdtsldt0(xn, xr), xn)),
% 1.10/0.95 inference(monotonicity,[status(thm)],[80, 35])).
% 1.10/0.95 tff(82,plain,
% 1.10/0.95 (sdtlseqdt0(sdtsldt0(xn, xr), xn) <=> sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(symmetry,[status(thm)],[81])).
% 1.10/0.95 tff(83,plain,
% 1.10/0.95 (sdtlseqdt0(sdtsldt0(xn, xr), xn) <=> sdtlseqdt0(sdtsldt0(xn, xr), xn)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(84,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2504')).
% 1.10/0.95 tff(85,plain,
% 1.10/0.95 (sdtlseqdt0(sdtsldt0(xn, xr), xn)),
% 1.10/0.95 inference(and_elim,[status(thm)],[84])).
% 1.10/0.95 tff(86,plain,
% 1.10/0.95 (sdtlseqdt0(sdtsldt0(xn, xr), xn)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[85, 83])).
% 1.10/0.95 tff(87,plain,
% 1.10/0.95 (sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.10/0.95 tff(88,plain,
% 1.10/0.95 (aNaturalNumber0(sdtasdt0(xr, W0!15)) <=> aNaturalNumber0(xn)),
% 1.10/0.95 inference(monotonicity,[status(thm)],[35])).
% 1.10/0.95 tff(89,plain,
% 1.10/0.95 (aNaturalNumber0(xn) <=> aNaturalNumber0(sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(symmetry,[status(thm)],[88])).
% 1.10/0.95 tff(90,plain,
% 1.10/0.95 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(91,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 1.10/0.95 tff(92,plain,
% 1.10/0.95 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 1.10/0.95 inference(and_elim,[status(thm)],[91])).
% 1.10/0.95 tff(93,plain,
% 1.10/0.95 (aNaturalNumber0(xn)),
% 1.10/0.95 inference(and_elim,[status(thm)],[92])).
% 1.10/0.95 tff(94,plain,
% 1.10/0.95 (aNaturalNumber0(xn)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[93, 90])).
% 1.10/0.95 tff(95,plain,
% 1.10/0.95 (aNaturalNumber0(sdtasdt0(xr, W0!15))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[94, 89])).
% 1.10/0.95 tff(96,plain,
% 1.10/0.95 (aNaturalNumber0(sdtasdt0(xp, W0!18)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.10/0.95 inference(monotonicity,[status(thm)],[80])).
% 1.10/0.95 tff(97,plain,
% 1.10/0.95 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtasdt0(xp, W0!18))),
% 1.10/0.95 inference(symmetry,[status(thm)],[96])).
% 1.10/0.95 tff(98,plain,
% 1.10/0.95 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(99,plain,
% 1.10/0.95 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(100,plain,
% 1.10/0.95 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 1.10/0.95 inference(and_elim,[status(thm)],[84])).
% 1.10/0.95 tff(101,plain,
% 1.10/0.95 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(and_elim,[status(thm)],[100])).
% 1.10/0.95 tff(102,plain,
% 1.10/0.95 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.10/0.95 inference(and_elim,[status(thm)],[101])).
% 1.10/0.95 tff(103,plain,
% 1.10/0.95 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 1.10/0.95 inference(and_elim,[status(thm)],[102])).
% 1.10/0.95 tff(104,plain,
% 1.10/0.95 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.10/0.95 tff(105,plain,
% 1.10/0.95 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 1.10/0.95 inference(or_elim,[status(thm)],[104])).
% 1.10/0.95 tff(106,plain,
% 1.10/0.95 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.10/0.95 inference(and_elim,[status(thm)],[105])).
% 1.10/0.95 tff(107,plain,
% 1.10/0.95 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[106, 98])).
% 1.10/0.95 tff(108,plain,
% 1.10/0.95 (aNaturalNumber0(sdtasdt0(xp, W0!18))),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[107, 97])).
% 1.10/0.95 tff(109,plain,
% 1.10/0.95 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(110,plain,
% 1.10/0.95 (aNaturalNumber0(xp)),
% 1.10/0.95 inference(and_elim,[status(thm)],[91])).
% 1.10/0.95 tff(111,plain,
% 1.10/0.95 (aNaturalNumber0(xp)),
% 1.10/0.95 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.10/0.95 tff(112,plain,
% 1.10/0.95 (^[W0: $i, W1: $i, W2: $i] : refl((sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1))) <=> (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(113,plain,
% 1.10/0.95 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[112])).
% 1.10/0.95 tff(114,plain,
% 1.10/0.95 (^[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(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) <=> (~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) <=> (~(~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))))), rewrite((~(~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))) <=> ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) <=> ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))), ((sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)))) <=> (sdtlseqdt0(W0, W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)))))), rewrite((sdtlseqdt0(W0, W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)))) <=> (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))), ((sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)))) <=> (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))))),
% 1.10/0.95 inference(bind,[status(th)],[])).
% 1.10/0.95 tff(115,plain,
% 1.10/0.95 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))),
% 1.10/0.95 inference(quant_intro,[status(thm)],[114])).
% 1.10/0.95 tff(116,plain,
% 1.10/0.95 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))),
% 1.10/0.95 inference(rewrite,[status(thm)],[])).
% 1.10/0.95 tff(117,plain,
% 1.10/0.95 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))) <=> (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(118,plain,
% 1.10/0.96 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[117])).
% 1.10/0.96 tff(119,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mLETran')).
% 1.10/0.96 tff(120,plain,
% 1.10/0.96 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.10/0.96 tff(121,plain,
% 1.10/0.96 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[120, 116])).
% 1.10/0.96 tff(122,plain,(
% 1.10/0.96 ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))))),
% 1.10/0.96 inference(skolemize,[status(sab)],[121])).
% 1.10/0.96 tff(123,plain,
% 1.10/0.96 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[122, 115])).
% 1.10/0.96 tff(124,plain,
% 1.10/0.96 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[123, 113])).
% 1.10/0.96 tff(125,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(126,plain,
% 1.10/0.96 ((sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(127,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15))))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[126])).
% 1.10/0.96 tff(128,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15)))),
% 1.10/0.96 inference(transitivity,[status(thm)],[127, 125])).
% 1.10/0.96 tff(129,plain,
% 1.10/0.96 ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (sdtlseqdt0(xp, sdtasdt0(xr, W0!15)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(130,plain,
% 1.10/0.96 ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aNaturalNumber0(W2)) | (~sdtlseqdt0(W1, W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)) | (~sdtlseqdt0(W0, W1)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.10/0.96 tff(131,plain,
% 1.10/0.96 ((~aNaturalNumber0(sdtasdt0(xr, W0!15))) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~sdtlseqdt0(sdtasdt0(xp, W0!18), sdtasdt0(xr, W0!15))) | (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))) | sdtlseqdt0(xp, sdtasdt0(xr, W0!15))),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[130, 124, 111])).
% 1.10/0.96 tff(132,plain,
% 1.10/0.96 (~sdtlseqdt0(xp, sdtasdt0(xp, W0!18))),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[131, 108, 95, 87, 43])).
% 1.10/0.96 tff(133,plain,
% 1.10/0.96 (doDivides0(xp, sdtasdt0(xp, W0!18)) <=> doDivides0(xp, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[80])).
% 1.10/0.96 tff(134,plain,
% 1.10/0.96 (doDivides0(xp, sdtsldt0(xn, xr)) <=> doDivides0(xp, sdtasdt0(xp, W0!18))),
% 1.10/0.96 inference(symmetry,[status(thm)],[133])).
% 1.10/0.96 tff(135,plain,
% 1.10/0.96 (doDivides0(xp, sdtsldt0(xn, xr)) <=> doDivides0(xp, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(136,plain,
% 1.10/0.96 (doDivides0(xp, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(and_elim,[status(thm)],[75])).
% 1.10/0.96 tff(137,plain,
% 1.10/0.96 (doDivides0(xp, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.10/0.96 tff(138,plain,
% 1.10/0.96 (doDivides0(xp, sdtasdt0(xp, W0!18))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[137, 134])).
% 1.10/0.96 tff(139,plain,
% 1.10/0.96 (^[W0: $i, W1: $i] : refl(((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(140,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[139])).
% 1.10/0.96 tff(141,plain,
% 1.10/0.96 (^[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((doDivides0(W0, W1) & (~(W1 = sz00))) <=> (~((~doDivides0(W0, W1)) | (W1 = sz00)))), ((~(doDivides0(W0, W1) & (~(W1 = sz00)))) <=> (~(~((~doDivides0(W0, W1)) | (W1 = sz00)))))), rewrite((~(~((~doDivides0(W0, W1)) | (W1 = sz00)))) <=> ((~doDivides0(W0, W1)) | (W1 = sz00))), ((~(doDivides0(W0, W1) & (~(W1 = sz00)))) <=> ((~doDivides0(W0, W1)) | (W1 = sz00)))), ((sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00))))) <=> (sdtlseqdt0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~doDivides0(W0, W1)) | (W1 = sz00))))), rewrite((sdtlseqdt0(W0, W1) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | ((~doDivides0(W0, W1)) | (W1 = sz00))) <=> ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))), ((sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00))))) <=> ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(142,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00))))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[141])).
% 1.10/0.96 tff(143,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00))))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(144,plain,
% 1.10/0.96 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((doDivides0(W0, W1) & (~(W1 = sz00))) => sdtlseqdt0(W0, W1)) <=> ((~(doDivides0(W0, W1) & (~(W1 = sz00)))) | sdtlseqdt0(W0, W1))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((doDivides0(W0, W1) & (~(W1 = sz00))) => sdtlseqdt0(W0, W1))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(doDivides0(W0, W1) & (~(W1 = sz00)))) | sdtlseqdt0(W0, W1))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((~(doDivides0(W0, W1) & (~(W1 = sz00)))) | sdtlseqdt0(W0, W1))) <=> (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))), (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((doDivides0(W0, W1) & (~(W1 = sz00))) => sdtlseqdt0(W0, W1))) <=> (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(145,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((doDivides0(W0, W1) & (~(W1 = sz00))) => sdtlseqdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[144])).
% 1.10/0.96 tff(146,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => ((doDivides0(W0, W1) & (~(W1 = sz00))) => sdtlseqdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDivLE')).
% 1.10/0.96 tff(147,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[146, 145])).
% 1.10/0.96 tff(148,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[147, 143])).
% 1.10/0.96 tff(149,plain,(
% 1.10/0.96 ![W0: $i, W1: $i] : (sdtlseqdt0(W0, W1) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (~(doDivides0(W0, W1) & (~(W1 = sz00)))))),
% 1.10/0.96 inference(skolemize,[status(sab)],[148])).
% 1.10/0.96 tff(150,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[149, 142])).
% 1.10/0.96 tff(151,plain,
% 1.10/0.96 (![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[150, 140])).
% 1.10/0.96 tff(152,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(153,plain,
% 1.10/0.96 (((sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(154,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18))))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[153])).
% 1.10/0.96 tff(155,plain,
% 1.10/0.96 (((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)))),
% 1.10/0.96 inference(transitivity,[status(thm)],[154, 152])).
% 1.10/0.96 tff(156,plain,
% 1.10/0.96 ((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (~aNaturalNumber0(xp)))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(157,plain,
% 1.10/0.96 ((~![W0: $i, W1: $i] : ((W1 = sz00) | sdtlseqdt0(W0, W1) | (~aNaturalNumber0(W1)) | (~doDivides0(W0, W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.10/0.96 tff(158,plain,
% 1.10/0.96 ((~aNaturalNumber0(sdtasdt0(xp, W0!18))) | (~doDivides0(xp, sdtasdt0(xp, W0!18))) | (sdtasdt0(xp, W0!18) = sz00) | sdtlseqdt0(xp, sdtasdt0(xp, W0!18))),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[157, 151, 111])).
% 1.10/0.96 tff(159,plain,
% 1.10/0.96 (sdtasdt0(xp, W0!18) = sz00),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[158, 138, 108, 132])).
% 1.10/0.96 tff(160,plain,
% 1.10/0.96 (sdtsldt0(xn, xr) = sz00),
% 1.10/0.96 inference(transitivity,[status(thm)],[79, 159])).
% 1.10/0.96 tff(161,plain,
% 1.10/0.96 (sdtasdt0(xr, sdtsldt0(xn, xr)) = sdtasdt0(xr, sz00)),
% 1.10/0.96 inference(monotonicity,[status(thm)],[160])).
% 1.10/0.96 tff(162,plain,
% 1.10/0.96 ((xn = sdtasdt0(xr, sdtsldt0(xn, xr))) <=> (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(163,plain,
% 1.10/0.96 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(and_elim,[status(thm)],[101])).
% 1.10/0.96 tff(164,plain,
% 1.10/0.96 (xn = sdtasdt0(xr, sdtsldt0(xn, xr))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[163, 162])).
% 1.10/0.96 tff(165,plain,
% 1.10/0.96 (sdtasdt0(xr, W0!15) = sz00),
% 1.10/0.96 inference(transitivity,[status(thm)],[35, 164, 161, 28])).
% 1.10/0.96 tff(166,plain,
% 1.10/0.96 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(167,plain,
% 1.10/0.96 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | ((~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(168,plain,
% 1.10/0.96 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~((~(sdtasdt0(W0, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, W0))))))) | (~aNaturalNumber0(xp)) | (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp)))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.10/0.96 tff(169,plain,
% 1.10/0.96 (~((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp))))),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[168, 22, 111])).
% 1.10/0.96 tff(170,plain,
% 1.10/0.96 (((~(sdtasdt0(xp, sz00) = sz00)) | (~(sz00 = sdtasdt0(sz00, xp)))) | (sdtasdt0(xp, sz00) = sz00)),
% 1.10/0.96 inference(tautology,[status(thm)],[])).
% 1.10/0.96 tff(171,plain,
% 1.10/0.96 (sdtasdt0(xp, sz00) = sz00),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[170, 169])).
% 1.10/0.96 tff(172,plain,
% 1.10/0.96 ((xn = sdtasdt0(xp, sz00)) <=> (sdtasdt0(xr, W0!15) = sz00)),
% 1.10/0.96 inference(monotonicity,[status(thm)],[34, 171])).
% 1.10/0.96 tff(173,plain,
% 1.10/0.96 ((~(xn = sdtasdt0(xp, sz00))) <=> (~(sdtasdt0(xr, W0!15) = sz00))),
% 1.10/0.96 inference(monotonicity,[status(thm)],[172])).
% 1.10/0.96 tff(174,plain,
% 1.10/0.96 (^[W0: $i] : refl(((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(175,plain,
% 1.10/0.96 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[174])).
% 1.10/0.96 tff(176,plain,
% 1.10/0.96 (^[W0: $i] : trans(monotonicity(rewrite((aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) <=> (~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))))), ((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) <=> (~(~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))))))), rewrite((~(~((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0)))))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))), ((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) <=> ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(177,plain,
% 1.10/0.96 (![W0: $i] : (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) <=> ![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(quant_intro,[status(thm)],[176])).
% 1.10/0.96 tff(178,plain,
% 1.10/0.96 ((~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) <=> (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(179,plain,
% 1.10/0.96 (~(?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) | doDivides0(xp, xn))),
% 1.10/0.96 inference(or_elim,[status(thm)],[52])).
% 1.10/0.96 tff(180,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(or_elim,[status(thm)],[179])).
% 1.10/0.96 tff(181,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[180, 178])).
% 1.10/0.96 tff(182,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[181, 178])).
% 1.10/0.96 tff(183,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[182, 178])).
% 1.10/0.96 tff(184,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[183, 178])).
% 1.10/0.96 tff(185,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[184, 178])).
% 1.10/0.96 tff(186,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[185, 178])).
% 1.10/0.96 tff(187,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[186, 178])).
% 1.10/0.96 tff(188,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[187, 178])).
% 1.10/0.96 tff(189,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[188, 178])).
% 1.10/0.96 tff(190,plain,
% 1.10/0.96 (~?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[189, 178])).
% 1.10/0.96 tff(191,plain,
% 1.10/0.96 (^[W0: $i] : refl($oeq((~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))), (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))))))),
% 1.10/0.96 inference(bind,[status(th)],[])).
% 1.10/0.96 tff(192,plain,(
% 1.10/0.96 ![W0: $i] : (~(aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(nnf-neg,[status(sab)],[190, 191])).
% 1.10/0.96 tff(193,plain,
% 1.10/0.96 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[192, 177])).
% 1.10/0.96 tff(194,plain,
% 1.10/0.96 (![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[193, 175])).
% 1.10/0.96 tff(195,plain,
% 1.10/0.96 (aNaturalNumber0(sz00) <=> aNaturalNumber0(sz00)),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(196,axiom,(aNaturalNumber0(sz00)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsC')).
% 1.10/0.96 tff(197,plain,
% 1.10/0.96 (aNaturalNumber0(sz00)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.10/0.96 tff(198,plain,
% 1.10/0.96 (((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(sz00)) | (~(xn = sdtasdt0(xp, sz00))))) <=> ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(sz00)) | (~(xn = sdtasdt0(xp, sz00))))),
% 1.10/0.96 inference(rewrite,[status(thm)],[])).
% 1.10/0.96 tff(199,plain,
% 1.10/0.96 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))) | ((~aNaturalNumber0(sz00)) | (~(xn = sdtasdt0(xp, sz00))))),
% 1.10/0.96 inference(quant_inst,[status(thm)],[])).
% 1.10/0.96 tff(200,plain,
% 1.10/0.96 ((~![W0: $i] : ((~aNaturalNumber0(W0)) | (~(xn = sdtasdt0(xp, W0))))) | (~aNaturalNumber0(sz00)) | (~(xn = sdtasdt0(xp, sz00)))),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.10/0.96 tff(201,plain,
% 1.10/0.96 (~(xn = sdtasdt0(xp, sz00))),
% 1.10/0.96 inference(unit_resolution,[status(thm)],[200, 197, 194])).
% 1.10/0.96 tff(202,plain,
% 1.10/0.96 (~(sdtasdt0(xr, W0!15) = sz00)),
% 1.10/0.96 inference(modus_ponens,[status(thm)],[201, 173])).
% 1.10/0.97 tff(203,plain,
% 1.10/0.97 ($false),
% 1.10/0.97 inference(unit_resolution,[status(thm)],[202, 165])).
% 1.10/0.97 % SZS output end Proof
%------------------------------------------------------------------------------