TSTP Solution File: NUM453+6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM453+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 14:26:21 EDT 2022
% Result : Theorem 7.92s 8.10s
% Output : Refutation 9.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM453+6 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n015.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 : 600
% 0.12/0.34 % DateTime : Tue Jul 5 21:22:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 7.92/8.10
% 7.92/8.10 SPASS V 3.9
% 7.92/8.10 SPASS beiseite: Proof found.
% 7.92/8.10 % SZS status Theorem
% 7.92/8.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.92/8.10 SPASS derived 20541 clauses, backtracked 8929 clauses, performed 109 splits and kept 15221 clauses.
% 7.92/8.10 SPASS allocated 117723 KBytes.
% 7.92/8.10 SPASS spent 0:00:07.72 on the problem.
% 7.92/8.10 0:00:00.04 for the input.
% 7.92/8.10 0:00:00.25 for the FLOTTER CNF translation.
% 7.92/8.10 0:00:00.23 for inferences.
% 7.92/8.10 0:00:00.28 for the backtracking.
% 7.92/8.10 0:00:06.78 for the reduction.
% 7.92/8.10
% 7.92/8.10
% 7.92/8.10 Here is a proof with depth 7, length 220 :
% 7.92/8.10 % SZS output start Refutation
% 7.92/8.10 1[0:Inp] || -> aInteger0(sz00)*.
% 7.92/8.10 2[0:Inp] || -> aInteger0(sz10)*.
% 7.92/8.10 5[0:Inp] || -> aInteger0(xp)*.
% 7.92/8.10 7[0:Inp] || -> aInteger0(skc42)*.
% 7.92/8.10 11[0:Inp] || -> aInteger0(skf49(u))*.
% 7.92/8.10 12[0:Inp] || -> aInteger0(skf46(u))*.
% 7.92/8.10 25[0:Inp] || equal(xp,sz00)** -> .
% 7.92/8.10 27[0:Inp] || -> equal(stldt0(sbsmnsldt0(xS)),cS2076)**.
% 7.92/8.10 28[0:Inp] aInteger0(u) || -> aInteger0(smndt0(u))*.
% 7.92/8.10 38[0:Inp] || -> aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))*.
% 7.92/8.10 39[0:Inp] || -> sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)*.
% 7.92/8.10 40[0:Inp] aInteger0(u) || -> equal(sdtpldt0(u,sz00),u)**.
% 7.92/8.10 41[0:Inp] aInteger0(u) || -> equal(sdtpldt0(sz00,u),u)**.
% 7.92/8.10 42[0:Inp] aInteger0(u) || -> equal(sdtasdt0(u,sz10),u)**.
% 7.92/8.10 43[0:Inp] aInteger0(u) || -> equal(sdtasdt0(sz10,u),u)**.
% 7.92/8.10 44[0:Inp] aInteger0(u) || -> equal(sdtasdt0(u,sz00),sz00)**.
% 7.92/8.10 45[0:Inp] aInteger0(u) || -> equal(sdtasdt0(sz00,u),sz00)**.
% 7.92/8.10 50[0:Inp] || aElementOf0(u,szAzrzSzezqlpdtcmdtrp0(sz10,xp))* -> aInteger0(u).
% 7.92/8.10 51[0:Inp] || aElementOf0(u,stldt0(sbsmnsldt0(xS)))* -> aInteger0(u).
% 7.92/8.10 53[0:Inp] || -> aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))*.
% 7.92/8.10 54[0:Inp] aInteger0(u) || -> equal(sdtpldt0(u,smndt0(u)),sz00)**.
% 7.92/8.10 55[0:Inp] aInteger0(u) || -> equal(sdtpldt0(smndt0(u),u),sz00)**.
% 7.92/8.10 65[0:Inp] || equal(u,sz10) -> aElementOf0(u,stldt0(sbsmnsldt0(xS)))*.
% 7.92/8.10 74[0:Inp] aInteger0(u) aInteger0(v) || -> aInteger0(sdtasdt0(v,u))*.
% 7.92/8.10 75[0:Inp] aInteger0(u) || -> equal(sdtasdt0(smndt0(sz10),u),smndt0(u))**.
% 7.92/8.10 76[0:Inp] aInteger0(u) || -> equal(sdtasdt0(u,smndt0(sz10)),smndt0(u))**.
% 7.92/8.10 84[0:Inp] || equal(u,smndt0(sz10)) -> aElementOf0(u,stldt0(sbsmnsldt0(xS)))*.
% 7.92/8.10 86[0:Inp] || -> equal(sdtasdt0(xp,skc42),sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))**.
% 7.92/8.10 87[0:Inp] || -> equal(sdtpldt0(sz10,xp),sz10) equal(sdtpldt0(sz10,smndt0(xp)),sz10)**.
% 7.92/8.10 95[0:Inp] || equal(skf46(u),sz00)** aElementOf0(u,stldt0(sbsmnsldt0(xS))) -> .
% 7.92/8.10 97[0:Inp] || equal(skf49(u),sz00)** aElementOf0(u,stldt0(sbsmnsldt0(xS))) -> .
% 7.92/8.10 100[0:Inp] || aElementOf0(u,szAzrzSzezqlpdtcmdtrp0(sz10,xp))* -> aElementOf0(u,stldt0(sbsmnsldt0(xS))).
% 7.92/8.10 109[0:Inp] aInteger0(u) || -> isPrime0(skf27(v))* equal(u,sz10) equal(u,smndt0(sz10))*.
% 7.92/8.10 113[0:Inp] || aElementOf0(u,stldt0(sbsmnsldt0(xS)))* -> equal(u,sz10) equal(u,smndt0(sz10)).
% 7.92/8.10 145[0:Inp] aInteger0(u) aInteger0(v) || equal(sdtasdt0(v,u),sz00)** -> equal(u,sz00) equal(v,sz00).
% 7.92/8.10 166[0:Inp] aInteger0(u) aInteger0(v) aInteger0(w) || -> equal(sdtpldt0(sdtpldt0(w,v),u),sdtpldt0(w,sdtpldt0(v,u)))**.
% 7.92/8.10 181[0:Inp] aInteger0(u) aInteger0(v) aInteger0(w) || -> equal(sdtasdt0(sdtpldt0(w,v),u),sdtpldt0(sdtasdt0(w,u),sdtasdt0(v,u)))**.
% 7.92/8.10 182[0:Inp] aInteger0(u) aInteger0(v) aInteger0(w) || -> equal(sdtasdt0(w,sdtpldt0(v,u)),sdtpldt0(sdtasdt0(w,v),sdtasdt0(w,u)))**.
% 7.92/8.10 213[0:Rew:27.0,51.0] || aElementOf0(u,cS2076)* -> aInteger0(u).
% 7.92/8.10 216[0:Rew:27.0,65.1] || equal(u,sz10) -> aElementOf0(u,cS2076)*.
% 7.92/8.10 217[0:Rew:27.0,84.1] || equal(u,smndt0(sz10))*+ -> aElementOf0(u,cS2076)*.
% 7.92/8.10 219[0:Rew:27.0,100.1] || aElementOf0(u,szAzrzSzezqlpdtcmdtrp0(sz10,xp))* -> aElementOf0(u,cS2076).
% 7.92/8.10 222[0:Rew:27.0,97.1] || aElementOf0(u,cS2076) equal(skf49(u),sz00)** -> .
% 7.92/8.10 224[0:Rew:27.0,95.1] || aElementOf0(u,cS2076) equal(skf46(u),sz00)** -> .
% 7.92/8.10 230[0:Rew:27.0,113.0] || aElementOf0(u,cS2076)*+ -> equal(u,sz10) equal(u,smndt0(sz10))*.
% 7.92/8.10 273[1:Spt:109.0,109.2,109.3] aInteger0(u) || -> equal(u,sz10) equal(u,smndt0(sz10))*.
% 7.92/8.10 291[2:Spt:87.0] || -> equal(sdtpldt0(sz10,xp),sz10)**.
% 7.92/8.10 295[2:Rew:291.0,38.0] || -> aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp))*.
% 7.92/8.10 302[1:SpR:273.2,12.0] aInteger0(skf46(u)) || -> equal(skf46(u),sz10)** aInteger0(smndt0(sz10)).
% 7.92/8.10 303[1:SSi:302.0,12.0] || -> equal(skf46(u),sz10)** aInteger0(smndt0(sz10)).
% 7.92/8.10 332[1:SpR:273.2,39.0] aInteger0(sdtpldt0(sz10,smndt0(xp))) || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10)** sdteqdtlpzmzozddtrp0(smndt0(sz10),sz10,xp).
% 7.92/8.10 340[3:Spt:303.0] || -> equal(skf46(u),sz10)**.
% 7.92/8.10 352[3:Rew:340.0,224.1] || aElementOf0(u,cS2076)* equal(sz10,sz00) -> .
% 7.92/8.10 404[3:Res:216.1,352.0] || equal(u,sz10)* equal(sz10,sz00)** -> .
% 7.92/8.10 405[3:AED:25.0,404.0] || equal(sz10,sz00)** -> .
% 7.92/8.10 414[0:EqR:217.0] || -> aElementOf0(smndt0(sz10),cS2076)*.
% 7.92/8.10 419[0:Res:414.0,213.0] || -> aInteger0(smndt0(sz10))*.
% 7.92/8.10 425[0:Res:53.0,50.0] || -> aInteger0(sdtpldt0(sz10,smndt0(xp)))*.
% 7.92/8.10 426[1:MRR:332.0,425.0] || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10)** sdteqdtlpzmzozddtrp0(smndt0(sz10),sz10,xp).
% 7.92/8.10 428[1:SpR:273.2,425.0] aInteger0(smndt0(xp)) || -> equal(smndt0(xp),sz10) aInteger0(sdtpldt0(sz10,smndt0(sz10)))*.
% 7.92/8.10 430[1:SSi:428.0,28.0,5.1] || -> equal(smndt0(xp),sz10) aInteger0(sdtpldt0(sz10,smndt0(sz10)))*.
% 7.92/8.10 460[4:Spt:430.0] || -> equal(smndt0(xp),sz10)**.
% 7.92/8.10 484[2:Res:295.0,219.0] || -> aElementOf0(sz10,cS2076)*.
% 7.92/8.10 496[0:SpR:55.1,40.1] aInteger0(sz00) aInteger0(smndt0(sz00)) || -> equal(smndt0(sz00),sz00)**.
% 7.92/8.10 499[4:SpR:460.0,55.1] aInteger0(xp) || -> equal(sdtpldt0(sz10,xp),sz00)**.
% 7.92/8.10 501[4:Rew:291.0,499.1] aInteger0(xp) || -> equal(sz10,sz00)**.
% 7.92/8.10 502[4:SSi:501.0,5.0] || -> equal(sz10,sz00)**.
% 7.92/8.10 503[4:MRR:502.0,405.0] || -> .
% 7.92/8.10 504[0:SSi:496.1,496.0,28.0,1.0,1.1] || -> equal(smndt0(sz00),sz00)**.
% 7.92/8.10 545[4:Spt:503.0,430.0,460.0] || equal(smndt0(xp),sz10)** -> .
% 7.92/8.10 546[4:Spt:503.0,430.1] || -> aInteger0(sdtpldt0(sz10,smndt0(sz10)))*.
% 7.92/8.10 569[0:Res:53.0,219.0] || -> aElementOf0(sdtpldt0(sz10,smndt0(xp)),cS2076)*.
% 7.92/8.10 571[1:SpR:273.2,569.0] aInteger0(smndt0(xp)) || -> equal(smndt0(xp),sz10) aElementOf0(sdtpldt0(sz10,smndt0(sz10)),cS2076)*.
% 7.92/8.10 574[1:SSi:571.0,28.0,5.1] || -> equal(smndt0(xp),sz10) aElementOf0(sdtpldt0(sz10,smndt0(sz10)),cS2076)*.
% 7.92/8.10 575[4:MRR:574.0,545.0] || -> aElementOf0(sdtpldt0(sz10,smndt0(sz10)),cS2076)*.
% 7.92/8.10 603[4:SpR:54.1,575.0] aInteger0(sz10) || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 612[4:SSi:603.0,2.0] || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 924[0:Res:569.0,230.0] || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10) equal(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))**.
% 7.92/8.10 926[4:Res:612.0,230.0] || -> equal(sz10,sz00) equal(smndt0(sz10),sz00)**.
% 7.92/8.10 931[4:MRR:926.0,405.0] || -> equal(smndt0(sz10),sz00)**.
% 7.92/8.10 951[4:Rew:931.0,75.1] aInteger0(u) || -> equal(sdtasdt0(sz00,u),smndt0(u))**.
% 7.92/8.10 1032[4:Rew:45.1,951.1] aInteger0(u) || -> equal(smndt0(u),sz00)**.
% 7.92/8.10 1034[4:Rew:1032.1,55.1] aInteger0(u) || -> equal(sdtpldt0(sz00,u),sz00)**.
% 7.92/8.10 1041[4:Rew:41.1,1034.1] aInteger0(u) || -> equal(u,sz00)*.
% 7.92/8.10 1086[4:EmS:1041.0,5.0] || -> equal(xp,sz00)**.
% 7.92/8.10 1091[4:MRR:1086.0,25.0] || -> .
% 7.92/8.10 1168[3:Spt:1091.0,303.1] || -> aInteger0(smndt0(sz10))*.
% 7.92/8.10 1220[4:Spt:574.0] || -> equal(smndt0(xp),sz10)**.
% 7.92/8.10 1240[4:SpR:1220.0,55.1] aInteger0(xp) || -> equal(sdtpldt0(sz10,xp),sz00)**.
% 7.92/8.10 1243[4:Rew:291.0,1240.1] aInteger0(xp) || -> equal(sz10,sz00)**.
% 7.92/8.10 1244[4:SSi:1243.0,5.0] || -> equal(sz10,sz00)**.
% 7.92/8.10 1258[4:Rew:1244.0,43.1] aInteger0(u) || -> equal(sdtasdt0(sz00,u),u)**.
% 7.92/8.10 1260[4:Rew:1244.0,484.0] || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 1371[4:Rew:45.1,1258.1] aInteger0(u) || -> equal(sz00,u)*.
% 7.92/8.10 1558[4:EmS:1371.0,11.0] || -> equal(skf49(u),sz00)**.
% 7.92/8.10 1582[4:Rew:1558.0,222.1] || aElementOf0(u,cS2076)* equal(sz00,sz00) -> .
% 7.92/8.10 1615[4:Obv:1582.1] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 1616[4:UnC:1615.0,1260.0] || -> .
% 7.92/8.10 1644[4:Spt:1616.0,574.0,1220.0] || equal(smndt0(xp),sz10)** -> .
% 7.92/8.10 1645[4:Spt:1616.0,574.1] || -> aElementOf0(sdtpldt0(sz10,smndt0(sz10)),cS2076)*.
% 7.92/8.10 1715[4:SpR:54.1,1645.0] aInteger0(sz10) || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 1724[4:SSi:1715.0,2.0] || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 1804[1:SpR:273.2,44.1] aInteger0(sdtasdt0(u,sz00)) aInteger0(u) || -> equal(sdtasdt0(u,sz00),sz10)** equal(smndt0(sz10),sz00).
% 7.92/8.10 1897[1:SpL:273.2,224.1] aInteger0(skf46(u)) || aElementOf0(u,cS2076) equal(smndt0(sz10),sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 1898[1:SpL:273.2,222.1] aInteger0(skf49(u)) || aElementOf0(u,cS2076) equal(smndt0(sz10),sz00) -> equal(skf49(u),sz10)**.
% 7.92/8.10 1919[1:Rew:44.1,1804.2] aInteger0(sdtasdt0(u,sz00)) aInteger0(u) || -> equal(sz10,sz00) equal(smndt0(sz10),sz00)**.
% 7.92/8.10 1926[1:SSi:1897.0,12.0] || aElementOf0(u,cS2076) equal(smndt0(sz10),sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 1927[1:SSi:1898.0,11.0] || aElementOf0(u,cS2076) equal(smndt0(sz10),sz00) -> equal(skf49(u),sz10)**.
% 7.92/8.10 1987[5:Spt:426.0] || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10)**.
% 7.92/8.10 2002[5:SpR:273.2,1987.0] aInteger0(smndt0(xp)) || -> equal(smndt0(xp),sz10) equal(sdtpldt0(sz10,smndt0(sz10)),sz10)**.
% 7.92/8.10 2003[5:SSi:2002.0,28.0,5.1] || -> equal(smndt0(xp),sz10) equal(sdtpldt0(sz10,smndt0(sz10)),sz10)**.
% 7.92/8.10 2004[5:MRR:2003.0,1644.0] || -> equal(sdtpldt0(sz10,smndt0(sz10)),sz10)**.
% 7.92/8.10 2025[5:SpR:2004.0,54.1] aInteger0(sz10) || -> equal(sz10,sz00)**.
% 7.92/8.10 2029[5:SSi:2025.0,2.0] || -> equal(sz10,sz00)**.
% 7.92/8.10 2135[5:Rew:2029.0,1926.1] || aElementOf0(u,cS2076) equal(smndt0(sz00),sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2243[5:Rew:504.0,2135.1] || aElementOf0(u,cS2076) equal(sz00,sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2244[5:Obv:2243.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2245[5:Rew:2029.0,2244.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz00)**.
% 7.92/8.10 2246[5:MRR:2245.1,224.1] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 2247[5:UnC:2246.0,1724.0] || -> .
% 7.92/8.10 2342[5:Spt:2247.0,426.0,1987.0] || equal(sdtpldt0(sz10,smndt0(xp)),sz10)** -> .
% 7.92/8.10 2343[5:Spt:2247.0,426.1] || -> sdteqdtlpzmzozddtrp0(smndt0(sz10),sz10,xp)*.
% 7.92/8.10 2358[1:SSi:1919.0,74.0,1.2] aInteger0(u) || -> equal(sz10,sz00) equal(smndt0(sz10),sz00)**.
% 7.92/8.10 2460[1:EmS:2358.0,419.0] || -> equal(sz10,sz00) equal(smndt0(sz10),sz00)**.
% 7.92/8.10 2485[6:Spt:2460.0] || -> equal(sz10,sz00)**.
% 7.92/8.10 2568[6:Rew:2485.0,1926.1] || aElementOf0(u,cS2076) equal(smndt0(sz00),sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2730[6:Rew:504.0,2568.1] || aElementOf0(u,cS2076) equal(sz00,sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2731[6:Obv:2730.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2732[6:Rew:2485.0,2731.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz00)**.
% 7.92/8.10 2733[6:MRR:2732.1,224.1] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 2734[6:UnC:2733.0,1724.0] || -> .
% 7.92/8.10 2848[6:Spt:2734.0,2460.0,2485.0] || equal(sz10,sz00)** -> .
% 7.92/8.10 2849[6:Spt:2734.0,2460.1] || -> equal(smndt0(sz10),sz00)**.
% 7.92/8.10 2871[6:Rew:2849.0,75.1] aInteger0(u) || -> equal(sdtasdt0(sz00,u),smndt0(u))**.
% 7.92/8.10 2872[6:Rew:45.1,2871.1] aInteger0(u) || -> equal(smndt0(u),sz00)**.
% 7.92/8.10 2874[6:Rew:2872.1,55.1] aInteger0(u) || -> equal(sdtpldt0(sz00,u),sz00)**.
% 7.92/8.10 2876[6:Rew:41.1,2874.1] aInteger0(u) || -> equal(u,sz00)*.
% 7.92/8.10 2897[6:Rew:2849.0,1926.1] || aElementOf0(u,cS2076) equal(sz00,sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 2898[6:Obv:2897.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz10)**.
% 7.92/8.10 3057[6:EmS:2876.0,12.0] || -> equal(skf46(u),sz00)**.
% 7.92/8.10 3074[6:Rew:3057.0,2898.1] || aElementOf0(u,cS2076)* -> equal(sz10,sz00).
% 7.92/8.10 3125[6:MRR:3074.1,2848.0] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 3126[6:UnC:3125.0,484.0] || -> .
% 7.92/8.10 3149[2:Spt:3126.0,87.0,291.0] || equal(sdtpldt0(sz10,xp),sz10)** -> .
% 7.92/8.10 3150[2:Spt:3126.0,87.1] || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10)**.
% 7.92/8.10 3152[2:Rew:3150.0,569.0] || -> aElementOf0(sz10,cS2076)*.
% 7.92/8.10 3173[3:Spt:2460.0] || -> equal(sz10,sz00)**.
% 7.92/8.10 3181[3:Rew:3173.0,3152.0] || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 3228[3:Rew:3173.0,1926.1] || aElementOf0(u,cS2076) equal(smndt0(sz00),sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 3391[3:Rew:504.0,3228.1] || aElementOf0(u,cS2076) equal(sz00,sz00) -> equal(skf46(u),sz10)**.
% 7.92/8.10 3392[3:Obv:3391.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz10)**.
% 7.92/8.10 3393[3:Rew:3173.0,3392.1] || aElementOf0(u,cS2076) -> equal(skf46(u),sz00)**.
% 7.92/8.10 3394[3:MRR:3393.1,224.1] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 3395[3:UnC:3394.0,3181.0] || -> .
% 7.92/8.10 3493[3:Spt:3395.0,2460.0,3173.0] || equal(sz10,sz00)** -> .
% 7.92/8.10 3494[3:Spt:3395.0,2460.1] || -> equal(smndt0(sz10),sz00)**.
% 7.92/8.10 3496[3:Rew:3494.0,414.0] || -> aElementOf0(sz00,cS2076)*.
% 7.92/8.10 3505[3:Rew:3494.0,76.1] aInteger0(u) || -> equal(sdtasdt0(u,sz00),smndt0(u))**.
% 7.92/8.10 3506[3:Rew:44.1,3505.1] aInteger0(u) || -> equal(smndt0(u),sz00)**.
% 7.92/8.10 3508[3:Rew:3506.1,55.1] aInteger0(u) || -> equal(sdtpldt0(sz00,u),sz00)**.
% 7.92/8.10 3510[3:Rew:41.1,3508.1] aInteger0(u) || -> equal(u,sz00)*.
% 7.92/8.10 3549[3:Rew:3494.0,1927.1] || aElementOf0(u,cS2076) equal(sz00,sz00) -> equal(skf49(u),sz10)**.
% 7.92/8.10 3550[3:Obv:3549.1] || aElementOf0(u,cS2076) -> equal(skf49(u),sz10)**.
% 7.92/8.10 3666[3:EmS:3510.0,11.0] || -> equal(skf49(u),sz00)**.
% 7.92/8.10 3684[3:Rew:3666.0,3550.1] || aElementOf0(u,cS2076)* -> equal(sz10,sz00).
% 7.92/8.10 3713[3:MRR:3684.1,3493.0] || aElementOf0(u,cS2076)* -> .
% 7.92/8.10 3714[3:UnC:3713.0,3496.0] || -> .
% 7.92/8.10 3745[1:Spt:3714.0,109.1] || -> isPrime0(skf27(u))*.
% 7.92/8.10 3746[2:Spt:87.1] || -> equal(sdtpldt0(sz10,smndt0(xp)),sz10)**.
% 7.92/8.10 12064[0:SpR:54.1,166.3] aInteger0(u) aInteger0(v) aInteger0(smndt0(u)) aInteger0(u) || -> equal(sdtpldt0(u,sdtpldt0(smndt0(u),v)),sdtpldt0(sz00,v))**.
% 7.92/8.10 12170[0:Obv:12064.0] aInteger0(u) aInteger0(smndt0(v)) aInteger0(v) || -> equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),sdtpldt0(sz00,u))**.
% 7.92/8.10 12171[0:Rew:41.1,12170.3] aInteger0(u) aInteger0(smndt0(v)) aInteger0(v) || -> equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u)**.
% 7.92/8.10 12172[0:SSi:12171.1,28.1] aInteger0(u) aInteger0(v) || -> equal(sdtpldt0(v,sdtpldt0(smndt0(v),u)),u)**.
% 7.92/8.10 12998[2:SpR:3746.0,182.3] aInteger0(smndt0(xp)) aInteger0(sz10) aInteger0(u) || -> equal(sdtpldt0(sdtasdt0(u,sz10),sdtasdt0(u,smndt0(xp))),sdtasdt0(u,sz10))**.
% 7.92/8.10 13006[2:Rew:42.1,12998.3] aInteger0(smndt0(xp)) aInteger0(sz10) aInteger0(u) || -> equal(sdtpldt0(u,sdtasdt0(u,smndt0(xp))),u)**.
% 7.92/8.10 13007[2:SSi:13006.1,13006.0,2.0,28.1,5.0] aInteger0(u) || -> equal(sdtpldt0(u,sdtasdt0(u,smndt0(xp))),u)**.
% 7.92/8.10 14718[2:SpR:75.1,13007.1] aInteger0(smndt0(xp)) aInteger0(smndt0(sz10)) || -> equal(sdtpldt0(smndt0(sz10),smndt0(smndt0(xp))),smndt0(sz10))**.
% 7.92/8.10 14723[2:SSi:14718.1,14718.0,419.0,28.1,5.0] || -> equal(sdtpldt0(smndt0(sz10),smndt0(smndt0(xp))),smndt0(sz10))**.
% 7.92/8.10 16593[2:SpR:14723.0,12172.2] aInteger0(smndt0(smndt0(xp))) aInteger0(sz10) || -> equal(sdtpldt0(sz10,smndt0(sz10)),smndt0(smndt0(xp)))**.
% 7.92/8.10 16758[2:Rew:54.1,16593.2] aInteger0(smndt0(smndt0(xp))) aInteger0(sz10) || -> equal(smndt0(smndt0(xp)),sz00)**.
% 7.92/8.10 16759[2:SSi:16758.1,2.0] aInteger0(smndt0(smndt0(xp))) || -> equal(smndt0(smndt0(xp)),sz00)**.
% 7.92/8.10 18777[2:SoR:16759.0,28.1] aInteger0(smndt0(xp)) || -> equal(smndt0(smndt0(xp)),sz00)**.
% 7.92/8.10 18779[2:SSi:18777.0,28.0,5.1] || -> equal(smndt0(smndt0(xp)),sz00)**.
% 7.92/8.10 18788[2:SpR:18779.0,55.1] aInteger0(smndt0(xp)) || -> equal(sdtpldt0(sz00,smndt0(xp)),sz00)**.
% 7.92/8.10 18798[2:Rew:41.1,18788.1] aInteger0(smndt0(xp)) || -> equal(smndt0(xp),sz00)**.
% 7.92/8.10 18799[2:SSi:18798.0,28.0,5.1] || -> equal(smndt0(xp),sz00)**.
% 7.92/8.10 18876[2:SpR:18799.0,54.1] aInteger0(xp) || -> equal(sdtpldt0(xp,sz00),sz00)**.
% 7.92/8.10 18888[2:Rew:40.1,18876.1] aInteger0(xp) || -> equal(xp,sz00)**.
% 7.92/8.10 18889[2:SSi:18888.0,5.0] || -> equal(xp,sz00)**.
% 7.92/8.10 18890[2:MRR:18889.0,25.0] || -> .
% 7.92/8.10 18901[2:Spt:18890.0,87.1,3746.0] || equal(sdtpldt0(sz10,smndt0(xp)),sz10)** -> .
% 7.92/8.10 18902[2:Spt:18890.0,87.0] || -> equal(sdtpldt0(sz10,xp),sz10)**.
% 7.92/8.10 18909[2:Rew:18902.0,86.0] || -> equal(sdtasdt0(xp,skc42),sdtpldt0(sz10,smndt0(sz10)))**.
% 7.92/8.10 18922[2:MRR:924.0,18901.0] || -> equal(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))**.
% 7.92/8.10 18926[2:Rew:18922.0,18901.0] || equal(smndt0(sz10),sz10)** -> .
% 7.92/8.10 19003[2:SpR:18902.0,181.3] aInteger0(u) aInteger0(xp) aInteger0(sz10) || -> equal(sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(xp,u)),sdtasdt0(sz10,u))**.
% 7.92/8.10 19006[2:Rew:43.1,19003.3] aInteger0(u) aInteger0(xp) aInteger0(sz10) || -> equal(sdtpldt0(u,sdtasdt0(xp,u)),u)**.
% 7.92/8.10 19007[2:SSi:19006.2,19006.1,2.0,5.0] aInteger0(u) || -> equal(sdtpldt0(u,sdtasdt0(xp,u)),u)**.
% 7.92/8.10 19120[2:SpR:18922.0,181.3] aInteger0(u) aInteger0(smndt0(xp)) aInteger0(sz10) || -> equal(sdtpldt0(sdtasdt0(sz10,u),sdtasdt0(smndt0(xp),u)),sdtasdt0(smndt0(sz10),u))**.
% 7.92/8.10 19128[2:Rew:43.1,19120.3,75.1,19120.3] aInteger0(u) aInteger0(smndt0(xp)) aInteger0(sz10) || -> equal(sdtpldt0(u,sdtasdt0(smndt0(xp),u)),smndt0(u))**.
% 7.92/8.10 19129[2:SSi:19128.2,19128.1,2.0,28.1,5.0] aInteger0(u) || -> equal(sdtpldt0(u,sdtasdt0(smndt0(xp),u)),smndt0(u))**.
% 7.92/8.10 19136[2:SpL:18909.0,145.2] aInteger0(skc42) aInteger0(xp) || equal(sdtpldt0(sz10,smndt0(sz10)),sz00)** -> equal(skc42,sz00) equal(xp,sz00).
% 7.92/8.10 19142[2:SSi:19136.1,19136.0,5.0,7.0] || equal(sdtpldt0(sz10,smndt0(sz10)),sz00)** -> equal(skc42,sz00) equal(xp,sz00).
% 7.92/8.10 19143[2:MRR:19142.2,25.0] || equal(sdtpldt0(sz10,smndt0(sz10)),sz00)** -> equal(skc42,sz00).
% 9.23/9.43 19592[2:SpL:54.1,19143.0] aInteger0(sz10) || equal(sz00,sz00) -> equal(skc42,sz00)**.
% 9.23/9.43 19593[2:Obv:19592.1] aInteger0(sz10) || -> equal(skc42,sz00)**.
% 9.23/9.43 19594[2:SSi:19593.0,2.0] || -> equal(skc42,sz00)**.
% 9.23/9.43 19596[2:Rew:19594.0,18909.0] || -> equal(sdtasdt0(xp,sz00),sdtpldt0(sz10,smndt0(sz10)))**.
% 9.23/9.43 19604[2:SpR:19596.0,44.1] aInteger0(xp) || -> equal(sdtpldt0(sz10,smndt0(sz10)),sz00)**.
% 9.23/9.43 19616[2:SSi:19604.0,5.0] || -> equal(sdtpldt0(sz10,smndt0(sz10)),sz00)**.
% 9.23/9.43 23232[2:SpR:76.1,19007.1] aInteger0(xp) aInteger0(smndt0(sz10)) || -> equal(sdtpldt0(smndt0(sz10),smndt0(xp)),smndt0(sz10))**.
% 9.23/9.43 23236[2:SSi:23232.1,23232.0,419.0,5.0] || -> equal(sdtpldt0(smndt0(sz10),smndt0(xp)),smndt0(sz10))**.
% 9.23/9.43 31555[2:SpR:23236.0,12172.2] aInteger0(smndt0(xp)) aInteger0(sz10) || -> equal(sdtpldt0(sz10,smndt0(sz10)),smndt0(xp))**.
% 9.23/9.43 31560[2:Rew:19616.0,31555.2] aInteger0(smndt0(xp)) aInteger0(sz10) || -> equal(smndt0(xp),sz00)**.
% 9.23/9.43 31561[2:SSi:31560.1,31560.0,2.0,28.1,5.0] || -> equal(smndt0(xp),sz00)**.
% 9.23/9.43 31564[2:Rew:31561.0,19129.1] aInteger0(u) || -> equal(sdtpldt0(u,sdtasdt0(sz00,u)),smndt0(u))**.
% 9.23/9.43 31571[2:Rew:40.1,31564.1,45.1,31564.1] aInteger0(u) || -> equal(smndt0(u),u)**.
% 9.23/9.43 32220[2:SpL:31571.1,18926.0] aInteger0(sz10) || equal(sz10,sz10)* -> .
% 9.23/9.43 32261[2:Obv:32220.1] aInteger0(sz10) || -> .
% 9.23/9.43 32262[2:SSi:32261.0,2.0] || -> .
% 9.23/9.43 % SZS output end Refutation
% 9.23/9.43 Formulae used in the proof : mIntZero mIntOne m__2171 m__2232 m__2144 m__2079 mIntNeg mAddZero mMulOne mMulZero mAddNeg mIntMult mMulMinOne m__ mPrimeDivisor mZeroDiv mAddAsso mDistrib
% 9.23/9.43
%------------------------------------------------------------------------------