TSTP Solution File: SWC183+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC183+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Tue Jul 19 22:02:18 EDT 2022
% Result : Theorem 7.57s 7.79s
% Output : Refutation 8.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC183+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 16:45:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.57/7.79
% 7.57/7.79 SPASS V 3.9
% 7.57/7.79 SPASS beiseite: Proof found.
% 7.57/7.79 % SZS status Theorem
% 7.57/7.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.57/7.79 SPASS derived 7596 clauses, backtracked 3163 clauses, performed 40 splits and kept 5758 clauses.
% 7.57/7.79 SPASS allocated 109022 KBytes.
% 7.57/7.79 SPASS spent 0:00:07.43 on the problem.
% 7.57/7.79 0:00:00.04 for the input.
% 7.57/7.79 0:00:00.07 for the FLOTTER CNF translation.
% 7.57/7.79 0:00:00.08 for inferences.
% 7.57/7.79 0:00:00.18 for the backtracking.
% 7.57/7.79 0:00:06.85 for the reduction.
% 7.57/7.79
% 7.57/7.79
% 7.57/7.79 Here is a proof with depth 8, length 240 :
% 7.57/7.79 % SZS output start Refutation
% 7.57/7.79 1[0:Inp] || -> ssList(skc11)*.
% 7.57/7.79 2[0:Inp] || -> ssList(skc10)*.
% 7.57/7.79 3[0:Inp] || -> ssItem(skc9)*.
% 7.57/7.79 5[0:Inp] || -> ssList(skc7)*.
% 7.57/7.79 6[0:Inp] || -> ssItem(skc13)*.
% 7.57/7.79 7[0:Inp] || -> ssItem(skc12)*.
% 7.57/7.79 8[0:Inp] || -> ssList(nil)*.
% 7.57/7.79 9[0:Inp] || -> cyclefreeP(nil)*.
% 7.57/7.79 10[0:Inp] || -> totalorderP(nil)*.
% 7.57/7.79 11[0:Inp] || -> strictorderP(nil)*.
% 7.57/7.79 12[0:Inp] || -> totalorderedP(nil)*.
% 7.57/7.79 13[0:Inp] || -> strictorderedP(nil)*.
% 7.57/7.79 14[0:Inp] || -> duplicatefreeP(nil)*.
% 7.57/7.79 15[0:Inp] || -> equalelemsP(nil)*.
% 7.57/7.79 16[0:Inp] || -> ssItem(skf47(u))*.
% 7.57/7.79 54[0:Inp] || -> ssItem(skf44(u,v))*.
% 7.57/7.79 55[0:Inp] || equal(skc13,skc12)** -> .
% 7.57/7.79 62[0:Inp] || -> memberP(skc11,skc9)* memberP(skc10,skc9).
% 7.57/7.79 64[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 7.57/7.79 72[0:Inp] || SkP0(skc8,skc7)* -> equal(nil,skc7).
% 7.57/7.79 73[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 7.57/7.79 74[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 7.57/7.79 75[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 7.57/7.79 76[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 7.57/7.79 77[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 7.57/7.79 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 7.57/7.79 79[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 7.57/7.79 80[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 7.57/7.79 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 7.57/7.79 85[0:Inp] || -> equal(app(app(skc10,cons(skc9,nil)),skc11),skc7)**.
% 7.57/7.79 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 7.57/7.79 90[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 7.57/7.79 91[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf53(u),skf52(u))*.
% 7.57/7.79 93[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(skf78(u),skf77(u))**.
% 7.57/7.79 94[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 7.57/7.79 95[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 7.57/7.79 110[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 7.57/7.79 113[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 7.57/7.79 114[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 7.57/7.79 115[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 7.57/7.79 121[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 7.57/7.79 124[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 7.57/7.79 131[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 7.57/7.79 133[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 7.57/7.79 136[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 7.57/7.79 142[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(v,u).
% 7.57/7.79 146[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 7.57/7.79 153[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(w,v) -> frontsegP(app(w,u),v)*.
% 7.57/7.79 157[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 7.57/7.79 162[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 7.57/7.79 176[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf74(u),cons(skf72(u),skf75(u))),cons(skf73(u),skf76(u))),u)**.
% 7.57/7.79 177[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf69(u),cons(skf67(u),skf70(u))),cons(skf68(u),skf71(u))),u)**.
% 7.57/7.79 178[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf64(u),cons(skf62(u),skf65(u))),cons(skf63(u),skf66(u))),u)**.
% 7.57/7.79 179[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf59(u),cons(skf57(u),skf60(u))),cons(skf58(u),skf61(u))),u)**.
% 7.57/7.79 190[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 7.57/7.79 191[0:Inp] ssList(u) ssList(v) || equal(tl(u),tl(v))* equal(hd(u),hd(v)) -> equal(u,v) equal(nil,v) equal(nil,u).
% 7.57/7.79 222[0:Res:5.0,179.0] || -> totalorderP(skc7) equal(app(app(skf59(skc7),cons(skf57(skc7),skf60(skc7))),cons(skf58(skc7),skf61(skc7))),skc7)**.
% 7.57/7.79 223[0:Res:5.0,178.0] || -> strictorderP(skc7) equal(app(app(skf64(skc7),cons(skf62(skc7),skf65(skc7))),cons(skf63(skc7),skf66(skc7))),skc7)**.
% 7.57/7.79 224[0:Res:5.0,177.0] || -> totalorderedP(skc7) equal(app(app(skf69(skc7),cons(skf67(skc7),skf70(skc7))),cons(skf68(skc7),skf71(skc7))),skc7)**.
% 7.57/7.79 225[0:Res:5.0,176.0] || -> strictorderedP(skc7) equal(app(app(skf74(skc7),cons(skf72(skc7),skf75(skc7))),cons(skf73(skc7),skf76(skc7))),skc7)**.
% 7.57/7.79 242[0:Res:5.0,157.0] ssList(u) || -> equal(nil,skc7) equal(app(tl(skc7),u),tl(app(skc7,u)))**.
% 7.57/7.79 248[0:Res:5.0,136.0] ssList(u) || -> equal(nil,skc7) equal(hd(app(skc7,u)),hd(skc7))**.
% 7.57/7.79 251[0:Res:5.0,133.0] ssList(u) || equal(app(skc7,u),nil)** -> equal(nil,skc7).
% 7.57/7.79 254[0:Res:5.0,121.0] || -> equal(nil,skc7) equal(cons(hd(skc7),tl(skc7)),skc7)**.
% 7.57/7.79 255[0:Res:5.0,110.1] singletonP(skc7) || -> equal(cons(skf47(skc7),nil),skc7)**.
% 7.57/7.79 259[0:Res:5.0,114.0] ssItem(u) || -> equal(hd(cons(u,skc7)),u)**.
% 7.57/7.79 268[0:Res:5.0,91.0] || -> cyclefreeP(skc7) leq(skf53(skc7),skf52(skc7))*.
% 7.57/7.79 270[0:Res:5.0,93.0] || -> duplicatefreeP(skc7) equal(skf78(skc7),skf77(skc7))**.
% 7.57/7.79 271[0:Res:5.0,94.0] ssItem(u) || -> ssList(cons(u,skc7))*.
% 7.57/7.79 289[0:Res:5.0,191.1] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u) equal(nil,skc7).
% 7.57/7.79 324[0:Res:5.0,124.1] ssItem(u) || equal(cons(u,nil),skc7)** -> singletonP(skc7).
% 7.57/7.79 554[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc7,u)),hd(skc7))**.
% 7.57/7.79 558[2:Spt:242.0,242.2] ssList(u) || -> equal(app(tl(skc7),u),tl(app(skc7,u)))**.
% 7.57/7.79 1500[3:Spt:289.5] || -> equal(nil,skc7)**.
% 7.57/7.79 1536[3:Rew:1500.0,74.1] ssItem(u) || -> cyclefreeP(cons(u,skc7))*.
% 7.57/7.79 1537[3:Rew:1500.0,75.1] ssItem(u) || -> totalorderP(cons(u,skc7))*.
% 7.57/7.79 1538[3:Rew:1500.0,76.1] ssItem(u) || -> strictorderP(cons(u,skc7))*.
% 7.57/7.79 1539[3:Rew:1500.0,77.1] ssItem(u) || -> totalorderedP(cons(u,skc7))*.
% 7.57/7.79 1540[3:Rew:1500.0,78.1] ssItem(u) || -> strictorderedP(cons(u,skc7))*.
% 7.57/7.79 1541[3:Rew:1500.0,79.1] ssItem(u) || -> duplicatefreeP(cons(u,skc7))*.
% 7.57/7.79 1542[3:Rew:1500.0,80.1] ssItem(u) || -> equalelemsP(cons(u,skc7))*.
% 7.57/7.79 1548[3:Rew:1500.0,83.1] ssList(u) || -> equal(app(skc7,u),u)**.
% 7.57/7.79 1628[3:Rew:1548.1,554.1] ssList(u) || -> equal(hd(u),hd(skc7))*.
% 7.57/7.79 1701[3:SpR:1628.1,259.1] ssList(cons(u,skc7)) ssItem(u) || -> equal(hd(skc7),u)*.
% 7.57/7.79 1710[3:SSi:1701.0,271.1,1536.1,1537.1,1538.1,1539.1,1540.1,1541.1,1542.1] ssItem(u) || -> equal(hd(skc7),u)*.
% 7.57/7.79 1728[3:SpR:1710.1,1710.1] ssItem(u) ssItem(v) || -> equal(u,v)*.
% 7.57/7.79 1919[3:EmS:1728.0,7.0] ssItem(u) || -> equal(skc12,u)*.
% 7.57/7.79 1943[3:EmS:1919.0,6.0] || -> equal(skc13,skc12)**.
% 7.57/7.79 1945[3:MRR:1943.0,55.0] || -> .
% 7.57/7.79 2155[3:Spt:1945.0,289.5,1500.0] || equal(nil,skc7)** -> .
% 7.57/7.79 2156[3:Spt:1945.0,289.0,289.1,289.2,289.3,289.4] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u).
% 7.57/7.79 2162[3:MRR:72.1,2155.0] || SkP0(skc8,skc7)* -> .
% 7.57/7.79 2163[3:MRR:254.0,2155.0] || -> equal(cons(hd(skc7),tl(skc7)),skc7)**.
% 7.57/7.79 2166[3:MRR:251.2,2155.0] ssList(u) || equal(app(skc7,u),nil)** -> .
% 7.57/7.79 2188[4:Spt:224.0] || -> totalorderedP(skc7)*.
% 7.57/7.79 2192[5:Spt:225.0] || -> strictorderedP(skc7)*.
% 7.57/7.79 2197[6:Spt:268.0] || -> cyclefreeP(skc7)*.
% 7.57/7.79 2201[7:Spt:222.0] || -> totalorderP(skc7)*.
% 7.57/7.79 2202[8:Spt:223.0] || -> strictorderP(skc7)*.
% 7.57/7.79 2215[9:Spt:270.0] || -> duplicatefreeP(skc7)*.
% 7.57/7.79 2282[0:SpR:90.1,80.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 7.57/7.79 2283[0:SpR:90.1,79.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* duplicatefreeP(v).
% 7.57/7.79 2284[0:SpR:90.1,78.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderedP(v).
% 7.57/7.79 2285[0:SpR:90.1,77.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderedP(v).
% 7.57/7.79 2286[0:SpR:90.1,76.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderP(v).
% 7.57/7.79 2287[0:SpR:90.1,75.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderP(v).
% 7.57/7.79 2288[0:SpR:90.1,74.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* cyclefreeP(v).
% 7.57/7.79 2290[0:SSi:2282.0,54.0] || -> SkP0(u,v)* equalelemsP(v).
% 7.57/7.79 2291[0:SSi:2283.0,54.0] || -> SkP0(u,v)* duplicatefreeP(v).
% 7.57/7.79 2292[0:SSi:2284.0,54.0] || -> SkP0(u,v)* strictorderedP(v).
% 7.57/7.79 2293[0:SSi:2285.0,54.0] || -> SkP0(u,v)* totalorderedP(v).
% 7.57/7.79 2294[0:SSi:2286.0,54.0] || -> SkP0(u,v)* strictorderP(v).
% 7.57/7.79 2295[0:SSi:2287.0,54.0] || -> SkP0(u,v)* totalorderP(v).
% 7.57/7.79 2296[0:SSi:2288.0,54.0] || -> SkP0(u,v)* cyclefreeP(v).
% 7.57/7.79 2298[3:Res:2290.0,2162.0] || -> equalelemsP(skc7)*.
% 7.57/7.79 2300[3:Res:2291.0,2162.0] || -> duplicatefreeP(skc7)*.
% 7.57/7.79 2301[3:Res:2292.0,2162.0] || -> strictorderedP(skc7)*.
% 7.57/7.79 2302[3:Res:2293.0,2162.0] || -> totalorderedP(skc7)*.
% 7.57/7.79 2303[3:Res:2294.0,2162.0] || -> strictorderP(skc7)*.
% 7.57/7.79 2304[3:Res:2295.0,2162.0] || -> totalorderP(skc7)*.
% 7.57/7.79 2305[3:Res:2296.0,2162.0] || -> cyclefreeP(skc7)*.
% 7.57/7.79 2311[0:SpL:90.1,324.1] ssItem(skf44(u,v)) || equal(v,skc7) -> SkP0(u,v)* singletonP(skc7).
% 7.57/7.79 2312[0:SSi:2311.0,54.0] || equal(u,skc7) -> SkP0(v,u)* singletonP(skc7).
% 7.57/7.79 2313[10:Spt:2312.0,2312.1] || equal(u,skc7) -> SkP0(v,u)*.
% 7.57/7.79 2314[10:Res:2313.1,2162.0] || equal(skc7,skc7)* -> .
% 7.57/7.79 2315[10:Obv:2314.0] || -> .
% 7.57/7.79 2316[10:Spt:2315.0,2312.2] || -> singletonP(skc7)*.
% 7.57/7.79 2317[10:MRR:255.0,2316.0] || -> equal(cons(skf47(skc7),nil),skc7)**.
% 7.57/7.79 2393[10:SpR:2317.0,115.2] ssItem(skf47(skc7)) ssList(nil) || -> equal(tl(skc7),nil)**.
% 7.57/7.79 2397[10:SSi:2393.1,2393.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,8.0,16.0,5.0,2188.0,2192.0,2197.0,2201.0,2202.0,2215.0,2298.0,2316.0] || -> equal(tl(skc7),nil)**.
% 7.57/7.79 2400[10:Rew:2397.0,2163.0] || -> equal(cons(hd(skc7),nil),skc7)**.
% 7.57/7.79 2401[10:Rew:2397.0,558.1] ssList(u) || -> equal(tl(app(skc7,u)),app(nil,u))**.
% 7.57/7.79 2404[10:Rew:83.1,2401.1] ssList(u) || -> equal(tl(app(skc7,u)),u)**.
% 7.57/7.79 2440[0:SpR:90.1,114.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 7.57/7.79 2444[0:SSi:2440.1,2440.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,8.0,54.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 7.57/7.79 2446[0:Rew:2444.1,90.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 7.57/7.79 2633[10:SpR:2404.1,121.2] ssList(u) ssList(app(skc7,u)) || -> equal(app(skc7,u),nil) equal(cons(hd(app(skc7,u)),u),app(skc7,u))**.
% 7.57/7.79 2649[10:Rew:554.1,2633.3] ssList(u) ssList(app(skc7,u)) || -> equal(app(skc7,u),nil) equal(cons(hd(skc7),u),app(skc7,u))**.
% 7.57/7.79 2650[10:SSi:2649.1,95.0,5.0,2188.0,2192.0,2197.0,2201.0,2202.0,2215.0,2298.0,2316.2] ssList(u) || -> equal(app(skc7,u),nil) equal(cons(hd(skc7),u),app(skc7,u))**.
% 7.57/7.79 2651[10:MRR:2650.1,2166.1] ssList(u) || -> equal(cons(hd(skc7),u),app(skc7,u))**.
% 7.57/7.79 3005[0:EqR:124.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 7.57/7.79 3010[0:SSi:3005.0,80.0,79.0,78.0,77.0,76.0,75.0,74.0,94.0,15.2,14.1,13.1,12.1,11.1,10.1,9.1,8.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 7.57/7.79 4575[0:EqR:146.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 7.57/7.79 4590[0:SSi:4575.1,95.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 7.57/7.79 5048[0:SpR:162.3,85.0] ssList(skc11) ssList(cons(skc9,nil)) ssList(skc10) || -> equal(app(skc10,app(cons(skc9,nil),skc11)),skc7)**.
% 7.57/7.79 5081[0:SSi:5048.2,5048.1,5048.0,2.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.0,3.2,75.0,3.1,74.0,3.1,3010.0,3.1,94.0,3.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,8.1,1.0] || -> equal(app(skc10,app(cons(skc9,nil),skc11)),skc7)**.
% 7.57/7.79 5144[0:SpR:5081.0,136.3] ssList(app(cons(skc9,nil),skc11)) ssList(skc10) || -> equal(skc10,nil) equal(hd(skc10),hd(skc7))**.
% 7.57/7.79 5147[0:SpR:5081.0,153.4] ssList(app(cons(skc9,nil),skc11)) ssList(u) ssList(skc10) || frontsegP(skc10,u)* -> frontsegP(skc7,u).
% 7.57/7.79 5152[0:SpR:131.2,5081.0] ssItem(skc9) ssList(skc11) || -> equal(app(skc10,cons(skc9,skc11)),skc7)**.
% 7.57/7.79 5158[0:SSi:5152.1,5152.0,1.0,3.0] || -> equal(app(skc10,cons(skc9,skc11)),skc7)**.
% 7.57/7.79 5159[0:SSi:5144.1,5144.0,2.0,95.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.2,3.0,75.1,3.0,74.1,3.0,3010.1,3.0,94.1,3.0,15.1,14.0,13.1,12.0,11.1,10.0,9.1,8.2,1.0] || -> equal(skc10,nil) equal(hd(skc10),hd(skc7))**.
% 7.57/7.79 5162[0:SSi:5147.2,5147.0,2.0,95.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.2,3.0,75.1,3.0,74.1,3.0,3010.1,3.0,94.1,3.0,15.1,14.0,13.1,12.0,11.1,10.0,9.1,8.2,1.0] ssList(u) || frontsegP(skc10,u)* -> frontsegP(skc7,u).
% 7.57/7.79 5190[11:Spt:5159.0] || -> equal(skc10,nil)**.
% 7.57/7.79 5193[11:Rew:5190.0,62.1] || -> memberP(skc11,skc9)* memberP(nil,skc9).
% 7.57/7.79 5199[11:Rew:5190.0,5158.0] || -> equal(app(nil,cons(skc9,skc11)),skc7)**.
% 7.57/7.79 5236[11:SpR:5199.0,83.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),skc7)**.
% 7.57/7.79 5245[11:SSi:5236.0,94.0,3.0,1.2] || -> equal(cons(skc9,skc11),skc7)**.
% 7.57/7.79 5259[11:SpR:5245.0,115.2] ssItem(skc9) ssList(skc11) || -> equal(tl(skc7),skc11)**.
% 7.57/7.79 5275[11:Rew:2397.0,5259.2] ssItem(skc9) ssList(skc11) || -> equal(skc11,nil)**.
% 7.57/7.79 5276[11:SSi:5275.1,5275.0,1.0,3.0] || -> equal(skc11,nil)**.
% 7.57/7.79 5291[11:Rew:5276.0,5193.0] || -> memberP(nil,skc9)* memberP(nil,skc9)*.
% 7.57/7.79 5316[11:Obv:5291.0] || -> memberP(nil,skc9)*.
% 7.57/7.79 5361[11:Res:5316.0,73.1] ssItem(skc9) || -> .
% 7.57/7.79 5362[11:SSi:5361.0,3.0] || -> .
% 7.57/7.79 5363[11:Spt:5362.0,5159.0,5190.0] || equal(skc10,nil)** -> .
% 7.57/7.79 5364[11:Spt:5362.0,5159.1] || -> equal(hd(skc10),hd(skc7))**.
% 7.57/7.79 5368[11:SpR:5364.0,121.2] ssList(skc10) || -> equal(skc10,nil) equal(cons(hd(skc7),tl(skc10)),skc10)**.
% 7.57/7.79 5370[11:SpR:5364.0,2446.1] || -> SkP0(u,skc10)* equal(cons(hd(skc7),nil),skc10)**.
% 7.57/7.79 5374[11:Rew:2400.0,5370.1] || -> SkP0(u,skc10)* equal(skc10,skc7).
% 7.57/7.79 5379[11:MRR:5368.0,5368.1,2.0,5363.0] || -> equal(cons(hd(skc7),tl(skc10)),skc10)**.
% 7.57/7.79 5398[12:Spt:5374.1] || -> equal(skc10,skc7)**.
% 7.57/7.79 5404[12:Rew:5398.0,5158.0] || -> equal(app(skc7,cons(skc9,skc11)),skc7)**.
% 7.57/7.79 5452[12:SpR:5404.0,2404.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),tl(skc7))**.
% 7.57/7.79 5465[12:Rew:2397.0,5452.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),nil)**.
% 7.57/7.79 5466[12:SSi:5465.0,94.0,3.0,1.2] || -> equal(cons(skc9,skc11),nil)**.
% 7.57/7.79 5490[12:SpL:5466.0,113.2] ssItem(skc9) ssList(skc11) || equal(nil,nil)* -> .
% 7.57/7.79 5498[12:Obv:5490.2] ssItem(skc9) ssList(skc11) || -> .
% 7.57/7.79 5499[12:SSi:5498.1,5498.0,1.0,3.0] || -> .
% 7.57/7.79 5519[12:Spt:5499.0,5374.1,5398.0] || equal(skc10,skc7)** -> .
% 7.57/7.79 5520[12:Spt:5499.0,5374.0] || -> SkP0(u,skc10)*.
% 7.57/7.79 5544[11:SpR:5379.0,2651.1] ssList(tl(skc10)) || -> equal(app(skc7,tl(skc10)),skc10)**.
% 7.57/7.79 5812[11:SoR:5544.0,89.1] ssList(skc10) || -> equal(app(skc7,tl(skc10)),skc10)** equal(skc10,nil).
% 7.57/7.79 5814[11:SSi:5812.0,2.0] || -> equal(app(skc7,tl(skc10)),skc10)** equal(skc10,nil).
% 7.57/7.79 5815[11:MRR:5814.1,5363.0] || -> equal(app(skc7,tl(skc10)),skc10)**.
% 7.57/7.79 5917[0:Res:64.1,5162.1] ssList(skc10) ssList(skc10) || -> frontsegP(skc7,skc10)*.
% 7.57/7.79 5922[0:Obv:5917.0] ssList(skc10) || -> frontsegP(skc7,skc10)*.
% 7.57/7.79 5923[0:SSi:5922.0,2.0] || -> frontsegP(skc7,skc10)*.
% 7.57/7.79 5926[0:Res:5923.0,142.2] ssList(skc7) ssList(skc10) || frontsegP(skc10,skc7)* -> equal(skc10,skc7).
% 7.57/7.79 5927[10:SSi:5926.1,5926.0,2.0,5.0,2188.0,2192.0,2197.0,2201.0,2202.0,2215.0,2298.0,2316.0] || frontsegP(skc10,skc7)* -> equal(skc10,skc7).
% 7.57/7.79 5928[12:MRR:5927.1,5519.0] || frontsegP(skc10,skc7)* -> .
% 7.57/7.79 7434[0:SpL:5158.0,190.4] ssItem(skc9) ssList(u) ssList(skc11) ssList(skc10) || equal(skc7,u) -> memberP(u,skc9)*.
% 7.57/7.79 7444[0:SSi:7434.3,7434.2,7434.0,2.0,1.0,3.0] ssList(u) || equal(skc7,u) -> memberP(u,skc9)*.
% 7.57/7.79 10022[11:SpR:5815.0,4590.2] ssList(skc7) ssList(tl(skc10)) || -> frontsegP(skc10,skc7)*.
% 7.57/7.79 10031[11:SSi:10022.0,5.0,2188.0,2192.0,2197.0,2201.0,2202.0,2215.0,2298.0,2316.0] ssList(tl(skc10)) || -> frontsegP(skc10,skc7)*.
% 7.57/7.79 10032[12:MRR:10031.1,5928.0] ssList(tl(skc10)) || -> .
% 7.57/7.79 10068[12:SoR:10032.0,89.1] ssList(skc10) || -> equal(skc10,nil)**.
% 7.57/7.79 10070[12:SSi:10068.0,2.0] || -> equal(skc10,nil)**.
% 7.57/7.79 10071[12:MRR:10070.0,5363.0] || -> .
% 7.57/7.79 10072[9:Spt:10071.0,270.0,2215.0] || duplicatefreeP(skc7)* -> .
% 7.57/7.79 10073[9:Spt:10071.0,270.1] || -> equal(skf78(skc7),skf77(skc7))**.
% 7.57/7.79 10074[9:MRR:10072.0,2300.0] || -> .
% 7.57/7.79 10221[8:Spt:10074.0,223.0,2202.0] || strictorderP(skc7)* -> .
% 7.57/7.79 10222[8:Spt:10074.0,223.1] || -> equal(app(app(skf64(skc7),cons(skf62(skc7),skf65(skc7))),cons(skf63(skc7),skf66(skc7))),skc7)**.
% 7.57/7.79 10223[8:MRR:10221.0,2303.0] || -> .
% 7.57/7.79 10413[7:Spt:10223.0,222.0,2201.0] || totalorderP(skc7)* -> .
% 7.57/7.79 10414[7:Spt:10223.0,222.1] || -> equal(app(app(skf59(skc7),cons(skf57(skc7),skf60(skc7))),cons(skf58(skc7),skf61(skc7))),skc7)**.
% 7.57/7.79 10415[7:MRR:10413.0,2304.0] || -> .
% 7.57/7.79 10505[6:Spt:10415.0,268.0,2197.0] || cyclefreeP(skc7)* -> .
% 7.57/7.79 10506[6:Spt:10415.0,268.1] || -> leq(skf53(skc7),skf52(skc7))*.
% 7.57/7.79 10507[6:MRR:10505.0,2305.0] || -> .
% 7.57/7.79 10682[5:Spt:10507.0,225.0,2192.0] || strictorderedP(skc7)* -> .
% 7.57/7.79 10683[5:Spt:10507.0,225.1] || -> equal(app(app(skf74(skc7),cons(skf72(skc7),skf75(skc7))),cons(skf73(skc7),skf76(skc7))),skc7)**.
% 7.57/7.79 10684[5:MRR:10682.0,2301.0] || -> .
% 8.13/8.31 10861[4:Spt:10684.0,224.0,2188.0] || totalorderedP(skc7)* -> .
% 8.13/8.31 10862[4:Spt:10684.0,224.1] || -> equal(app(app(skf69(skc7),cons(skf67(skc7),skf70(skc7))),cons(skf68(skc7),skf71(skc7))),skc7)**.
% 8.13/8.31 10863[4:MRR:10861.0,2302.0] || -> .
% 8.13/8.31 10958[2:Spt:10863.0,242.1] || -> equal(nil,skc7)**.
% 8.13/8.31 10981[2:Rew:10958.0,15.0] || -> equalelemsP(skc7)*.
% 8.13/8.31 10982[2:Rew:10958.0,14.0] || -> duplicatefreeP(skc7)*.
% 8.13/8.31 10983[2:Rew:10958.0,13.0] || -> strictorderedP(skc7)*.
% 8.13/8.31 10984[2:Rew:10958.0,12.0] || -> totalorderedP(skc7)*.
% 8.13/8.31 10985[2:Rew:10958.0,11.0] || -> strictorderP(skc7)*.
% 8.13/8.31 10986[2:Rew:10958.0,10.0] || -> totalorderP(skc7)*.
% 8.13/8.31 10987[2:Rew:10958.0,9.0] || -> cyclefreeP(skc7)*.
% 8.13/8.31 11014[2:Rew:10958.0,73.1] ssItem(u) || memberP(skc7,u)* -> .
% 8.13/8.31 12242[2:Res:7444.2,11014.1] ssList(skc7) ssItem(skc9) || equal(skc7,skc7)* -> .
% 8.13/8.31 12244[2:Obv:12242.2] ssList(skc7) ssItem(skc9) || -> .
% 8.13/8.31 12245[2:SSi:12244.1,12244.0,3.0,5.0,10981.0,10982.0,10983.0,10984.0,10985.0,10986.0,10987.0] || -> .
% 8.13/8.31 12246[1:Spt:12245.0,248.1] || -> equal(nil,skc7)**.
% 8.13/8.31 12248[1:Rew:12246.0,9.0] || -> cyclefreeP(skc7)*.
% 8.13/8.31 12249[1:Rew:12246.0,10.0] || -> totalorderP(skc7)*.
% 8.13/8.31 12250[1:Rew:12246.0,11.0] || -> strictorderP(skc7)*.
% 8.13/8.31 12251[1:Rew:12246.0,12.0] || -> totalorderedP(skc7)*.
% 8.13/8.31 12252[1:Rew:12246.0,13.0] || -> strictorderedP(skc7)*.
% 8.13/8.31 12253[1:Rew:12246.0,14.0] || -> duplicatefreeP(skc7)*.
% 8.13/8.31 12254[1:Rew:12246.0,15.0] || -> equalelemsP(skc7)*.
% 8.13/8.31 12277[1:Rew:12246.0,73.1] ssItem(u) || memberP(skc7,u)* -> .
% 8.13/8.31 13191[1:Res:7444.2,12277.1] ssList(skc7) ssItem(skc9) || equal(skc7,skc7)* -> .
% 8.13/8.31 13193[1:Obv:13191.2] ssList(skc7) ssItem(skc9) || -> .
% 8.13/8.31 13194[1:SSi:13193.1,13193.0,3.0,5.0,12248.0,12249.0,12250.0,12251.0,12252.0,12253.0,12254.0] || -> .
% 8.13/8.31 % SZS output end Refutation
% 8.13/8.31 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax42 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax76 ax8 ax13 ax16 ax26 ax21 ax23 ax25 ax78 ax81 ax83 ax85 ax41 ax5 ax43 ax86 ax82 ax12 ax11 ax10 ax9 ax3 ax77
% 8.13/8.31
%------------------------------------------------------------------------------