TSTP Solution File: NUM507+3 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM507+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 14:26:55 EDT 2022
% Result : Theorem 1.68s 1.85s
% Output : Refutation 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : NUM507+3 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.15 % Command : run_spass %d %s
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Wed Jul 6 19:54:29 EDT 2022
% 0.16/0.37 % CPUTime :
% 1.68/1.85
% 1.68/1.85 SPASS V 3.9
% 1.68/1.85 SPASS beiseite: Proof found.
% 1.68/1.85 % SZS status Theorem
% 1.68/1.85 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.68/1.85 SPASS derived 2968 clauses, backtracked 573 clauses, performed 15 splits and kept 1990 clauses.
% 1.68/1.85 SPASS allocated 101916 KBytes.
% 1.68/1.85 SPASS spent 0:00:01.47 on the problem.
% 1.68/1.85 0:00:00.04 for the input.
% 1.68/1.85 0:00:00.04 for the FLOTTER CNF translation.
% 1.68/1.85 0:00:00.04 for inferences.
% 1.68/1.85 0:00:00.01 for the backtracking.
% 1.68/1.85 0:00:01.30 for the reduction.
% 1.68/1.85
% 1.68/1.85
% 1.68/1.85 Here is a proof with depth 5, length 166 :
% 1.68/1.85 % SZS output start Refutation
% 1.68/1.85 1[0:Inp] || -> aNaturalNumber0(sz00)*.
% 1.68/1.85 3[0:Inp] || -> aNaturalNumber0(xn)*.
% 1.68/1.85 4[0:Inp] || -> aNaturalNumber0(xm)*.
% 1.68/1.85 5[0:Inp] || -> aNaturalNumber0(xp)*.
% 1.68/1.85 7[0:Inp] || -> isPrime0(xp)*.
% 1.68/1.85 10[0:Inp] || -> aNaturalNumber0(xk)*.
% 1.68/1.85 11[0:Inp] || -> aNaturalNumber0(skc10)*.
% 1.68/1.85 12[0:Inp] || -> aNaturalNumber0(xr)*.
% 1.68/1.85 13[0:Inp] || -> isPrime0(xr)*.
% 1.68/1.85 16[0:Inp] || -> aNaturalNumber0(skc13)*.
% 1.68/1.85 17[0:Inp] || -> aNaturalNumber0(skf9(u))*.
% 1.68/1.85 20[0:Inp] || -> aNaturalNumber0(skf11(u))*.
% 1.68/1.85 23[0:Inp] || -> doDivides0(xr,xk)*.
% 1.68/1.85 24[0:Inp] || -> sdtlseqdt0(xk,xp)*.
% 1.68/1.85 29[0:Inp] || equal(xp,sz00)** -> .
% 1.68/1.85 30[0:Inp] || equal(xp,sz10)** -> .
% 1.68/1.85 37[0:Inp] || equal(xk,sz00)** -> .
% 1.68/1.85 38[0:Inp] || equal(xk,sz10)** -> .
% 1.68/1.85 39[0:Inp] || equal(xr,sz00)** -> .
% 1.68/1.85 40[0:Inp] || equal(xr,sz10)** -> .
% 1.68/1.85 41[0:Inp] || equal(xk,xp)** -> .
% 1.68/1.85 42[0:Inp] isPrime0(u) || -> SkP1(u)*.
% 1.68/1.85 43[0:Inp] || -> doDivides0(xp,sdtasdt0(xn,xm))*.
% 1.68/1.85 46[0:Inp] || -> equal(sdtasdt0(xr,skc10),xk)**.
% 1.68/1.85 49[0:Inp] || -> equal(sdtpldt0(xk,skc13),xp)**.
% 1.68/1.85 54[0:Inp] || -> equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk)**.
% 1.68/1.85 61[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(sz00,u),sz00)**.
% 1.68/1.85 64[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtpldt0(v,u))*.
% 1.68/1.85 65[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtasdt0(v,u))*.
% 1.68/1.85 69[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(v,u)* sdtlseqdt0(u,v)*.
% 1.68/1.85 72[0:Inp] || -> SkP1(u) equal(u,sz10) equal(u,sz00) doDivides0(skf11(u),u)*.
% 1.68/1.85 73[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtpldt0(v,u),sdtpldt0(u,v))*.
% 1.68/1.85 74[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtasdt0(v,u),sdtasdt0(u,v))*.
% 1.68/1.85 75[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(u,v) -> sdtlseqdt0(v,u)*.
% 1.68/1.85 79[0:Inp] || equal(skf11(u),sz10)** -> SkP1(u) equal(u,sz10) equal(u,sz00).
% 1.68/1.85 80[0:Inp] || equal(skf11(u),u)** -> SkP1(u) equal(u,sz10) equal(u,sz00).
% 1.68/1.85 81[0:Inp] aNaturalNumber0(u) || doDivides0(u,xp)* -> equal(u,xp) equal(u,sz10).
% 1.68/1.85 82[0:Inp] aNaturalNumber0(u) || doDivides0(u,xr)* -> equal(u,xr) equal(u,sz10).
% 1.68/1.85 83[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(u,v))*.
% 1.68/1.85 86[0:Inp] aNaturalNumber0(u) || -> isPrime0(u) equal(u,sz10) equal(u,sz00) doDivides0(skf9(u),u)*.
% 1.68/1.85 89[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> sdtlseqdt0(v,u) equal(u,sz00).
% 1.68/1.85 93[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 1.68/1.85 96[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> sdtlseqdt0(v,u)*.
% 1.68/1.85 102[0:Inp] aNaturalNumber0(u) isPrime0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> equal(v,u) equal(v,sz10).
% 1.68/1.85 104[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)*+ sdtlseqdt0(w,v)* -> sdtlseqdt0(w,u)*.
% 1.68/1.85 108[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || -> equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u)))**.
% 1.68/1.85 109[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> aNaturalNumber0(w)* equal(v,sz00).
% 1.68/1.85 116[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,u) -> equal(w,u) sdtlseqdt0(sdtpldt0(v,w),sdtpldt0(v,u))*.
% 1.68/1.85 119[0:Inp] || sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))* -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)).
% 1.68/1.85 123[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,w) equal(sdtpldt0(v,u),w)* -> equal(u,sdtmndt0(w,v))*.
% 1.68/1.85 132[0:MRR:123.3,96.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> equal(w,sdtmndt0(u,v))*.
% 1.68/1.85 157[1:Spt:119.1] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))**.
% 1.68/1.85 253[0:Res:72.3,82.1] aNaturalNumber0(skf11(xr)) || -> SkP1(xr) equal(xr,sz10) equal(xr,sz00) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 1.68/1.85 254[0:SSi:253.0,20.0,13.0,12.0] || -> SkP1(xr) equal(xr,sz10) equal(xr,sz00) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 1.68/1.85 255[0:MRR:254.1,254.2,40.0,39.0] || -> SkP1(xr) equal(skf11(xr),xr)** equal(skf11(xr),sz10).
% 1.68/1.85 256[0:Res:72.3,81.1] aNaturalNumber0(skf11(xp)) || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 1.68/1.85 257[0:SSi:256.0,20.0,7.0,5.0] || -> SkP1(xp) equal(xp,sz10) equal(xp,sz00) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 1.68/1.85 258[0:MRR:257.1,257.2,30.0,29.0] || -> SkP1(xp) equal(skf11(xp),xp)** equal(skf11(xp),sz10).
% 1.68/1.85 261[0:SpR:255.1,72.3] || -> SkP1(xr) equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00) doDivides0(xr,xr).
% 1.68/1.85 263[0:Obv:261.0] || -> equal(skf11(xr),sz10)** SkP1(xr) equal(xr,sz10) equal(xr,sz00) doDivides0(xr,xr).
% 1.68/1.85 264[0:MRR:263.2,263.3,40.0,39.0] || -> equal(skf11(xr),sz10)** SkP1(xr) doDivides0(xr,xr).
% 1.68/1.85 266[0:SpR:264.0,72.3] || -> SkP1(xr)* doDivides0(xr,xr) SkP1(xr)* equal(xr,sz10) equal(xr,sz00) doDivides0(sz10,xr).
% 1.68/1.85 270[0:Obv:266.0] || -> doDivides0(xr,xr) SkP1(xr)* equal(xr,sz10) equal(xr,sz00) doDivides0(sz10,xr).
% 1.68/1.85 271[0:MRR:270.2,270.3,40.0,39.0] || -> doDivides0(xr,xr) SkP1(xr)* doDivides0(sz10,xr).
% 1.68/1.85 272[2:Spt:271.1] || -> SkP1(xr)*.
% 1.68/1.85 303[0:SpL:258.1,80.0] || equal(xp,xp) -> SkP1(xp) equal(skf11(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00).
% 1.68/1.85 304[0:Obv:303.1] || -> equal(skf11(xp),sz10)** SkP1(xp) equal(xp,sz10) equal(xp,sz00).
% 1.68/1.85 305[0:MRR:304.0,304.2,304.3,79.0,30.0,29.0] || -> SkP1(xp)*.
% 1.68/1.85 362[1:SpR:73.2,157.0] aNaturalNumber0(xr) aNaturalNumber0(sdtpldt0(xn,xm)) || -> equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xn,xm)))**.
% 1.68/1.85 394[2:SSi:362.1,362.0,64.0,3.0,4.0,13.0,12.0,272.2] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xr,sdtpldt0(xn,xm)))**.
% 1.68/1.85 395[2:Rew:394.0,157.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xr,sdtpldt0(xn,xm)))**.
% 1.68/1.85 415[2:SpR:394.0,73.2] aNaturalNumber0(xp) aNaturalNumber0(sdtpldt0(xn,xm)) || -> equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))**.
% 1.68/1.85 422[2:SSi:415.1,415.0,64.0,3.0,4.0,7.0,5.0,305.2] || -> equal(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))**.
% 1.68/1.85 424[2:Rew:422.0,394.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xp,sdtpldt0(xn,xm)))**.
% 1.68/1.85 425[2:Rew:422.0,395.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xp,sdtpldt0(xn,xm)))**.
% 1.68/1.85 449[0:SpR:46.0,83.3] aNaturalNumber0(xr) aNaturalNumber0(skc10) || -> equal(skc10,sz00) sdtlseqdt0(xr,xk)*.
% 1.68/1.85 461[2:SSi:449.1,449.0,11.0,13.0,12.0,272.0] || -> equal(skc10,sz00) sdtlseqdt0(xr,xk)*.
% 1.68/1.85 472[3:Spt:461.0] || -> equal(skc10,sz00)**.
% 1.68/1.85 474[3:Rew:472.0,46.0] || -> equal(sdtasdt0(xr,sz00),xk)**.
% 1.68/1.85 481[3:SpR:474.0,74.2] aNaturalNumber0(xr) aNaturalNumber0(sz00) || -> equal(sdtasdt0(sz00,xr),xk)**.
% 1.68/1.85 489[3:Rew:61.1,481.2] aNaturalNumber0(xr) aNaturalNumber0(sz00) || -> equal(xk,sz00)**.
% 1.68/1.85 490[3:SSi:489.1,489.0,1.0,13.0,12.0,272.0] || -> equal(xk,sz00)**.
% 1.68/1.85 491[3:MRR:490.0,37.0] || -> .
% 1.68/1.85 492[3:Spt:491.0,461.0,472.0] || equal(skc10,sz00)** -> .
% 1.68/1.85 493[3:Spt:491.0,461.1] || -> sdtlseqdt0(xr,xk)*.
% 1.68/1.85 742[0:Res:23.0,89.2] aNaturalNumber0(xk) aNaturalNumber0(xr) || -> sdtlseqdt0(xr,xk)* equal(xk,sz00).
% 1.68/1.85 749[0:Res:86.4,89.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(skf9(u)) || -> isPrime0(u) equal(u,sz10) equal(u,sz00) sdtlseqdt0(skf9(u),u)* equal(u,sz00).
% 1.68/1.85 757[0:Obv:749.5] aNaturalNumber0(u) aNaturalNumber0(skf9(u)) || -> isPrime0(u) equal(u,sz10) sdtlseqdt0(skf9(u),u)* equal(u,sz00).
% 1.68/1.85 758[0:SSi:757.1,17.0] aNaturalNumber0(u) || -> isPrime0(u) equal(u,sz10) sdtlseqdt0(skf9(u),u)* equal(u,sz00).
% 1.68/1.85 861[3:Res:493.0,93.2] aNaturalNumber0(xk) aNaturalNumber0(xr) || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 1.68/1.85 872[3:SSi:861.1,861.0,13.0,12.0,272.0,10.0] || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 1.68/1.85 1083[0:SpL:49.0,96.3] aNaturalNumber0(u) aNaturalNumber0(xk) aNaturalNumber0(skc13) || equal(xp,u) -> sdtlseqdt0(xk,u)*.
% 1.77/1.93 1097[0:SSi:1083.2,1083.1,16.0,10.0] aNaturalNumber0(u) || equal(xp,u) -> sdtlseqdt0(xk,u)*.
% 1.77/1.93 1161[3:Res:1097.2,872.0] aNaturalNumber0(xr) || equal(xr,xp) -> equal(xk,xr)**.
% 1.77/1.93 1163[3:SSi:1161.0,13.0,12.0,272.0] || equal(xr,xp) -> equal(xk,xr)**.
% 1.77/1.93 1178[3:SpL:1163.1,41.0] || equal(xr,xp)** equal(xr,xp)** -> .
% 1.77/1.93 1184[3:Obv:1178.0] || equal(xr,xp)** -> .
% 1.77/1.93 1235[0:Res:23.0,102.3] aNaturalNumber0(xk) isPrime0(xk) aNaturalNumber0(xr) || -> equal(xk,xr)** equal(xr,sz10).
% 1.77/1.93 1276[2:SpR:108.3,424.0] aNaturalNumber0(xp) aNaturalNumber0(xm) aNaturalNumber0(xn) || -> equal(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,sdtpldt0(xm,xp)))**.
% 1.77/1.93 1277[2:SpR:108.3,425.0] aNaturalNumber0(xr) aNaturalNumber0(xm) aNaturalNumber0(xn) || -> equal(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,sdtpldt0(xm,xr)))**.
% 1.77/1.93 1304[2:SSi:1277.2,1277.1,1277.0,3.0,4.0,13.0,12.0,272.0] || -> equal(sdtpldt0(xp,sdtpldt0(xn,xm)),sdtpldt0(xn,sdtpldt0(xm,xr)))**.
% 1.77/1.93 1310[2:Rew:1304.0,424.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xr)))**.
% 1.77/1.93 1311[2:Rew:1304.0,425.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xn,sdtpldt0(xm,xr)))**.
% 1.77/1.93 1316[2:Rew:1304.0,1276.3] aNaturalNumber0(xp) aNaturalNumber0(xm) aNaturalNumber0(xn) || -> equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xp)))**.
% 1.77/1.93 1317[2:SSi:1316.2,1316.1,1316.0,3.0,4.0,7.0,5.0,305.0] || -> equal(sdtpldt0(xn,sdtpldt0(xm,xr)),sdtpldt0(xn,sdtpldt0(xm,xp)))**.
% 1.77/1.93 1324[2:Rew:1317.0,1310.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(xn,sdtpldt0(xm,xp)))**.
% 1.77/1.93 1325[2:Rew:1317.0,1311.0] || -> equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xn,sdtpldt0(xm,xp)))**.
% 1.77/1.93 1675[0:Res:24.0,104.3] aNaturalNumber0(xp) aNaturalNumber0(xk) aNaturalNumber0(u) || sdtlseqdt0(u,xk)* -> sdtlseqdt0(u,xp).
% 1.77/1.93 1704[0:SSi:1675.1,1675.0,10.0,7.0,5.0,305.0] aNaturalNumber0(u) || sdtlseqdt0(u,xk)* -> sdtlseqdt0(u,xp).
% 1.77/1.93 1753[0:Res:75.3,1704.1] aNaturalNumber0(xk) aNaturalNumber0(u) aNaturalNumber0(u) || equal(xk,u) -> sdtlseqdt0(u,xp)*.
% 1.77/1.93 1754[0:Res:69.2,1704.1] aNaturalNumber0(xk) aNaturalNumber0(u) aNaturalNumber0(u) || -> sdtlseqdt0(xk,u)* sdtlseqdt0(u,xp)*.
% 1.77/1.93 1758[0:Res:758.3,1704.1] aNaturalNumber0(xk) aNaturalNumber0(skf9(xk)) || -> isPrime0(xk) equal(xk,sz10) equal(xk,sz00) sdtlseqdt0(skf9(xk),xp)*.
% 1.77/1.93 1777[0:Obv:1754.1] aNaturalNumber0(xk) aNaturalNumber0(u) || -> sdtlseqdt0(xk,u)* sdtlseqdt0(u,xp)*.
% 1.77/1.93 1778[0:SSi:1777.0,10.0] aNaturalNumber0(u) || -> sdtlseqdt0(xk,u)* sdtlseqdt0(u,xp)*.
% 1.77/1.93 1780[0:Obv:1753.1] aNaturalNumber0(xk) aNaturalNumber0(u) || equal(xk,u) -> sdtlseqdt0(u,xp)*.
% 1.77/1.93 1781[0:SSi:1780.0,10.0] aNaturalNumber0(u) || equal(xk,u) -> sdtlseqdt0(u,xp)*.
% 1.77/1.93 1786[0:SSi:1758.1,1758.0,17.0,10.0,10.0] || -> isPrime0(xk) equal(xk,sz10) equal(xk,sz00) sdtlseqdt0(skf9(xk),xp)*.
% 1.77/1.93 1787[0:MRR:1786.1,1786.2,38.0,37.0] || -> isPrime0(xk) sdtlseqdt0(skf9(xk),xp)*.
% 1.77/1.93 1803[0:SpL:54.0,109.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 1.77/1.93 1804[0:SSi:1803.1,1803.0,7.0,5.0,305.2,65.0,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 1.77/1.93 1805[0:MRR:1804.0,1804.3,43.0,29.0] || equal(u,xk) -> aNaturalNumber0(u)*.
% 1.77/1.93 1816[0:MRR:1781.0,1805.1] || equal(xk,u) -> sdtlseqdt0(u,xp)*.
% 1.77/1.93 3368[2:SpL:1324.0,132.3] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(xn,xm)) aNaturalNumber0(xp) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> equal(sdtmndt0(u,sdtpldt0(xn,xm)),xp)**.
% 1.77/1.93 3374[2:SSi:3368.2,3368.1,7.0,5.0,305.2,64.0,3.0,4.0] aNaturalNumber0(u) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> equal(sdtmndt0(u,sdtpldt0(xn,xm)),xp)**.
% 1.77/1.93 3401[2:SpL:1325.0,132.3] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(xn,xm)) aNaturalNumber0(xr) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> equal(sdtmndt0(u,sdtpldt0(xn,xm)),xr)**.
% 1.77/1.93 3407[2:Rew:3374.2,3401.4] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(xn,xm)) aNaturalNumber0(xr) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> equal(xr,xp).
% 1.77/1.93 3408[2:SSi:3407.2,3407.1,13.0,12.0,272.2,64.0,3.0,4.0] aNaturalNumber0(u) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> equal(xr,xp).
% 1.77/1.93 3409[3:MRR:3408.2,1184.0] aNaturalNumber0(u) || equal(sdtpldt0(xn,sdtpldt0(xm,xp)),u)* -> .
% 1.77/1.93 3567[3:EqR:3409.1] aNaturalNumber0(sdtpldt0(xn,sdtpldt0(xm,xp))) || -> .
% 1.77/1.93 3568[3:SSi:3567.0,64.0,3.0,64.0,4.0,7.2,5.0,305.2] || -> .
% 1.77/1.93 3569[2:Spt:3568.0,271.1,272.0] || SkP1(xr)* -> .
% 1.77/1.93 3570[2:Spt:3568.0,271.0,271.2] || -> doDivides0(xr,xr)* doDivides0(sz10,xr).
% 1.77/1.93 3576[0:SSi:742.1,13.0,12.0] aNaturalNumber0(xk) || -> sdtlseqdt0(xr,xk)* equal(xk,sz00).
% 1.77/1.93 3577[0:MRR:3576.0,3576.2,10.0,37.0] || -> sdtlseqdt0(xr,xk)*.
% 1.77/1.93 3585[0:SSi:1235.2,13.0,12.0] aNaturalNumber0(xk) isPrime0(xk) || -> equal(xk,xr)** equal(xr,sz10).
% 1.77/1.93 3586[0:MRR:3585.3,40.0] aNaturalNumber0(xk) isPrime0(xk) || -> equal(xk,xr)**.
% 1.77/1.93 3587[0:MRR:3586.0,10.0] isPrime0(xk) || -> equal(xk,xr)**.
% 1.77/1.93 3696[2:Res:42.1,3569.0] isPrime0(xr) || -> .
% 1.77/1.93 3697[2:SSi:3696.0,13.0,12.0] || -> .
% 1.77/1.93 3698[1:Spt:3697.0,119.1,157.0] || equal(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))** -> .
% 1.77/1.93 3699[1:Spt:3697.0,119.0] || sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))* -> .
% 1.77/1.93 3730[1:Res:116.5,3699.0] aNaturalNumber0(xp) aNaturalNumber0(sdtpldt0(xn,xm)) aNaturalNumber0(xr) || sdtlseqdt0(xr,xp)* -> equal(xr,xp).
% 1.77/1.93 3731[1:SSi:3730.2,3730.1,3730.0,13.0,12.0,64.0,3.0,4.0,7.2,5.0,305.0] || sdtlseqdt0(xr,xp)* -> equal(xr,xp).
% 1.77/1.93 3738[0:Res:3577.0,93.2] aNaturalNumber0(xk) aNaturalNumber0(xr) || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 1.77/1.93 3739[0:SSi:3738.1,3738.0,13.0,12.0,10.0] || sdtlseqdt0(xk,xr)* -> equal(xk,xr).
% 1.77/1.93 3876[2:Spt:1787.0] || -> isPrime0(xk)*.
% 1.77/1.93 3877[2:MRR:3587.0,3876.0] || -> equal(xk,xr)**.
% 1.77/1.93 3879[2:Rew:3877.0,24.0] || -> sdtlseqdt0(xr,xp)*.
% 1.77/1.93 3963[2:MRR:3731.0,3879.0] || -> equal(xr,xp)**.
% 1.77/1.93 4011[2:Rew:3963.0,3698.0] || equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))* -> .
% 1.77/1.93 4118[2:Obv:4011.0] || -> .
% 1.77/1.93 4180[2:Spt:4118.0,1787.0,3876.0] || isPrime0(xk)* -> .
% 1.77/1.93 4181[2:Spt:4118.0,1787.1] || -> sdtlseqdt0(skf9(xk),xp)*.
% 1.77/1.93 4348[1:Res:69.2,3731.0] aNaturalNumber0(xp) aNaturalNumber0(xr) || -> sdtlseqdt0(xp,xr)* equal(xr,xp).
% 1.77/1.93 4361[1:SSi:4348.1,4348.0,12.0,13.0,7.0,5.0,305.0] || -> sdtlseqdt0(xp,xr)* equal(xr,xp).
% 1.77/1.93 4383[3:Spt:4361.1] || -> equal(xr,xp)**.
% 1.77/1.93 4430[3:Rew:4383.0,3698.0] || equal(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))* -> .
% 1.77/1.93 4503[3:Obv:4430.0] || -> .
% 1.77/1.93 4521[3:Spt:4503.0,4361.1,4383.0] || equal(xr,xp)** -> .
% 1.77/1.93 4522[3:Spt:4503.0,4361.0] || -> sdtlseqdt0(xp,xr)*.
% 1.77/1.93 4523[3:MRR:3731.1,4521.0] || sdtlseqdt0(xr,xp)* -> .
% 1.77/1.93 4727[3:Res:1816.1,4523.0] || equal(xk,xr)** -> .
% 1.77/1.93 4734[3:MRR:3739.1,4727.0] || sdtlseqdt0(xk,xr)* -> .
% 1.77/1.93 4901[3:Res:1778.1,4734.0] aNaturalNumber0(xr) || -> sdtlseqdt0(xr,xp)*.
% 1.77/1.93 4905[3:SSi:4901.0,13.0,12.0] || -> sdtlseqdt0(xr,xp)*.
% 1.77/1.93 4906[3:MRR:4905.0,4523.0] || -> .
% 1.77/1.93 % SZS output end Refutation
% 1.77/1.93 Formulae used in the proof : mSortsC m__1837 m__1860 m__2306 m__2342 m__2377 mDefPrime m__1799 m__2327 m_MulZero mSortsB mSortsB_02 mLETotal mAddComm mMulComm mMonMul2 mDivLE mLEAsym mDefLE mLETran mAddAsso mDefQuot mMonAdd m__ mDefDiff
% 1.77/1.93
%------------------------------------------------------------------------------