TSTP Solution File: NUM500+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : 600s
% DateTime : Mon Jul 18 14:26:51 EDT 2022
% Result : Theorem 1.67s 1.91s
% Output : Refutation 1.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : 600
% 0.12/0.33 % DateTime : Thu Jul 7 02:19:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.91
% 1.67/1.91 SPASS V 3.9
% 1.67/1.91 SPASS beiseite: Proof found.
% 1.67/1.91 % SZS status Theorem
% 1.67/1.91 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.67/1.91 SPASS derived 3284 clauses, backtracked 546 clauses, performed 14 splits and kept 1929 clauses.
% 1.67/1.91 SPASS allocated 102640 KBytes.
% 1.67/1.91 SPASS spent 0:00:01.57 on the problem.
% 1.67/1.91 0:00:00.04 for the input.
% 1.67/1.91 0:00:00.05 for the FLOTTER CNF translation.
% 1.67/1.91 0:00:00.05 for inferences.
% 1.67/1.91 0:00:00.02 for the backtracking.
% 1.67/1.91 0:00:01.37 for the reduction.
% 1.67/1.91
% 1.67/1.91
% 1.67/1.91 Here is a proof with depth 9, length 207 :
% 1.67/1.91 % SZS output start Refutation
% 1.67/1.91 1[0:Inp] || -> aNaturalNumber0(sz00)*.
% 1.67/1.91 2[0:Inp] || -> aNaturalNumber0(sz10)*.
% 1.67/1.91 3[0:Inp] || -> aNaturalNumber0(xn)*.
% 1.67/1.91 4[0:Inp] || -> aNaturalNumber0(xm)*.
% 1.67/1.91 5[0:Inp] || -> aNaturalNumber0(xp)*.
% 1.67/1.91 6[0:Inp] || -> aNaturalNumber0(skc3)*.
% 1.67/1.91 7[0:Inp] || -> isPrime0(xp)*.
% 1.67/1.91 10[0:Inp] || -> aNaturalNumber0(xk)*.
% 1.67/1.91 12[0:Inp] || -> aNaturalNumber0(skf9(u))*.
% 1.67/1.91 14[0:Inp] || -> aNaturalNumber0(skf14(u))*.
% 1.67/1.91 16[0:Inp] || -> aNaturalNumber0(skf15(u))*.
% 1.67/1.91 17[0:Inp] || -> sdtlseqdt0(xn,xp)*.
% 1.67/1.91 21[0:Inp] || -> aNaturalNumber0(skf12(u,v))*.
% 1.67/1.91 23[0:Inp] || equal(xp,sz00)** -> .
% 1.67/1.91 24[0:Inp] || equal(xp,sz10)** -> .
% 1.67/1.91 25[0:Inp] || sdtlseqdt0(xp,xn)* -> .
% 1.67/1.91 26[0:Inp] || sdtlseqdt0(xp,xm)* -> .
% 1.67/1.91 27[0:Inp] || equal(xp,xn)** -> .
% 1.67/1.91 31[0:Inp] || equal(xk,sz00)** -> .
% 1.67/1.91 32[0:Inp] || equal(xk,sz10)** -> .
% 1.67/1.91 33[0:Inp] isPrime0(u) || -> SkP1(u)*.
% 1.67/1.91 34[0:Inp] || -> doDivides0(xp,sdtasdt0(xn,xm))*.
% 1.67/1.91 37[0:Inp] || doDivides0(u,xk) -> SkP3(u)*.
% 1.67/1.91 40[0:Inp] || -> equal(sdtasdt0(xp,skc3),sdtasdt0(xn,xm))**.
% 1.67/1.91 41[0:Inp] || -> equal(sdtasdt0(xp,xk),sdtasdt0(xn,xm))**.
% 1.67/1.91 42[0:Inp] || -> equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk)**.
% 1.67/1.91 45[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(u,sz10),u)**.
% 1.67/1.91 46[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(sz10,u),u)**.
% 1.67/1.91 47[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(u,sz00),sz00)**.
% 1.67/1.91 48[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(sz00,u),sz00)**.
% 1.67/1.91 49[0:Inp] SkP3(u) aNaturalNumber0(u) isPrime0(u) || -> .
% 1.67/1.91 53[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtasdt0(v,u))*.
% 1.67/1.91 56[0:Inp] aNaturalNumber0(u) || equal(sdtasdt0(v,u),xk)** -> SkP3(v).
% 1.67/1.91 58[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(v,u)* sdtlseqdt0(u,v)*.
% 1.67/1.91 60[0:Inp] aNaturalNumber0(u) || -> isPrime0(skf14(u))* equal(u,sz10) equal(u,sz00).
% 1.67/1.91 61[0:Inp] || -> SkP1(u) equal(u,sz10) equal(u,sz00) doDivides0(skf15(u),u)*.
% 1.67/1.91 63[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtasdt0(v,u),sdtasdt0(u,v))*.
% 1.67/1.91 66[0:Inp] aNaturalNumber0(u) || -> equal(u,sz10) equal(u,sz00) doDivides0(skf14(u),u)*.
% 1.67/1.91 70[0:Inp] aNaturalNumber0(u) || doDivides0(u,xp)* -> equal(u,xp) equal(u,sz10).
% 1.67/1.91 71[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(u,v))*.
% 1.67/1.91 76[0:Inp] SkP3(u) aNaturalNumber0(u) || -> equal(u,sz10) equal(u,sz00) doDivides0(skf9(u),u)*.
% 1.67/1.91 78[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> sdtlseqdt0(v,u) equal(u,sz00).
% 1.67/1.91 81[0:Inp] SkP3(u) aNaturalNumber0(u) || equal(skf9(u),sz10)** -> equal(u,sz10) equal(u,sz00).
% 1.67/1.91 84[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 1.67/1.91 85[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) -> equal(sdtasdt0(v,skf12(v,u)),u)**.
% 1.67/1.91 86[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(sdtasdt0(v,u),sz00)** -> equal(u,sz00) equal(v,sz00).
% 1.67/1.91 91[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(sdtasdt0(u,v),xp)** -> equal(u,xp) equal(u,sz10).
% 1.67/1.91 94[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || doDivides0(v,u)*+ doDivides0(w,v)* -> doDivides0(w,u)*.
% 1.67/1.91 95[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)*+ sdtlseqdt0(w,v)* -> sdtlseqdt0(w,u)*.
% 1.67/1.91 100[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> aNaturalNumber0(w)* equal(v,sz00).
% 1.67/1.91 404[0:Res:14.0,49.1] SkP3(skf14(u)) isPrime0(skf14(u)) || -> .
% 1.67/1.91 411[0:Res:10.0,56.0] || equal(sdtasdt0(u,xk),xk)** -> SkP3(u).
% 1.67/1.91 418[0:Res:2.0,56.0] || equal(sdtasdt0(u,sz10),xk)** -> SkP3(u).
% 1.67/1.91 429[0:Res:10.0,76.0] SkP3(xk) || -> doDivides0(skf9(xk),xk)* equal(xk,sz00) equal(xk,sz10).
% 1.67/1.91 432[0:Res:6.0,76.0] SkP3(skc3) || -> equal(skc3,sz10) equal(skc3,sz00) doDivides0(skf9(skc3),skc3)*.
% 1.67/1.91 434[0:Res:4.0,76.0] SkP3(xm) || -> equal(xm,sz10) equal(xm,sz00) doDivides0(skf9(xm),xm)*.
% 1.67/1.91 435[0:Res:3.0,76.0] SkP3(xn) || -> equal(xn,sz10) equal(xn,sz00) doDivides0(skf9(xn),xn)*.
% 1.67/1.91 478[0:MRR:429.2,429.3,31.0,32.0] SkP3(xk) || -> doDivides0(skf9(xk),xk)*.
% 1.67/1.91 505[0:SpL:45.1,418.0] aNaturalNumber0(u) || equal(u,xk) -> SkP3(u)*.
% 1.67/1.91 528[0:SpL:46.1,411.0] aNaturalNumber0(xk) || equal(xk,xk) -> SkP3(sz10)*.
% 1.67/1.91 529[0:Obv:528.1] aNaturalNumber0(xk) || -> SkP3(sz10)*.
% 1.67/1.91 530[0:SSi:529.0,10.0] || -> SkP3(sz10)*.
% 1.67/1.91 537[0:SoR:478.0,505.2] aNaturalNumber0(xk) || equal(xk,xk) -> doDivides0(skf9(xk),xk)*.
% 1.67/1.91 539[0:Obv:537.1] aNaturalNumber0(xk) || -> doDivides0(skf9(xk),xk)*.
% 1.67/1.91 540[0:SSi:539.0,10.0] || -> doDivides0(skf9(xk),xk)*.
% 1.67/1.91 613[0:SoR:435.0,37.1] || doDivides0(xn,xk) -> equal(xn,sz10) equal(xn,sz00) doDivides0(skf9(xn),xn)*.
% 1.67/1.91 617[0:SoR:434.0,37.1] || doDivides0(xm,xk) -> equal(xm,sz10) equal(xm,sz00) doDivides0(skf9(xm),xm)*.
% 1.67/1.91 621[0:SoR:432.0,37.1] || doDivides0(skc3,xk) -> equal(skc3,sz10) equal(skc3,sz00) doDivides0(skf9(skc3),skc3)*.
% 1.67/1.91 654[0:Res:61.3,70.1] aNaturalNumber0(skf15(xp)) || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf15(xp),xp)** equal(skf15(xp),sz10).
% 1.67/1.91 655[0:SSi:654.0,16.0,7.0,5.0] || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf15(xp),xp)** equal(skf15(xp),sz10).
% 1.67/1.91 656[0:MRR:655.1,655.2,24.0,23.0] || -> SkP1(xp) equal(skf15(xp),xp)** equal(skf15(xp),sz10).
% 1.67/1.91 659[0:SpR:656.1,61.3] || -> SkP1(xp) equal(skf15(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00) doDivides0(xp,xp).
% 1.67/1.91 661[0:Obv:659.0] || -> equal(skf15(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00) doDivides0(xp,xp).
% 1.67/1.91 662[0:MRR:661.2,661.3,24.0,23.0] || -> equal(skf15(xp),sz10)** SkP1(xp) doDivides0(xp,xp).
% 1.67/1.91 664[0:SpR:662.0,61.3] || -> SkP1(xp)* doDivides0(xp,xp) SkP1(xp)* equal(xp,sz10) equal(xp,sz00) doDivides0(sz10,xp).
% 1.67/1.91 668[0:Obv:664.0] || -> doDivides0(xp,xp) SkP1(xp)* equal(xp,sz10) equal(xp,sz00) doDivides0(sz10,xp).
% 1.67/1.91 669[0:MRR:668.2,668.3,24.0,23.0] || -> doDivides0(xp,xp) SkP1(xp)* doDivides0(sz10,xp).
% 1.67/1.91 670[1:Spt:669.1] || -> SkP1(xp)*.
% 1.67/1.91 858[0:SpR:41.0,71.3] aNaturalNumber0(xp) aNaturalNumber0(xk) || -> equal(xk,sz00) sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 1.67/1.91 862[0:SpR:46.1,71.3] aNaturalNumber0(u) aNaturalNumber0(sz10) aNaturalNumber0(u) || -> equal(u,sz00) sdtlseqdt0(sz10,u)*.
% 1.67/1.91 868[1:SSi:858.1,858.0,10.0,7.0,5.0,670.0] || -> equal(xk,sz00) sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 1.67/1.91 869[1:MRR:868.0,31.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 1.67/1.91 871[0:Obv:862.0] aNaturalNumber0(sz10) aNaturalNumber0(u) || -> equal(u,sz00) sdtlseqdt0(sz10,u)*.
% 1.67/1.91 872[0:SSi:871.0,2.0,530.0] aNaturalNumber0(u) || -> equal(u,sz00) sdtlseqdt0(sz10,u)*.
% 1.67/1.91 923[2:Spt:613.1] || -> equal(xn,sz10)**.
% 1.67/1.91 935[2:Rew:923.0,869.0] || -> sdtlseqdt0(xp,sdtasdt0(sz10,xm))*.
% 1.67/1.91 974[2:SpR:46.1,935.0] aNaturalNumber0(xm) || -> sdtlseqdt0(xp,xm)*.
% 1.67/1.91 975[2:SSi:974.0,4.0] || -> sdtlseqdt0(xp,xm)*.
% 1.67/1.91 976[2:MRR:975.0,26.0] || -> .
% 1.67/1.91 978[2:Spt:976.0,613.1,923.0] || equal(xn,sz10)** -> .
% 1.67/1.91 979[2:Spt:976.0,613.0,613.2,613.3] || doDivides0(xn,xk) -> equal(xn,sz00) doDivides0(skf9(xn),xn)*.
% 1.67/1.91 987[3:Spt:979.1] || -> equal(xn,sz00)**.
% 1.67/1.91 992[3:Rew:987.0,869.0] || -> sdtlseqdt0(xp,sdtasdt0(sz00,xm))*.
% 1.67/1.91 1004[3:Rew:987.0,25.0] || sdtlseqdt0(xp,sz00)* -> .
% 1.67/1.91 1028[3:SpR:48.1,992.0] aNaturalNumber0(xm) || -> sdtlseqdt0(xp,sz00)*.
% 1.67/1.91 1029[3:SSi:1028.0,4.0] || -> sdtlseqdt0(xp,sz00)*.
% 1.67/1.91 1030[3:MRR:1029.0,1004.0] || -> .
% 1.67/1.91 1031[3:Spt:1030.0,979.1,987.0] || equal(xn,sz00)** -> .
% 1.67/1.91 1032[3:Spt:1030.0,979.0,979.2] || doDivides0(xn,xk) -> doDivides0(skf9(xn),xn)*.
% 1.67/1.91 1114[4:Spt:617.1] || -> equal(xm,sz10)**.
% 1.67/1.91 1127[4:Rew:1114.0,869.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,sz10))*.
% 1.67/1.91 1181[4:SpR:63.2,1127.0] aNaturalNumber0(xn) aNaturalNumber0(sz10) || -> sdtlseqdt0(xp,sdtasdt0(sz10,xn))*.
% 1.67/1.91 1187[4:Rew:46.1,1181.2] aNaturalNumber0(xn) aNaturalNumber0(sz10) || -> sdtlseqdt0(xp,xn)*.
% 1.67/1.91 1188[4:SSi:1187.1,1187.0,2.0,530.0,3.0] || -> sdtlseqdt0(xp,xn)*.
% 1.67/1.91 1189[4:MRR:1188.0,25.0] || -> .
% 1.67/1.91 1190[4:Spt:1189.0,617.1,1114.0] || equal(xm,sz10)** -> .
% 1.67/1.91 1191[4:Spt:1189.0,617.0,617.2,617.3] || doDivides0(xm,xk) -> equal(xm,sz00) doDivides0(skf9(xm),xm)*.
% 1.67/1.91 1199[5:Spt:1191.1] || -> equal(xm,sz00)**.
% 1.67/1.91 1204[5:Rew:1199.0,869.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,sz00))*.
% 1.67/1.91 1218[5:Rew:1199.0,26.0] || sdtlseqdt0(xp,sz00)* -> .
% 1.67/1.91 1248[5:SpR:63.2,1204.0] aNaturalNumber0(xn) aNaturalNumber0(sz00) || -> sdtlseqdt0(xp,sdtasdt0(sz00,xn))*.
% 1.67/1.91 1254[5:Rew:48.1,1248.2] aNaturalNumber0(xn) aNaturalNumber0(sz00) || -> sdtlseqdt0(xp,sz00)*.
% 1.67/1.91 1255[5:SSi:1254.1,1254.0,1.0,3.0] || -> sdtlseqdt0(xp,sz00)*.
% 1.67/1.91 1256[5:MRR:1255.0,1218.0] || -> .
% 1.67/1.91 1257[5:Spt:1256.0,1191.1,1199.0] || equal(xm,sz00)** -> .
% 1.67/1.91 1258[5:Spt:1256.0,1191.0,1191.2] || doDivides0(xm,xk) -> doDivides0(skf9(xm),xm)*.
% 1.67/1.91 1335[6:Spt:621.1] || -> equal(skc3,sz10)**.
% 1.67/1.91 1341[6:Rew:1335.0,40.0] || -> equal(sdtasdt0(xp,sz10),sdtasdt0(xn,xm))**.
% 1.67/1.91 1353[6:SpR:1341.0,45.1] aNaturalNumber0(xp) || -> equal(sdtasdt0(xn,xm),xp)**.
% 1.67/1.91 1361[6:SSi:1353.0,7.0,5.0,670.0] || -> equal(sdtasdt0(xn,xm),xp)**.
% 1.67/1.91 1439[0:Res:540.0,78.2] aNaturalNumber0(xk) aNaturalNumber0(skf9(xk)) || -> sdtlseqdt0(skf9(xk),xk)* equal(xk,sz00).
% 1.67/1.91 1441[0:Res:66.3,78.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(skf14(u)) || -> equal(u,sz10) equal(u,sz00) sdtlseqdt0(skf14(u),u)* equal(u,sz00).
% 1.67/1.91 1452[0:SSi:1439.1,1439.0,12.0,10.0,10.0] || -> sdtlseqdt0(skf9(xk),xk)* equal(xk,sz00).
% 1.67/1.91 1453[0:MRR:1452.1,31.0] || -> sdtlseqdt0(skf9(xk),xk)*.
% 1.67/1.91 1469[0:Obv:1441.4] aNaturalNumber0(u) aNaturalNumber0(skf14(u)) || -> equal(u,sz10) sdtlseqdt0(skf14(u),u)* equal(u,sz00).
% 1.67/1.91 1470[0:SSi:1469.1,14.0] aNaturalNumber0(u) || -> equal(u,sz10) sdtlseqdt0(skf14(u),u)* equal(u,sz00).
% 1.67/1.91 1486[0:SpR:85.3,48.1] aNaturalNumber0(u) aNaturalNumber0(sz00) aNaturalNumber0(skf12(sz00,u)) || doDivides0(sz00,u)* -> equal(u,sz00).
% 1.67/1.91 1492[0:SpL:85.3,56.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(skf12(v,u)) || doDivides0(v,u)* equal(u,xk) -> SkP3(v)*.
% 1.67/1.91 1500[0:SSi:1486.2,1486.1,21.0,1.0,1.0] aNaturalNumber0(u) || doDivides0(sz00,u)* -> equal(u,sz00).
% 1.67/1.91 1502[0:SSi:1492.2,21.0] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u)* equal(u,xk) -> SkP3(v)*.
% 1.67/1.91 1646[6:SpL:1361.0,91.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || equal(xp,xp)* -> equal(xp,xn) equal(xn,sz10).
% 1.67/1.91 1649[6:Obv:1646.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || -> equal(xp,xn)** equal(xn,sz10).
% 1.67/1.91 1650[6:SSi:1649.1,1649.0,4.0,3.0] || -> equal(xp,xn)** equal(xn,sz10).
% 1.67/1.91 1651[6:MRR:1650.0,1650.1,27.0,978.0] || -> .
% 1.67/1.91 1660[6:Spt:1651.0,621.1,1335.0] || equal(skc3,sz10)** -> .
% 1.67/1.91 1661[6:Spt:1651.0,621.0,621.2,621.3] || doDivides0(skc3,xk) -> equal(skc3,sz00) doDivides0(skf9(skc3),skc3)*.
% 1.67/1.91 1669[7:Spt:1661.1] || -> equal(skc3,sz00)**.
% 1.67/1.91 1673[7:Rew:1669.0,40.0] || -> equal(sdtasdt0(xp,sz00),sdtasdt0(xn,xm))**.
% 1.67/1.91 1693[1:Res:869.0,84.2] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 1696[1:SSi:1693.1,1693.0,7.0,5.0,670.2,53.0,3.0,4.0] || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 1708[7:SpR:1673.0,47.1] aNaturalNumber0(xp) || -> equal(sdtasdt0(xn,xm),sz00)**.
% 1.67/1.91 1717[7:SSi:1708.0,7.0,5.0,670.0] || -> equal(sdtasdt0(xn,xm),sz00)**.
% 1.67/1.91 1819[7:SpL:1717.0,86.2] aNaturalNumber0(xm) aNaturalNumber0(xn) || equal(sz00,sz00) -> equal(xm,sz00)** equal(xn,sz00).
% 1.67/1.91 1823[7:Obv:1819.2] aNaturalNumber0(xm) aNaturalNumber0(xn) || -> equal(xm,sz00)** equal(xn,sz00).
% 1.67/1.91 1824[7:SSi:1823.1,1823.0,3.0,4.0] || -> equal(xm,sz00)** equal(xn,sz00).
% 1.67/1.91 1825[7:MRR:1824.0,1824.1,1257.0,1031.0] || -> .
% 1.67/1.91 1831[7:Spt:1825.0,1661.1,1669.0] || equal(skc3,sz00)** -> .
% 1.67/1.91 1832[7:Spt:1825.0,1661.0,1661.2] || doDivides0(skc3,xk) -> doDivides0(skf9(skc3),skc3)*.
% 1.67/1.91 2379[0:Res:17.0,95.3] aNaturalNumber0(xp) aNaturalNumber0(xn) aNaturalNumber0(u) || sdtlseqdt0(u,xn) -> sdtlseqdt0(u,xp)*.
% 1.67/1.91 2388[0:Res:1453.0,95.3] aNaturalNumber0(xk) aNaturalNumber0(skf9(xk)) aNaturalNumber0(u) || sdtlseqdt0(u,skf9(xk))* -> sdtlseqdt0(u,xk).
% 1.67/1.91 2415[1:SSi:2379.1,2379.0,3.0,7.0,5.0,670.0] aNaturalNumber0(u) || sdtlseqdt0(u,xn) -> sdtlseqdt0(u,xp)*.
% 1.67/1.91 2417[0:SSi:2388.1,2388.0,12.0,10.0,10.0] aNaturalNumber0(u) || sdtlseqdt0(u,skf9(xk))* -> sdtlseqdt0(u,xk).
% 1.67/1.91 2457[1:Res:2415.2,1696.0] aNaturalNumber0(sdtasdt0(xn,xm)) || sdtlseqdt0(sdtasdt0(xn,xm),xn)* -> equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 2464[1:SSi:2457.0,53.0,3.0,4.2] || sdtlseqdt0(sdtasdt0(xn,xm),xn)* -> equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 2469[0:Res:540.0,94.3] aNaturalNumber0(xk) aNaturalNumber0(skf9(xk)) aNaturalNumber0(u) || doDivides0(u,skf9(xk))* -> doDivides0(u,xk).
% 1.67/1.91 2485[0:SSi:2469.1,2469.0,12.0,10.0,10.0] aNaturalNumber0(u) || doDivides0(u,skf9(xk))* -> doDivides0(u,xk).
% 1.67/1.91 2519[1:Res:58.3,2464.0] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xn) || -> sdtlseqdt0(xn,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 2522[1:SSi:2519.1,2519.0,3.0,53.0,3.2,4.0] || -> sdtlseqdt0(xn,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),xp).
% 1.67/1.91 2523[8:Spt:2522.1] || -> equal(sdtasdt0(xn,xm),xp)**.
% 1.67/1.91 2571[8:SpL:2523.0,91.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || equal(xp,xp)* -> equal(xp,xn) equal(xn,sz10).
% 1.67/1.91 2577[8:Obv:2571.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || -> equal(xp,xn)** equal(xn,sz10).
% 1.67/1.91 2578[8:SSi:2577.1,2577.0,4.0,3.0] || -> equal(xp,xn)** equal(xn,sz10).
% 1.67/1.91 2579[8:MRR:2578.0,2578.1,27.0,978.0] || -> .
% 1.67/1.91 2588[8:Spt:2579.0,2522.1,2523.0] || equal(sdtasdt0(xn,xm),xp)** -> .
% 1.67/1.91 2589[8:Spt:2579.0,2522.0] || -> sdtlseqdt0(xn,sdtasdt0(xn,xm))*.
% 1.67/1.91 2667[0:SpL:42.0,100.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 1.67/1.91 2668[1:SSi:2667.1,2667.0,7.0,5.0,670.2,53.0,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 1.67/1.91 2669[1:MRR:2668.0,2668.3,34.0,23.0] || equal(u,xk) -> aNaturalNumber0(u)*.
% 1.67/1.91 2670[1:MRR:505.0,2669.1] || equal(u,xk) -> SkP3(u)*.
% 1.67/1.91 2671[1:MRR:1502.0,2669.1] aNaturalNumber0(u) || doDivides0(u,v)*+ equal(v,xk) -> SkP3(u)*.
% 1.67/1.91 2730[0:Res:872.2,2417.1] aNaturalNumber0(skf9(xk)) aNaturalNumber0(sz10) || -> equal(skf9(xk),sz00)** sdtlseqdt0(sz10,xk).
% 1.67/1.91 2734[0:Res:1470.2,2417.1] aNaturalNumber0(skf9(xk)) aNaturalNumber0(skf14(skf9(xk))) || -> equal(skf9(xk),sz10) equal(skf9(xk),sz00) sdtlseqdt0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 2741[0:SSi:2730.1,2730.0,2.0,530.0,12.0,10.0] || -> equal(skf9(xk),sz00)** sdtlseqdt0(sz10,xk).
% 1.67/1.91 2748[0:SSi:2734.1,2734.0,14.0,12.0,10.0,12.0,10.0] || -> equal(skf9(xk),sz10) equal(skf9(xk),sz00) sdtlseqdt0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 2750[9:Spt:2741.0] || -> equal(skf9(xk),sz00)**.
% 1.67/1.91 2751[9:Rew:2750.0,540.0] || -> doDivides0(sz00,xk)*.
% 1.67/1.91 2789[9:Res:2751.0,1500.1] aNaturalNumber0(xk) || -> equal(xk,sz00)**.
% 1.67/1.91 2790[9:SSi:2789.0,10.0] || -> equal(xk,sz00)**.
% 1.67/1.91 2791[9:MRR:2790.0,31.0] || -> .
% 1.67/1.91 2792[9:Spt:2791.0,2741.0,2750.0] || equal(skf9(xk),sz00)** -> .
% 1.67/1.91 2793[9:Spt:2791.0,2741.1] || -> sdtlseqdt0(sz10,xk)*.
% 1.67/1.91 2794[9:MRR:2748.1,2792.0] || -> equal(skf9(xk),sz10) sdtlseqdt0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 2894[10:Spt:2794.0] || -> equal(skf9(xk),sz10)**.
% 1.67/1.91 2916[10:SpL:2894.0,81.2] SkP3(xk) aNaturalNumber0(xk) || equal(sz10,sz10) -> equal(xk,sz10)** equal(xk,sz00).
% 1.67/1.91 2925[10:Obv:2916.2] SkP3(xk) aNaturalNumber0(xk) || -> equal(xk,sz10)** equal(xk,sz00).
% 1.67/1.91 2926[10:SSi:2925.1,10.0] SkP3(xk) || -> equal(xk,sz10)** equal(xk,sz00).
% 1.67/1.91 2927[10:MRR:2926.1,2926.2,32.0,31.0] SkP3(xk) || -> .
% 1.67/1.91 3014[10:SoR:2927.0,2670.1] || equal(xk,xk)* -> .
% 1.67/1.91 3015[10:Obv:3014.0] || -> .
% 1.67/1.91 3016[10:Spt:3015.0,2794.0,2894.0] || equal(skf9(xk),sz10)** -> .
% 1.67/1.91 3017[10:Spt:3015.0,2794.1] || -> sdtlseqdt0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 3140[0:Res:66.3,2485.1] aNaturalNumber0(skf9(xk)) aNaturalNumber0(skf14(skf9(xk))) || -> equal(skf9(xk),sz10) equal(skf9(xk),sz00) doDivides0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 3146[0:SSi:3140.1,3140.0,14.0,12.0,10.0,12.0,10.0] || -> equal(skf9(xk),sz10) equal(skf9(xk),sz00) doDivides0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 3147[10:MRR:3146.0,3146.1,3016.0,2792.0] || -> doDivides0(skf14(skf9(xk)),xk)*.
% 1.67/1.91 5532[10:Res:3147.0,2671.1] aNaturalNumber0(skf14(skf9(xk))) || equal(xk,xk) -> SkP3(skf14(skf9(xk)))*.
% 1.67/1.91 5551[1:Res:540.0,2671.1] aNaturalNumber0(skf9(xk)) || equal(xk,xk) -> SkP3(skf9(xk))*.
% 1.67/1.91 5564[1:Obv:5551.1] aNaturalNumber0(skf9(xk)) || -> SkP3(skf9(xk))*.
% 1.67/1.91 5568[10:Obv:5532.1] aNaturalNumber0(skf14(skf9(xk))) || -> SkP3(skf14(skf9(xk)))*.
% 1.67/1.91 5614[1:SSi:5564.0,12.0,10.0] || -> SkP3(skf9(xk))*.
% 1.67/1.91 5616[10:SSi:5568.0,14.0,12.0,10.0] || -> SkP3(skf14(skf9(xk)))*.
% 1.80/1.99 5657[10:SoR:404.0,404.1,5616.0,60.1] aNaturalNumber0(skf9(xk)) || -> equal(skf9(xk),sz00) equal(skf9(xk),sz10)**.
% 1.80/1.99 5660[10:SSi:5657.0,5614.0,12.0,10.0] || -> equal(skf9(xk),sz00) equal(skf9(xk),sz10)**.
% 1.80/1.99 5661[10:MRR:5660.0,5660.1,2792.0,3016.0] || -> .
% 1.80/1.99 5666[1:Spt:5661.0,669.1,670.0] || SkP1(xp)* -> .
% 1.80/1.99 5667[1:Spt:5661.0,669.0,669.2] || -> doDivides0(xp,xp)* doDivides0(sz10,xp).
% 1.80/1.99 5790[1:Res:33.1,5666.0] isPrime0(xp) || -> .
% 1.80/1.99 5791[1:SSi:5790.0,7.0,5.0] || -> .
% 1.80/1.99 % SZS output end Refutation
% 1.80/1.99 Formulae used in the proof : mSortsC mSortsC_01 m__1837 m__1860 m__2306 m__ mPrimDiv m__1799 m__2287 mDefDiv m__1870 m__2075 m__2327 m_MulUnit m_MulZero mSortsB_02 mLETotal mMulComm mMonMul2 mDivLE mLEAsym mZeroMul mDivTrans mLETran mDefQuot
% 1.80/1.99
%------------------------------------------------------------------------------