TSTP Solution File: NUM503+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM503+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 14:26:52 EDT 2022
% Result : Theorem 174.01s 174.27s
% Output : Refutation 226.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : NUM503+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 5 17:07:43 EDT 2022
% 0.13/0.36 % CPUTime :
% 174.01/174.27
% 174.01/174.27 SPASS V 3.9
% 174.01/174.27 SPASS beiseite: Proof found.
% 174.01/174.27 % SZS status Theorem
% 174.01/174.27 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 174.01/174.27 SPASS derived 48372 clauses, backtracked 10780 clauses, performed 21 splits and kept 23359 clauses.
% 174.01/174.27 SPASS allocated 164268 KBytes.
% 174.01/174.27 SPASS spent 0:2:53.82 on the problem.
% 174.01/174.27 0:00:00.04 for the input.
% 174.01/174.27 0:00:00.04 for the FLOTTER CNF translation.
% 174.01/174.27 0:00:00.67 for inferences.
% 174.01/174.27 0:00:02.07 for the backtracking.
% 174.01/174.27 0:2:50.53 for the reduction.
% 174.01/174.27
% 174.01/174.27
% 174.01/174.27 Here is a proof with depth 9, length 268 :
% 174.01/174.27 % SZS output start Refutation
% 174.01/174.27 1[0:Inp] || -> aNaturalNumber0(sz00)*.
% 174.01/174.27 2[0:Inp] || -> aNaturalNumber0(sz10)*.
% 174.01/174.27 3[0:Inp] || -> aNaturalNumber0(xn)*.
% 174.01/174.27 4[0:Inp] || -> aNaturalNumber0(xm)*.
% 174.01/174.27 5[0:Inp] || -> aNaturalNumber0(xp)*.
% 174.01/174.27 6[0:Inp] || -> isPrime0(xp)*.
% 174.01/174.27 7[0:Inp] || -> aNaturalNumber0(xr)*.
% 174.01/174.27 8[0:Inp] || -> isPrime0(xr)*.
% 174.01/174.27 11[0:Inp] || -> sdtlseqdt0(xn,xp)*.
% 174.01/174.27 12[0:Inp] || -> sdtlseqdt0(xm,xp)*.
% 174.01/174.27 15[0:Inp] || -> sdtlseqdt0(xp,xk)*.
% 174.01/174.27 16[0:Inp] || equal(sz10,sz00)** -> .
% 174.01/174.27 17[0:Inp] || -> aNaturalNumber0(skf4(u,v))*.
% 174.01/174.27 18[0:Inp] || -> aNaturalNumber0(skf5(u,v))*.
% 174.01/174.27 20[0:Inp] || sdtlseqdt0(xp,xm)* -> .
% 174.01/174.27 21[0:Inp] || equal(xp,xn)** -> .
% 174.01/174.27 22[0:Inp] || equal(xp,xm)** -> .
% 174.01/174.27 25[0:Inp] || equal(xk,sz00)** -> .
% 174.01/174.27 27[0:Inp] || -> doDivides0(xp,sdtasdt0(xn,xm))*.
% 174.01/174.27 28[0:Inp] || -> doDivides0(xr,sdtasdt0(xn,xm))*.
% 174.01/174.27 30[0:Inp] || -> equal(sdtsldt0(sdtasdt0(xn,xm),xp),xk)**.
% 174.01/174.27 32[0:Inp] aNaturalNumber0(u) || -> equal(sdtpldt0(sz00,u),u)**.
% 174.01/174.27 33[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(u,sz10),u)**.
% 174.01/174.27 36[0:Inp] aNaturalNumber0(u) || -> equal(sdtasdt0(sz00,u),sz00)**.
% 174.01/174.27 37[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtpldt0(v,u))*.
% 174.01/174.27 38[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> aNaturalNumber0(sdtasdt0(v,u))*.
% 174.01/174.27 39[0:Inp] aNaturalNumber0(u) isPrime0(u) || equal(u,sz00)* -> .
% 174.01/174.27 40[0:Inp] aNaturalNumber0(u) isPrime0(u) || equal(u,sz10)* -> .
% 174.01/174.27 41[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(v,u)* sdtlseqdt0(u,v)*.
% 174.01/174.27 45[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtasdt0(v,u),sdtasdt0(u,v))*.
% 174.01/174.27 46[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || equal(u,v) -> sdtlseqdt0(v,u)*.
% 174.01/174.27 49[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(u,v))*.
% 174.01/174.27 54[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> sdtlseqdt0(v,u) equal(u,sz00).
% 174.01/174.27 57[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) -> equal(sdtpldt0(v,skf4(u,v)),u)**.
% 174.01/174.27 58[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ sdtlseqdt0(u,v)* -> equal(v,u).
% 174.01/174.27 59[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) -> equal(sdtasdt0(v,skf5(v,u)),u)**.
% 174.01/174.27 61[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> sdtlseqdt0(v,u)*.
% 174.01/174.27 62[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u) equal(w,sdtmndt0(u,v))*+ -> aNaturalNumber0(w)*.
% 174.01/174.27 63[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(u,sdtasdt0(v,w))*+ -> doDivides0(v,u)*.
% 174.01/174.27 64[0:Inp] aNaturalNumber0(u) isPrime0(u) aNaturalNumber0(v) || doDivides0(v,u)* -> equal(v,u) equal(v,sz10).
% 174.01/174.27 65[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || doDivides0(v,u)*+ doDivides0(w,v)* -> doDivides0(w,u)*.
% 174.01/174.27 66[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)*+ sdtlseqdt0(w,v)* -> sdtlseqdt0(w,u)*.
% 174.01/174.27 71[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> aNaturalNumber0(w)* equal(v,sz00).
% 174.01/174.27 79[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtasdt0(v,w),sdtasdt0(u,w))* -> equal(v,u) equal(w,sz00).
% 174.01/174.27 81[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) equal(w,sdtsldt0(u,v))*+ -> equal(v,sz00) equal(u,sdtasdt0(v,w))*.
% 174.01/174.27 84[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,w) equal(sdtpldt0(v,u),w)* -> equal(u,sdtmndt0(w,v))*.
% 174.01/174.27 85[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u) -> equal(v,u) equal(w,sz00) sdtlseqdt0(sdtasdt0(v,w),sdtasdt0(u,w))*.
% 174.01/174.27 86[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u) -> equal(v,u) equal(w,sz00) sdtlseqdt0(sdtasdt0(w,v),sdtasdt0(w,u))*.
% 174.01/174.27 88[0:Inp] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || doDivides0(v,w) equal(w,sdtasdt0(v,u))* -> equal(u,sdtsldt0(w,v))* equal(v,sz00).
% 174.01/174.27 91[0:Inp] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))* sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 93[0:MRR:84.3,61.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(sdtpldt0(v,w),u)*+ -> equal(w,sdtmndt0(u,v))*.
% 174.01/174.27 94[0:MRR:88.3,63.4] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || equal(u,sdtasdt0(v,w))*+ -> equal(v,sz00) equal(w,sdtsldt0(u,v))*.
% 174.01/174.27 108[0:EmS:40.0,40.1,5.0,6.0] || equal(xp,sz10)** -> .
% 174.01/174.27 110[0:EmS:39.0,39.1,5.0,6.0] || equal(xp,sz00)** -> .
% 174.01/174.27 185[0:SpR:45.2,49.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(v,u))*.
% 174.01/174.27 190[0:Obv:185.1] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(v,sz00) sdtlseqdt0(u,sdtasdt0(v,u))*.
% 174.01/174.27 216[0:Res:28.0,54.2] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xr) || -> sdtlseqdt0(xr,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),sz00).
% 174.01/174.27 217[0:Res:27.0,54.2] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || -> sdtlseqdt0(xp,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),sz00).
% 174.01/174.27 220[0:SSi:216.1,216.0,8.0,7.0,38.2,3.0,4.0] || -> sdtlseqdt0(xr,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),sz00).
% 174.01/174.27 221[0:SSi:217.1,217.0,6.0,5.0,38.2,3.0,4.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),sz00).
% 174.01/174.27 226[1:Spt:220.1] || -> equal(sdtasdt0(xn,xm),sz00)**.
% 174.01/174.27 228[1:Rew:226.0,27.0] || -> doDivides0(xp,sz00)*.
% 174.01/174.27 229[1:Rew:226.0,30.0] || -> equal(sdtsldt0(sz00,xp),xk)**.
% 174.01/174.27 278[0:SpR:59.3,36.1] aNaturalNumber0(u) aNaturalNumber0(sz00) aNaturalNumber0(skf5(sz00,u)) || doDivides0(sz00,u)* -> equal(u,sz00).
% 174.01/174.27 284[0:SSi:278.2,278.1,18.0,1.0,1.0] aNaturalNumber0(u) || doDivides0(sz00,u)* -> equal(u,sz00).
% 174.01/174.27 308[0:Res:15.0,58.2] aNaturalNumber0(xk) aNaturalNumber0(xp) || sdtlseqdt0(xk,xp)* -> equal(xk,xp).
% 174.01/174.27 320[0:SSi:308.1,6.0,5.0] aNaturalNumber0(xk) || sdtlseqdt0(xk,xp)* -> equal(xk,xp).
% 174.01/174.27 406[0:EqR:61.3] aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 174.01/174.27 411[0:SpL:57.3,61.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(skf4(u,v)) || sdtlseqdt0(v,u)* equal(u,w)* -> sdtlseqdt0(v,w)*.
% 174.01/174.27 412[0:SSi:406.0,37.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> sdtlseqdt0(u,sdtpldt0(u,v))*.
% 174.01/174.27 418[0:Obv:411.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(skf4(u,w)) || sdtlseqdt0(w,u)* equal(u,v)* -> sdtlseqdt0(w,v)*.
% 174.01/174.27 419[0:SSi:418.3,17.0] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,u)* equal(u,v)* -> sdtlseqdt0(w,v)*.
% 174.01/174.27 420[0:SpR:32.1,412.2] aNaturalNumber0(u) aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 174.01/174.27 426[0:Obv:420.0] aNaturalNumber0(sz00) aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 174.01/174.27 427[0:SSi:426.0,1.0] aNaturalNumber0(u) || -> sdtlseqdt0(sz00,u)*.
% 174.01/174.27 434[0:Res:427.1,58.2] aNaturalNumber0(u) aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 174.01/174.27 436[0:Obv:434.0] aNaturalNumber0(u) aNaturalNumber0(sz00) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 174.01/174.27 437[0:SSi:436.1,1.0] aNaturalNumber0(u) || sdtlseqdt0(u,sz00)* -> equal(sz00,u).
% 174.01/174.27 452[0:EqR:63.3] aNaturalNumber0(sdtasdt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> doDivides0(u,sdtasdt0(u,v))*.
% 174.01/174.27 457[0:SpL:33.1,63.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(u) aNaturalNumber0(sz10) || equal(v,u) -> doDivides0(u,v)*.
% 174.01/174.27 461[0:SSi:452.0,38.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> doDivides0(u,sdtasdt0(u,v))*.
% 174.01/174.27 471[0:Obv:457.0] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(sz10) || equal(u,v) -> doDivides0(v,u)*.
% 174.01/174.27 472[0:SSi:471.2,2.0] aNaturalNumber0(u) aNaturalNumber0(v) || equal(u,v) -> doDivides0(v,u)*.
% 174.01/174.27 495[0:SpR:45.2,461.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(v) aNaturalNumber0(u) || -> doDivides0(v,sdtasdt0(u,v))*.
% 174.01/174.27 514[0:Obv:495.1] aNaturalNumber0(u) aNaturalNumber0(v) || -> doDivides0(u,sdtasdt0(v,u))*.
% 174.01/174.27 797[0:EqR:93.3] aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtmndt0(sdtpldt0(u,v),u),v)**.
% 174.01/174.27 804[0:SSi:797.0,37.2] aNaturalNumber0(u) aNaturalNumber0(v) || -> equal(sdtmndt0(sdtpldt0(u,v),u),v)**.
% 174.01/174.27 823[0:SpL:804.2,62.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(sdtpldt0(u,v)) aNaturalNumber0(u) || sdtlseqdt0(u,sdtpldt0(u,v))* equal(w,v)* -> aNaturalNumber0(w)*.
% 174.01/174.27 838[0:Obv:823.0] aNaturalNumber0(u) aNaturalNumber0(sdtpldt0(v,u)) aNaturalNumber0(v) || sdtlseqdt0(v,sdtpldt0(v,u))* equal(w,u)* -> aNaturalNumber0(w)*.
% 174.01/174.27 839[0:SSi:838.1,37.2] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,sdtpldt0(v,u))* equal(w,u)* -> aNaturalNumber0(w)*.
% 174.01/174.27 840[0:MRR:839.2,412.2] aNaturalNumber0(u) aNaturalNumber0(v) || equal(w,u)* -> aNaturalNumber0(w)*.
% 174.01/174.27 844[0:MRR:419.1,840.3] aNaturalNumber0(u) aNaturalNumber0(v) || sdtlseqdt0(v,u)*+ equal(u,w)* -> sdtlseqdt0(v,w)*.
% 174.01/174.27 936[0:EmS:840.1,17.0] aNaturalNumber0(u) || equal(v,u)*+ -> aNaturalNumber0(v)*.
% 174.01/174.27 947[0:MRR:46.1,936.2] aNaturalNumber0(u) || equal(u,v) -> sdtlseqdt0(v,u)*.
% 174.01/174.27 949[0:MRR:472.1,936.2] aNaturalNumber0(u) || equal(u,v) -> doDivides0(v,u)*.
% 174.01/174.27 965[0:SoR:320.0,936.2] aNaturalNumber0(u) || sdtlseqdt0(xk,xp)*+ equal(xk,u)* -> equal(xk,xp).
% 174.01/174.27 1195[0:Res:41.3,66.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(v) aNaturalNumber0(u) aNaturalNumber0(w) || sdtlseqdt0(w,u)* -> sdtlseqdt0(v,u)* sdtlseqdt0(w,v)*.
% 174.01/174.27 1209[0:Obv:1195.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(w,v)*+ -> sdtlseqdt0(u,v)* sdtlseqdt0(w,u)*.
% 174.01/174.27 1262[0:EqR:71.3] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) -> aNaturalNumber0(sdtsldt0(u,v))* equal(v,sz00).
% 174.01/174.27 1263[1:SpL:229.0,71.3] aNaturalNumber0(sz00) aNaturalNumber0(xp) || doDivides0(xp,sz00)* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 174.01/174.27 1264[1:SSi:1263.1,1263.0,6.0,5.0,1.0] || doDivides0(xp,sz00)* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 174.01/174.27 1265[1:MRR:1264.0,1264.3,228.0,110.0] || equal(u,xk) -> aNaturalNumber0(u)*.
% 174.01/174.27 2311[0:EqR:81.3] aNaturalNumber0(u) aNaturalNumber0(v) || doDivides0(v,u) -> equal(v,sz00) equal(sdtasdt0(v,sdtsldt0(u,v)),u)**.
% 174.01/174.27 2313[1:SpL:229.0,81.3] aNaturalNumber0(sz00) aNaturalNumber0(xp) || doDivides0(xp,sz00) equal(u,xk) -> equal(xp,sz00) equal(sdtasdt0(xp,u),sz00)**.
% 174.01/174.27 2314[1:SSi:2313.1,2313.0,6.0,5.0,1.0] || doDivides0(xp,sz00) equal(u,xk) -> equal(xp,sz00) equal(sdtasdt0(xp,u),sz00)**.
% 174.01/174.27 2315[1:MRR:2314.0,2314.2,228.0,110.0] || equal(u,xk) -> equal(sdtasdt0(xp,u),sz00)**.
% 174.01/174.27 2319[1:SpR:2315.1,190.3] aNaturalNumber0(u) aNaturalNumber0(xp) || equal(u,xk) -> equal(xp,sz00) sdtlseqdt0(u,sz00)*.
% 174.01/174.27 2340[1:SSi:2319.1,6.0,5.0] aNaturalNumber0(u) || equal(u,xk) -> equal(xp,sz00) sdtlseqdt0(u,sz00)*.
% 174.01/174.27 2341[1:MRR:2340.0,2340.2,1265.1,110.0] || equal(u,xk) -> sdtlseqdt0(u,sz00)*.
% 174.01/174.27 2357[1:Res:2341.1,437.1] aNaturalNumber0(u) || equal(u,xk)* -> equal(sz00,u).
% 174.01/174.27 2368[1:MRR:2357.0,1265.1] || equal(u,xk)* -> equal(sz00,u).
% 174.01/174.27 2391[0:Res:11.0,66.3] aNaturalNumber0(xp) aNaturalNumber0(xn) aNaturalNumber0(u) || sdtlseqdt0(u,xn) -> sdtlseqdt0(u,xp)*.
% 174.01/174.27 2393[0:SSi:2391.1,2391.0,3.0,6.0,5.0] aNaturalNumber0(u) || sdtlseqdt0(u,xn) -> sdtlseqdt0(u,xp)*.
% 174.01/174.27 2449[1:EqR:2368.0] || -> equal(xk,sz00)**.
% 174.01/174.27 2450[1:MRR:2449.0,25.0] || -> .
% 174.01/174.27 2451[1:Spt:2450.0,220.1,226.0] || equal(sdtasdt0(xn,xm),sz00)** -> .
% 174.01/174.27 2452[1:Spt:2450.0,220.0] || -> sdtlseqdt0(xr,sdtasdt0(xn,xm))*.
% 174.01/174.27 2453[1:MRR:221.1,2451.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,xm))*.
% 174.01/174.27 2461[0:Res:12.0,66.3] aNaturalNumber0(xp) aNaturalNumber0(xm) aNaturalNumber0(u) || sdtlseqdt0(u,xm) -> sdtlseqdt0(u,xp)*.
% 174.01/174.27 2463[0:SSi:2461.1,2461.0,4.0,6.0,5.0] aNaturalNumber0(u) || sdtlseqdt0(u,xm) -> sdtlseqdt0(u,xp)*.
% 174.01/174.27 2488[1:Res:2453.0,58.2] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2490[1:SSi:2488.1,2488.0,6.0,5.0,38.2,3.0,4.0] || sdtlseqdt0(sdtasdt0(xn,xm),xp)* -> equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2496[0:SpL:30.0,81.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm)) equal(u,xk) -> equal(xp,sz00) equal(sdtasdt0(xp,u),sdtasdt0(xn,xm))**.
% 174.01/174.27 2497[0:SpL:30.0,71.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 174.01/174.27 2499[0:SSi:2497.1,2497.0,6.0,5.0,38.2,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm))* equal(u,xk) -> aNaturalNumber0(u)* equal(xp,sz00).
% 174.01/174.27 2500[0:MRR:2499.0,2499.3,27.0,110.0] || equal(u,xk) -> aNaturalNumber0(u)*.
% 174.01/174.27 2501[0:MRR:965.0,2500.1] || sdtlseqdt0(xk,xp)* equal(xk,u)* -> equal(xk,xp).
% 174.01/174.27 2506[0:AED:16.0,2501.1] || sdtlseqdt0(xk,xp)* -> equal(xk,xp).
% 174.01/174.27 2511[0:SSi:2496.1,2496.0,6.0,5.0,38.2,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm)) equal(u,xk) -> equal(xp,sz00) equal(sdtasdt0(xp,u),sdtasdt0(xn,xm))**.
% 174.01/174.27 2512[0:MRR:2511.0,2511.2,27.0,110.0] || equal(u,xk) -> equal(sdtasdt0(xp,u),sdtasdt0(xn,xm))**.
% 174.01/174.27 2545[0:SpR:45.2,86.6] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(v) aNaturalNumber0(u) || sdtlseqdt0(v,w) -> equal(v,w) equal(u,sz00) sdtlseqdt0(sdtasdt0(v,u),sdtasdt0(u,w))*.
% 174.01/174.27 2561[0:Obv:2545.1] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u) -> equal(v,u) equal(w,sz00) sdtlseqdt0(sdtasdt0(v,w),sdtasdt0(w,u))*.
% 174.01/174.27 2591[0:Res:2393.2,2506.0] aNaturalNumber0(xk) || sdtlseqdt0(xk,xn)* -> equal(xk,xp).
% 174.01/174.27 2621[0:Res:85.6,58.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) aNaturalNumber0(sdtasdt0(u,w)) aNaturalNumber0(sdtasdt0(v,w)) || sdtlseqdt0(v,u)* sdtlseqdt0(sdtasdt0(u,w),sdtasdt0(v,w))* -> equal(v,u) equal(w,sz00) equal(sdtasdt0(v,w),sdtasdt0(u,w)).
% 174.01/174.27 2646[0:SSi:2621.4,2621.3,38.2,38.2] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)* sdtlseqdt0(sdtasdt0(u,w),sdtasdt0(v,w))* -> equal(v,u) equal(w,sz00) equal(sdtasdt0(v,w),sdtasdt0(u,w)).
% 174.01/174.27 2647[0:MRR:2646.7,79.3] aNaturalNumber0(u) aNaturalNumber0(v) aNaturalNumber0(w) || sdtlseqdt0(v,u)* sdtlseqdt0(sdtasdt0(u,w),sdtasdt0(v,w))*+ -> equal(v,u) equal(w,sz00).
% 174.01/174.27 2661[0:SoR:2591.0,2500.1] || sdtlseqdt0(xk,xn)* equal(xk,xk) -> equal(xk,xp).
% 174.01/174.27 2662[0:Obv:2661.1] || sdtlseqdt0(xk,xn)* -> equal(xk,xp).
% 174.01/174.27 2665[0:Res:41.2,2662.0] aNaturalNumber0(xn) aNaturalNumber0(xk) || -> sdtlseqdt0(xn,xk)* equal(xk,xp).
% 174.01/174.27 2669[0:SSi:2665.0,3.0] aNaturalNumber0(xk) || -> sdtlseqdt0(xn,xk)* equal(xk,xp).
% 174.01/174.27 2674[0:SoR:2669.0,2500.1] || equal(xk,xk) -> sdtlseqdt0(xn,xk)* equal(xk,xp).
% 174.01/174.27 2675[0:Obv:2674.0] || -> sdtlseqdt0(xn,xk)* equal(xk,xp).
% 174.01/174.27 2756[2:Spt:2675.1] || -> equal(xk,xp)**.
% 174.01/174.27 2765[2:Rew:2756.0,2500.0] || equal(u,xp) -> aNaturalNumber0(u)*.
% 174.01/174.27 2768[2:Rew:2756.0,91.0] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xp)) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm))** equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 2770[2:Rew:2756.0,2512.0] || equal(u,xp) -> equal(sdtasdt0(xp,u),sdtasdt0(xn,xm))**.
% 174.01/174.27 2775[2:Rew:2756.0,2768.2] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xp))* sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xp),sdtasdt0(xp,xm)) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 2829[1:Res:2463.2,2490.0] aNaturalNumber0(sdtasdt0(xn,xm)) || sdtlseqdt0(sdtasdt0(xn,xm),xm)* -> equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2831[1:SSi:2829.0,38.0,3.0,4.2] || sdtlseqdt0(sdtasdt0(xn,xm),xm)* -> equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2859[1:Res:41.2,2831.0] aNaturalNumber0(xm) aNaturalNumber0(sdtasdt0(xn,xm)) || -> sdtlseqdt0(xm,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2863[1:SSi:2859.1,2859.0,38.0,3.0,4.0,4.2] || -> sdtlseqdt0(xm,sdtasdt0(xn,xm))* equal(sdtasdt0(xn,xm),xp).
% 174.01/174.27 2865[3:Spt:2863.1] || -> equal(sdtasdt0(xn,xm),xp)**.
% 174.01/174.27 2890[3:SpR:2865.0,514.2] aNaturalNumber0(xm) aNaturalNumber0(xn) || -> doDivides0(xm,xp)*.
% 174.01/174.27 2893[3:SpR:2865.0,461.2] aNaturalNumber0(xn) aNaturalNumber0(xm) || -> doDivides0(xn,xp)*.
% 174.01/174.27 2907[3:SSi:2890.1,2890.0,3.0,4.0] || -> doDivides0(xm,xp)*.
% 174.01/174.27 2908[3:SSi:2893.1,2893.0,4.0,3.0] || -> doDivides0(xn,xp)*.
% 174.01/174.27 2922[3:Res:2907.0,64.3] aNaturalNumber0(xp) isPrime0(xp) aNaturalNumber0(xm) || -> equal(xp,xm)** equal(xm,sz10).
% 174.01/174.27 2924[3:SSi:2922.2,2922.1,2922.0,4.0,6.0,5.0,6.0,5.0] || -> equal(xp,xm)** equal(xm,sz10).
% 174.01/174.27 2925[3:MRR:2924.0,22.0] || -> equal(xm,sz10)**.
% 174.01/174.27 2932[3:Rew:2925.0,2865.0] || -> equal(sdtasdt0(xn,sz10),xp)**.
% 174.01/174.27 2968[3:Res:2908.0,64.3] aNaturalNumber0(xp) isPrime0(xp) aNaturalNumber0(xn) || -> equal(xp,xn)** equal(xn,sz10).
% 174.01/174.27 2970[3:SSi:2968.2,2968.1,2968.0,3.0,6.0,5.0,6.0,5.0] || -> equal(xp,xn)** equal(xn,sz10).
% 174.01/174.27 2971[3:MRR:2970.0,21.0] || -> equal(xn,sz10)**.
% 174.01/174.27 2982[3:Rew:2971.0,2932.0] || -> equal(sdtasdt0(sz10,sz10),xp)**.
% 174.01/174.27 3046[3:SpR:2982.0,33.1] aNaturalNumber0(sz10) || -> equal(xp,sz10)**.
% 174.01/174.27 3065[3:SSi:3046.0,2.0] || -> equal(xp,sz10)**.
% 174.01/174.27 3066[3:MRR:3065.0,108.0] || -> .
% 174.01/174.27 3096[3:Spt:3066.0,2863.1,2865.0] || equal(sdtasdt0(xn,xm),xp)** -> .
% 174.01/174.27 3097[3:Spt:3066.0,2863.0] || -> sdtlseqdt0(xm,sdtasdt0(xn,xm))*.
% 174.01/174.27 3172[4:Spt:2775.2] || -> equal(sdtasdt0(xp,xp),sdtasdt0(xp,xm))**.
% 174.01/174.27 3190[4:SpL:3172.0,94.3] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(xp) || equal(u,sdtasdt0(xp,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xp)**.
% 174.01/174.27 3222[4:Obv:3190.1] aNaturalNumber0(u) aNaturalNumber0(xp) || equal(u,sdtasdt0(xp,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xp)**.
% 174.01/174.27 3223[4:SSi:3222.1,6.0,5.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xp,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xp)**.
% 174.01/174.27 3224[4:MRR:3223.2,110.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xp,xm))* -> equal(sdtsldt0(u,xp),xp)**.
% 174.01/174.27 3400[2:SpR:2770.1,38.2] aNaturalNumber0(u) aNaturalNumber0(xp) || equal(u,xp)* -> aNaturalNumber0(sdtasdt0(xn,xm))*.
% 174.01/174.27 3401[2:SpR:2770.1,45.2] aNaturalNumber0(u) aNaturalNumber0(xp) || equal(u,xp) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 174.01/174.27 3423[4:SpR:2770.1,3172.0] || equal(xp,xp) -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm))**.
% 174.01/174.27 3434[4:Obv:3423.0] || -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm))**.
% 174.01/174.27 3452[4:Rew:3434.0,3224.1] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(sdtsldt0(u,xp),xp)**.
% 174.01/174.27 3477[2:SSi:3401.1,6.0,5.0] aNaturalNumber0(u) || equal(u,xp) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 174.01/174.27 3478[2:MRR:3477.0,2765.1] || equal(u,xp) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 174.01/174.27 3520[4:SpL:3434.0,94.3] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(xm) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(sdtsldt0(u,xp),xm)**.
% 174.01/174.27 3544[4:Rew:3452.2,3520.5] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(xm) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(xp,xm).
% 174.01/174.27 3545[4:SSi:3544.2,3544.1,4.0,6.0,5.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> equal(xp,sz00) equal(xp,xm).
% 174.01/174.27 3546[4:MRR:3545.2,3545.3,110.0,22.0] aNaturalNumber0(u) || equal(u,sdtasdt0(xn,xm))* -> .
% 174.01/174.27 3687[4:EqR:3546.1] aNaturalNumber0(sdtasdt0(xn,xm)) || -> .
% 174.01/174.27 3689[4:SSi:3687.0,38.0,3.0,4.2] || -> .
% 174.01/174.27 3691[4:Spt:3689.0,2775.2,3172.0] || equal(sdtasdt0(xp,xp),sdtasdt0(xp,xm))** -> .
% 174.01/174.27 3692[4:Spt:3689.0,2775.0,2775.1,2775.3] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xp))* sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 3693[2:SSi:3400.1,6.0,5.0] aNaturalNumber0(u) || equal(u,xp)* -> aNaturalNumber0(sdtasdt0(xn,xm))*.
% 174.01/174.27 3694[2:MRR:3693.0,2765.1] || equal(u,xp)*+ -> aNaturalNumber0(sdtasdt0(xn,xm))*.
% 174.01/174.27 3719[4:Res:86.6,3692.0] aNaturalNumber0(xp) aNaturalNumber0(xm) aNaturalNumber0(xp) || sdtlseqdt0(xm,xp) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))* -> equal(xp,xm) equal(xp,sz00) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 3728[4:Obv:3719.0] aNaturalNumber0(xm) aNaturalNumber0(xp) || sdtlseqdt0(xm,xp) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))* -> equal(xp,xm) equal(xp,sz00) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 3729[4:Rew:45.2,3728.6,45.2,3728.3] aNaturalNumber0(xm) aNaturalNumber0(xp) || sdtlseqdt0(xm,xp) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))* -> equal(xp,xm) equal(xp,sz00) equal(sdtasdt0(xm,xp),sdtasdt0(xn,xm)).
% 174.01/174.27 3730[4:SSi:3729.1,3729.0,6.0,5.0,4.0] || sdtlseqdt0(xm,xp) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))* -> equal(xp,xm) equal(xp,sz00) equal(sdtasdt0(xm,xp),sdtasdt0(xn,xm)).
% 174.01/174.27 3731[4:MRR:3730.0,3730.2,3730.3,12.0,22.0,110.0] || sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))* -> equal(sdtasdt0(xm,xp),sdtasdt0(xn,xm)).
% 174.01/174.27 3734[4:SpL:2770.1,3691.0] || equal(xp,xp) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm))** -> .
% 174.01/174.27 3736[4:Obv:3734.0] || equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm))** -> .
% 174.01/174.27 3746[4:SpL:45.2,3736.0] aNaturalNumber0(xm) aNaturalNumber0(xp) || equal(sdtasdt0(xm,xp),sdtasdt0(xn,xm))** -> .
% 174.01/174.27 3750[4:SSi:3746.1,3746.0,6.0,5.0,4.0] || equal(sdtasdt0(xm,xp),sdtasdt0(xn,xm))** -> .
% 174.01/174.27 3751[4:MRR:3731.1,3750.0] || sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))* -> .
% 174.01/174.27 4055[2:EqR:3694.0] || -> aNaturalNumber0(sdtasdt0(xn,xm))*.
% 174.01/174.27 7004[2:SpR:3478.1,514.2] aNaturalNumber0(xm) aNaturalNumber0(xn) || equal(u,xp) -> doDivides0(xm,sdtasdt0(u,xp))*.
% 174.01/174.27 7020[2:SSi:7004.1,7004.0,3.0,4.0] || equal(u,xp) -> doDivides0(xm,sdtasdt0(u,xp))*.
% 174.01/174.27 7032[2:SpR:2770.1,7020.1] || equal(xp,xp) equal(xp,xp) -> doDivides0(xm,sdtasdt0(xn,xm))*.
% 174.01/174.27 7041[2:Obv:7032.1] || -> doDivides0(xm,sdtasdt0(xn,xm))*.
% 174.01/174.27 7052[2:Res:7041.0,65.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xm) aNaturalNumber0(u) || doDivides0(u,xm) -> doDivides0(u,sdtasdt0(xn,xm))*.
% 174.01/174.27 7056[2:SSi:7052.1,7052.0,4.0,4055.0] aNaturalNumber0(u) || doDivides0(u,xm) -> doDivides0(u,sdtasdt0(xn,xm))*.
% 174.01/174.27 10910[2:Res:7056.2,284.1] aNaturalNumber0(sz00) aNaturalNumber0(sdtasdt0(xn,xm)) || doDivides0(sz00,xm) -> equal(sdtasdt0(xn,xm),sz00)**.
% 174.01/174.27 10911[2:SSi:10910.1,10910.0,4055.0,1.0] || doDivides0(sz00,xm) -> equal(sdtasdt0(xn,xm),sz00)**.
% 174.01/174.27 10912[2:MRR:10911.1,2451.0] || doDivides0(sz00,xm)* -> .
% 174.01/174.27 10939[2:Res:949.2,10912.0] aNaturalNumber0(xm) || equal(xm,sz00)** -> .
% 174.01/174.27 10942[2:SSi:10939.0,4.0] || equal(xm,sz00)** -> .
% 174.01/174.27 15939[0:Res:12.0,1209.3] aNaturalNumber0(u) aNaturalNumber0(xp) aNaturalNumber0(xm) || -> sdtlseqdt0(u,xp)* sdtlseqdt0(xm,u)*.
% 174.01/174.27 15944[0:SSi:15939.2,15939.1,4.0,6.0,5.0] aNaturalNumber0(u) || -> sdtlseqdt0(u,xp)* sdtlseqdt0(xm,u)*.
% 174.01/174.27 16030[0:Res:15944.2,437.1] aNaturalNumber0(sz00) aNaturalNumber0(xm) || -> sdtlseqdt0(sz00,xp)* equal(xm,sz00).
% 174.01/174.27 16034[0:SSi:16030.1,16030.0,4.0,1.0] || -> sdtlseqdt0(sz00,xp)* equal(xm,sz00).
% 174.01/174.27 31071[4:Res:2561.6,3751.0] aNaturalNumber0(xp) aNaturalNumber0(xn) aNaturalNumber0(xm) || sdtlseqdt0(xn,xp)* -> equal(xp,xn) equal(xm,sz00).
% 174.01/174.27 31075[4:SSi:31071.2,31071.1,31071.0,4.0,3.0,6.0,5.0] || sdtlseqdt0(xn,xp)* -> equal(xp,xn) equal(xm,sz00).
% 174.01/174.27 31076[4:MRR:31075.0,31075.1,31075.2,11.0,21.0,10942.0] || -> .
% 174.01/174.27 31168[2:Spt:31076.0,2675.1,2756.0] || equal(xk,xp)** -> .
% 174.01/174.27 31169[2:Spt:31076.0,2675.0] || -> sdtlseqdt0(xn,xk)*.
% 174.01/174.27 31170[2:MRR:2506.1,31168.0] || sdtlseqdt0(xk,xp)* -> .
% 174.01/174.27 31323[2:Res:15944.1,31170.0] aNaturalNumber0(xk) || -> sdtlseqdt0(xm,xk)*.
% 174.01/174.27 31324[2:Res:2463.2,31170.0] aNaturalNumber0(xk) || sdtlseqdt0(xk,xm)* -> .
% 174.01/174.27 31340[0:SpR:30.0,1262.3] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm))* -> aNaturalNumber0(xk) equal(xp,sz00).
% 174.01/174.27 31341[0:SpR:30.0,2311.4] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(xp) || doDivides0(xp,sdtasdt0(xn,xm)) -> equal(xp,sz00) equal(sdtasdt0(xp,xk),sdtasdt0(xn,xm))**.
% 174.01/174.27 31363[0:SSi:31340.1,31340.0,6.0,5.0,38.2,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm))* -> aNaturalNumber0(xk) equal(xp,sz00).
% 174.01/174.27 31364[0:MRR:31363.0,31363.2,27.0,110.0] || -> aNaturalNumber0(xk)*.
% 174.01/174.27 31370[2:MRR:31323.0,31364.0] || -> sdtlseqdt0(xm,xk)*.
% 174.01/174.27 31371[2:MRR:31324.0,31364.0] || sdtlseqdt0(xk,xm)* -> .
% 174.01/174.27 31372[0:SSi:31341.1,31341.0,6.0,5.0,38.2,3.0,4.0] || doDivides0(xp,sdtasdt0(xn,xm)) -> equal(xp,sz00) equal(sdtasdt0(xp,xk),sdtasdt0(xn,xm))**.
% 174.01/174.27 31373[0:MRR:31372.0,31372.1,27.0,110.0] || -> equal(sdtasdt0(xp,xk),sdtasdt0(xn,xm))**.
% 174.01/174.27 31374[0:Rew:31373.0,91.0] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xk),sdtasdt0(xp,xm))** equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 31375[0:Rew:31373.0,31374.2] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))* sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)) equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 31376[0:Obv:31375.2] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))* sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 174.01/174.27 31378[2:Res:31370.0,844.2] aNaturalNumber0(xk) aNaturalNumber0(xm) || equal(xk,u) -> sdtlseqdt0(xm,u)*.
% 174.01/174.27 31384[2:SSi:31378.1,31378.0,4.0,31364.0] || equal(xk,u) -> sdtlseqdt0(xm,u)*.
% 174.01/174.27 31389[2:Res:947.2,31371.0] aNaturalNumber0(xm) || equal(xk,xm)** -> .
% 226.52/226.71 31392[2:SSi:31389.0,4.0] || equal(xk,xm)** -> .
% 226.52/226.71 31432[3:Spt:16034.1] || -> equal(xm,sz00)**.
% 226.52/226.71 31437[3:Rew:31432.0,2453.0] || -> sdtlseqdt0(xp,sdtasdt0(xn,sz00))*.
% 226.52/226.71 31456[3:Rew:31432.0,20.0] || sdtlseqdt0(xp,sz00)* -> .
% 226.52/226.71 31711[3:SpR:45.2,31437.0] aNaturalNumber0(xn) aNaturalNumber0(sz00) || -> sdtlseqdt0(xp,sdtasdt0(sz00,xn))*.
% 226.52/226.71 31723[3:Rew:36.1,31711.2] aNaturalNumber0(xn) aNaturalNumber0(sz00) || -> sdtlseqdt0(xp,sz00)*.
% 226.52/226.71 31724[3:SSi:31723.1,31723.0,1.0,3.0] || -> sdtlseqdt0(xp,sz00)*.
% 226.52/226.71 31725[3:MRR:31724.0,31456.0] || -> .
% 226.52/226.71 31726[3:Spt:31725.0,16034.1,31432.0] || equal(xm,sz00)** -> .
% 226.52/226.71 31727[3:Spt:31725.0,16034.0] || -> sdtlseqdt0(sz00,xp)*.
% 226.52/226.71 31869[4:Spt:31376.0] || sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))* -> .
% 226.52/226.71 31874[4:Res:41.2,31869.0] aNaturalNumber0(sdtasdt0(xn,xm)) aNaturalNumber0(sdtasdt0(xp,xm)) || -> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))*.
% 226.52/226.71 31886[4:SSi:31874.1,31874.0,38.0,6.0,5.2,4.0,38.0,3.0,4.2] || -> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))*.
% 226.52/226.71 32228[0:SpR:2512.1,45.2] aNaturalNumber0(u) aNaturalNumber0(xp) || equal(u,xk) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 226.52/226.71 32323[0:SSi:32228.1,6.0,5.0] aNaturalNumber0(u) || equal(u,xk) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 226.52/226.71 32324[0:MRR:32323.0,2500.1] || equal(u,xk) -> equal(sdtasdt0(xn,xm),sdtasdt0(u,xp))*.
% 226.52/226.71 33439[4:SpR:45.2,31886.0] aNaturalNumber0(xm) aNaturalNumber0(xp) || -> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))*.
% 226.52/226.71 33448[4:SSi:33439.1,33439.0,6.0,5.0,4.0] || -> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xm,xp))*.
% 226.52/226.71 49828[4:SpR:32324.1,33448.0] || equal(u,xk) -> sdtlseqdt0(sdtasdt0(u,xp),sdtasdt0(xm,xp))*.
% 226.52/226.71 77892[4:Res:49828.1,2647.4] aNaturalNumber0(u) aNaturalNumber0(xm) aNaturalNumber0(xp) || equal(u,xk) sdtlseqdt0(xm,u)* -> equal(xm,u) equal(xp,sz00).
% 226.52/226.71 78089[4:SSi:77892.2,77892.1,6.0,5.0,4.0] aNaturalNumber0(u) || equal(u,xk) sdtlseqdt0(xm,u)* -> equal(xm,u) equal(xp,sz00).
% 226.52/226.71 78090[4:MRR:78089.0,78089.2,78089.4,2500.1,31384.1,110.0] || equal(u,xk)* -> equal(xm,u).
% 226.52/226.71 78608[4:EqR:78090.0] || -> equal(xk,xm)**.
% 226.52/226.71 78609[4:MRR:78608.0,31392.0] || -> .
% 226.52/226.71 78610[4:Spt:78609.0,31376.0,31869.0] || -> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))*.
% 226.52/226.71 78611[4:Spt:78609.0,31376.1,31376.2] || sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))* -> equal(sdtasdt0(xp,xm),sdtasdt0(xn,xm)).
% 226.52/226.71 80022[4:Res:78610.0,2647.4] aNaturalNumber0(xp) aNaturalNumber0(xn) aNaturalNumber0(xm) || sdtlseqdt0(xn,xp)* -> equal(xp,xn) equal(xm,sz00).
% 226.52/226.71 80030[4:SSi:80022.2,80022.1,80022.0,4.0,3.0,6.0,5.0] || sdtlseqdt0(xn,xp)* -> equal(xp,xn) equal(xm,sz00).
% 226.52/226.71 80031[4:MRR:80030.0,80030.1,80030.2,11.0,21.0,31726.0] || -> .
% 226.52/226.71 % SZS output end Refutation
% 226.52/226.71 Formulae used in the proof : mSortsC mSortsC_01 m__1837 m__1860 m__2342 m__2287 m__2389 mDefLE mDefDiv m__2075 m__2327 m__2362 m__2306 m_AddZero m_MulUnit m_MulZero mSortsB mSortsB_02 mDefPrime mLETotal mMulComm mMonMul2 mDivLE mLEAsym mDefDiff mDivTrans mLETran mDefQuot mMulCanc mMonMul m__
% 226.52/226.71
%------------------------------------------------------------------------------