TSTP Solution File: SWC187+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC187+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 22:02:20 EDT 2022
% Result : Theorem 6.85s 7.03s
% Output : Refutation 7.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC187+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jun 11 22:07:37 EDT 2022
% 0.11/0.32 % CPUTime :
% 6.85/7.03
% 6.85/7.03 SPASS V 3.9
% 6.85/7.03 SPASS beiseite: Proof found.
% 6.85/7.03 % SZS status Theorem
% 6.85/7.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/7.03 SPASS derived 7249 clauses, backtracked 2769 clauses, performed 43 splits and kept 5469 clauses.
% 6.85/7.03 SPASS allocated 108110 KBytes.
% 6.85/7.03 SPASS spent 0:00:06.69 on the problem.
% 6.85/7.03 0:00:00.04 for the input.
% 6.85/7.03 0:00:00.07 for the FLOTTER CNF translation.
% 6.85/7.03 0:00:00.08 for inferences.
% 6.85/7.03 0:00:00.16 for the backtracking.
% 6.85/7.03 0:00:06.16 for the reduction.
% 6.85/7.03
% 6.85/7.03
% 6.85/7.03 Here is a proof with depth 8, length 240 :
% 6.85/7.03 % SZS output start Refutation
% 6.85/7.03 1[0:Inp] || -> ssList(skc11)*.
% 6.85/7.03 2[0:Inp] || -> ssList(skc10)*.
% 6.85/7.03 3[0:Inp] || -> ssItem(skc9)*.
% 6.85/7.03 5[0:Inp] || -> ssList(skc7)*.
% 6.85/7.03 6[0:Inp] || -> ssItem(skc13)*.
% 6.85/7.03 7[0:Inp] || -> ssItem(skc12)*.
% 6.85/7.03 8[0:Inp] || -> ssList(nil)*.
% 6.85/7.03 9[0:Inp] || -> cyclefreeP(nil)*.
% 6.85/7.03 10[0:Inp] || -> totalorderP(nil)*.
% 6.85/7.03 11[0:Inp] || -> strictorderP(nil)*.
% 6.85/7.03 12[0:Inp] || -> totalorderedP(nil)*.
% 6.85/7.03 13[0:Inp] || -> strictorderedP(nil)*.
% 6.85/7.03 14[0:Inp] || -> duplicatefreeP(nil)*.
% 6.85/7.03 15[0:Inp] || -> equalelemsP(nil)*.
% 6.85/7.03 16[0:Inp] || -> ssItem(skf47(u))*.
% 6.85/7.03 54[0:Inp] || -> ssItem(skf44(u,v))*.
% 6.85/7.03 55[0:Inp] || equal(skc13,skc12)** -> .
% 6.85/7.03 62[0:Inp] || -> memberP(skc11,skc9)* memberP(skc10,skc9).
% 6.85/7.03 64[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 6.85/7.03 72[0:Inp] || SkP0(skc8,skc7)* -> equal(nil,skc7).
% 6.85/7.03 73[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 6.85/7.03 74[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 6.85/7.03 75[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 6.85/7.03 76[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 6.85/7.03 77[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 6.85/7.03 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 6.85/7.03 79[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 6.85/7.03 80[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 6.85/7.03 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 6.85/7.03 85[0:Inp] || -> equal(app(app(skc10,cons(skc9,nil)),skc11),skc7)**.
% 6.85/7.03 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 6.85/7.03 90[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 6.85/7.03 91[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf53(u),skf52(u))*.
% 6.85/7.03 93[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(skf78(u),skf77(u))**.
% 6.85/7.03 94[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 6.85/7.03 95[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 6.85/7.03 110[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 6.85/7.03 113[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 6.85/7.03 114[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 6.85/7.03 115[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 6.85/7.03 121[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 6.85/7.03 124[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 6.85/7.03 131[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 6.85/7.03 133[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 6.85/7.03 136[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 6.85/7.03 142[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(v,u).
% 6.85/7.03 146[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 6.85/7.03 153[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(w,v) -> frontsegP(app(w,u),v)*.
% 6.85/7.03 157[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 6.85/7.03 162[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 6.85/7.03 176[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf74(u),cons(skf72(u),skf75(u))),cons(skf73(u),skf76(u))),u)**.
% 6.85/7.03 177[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf69(u),cons(skf67(u),skf70(u))),cons(skf68(u),skf71(u))),u)**.
% 6.85/7.03 178[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf64(u),cons(skf62(u),skf65(u))),cons(skf63(u),skf66(u))),u)**.
% 6.85/7.03 179[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf59(u),cons(skf57(u),skf60(u))),cons(skf58(u),skf61(u))),u)**.
% 6.85/7.03 189[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 6.85/7.03 190[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).
% 6.85/7.03 221[0:Res:5.0,179.0] || -> totalorderP(skc7) equal(app(app(skf59(skc7),cons(skf57(skc7),skf60(skc7))),cons(skf58(skc7),skf61(skc7))),skc7)**.
% 6.85/7.03 222[0:Res:5.0,178.0] || -> strictorderP(skc7) equal(app(app(skf64(skc7),cons(skf62(skc7),skf65(skc7))),cons(skf63(skc7),skf66(skc7))),skc7)**.
% 6.85/7.03 223[0:Res:5.0,177.0] || -> totalorderedP(skc7) equal(app(app(skf69(skc7),cons(skf67(skc7),skf70(skc7))),cons(skf68(skc7),skf71(skc7))),skc7)**.
% 6.85/7.03 224[0:Res:5.0,176.0] || -> strictorderedP(skc7) equal(app(app(skf74(skc7),cons(skf72(skc7),skf75(skc7))),cons(skf73(skc7),skf76(skc7))),skc7)**.
% 6.85/7.03 241[0:Res:5.0,157.0] ssList(u) || -> equal(nil,skc7) equal(app(tl(skc7),u),tl(app(skc7,u)))**.
% 6.85/7.03 247[0:Res:5.0,136.0] ssList(u) || -> equal(nil,skc7) equal(hd(app(skc7,u)),hd(skc7))**.
% 6.85/7.03 250[0:Res:5.0,133.0] ssList(u) || equal(app(skc7,u),nil)** -> equal(nil,skc7).
% 6.85/7.03 253[0:Res:5.0,121.0] || -> equal(nil,skc7) equal(cons(hd(skc7),tl(skc7)),skc7)**.
% 6.85/7.03 254[0:Res:5.0,110.1] singletonP(skc7) || -> equal(cons(skf47(skc7),nil),skc7)**.
% 6.85/7.03 258[0:Res:5.0,114.0] ssItem(u) || -> equal(hd(cons(u,skc7)),u)**.
% 6.85/7.03 267[0:Res:5.0,91.0] || -> cyclefreeP(skc7) leq(skf53(skc7),skf52(skc7))*.
% 6.85/7.03 269[0:Res:5.0,93.0] || -> duplicatefreeP(skc7) equal(skf78(skc7),skf77(skc7))**.
% 6.85/7.03 270[0:Res:5.0,94.0] ssItem(u) || -> ssList(cons(u,skc7))*.
% 6.85/7.03 288[0:Res:5.0,190.1] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u) equal(nil,skc7).
% 6.85/7.03 323[0:Res:5.0,124.1] ssItem(u) || equal(cons(u,nil),skc7)** -> singletonP(skc7).
% 6.85/7.03 553[1:Spt:247.0,247.2] ssList(u) || -> equal(hd(app(skc7,u)),hd(skc7))**.
% 6.85/7.03 557[2:Spt:241.0,241.2] ssList(u) || -> equal(app(tl(skc7),u),tl(app(skc7,u)))**.
% 6.85/7.03 1498[3:Spt:288.5] || -> equal(nil,skc7)**.
% 6.85/7.03 1534[3:Rew:1498.0,74.1] ssItem(u) || -> cyclefreeP(cons(u,skc7))*.
% 6.85/7.03 1535[3:Rew:1498.0,75.1] ssItem(u) || -> totalorderP(cons(u,skc7))*.
% 6.85/7.03 1536[3:Rew:1498.0,76.1] ssItem(u) || -> strictorderP(cons(u,skc7))*.
% 6.85/7.03 1537[3:Rew:1498.0,77.1] ssItem(u) || -> totalorderedP(cons(u,skc7))*.
% 6.85/7.03 1538[3:Rew:1498.0,78.1] ssItem(u) || -> strictorderedP(cons(u,skc7))*.
% 6.85/7.03 1539[3:Rew:1498.0,79.1] ssItem(u) || -> duplicatefreeP(cons(u,skc7))*.
% 6.85/7.03 1540[3:Rew:1498.0,80.1] ssItem(u) || -> equalelemsP(cons(u,skc7))*.
% 6.85/7.03 1546[3:Rew:1498.0,83.1] ssList(u) || -> equal(app(skc7,u),u)**.
% 6.85/7.03 1626[3:Rew:1546.1,553.1] ssList(u) || -> equal(hd(u),hd(skc7))*.
% 6.85/7.03 1699[3:SpR:1626.1,258.1] ssList(cons(u,skc7)) ssItem(u) || -> equal(hd(skc7),u)*.
% 6.85/7.03 1708[3:SSi:1699.0,270.1,1534.1,1535.1,1536.1,1537.1,1538.1,1539.1,1540.1] ssItem(u) || -> equal(hd(skc7),u)*.
% 6.85/7.03 1726[3:SpR:1708.1,1708.1] ssItem(u) ssItem(v) || -> equal(u,v)*.
% 6.85/7.03 1916[3:EmS:1726.0,7.0] ssItem(u) || -> equal(skc12,u)*.
% 6.85/7.03 1940[3:EmS:1916.0,6.0] || -> equal(skc13,skc12)**.
% 6.85/7.03 1942[3:MRR:1940.0,55.0] || -> .
% 6.85/7.03 2152[3:Spt:1942.0,288.5,1498.0] || equal(nil,skc7)** -> .
% 6.85/7.03 2153[3:Spt:1942.0,288.0,288.1,288.2,288.3,288.4] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u).
% 6.85/7.03 2159[3:MRR:72.1,2152.0] || SkP0(skc8,skc7)* -> .
% 6.85/7.03 2160[3:MRR:253.0,2152.0] || -> equal(cons(hd(skc7),tl(skc7)),skc7)**.
% 6.85/7.03 2163[3:MRR:250.2,2152.0] ssList(u) || equal(app(skc7,u),nil)** -> .
% 6.85/7.03 2185[4:Spt:223.0] || -> totalorderedP(skc7)*.
% 6.85/7.03 2189[5:Spt:224.0] || -> strictorderedP(skc7)*.
% 6.85/7.03 2194[6:Spt:267.0] || -> cyclefreeP(skc7)*.
% 6.85/7.03 2198[7:Spt:221.0] || -> totalorderP(skc7)*.
% 6.85/7.03 2199[8:Spt:222.0] || -> strictorderP(skc7)*.
% 6.85/7.03 2212[9:Spt:269.0] || -> duplicatefreeP(skc7)*.
% 6.85/7.03 2279[0:SpR:90.1,80.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 6.85/7.03 2280[0:SpR:90.1,79.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* duplicatefreeP(v).
% 6.85/7.03 2281[0:SpR:90.1,78.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderedP(v).
% 6.85/7.03 2282[0:SpR:90.1,77.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderedP(v).
% 6.85/7.03 2283[0:SpR:90.1,76.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderP(v).
% 6.85/7.03 2284[0:SpR:90.1,75.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderP(v).
% 6.85/7.03 2285[0:SpR:90.1,74.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* cyclefreeP(v).
% 6.85/7.03 2287[0:SSi:2279.0,54.0] || -> SkP0(u,v)* equalelemsP(v).
% 6.85/7.03 2288[0:SSi:2280.0,54.0] || -> SkP0(u,v)* duplicatefreeP(v).
% 6.85/7.03 2289[0:SSi:2281.0,54.0] || -> SkP0(u,v)* strictorderedP(v).
% 6.85/7.03 2290[0:SSi:2282.0,54.0] || -> SkP0(u,v)* totalorderedP(v).
% 6.85/7.03 2291[0:SSi:2283.0,54.0] || -> SkP0(u,v)* strictorderP(v).
% 6.85/7.03 2292[0:SSi:2284.0,54.0] || -> SkP0(u,v)* totalorderP(v).
% 6.85/7.03 2293[0:SSi:2285.0,54.0] || -> SkP0(u,v)* cyclefreeP(v).
% 6.85/7.03 2295[3:Res:2287.0,2159.0] || -> equalelemsP(skc7)*.
% 6.85/7.03 2297[3:Res:2288.0,2159.0] || -> duplicatefreeP(skc7)*.
% 6.85/7.03 2298[3:Res:2289.0,2159.0] || -> strictorderedP(skc7)*.
% 6.85/7.03 2299[3:Res:2290.0,2159.0] || -> totalorderedP(skc7)*.
% 6.85/7.03 2300[3:Res:2291.0,2159.0] || -> strictorderP(skc7)*.
% 6.85/7.03 2301[3:Res:2292.0,2159.0] || -> totalorderP(skc7)*.
% 6.85/7.03 2302[3:Res:2293.0,2159.0] || -> cyclefreeP(skc7)*.
% 6.85/7.03 2308[0:SpL:90.1,323.1] ssItem(skf44(u,v)) || equal(v,skc7) -> SkP0(u,v)* singletonP(skc7).
% 6.85/7.03 2309[0:SSi:2308.0,54.0] || equal(u,skc7) -> SkP0(v,u)* singletonP(skc7).
% 6.85/7.03 2310[10:Spt:2309.0,2309.1] || equal(u,skc7) -> SkP0(v,u)*.
% 6.85/7.03 2311[10:Res:2310.1,2159.0] || equal(skc7,skc7)* -> .
% 6.85/7.03 2312[10:Obv:2311.0] || -> .
% 6.85/7.03 2313[10:Spt:2312.0,2309.2] || -> singletonP(skc7)*.
% 6.85/7.03 2314[10:MRR:254.0,2313.0] || -> equal(cons(skf47(skc7),nil),skc7)**.
% 6.85/7.03 2390[10:SpR:2314.0,115.2] ssItem(skf47(skc7)) ssList(nil) || -> equal(tl(skc7),nil)**.
% 6.85/7.03 2394[10:SSi:2390.1,2390.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,8.0,16.0,5.0,2185.0,2189.0,2194.0,2198.0,2199.0,2212.0,2295.0,2313.0] || -> equal(tl(skc7),nil)**.
% 6.85/7.03 2397[10:Rew:2394.0,2160.0] || -> equal(cons(hd(skc7),nil),skc7)**.
% 6.85/7.03 2398[10:Rew:2394.0,557.1] ssList(u) || -> equal(tl(app(skc7,u)),app(nil,u))**.
% 6.85/7.03 2401[10:Rew:83.1,2398.1] ssList(u) || -> equal(tl(app(skc7,u)),u)**.
% 6.85/7.03 2437[0:SpR:90.1,114.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 6.85/7.03 2441[0:SSi:2437.1,2437.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,8.0,54.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 6.85/7.03 2443[0:Rew:2441.1,90.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 6.85/7.03 2632[10:SpR:2401.1,121.2] ssList(u) ssList(app(skc7,u)) || -> equal(app(skc7,u),nil) equal(cons(hd(app(skc7,u)),u),app(skc7,u))**.
% 6.85/7.03 2648[10:Rew:553.1,2632.3] ssList(u) ssList(app(skc7,u)) || -> equal(app(skc7,u),nil) equal(cons(hd(skc7),u),app(skc7,u))**.
% 6.85/7.03 2649[10:SSi:2648.1,95.0,5.0,2185.0,2189.0,2194.0,2198.0,2199.0,2212.0,2295.0,2313.2] ssList(u) || -> equal(app(skc7,u),nil) equal(cons(hd(skc7),u),app(skc7,u))**.
% 6.85/7.03 2650[10:MRR:2649.1,2163.1] ssList(u) || -> equal(cons(hd(skc7),u),app(skc7,u))**.
% 6.85/7.03 3007[0:EqR:124.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 6.85/7.03 3012[0:SSi:3007.0,80.0,79.0,78.0,77.0,76.0,75.0,74.0,94.0,15.2,14.1,13.1,12.1,11.1,10.1,9.1,8.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 6.85/7.03 4587[0:EqR:146.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 6.85/7.03 4602[0:SSi:4587.1,95.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 6.85/7.03 5037[0:SpR:162.3,85.0] ssList(skc11) ssList(cons(skc9,nil)) ssList(skc10) || -> equal(app(skc10,app(cons(skc9,nil),skc11)),skc7)**.
% 6.85/7.03 5070[0:SSi:5037.2,5037.1,5037.0,2.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.0,3.2,75.0,3.1,74.0,3.1,3012.0,3.1,94.0,3.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,8.1,1.0] || -> equal(app(skc10,app(cons(skc9,nil),skc11)),skc7)**.
% 6.85/7.03 5133[0:SpR:5070.0,136.3] ssList(app(cons(skc9,nil),skc11)) ssList(skc10) || -> equal(skc10,nil) equal(hd(skc10),hd(skc7))**.
% 6.85/7.03 5136[0:SpR:5070.0,153.4] ssList(app(cons(skc9,nil),skc11)) ssList(u) ssList(skc10) || frontsegP(skc10,u)* -> frontsegP(skc7,u).
% 6.85/7.03 5141[0:SpR:131.2,5070.0] ssItem(skc9) ssList(skc11) || -> equal(app(skc10,cons(skc9,skc11)),skc7)**.
% 6.85/7.03 5147[0:SSi:5141.1,5141.0,1.0,3.0] || -> equal(app(skc10,cons(skc9,skc11)),skc7)**.
% 6.85/7.03 5148[0:SSi:5133.1,5133.0,2.0,95.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.2,3.0,75.1,3.0,74.1,3.0,3012.1,3.0,94.1,3.0,15.1,14.0,13.1,12.0,11.1,10.0,9.1,8.2,1.0] || -> equal(skc10,nil) equal(hd(skc10),hd(skc7))**.
% 6.85/7.03 5151[0:SSi:5136.2,5136.0,2.0,95.0,80.0,3.0,79.0,3.0,78.0,3.0,77.0,3.0,76.2,3.0,75.1,3.0,74.1,3.0,3012.1,3.0,94.1,3.0,15.1,14.0,13.1,12.0,11.1,10.0,9.1,8.2,1.0] ssList(u) || frontsegP(skc10,u)* -> frontsegP(skc7,u).
% 6.85/7.03 5179[11:Spt:5148.0] || -> equal(skc10,nil)**.
% 6.85/7.03 5182[11:Rew:5179.0,62.1] || -> memberP(skc11,skc9)* memberP(nil,skc9).
% 6.85/7.03 5188[11:Rew:5179.0,5147.0] || -> equal(app(nil,cons(skc9,skc11)),skc7)**.
% 6.85/7.03 5225[11:SpR:5188.0,83.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),skc7)**.
% 6.85/7.03 5234[11:SSi:5225.0,94.0,3.0,1.2] || -> equal(cons(skc9,skc11),skc7)**.
% 6.85/7.03 5248[11:SpR:5234.0,115.2] ssItem(skc9) ssList(skc11) || -> equal(tl(skc7),skc11)**.
% 6.85/7.03 5264[11:Rew:2394.0,5248.2] ssItem(skc9) ssList(skc11) || -> equal(skc11,nil)**.
% 6.85/7.03 5265[11:SSi:5264.1,5264.0,1.0,3.0] || -> equal(skc11,nil)**.
% 6.85/7.03 5280[11:Rew:5265.0,5182.0] || -> memberP(nil,skc9)* memberP(nil,skc9)*.
% 6.85/7.03 5305[11:Obv:5280.0] || -> memberP(nil,skc9)*.
% 6.85/7.03 5350[11:Res:5305.0,73.1] ssItem(skc9) || -> .
% 6.85/7.03 5351[11:SSi:5350.0,3.0] || -> .
% 6.85/7.03 5352[11:Spt:5351.0,5148.0,5179.0] || equal(skc10,nil)** -> .
% 6.85/7.03 5353[11:Spt:5351.0,5148.1] || -> equal(hd(skc10),hd(skc7))**.
% 6.85/7.03 5357[11:SpR:5353.0,121.2] ssList(skc10) || -> equal(skc10,nil) equal(cons(hd(skc7),tl(skc10)),skc10)**.
% 6.85/7.03 5360[11:SpR:5353.0,2443.1] || -> SkP0(u,skc10)* equal(cons(hd(skc7),nil),skc10)**.
% 6.85/7.03 5364[11:Rew:2397.0,5360.1] || -> SkP0(u,skc10)* equal(skc10,skc7).
% 6.85/7.03 5369[11:MRR:5357.0,5357.1,2.0,5352.0] || -> equal(cons(hd(skc7),tl(skc10)),skc10)**.
% 6.85/7.03 5387[12:Spt:5364.1] || -> equal(skc10,skc7)**.
% 6.85/7.03 5393[12:Rew:5387.0,5147.0] || -> equal(app(skc7,cons(skc9,skc11)),skc7)**.
% 6.85/7.03 5441[12:SpR:5393.0,2401.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),tl(skc7))**.
% 6.85/7.03 5454[12:Rew:2394.0,5441.1] ssList(cons(skc9,skc11)) || -> equal(cons(skc9,skc11),nil)**.
% 6.85/7.03 5455[12:SSi:5454.0,94.0,3.0,1.2] || -> equal(cons(skc9,skc11),nil)**.
% 6.85/7.03 5479[12:SpL:5455.0,113.2] ssItem(skc9) ssList(skc11) || equal(nil,nil)* -> .
% 6.85/7.03 5487[12:Obv:5479.2] ssItem(skc9) ssList(skc11) || -> .
% 6.85/7.03 5488[12:SSi:5487.1,5487.0,1.0,3.0] || -> .
% 6.85/7.03 5508[12:Spt:5488.0,5364.1,5387.0] || equal(skc10,skc7)** -> .
% 6.85/7.03 5509[12:Spt:5488.0,5364.0] || -> SkP0(u,skc10)*.
% 6.85/7.03 5534[11:SpR:5369.0,2650.1] ssList(tl(skc10)) || -> equal(app(skc7,tl(skc10)),skc10)**.
% 6.85/7.03 5802[11:SoR:5534.0,89.1] ssList(skc10) || -> equal(app(skc7,tl(skc10)),skc10)** equal(skc10,nil).
% 6.85/7.03 5804[11:SSi:5802.0,2.0] || -> equal(app(skc7,tl(skc10)),skc10)** equal(skc10,nil).
% 6.85/7.03 5805[11:MRR:5804.1,5352.0] || -> equal(app(skc7,tl(skc10)),skc10)**.
% 6.85/7.03 5920[0:Res:64.1,5151.1] ssList(skc10) ssList(skc10) || -> frontsegP(skc7,skc10)*.
% 6.85/7.03 5925[0:Obv:5920.0] ssList(skc10) || -> frontsegP(skc7,skc10)*.
% 6.85/7.03 5926[0:SSi:5925.0,2.0] || -> frontsegP(skc7,skc10)*.
% 6.85/7.03 5929[0:Res:5926.0,142.2] ssList(skc7) ssList(skc10) || frontsegP(skc10,skc7)* -> equal(skc10,skc7).
% 6.85/7.03 5930[10:SSi:5929.1,5929.0,2.0,5.0,2185.0,2189.0,2194.0,2198.0,2199.0,2212.0,2295.0,2313.0] || frontsegP(skc10,skc7)* -> equal(skc10,skc7).
% 6.85/7.03 5931[12:MRR:5930.1,5508.0] || frontsegP(skc10,skc7)* -> .
% 6.85/7.03 7233[0:SpL:5147.0,189.4] ssItem(skc9) ssList(u) ssList(skc11) ssList(skc10) || equal(skc7,u) -> memberP(u,skc9)*.
% 6.85/7.03 7243[0:SSi:7233.3,7233.2,7233.0,2.0,1.0,3.0] ssList(u) || equal(skc7,u) -> memberP(u,skc9)*.
% 6.85/7.03 9604[11:SpR:5805.0,4602.2] ssList(skc7) ssList(tl(skc10)) || -> frontsegP(skc10,skc7)*.
% 6.85/7.03 9611[11:SSi:9604.0,5.0,2185.0,2189.0,2194.0,2198.0,2199.0,2212.0,2295.0,2313.0] ssList(tl(skc10)) || -> frontsegP(skc10,skc7)*.
% 6.85/7.03 9612[12:MRR:9611.1,5931.0] ssList(tl(skc10)) || -> .
% 6.85/7.03 9647[12:SoR:9612.0,89.1] ssList(skc10) || -> equal(skc10,nil)**.
% 6.85/7.03 9649[12:SSi:9647.0,2.0] || -> equal(skc10,nil)**.
% 6.85/7.03 9650[12:MRR:9649.0,5352.0] || -> .
% 6.85/7.03 9651[9:Spt:9650.0,269.0,2212.0] || duplicatefreeP(skc7)* -> .
% 6.85/7.03 9652[9:Spt:9650.0,269.1] || -> equal(skf78(skc7),skf77(skc7))**.
% 6.85/7.03 9653[9:MRR:9651.0,2297.0] || -> .
% 6.85/7.03 9727[8:Spt:9653.0,222.0,2199.0] || strictorderP(skc7)* -> .
% 6.85/7.03 9728[8:Spt:9653.0,222.1] || -> equal(app(app(skf64(skc7),cons(skf62(skc7),skf65(skc7))),cons(skf63(skc7),skf66(skc7))),skc7)**.
% 6.85/7.03 9729[8:MRR:9727.0,2300.0] || -> .
% 6.85/7.03 9846[7:Spt:9729.0,221.0,2198.0] || totalorderP(skc7)* -> .
% 6.85/7.03 9847[7:Spt:9729.0,221.1] || -> equal(app(app(skf59(skc7),cons(skf57(skc7),skf60(skc7))),cons(skf58(skc7),skf61(skc7))),skc7)**.
% 6.85/7.03 9848[7:MRR:9846.0,2301.0] || -> .
% 6.85/7.03 9868[6:Spt:9848.0,267.0,2194.0] || cyclefreeP(skc7)* -> .
% 6.85/7.03 9869[6:Spt:9848.0,267.1] || -> leq(skf53(skc7),skf52(skc7))*.
% 6.85/7.03 9870[6:MRR:9868.0,2302.0] || -> .
% 6.85/7.03 9975[5:Spt:9870.0,224.0,2189.0] || strictorderedP(skc7)* -> .
% 6.85/7.03 9976[5:Spt:9870.0,224.1] || -> equal(app(app(skf74(skc7),cons(skf72(skc7),skf75(skc7))),cons(skf73(skc7),skf76(skc7))),skc7)**.
% 6.85/7.03 9977[5:MRR:9975.0,2298.0] || -> .
% 6.85/7.03 10083[4:Spt:9977.0,223.0,2185.0] || totalorderedP(skc7)* -> .
% 7.31/7.47 10084[4:Spt:9977.0,223.1] || -> equal(app(app(skf69(skc7),cons(skf67(skc7),skf70(skc7))),cons(skf68(skc7),skf71(skc7))),skc7)**.
% 7.31/7.47 10085[4:MRR:10083.0,2299.0] || -> .
% 7.31/7.47 10108[2:Spt:10085.0,241.1] || -> equal(nil,skc7)**.
% 7.31/7.47 10131[2:Rew:10108.0,15.0] || -> equalelemsP(skc7)*.
% 7.31/7.47 10132[2:Rew:10108.0,14.0] || -> duplicatefreeP(skc7)*.
% 7.31/7.47 10133[2:Rew:10108.0,13.0] || -> strictorderedP(skc7)*.
% 7.31/7.47 10134[2:Rew:10108.0,12.0] || -> totalorderedP(skc7)*.
% 7.31/7.47 10135[2:Rew:10108.0,11.0] || -> strictorderP(skc7)*.
% 7.31/7.47 10136[2:Rew:10108.0,10.0] || -> totalorderP(skc7)*.
% 7.31/7.47 10137[2:Rew:10108.0,9.0] || -> cyclefreeP(skc7)*.
% 7.31/7.47 10164[2:Rew:10108.0,73.1] ssItem(u) || memberP(skc7,u)* -> .
% 7.31/7.47 11288[2:Res:7243.2,10164.1] ssList(skc7) ssItem(skc9) || equal(skc7,skc7)* -> .
% 7.31/7.47 11290[2:Obv:11288.2] ssList(skc7) ssItem(skc9) || -> .
% 7.31/7.47 11291[2:SSi:11290.1,11290.0,3.0,5.0,10131.0,10132.0,10133.0,10134.0,10135.0,10136.0,10137.0] || -> .
% 7.31/7.47 11292[1:Spt:11291.0,247.1] || -> equal(nil,skc7)**.
% 7.31/7.47 11294[1:Rew:11292.0,9.0] || -> cyclefreeP(skc7)*.
% 7.31/7.47 11295[1:Rew:11292.0,10.0] || -> totalorderP(skc7)*.
% 7.31/7.47 11296[1:Rew:11292.0,11.0] || -> strictorderP(skc7)*.
% 7.31/7.47 11297[1:Rew:11292.0,12.0] || -> totalorderedP(skc7)*.
% 7.31/7.47 11298[1:Rew:11292.0,13.0] || -> strictorderedP(skc7)*.
% 7.31/7.47 11299[1:Rew:11292.0,14.0] || -> duplicatefreeP(skc7)*.
% 7.31/7.47 11300[1:Rew:11292.0,15.0] || -> equalelemsP(skc7)*.
% 7.31/7.47 11322[1:Rew:11292.0,73.1] ssItem(u) || memberP(skc7,u)* -> .
% 7.31/7.47 12104[1:Res:7243.2,11322.1] ssList(skc7) ssItem(skc9) || equal(skc7,skc7)* -> .
% 7.31/7.47 12106[1:Obv:12104.2] ssList(skc7) ssItem(skc9) || -> .
% 7.31/7.47 12107[1:SSi:12106.1,12106.0,3.0,5.0,11294.0,11295.0,11296.0,11297.0,11298.0,11299.0,11300.0] || -> .
% 7.31/7.47 % SZS output end Refutation
% 7.31/7.47 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
% 7.31/7.47
%------------------------------------------------------------------------------