TSTP Solution File: SWC111+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC111+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:01:48 EDT 2022
% Result : Theorem 40.83s 41.05s
% Output : Refutation 47.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC111+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 12:07:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 40.83/41.05
% 40.83/41.05 SPASS V 3.9
% 40.83/41.05 SPASS beiseite: Proof found.
% 40.83/41.05 % SZS status Theorem
% 40.83/41.05 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.83/41.05 SPASS derived 21553 clauses, backtracked 8396 clauses, performed 86 splits and kept 12057 clauses.
% 40.83/41.05 SPASS allocated 130214 KBytes.
% 40.83/41.05 SPASS spent 0:0:40.68 on the problem.
% 40.83/41.05 0:00:00.04 for the input.
% 40.83/41.05 0:00:00.07 for the FLOTTER CNF translation.
% 40.83/41.05 0:00:00.34 for inferences.
% 40.83/41.05 0:00:01.61 for the backtracking.
% 40.83/41.05 0:0:38.29 for the reduction.
% 40.83/41.05
% 40.83/41.05
% 40.83/41.05 Here is a proof with depth 7, length 201 :
% 40.83/41.05 % SZS output start Refutation
% 40.83/41.05 1[0:Inp] || -> ssList(skc5)*.
% 40.83/41.05 2[0:Inp] || -> ssList(skc4)*.
% 40.83/41.05 3[0:Inp] || -> totalorderedP(skc4)*.
% 40.83/41.05 6[0:Inp] || -> ssList(nil)*.
% 40.83/41.05 7[0:Inp] || -> cyclefreeP(nil)*.
% 40.83/41.05 8[0:Inp] || -> totalorderP(nil)*.
% 40.83/41.05 9[0:Inp] || -> strictorderP(nil)*.
% 40.83/41.05 10[0:Inp] || -> totalorderedP(nil)*.
% 40.83/41.05 11[0:Inp] || -> strictorderedP(nil)*.
% 40.83/41.05 12[0:Inp] || -> duplicatefreeP(nil)*.
% 40.83/41.05 13[0:Inp] || -> equalelemsP(nil)*.
% 40.83/41.05 14[0:Inp] || -> segmentP(skc5,skc4)*.
% 40.83/41.05 19[0:Inp] || -> ssItem(skf51(u))*.
% 40.83/41.05 20[0:Inp] || -> ssItem(skf50(u))*.
% 40.83/41.05 34[0:Inp] || -> ssItem(skf66(u))*.
% 40.83/41.05 35[0:Inp] || -> ssItem(skf65(u))*.
% 40.83/41.05 56[0:Inp] || -> ssList(skf46(u,v))*.
% 40.83/41.05 60[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 40.83/41.05 61[0:Inp] ssItem(u) || -> leq(u,u)*.
% 40.83/41.05 66[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 40.83/41.05 67[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 40.83/41.05 69[0:Inp] || SkP0(skc4,skc5) -> neq(skc5,nil)*.
% 40.83/41.05 70[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 40.83/41.05 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 40.83/41.05 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 40.83/41.05 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 40.83/41.05 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 40.83/41.05 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 40.83/41.05 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 40.83/41.05 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 40.83/41.05 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 40.83/41.05 84[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 40.83/41.05 85[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 40.83/41.05 86[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 40.83/41.05 87[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf50(u),skf51(u))*.
% 40.83/41.05 89[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 40.83/41.05 90[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 40.83/41.05 95[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 40.83/41.05 101[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 40.83/41.05 104[0:Inp] || neq(skc4,nil) segmentP(skc5,skc4)* SkP0(skc4,skc5) -> .
% 40.83/41.05 107[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 40.83/41.05 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 40.83/41.05 110[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 40.83/41.05 117[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 40.83/41.05 120[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 40.83/41.05 127[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 40.83/41.05 132[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 40.83/41.05 135[0:Inp] ssList(u) ssList(v) || frontsegP(v,u) -> equal(app(u,skf46(v,u)),v)**.
% 40.83/41.05 142[0:Inp] totalorderedP(u) ssList(u) || segmentP(u,skc4)* neq(skc4,u) segmentP(skc5,u)* -> .
% 40.83/41.05 143[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 40.83/41.05 159[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 40.83/41.05 173[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 40.83/41.05 174[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 40.83/41.05 185[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(u,x),v),w)* -> segmentP(w,x)*.
% 40.83/41.05 187[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).
% 40.83/41.05 196[0:MRR:104.1,14.0] || SkP0(skc4,skc5) neq(skc4,nil)* -> .
% 40.83/41.05 201[0:Rew:159.3,185.4] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(x,app(u,w)),v)*+ -> segmentP(v,u)*.
% 40.83/41.05 204[0:Res:3.0,142.1] ssList(skc4) || segmentP(skc5,skc4)* segmentP(skc4,skc4) neq(skc4,skc4) -> .
% 40.83/41.05 248[0:Res:2.0,132.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 40.83/41.05 256[0:Res:2.0,107.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 40.83/41.05 258[0:Res:2.0,109.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 40.83/41.05 271[0:Res:2.0,89.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 40.83/41.05 277[0:Res:2.0,95.0] || segmentP(nil,skc4)* -> equal(skc4,nil).
% 40.83/41.05 287[0:Res:2.0,66.0] || -> segmentP(skc4,skc4)*.
% 40.83/41.05 289[0:Res:2.0,187.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(skc4,nil).
% 40.83/41.05 395[0:Res:1.0,174.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 40.83/41.05 396[0:Res:1.0,173.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 40.83/41.05 408[0:Res:1.0,142.0] totalorderedP(skc5) || segmentP(skc5,skc5)* segmentP(skc5,skc4) neq(skc4,skc5) -> .
% 40.83/41.05 415[0:Res:1.0,135.0] ssList(u) || frontsegP(skc5,u) -> equal(app(u,skf46(skc5,u)),skc5)**.
% 40.83/41.05 426[0:Res:1.0,117.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 40.83/41.05 431[0:Res:1.0,110.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 40.83/41.05 437[0:Res:1.0,101.0] || leq(skf65(skc5),skf66(skc5))* -> totalorderedP(skc5).
% 40.83/41.05 440[0:Res:1.0,86.0] || -> cyclefreeP(skc5) leq(skf51(skc5),skf50(skc5))*.
% 40.83/41.05 441[0:Res:1.0,87.0] || -> cyclefreeP(skc5) leq(skf50(skc5),skf51(skc5))*.
% 40.83/41.05 443[0:Res:1.0,89.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 40.83/41.05 451[0:Res:1.0,84.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 40.83/41.05 452[0:Res:1.0,85.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 40.83/41.05 459[0:Res:1.0,66.0] || -> segmentP(skc5,skc5)*.
% 40.83/41.05 461[0:Res:1.0,187.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(skc5,nil).
% 40.83/41.05 500[0:Res:1.0,107.1] ssList(u) || -> neq(u,skc5)* equal(u,skc5).
% 40.83/41.05 550[0:MRR:204.0,204.1,204.2,2.0,14.0,287.0] || neq(skc4,skc4)* -> .
% 40.83/41.05 551[0:MRR:408.1,408.2,459.0,14.0] totalorderedP(skc5) || neq(skc4,skc5)* -> .
% 40.83/41.05 558[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 40.83/41.05 562[2:Spt:461.5] || -> equal(skc5,nil)**.
% 40.83/41.05 566[2:Rew:562.0,69.0] || SkP0(skc4,nil) -> neq(skc5,nil)*.
% 40.83/41.05 675[2:Rew:562.0,14.0] || -> segmentP(nil,skc4)*.
% 40.83/41.05 718[2:MRR:277.0,675.0] || -> equal(skc4,nil)**.
% 40.83/41.05 826[2:Rew:718.0,550.0] || neq(nil,nil)* -> .
% 40.83/41.05 868[2:Rew:562.0,566.1,718.0,566.0] || SkP0(nil,nil) -> neq(nil,nil)*.
% 40.83/41.05 869[2:MRR:868.1,826.0] || SkP0(nil,nil)* -> .
% 40.83/41.05 1070[2:Res:70.1,869.0] || equal(nil,nil)* -> .
% 40.83/41.05 1071[2:Obv:1070.0] || -> .
% 40.83/41.05 1072[2:Spt:1071.0,461.5,562.0] || equal(skc5,nil)** -> .
% 40.83/41.05 1073[2:Spt:1071.0,461.0,461.1,461.2,461.3,461.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 40.83/41.05 1075[2:MRR:451.1,1072.0] || -> ssItem(hd(skc5))*.
% 40.83/41.05 1088[3:Spt:289.5] || -> equal(skc4,nil)**.
% 40.83/41.05 1110[3:Rew:1088.0,551.1] totalorderedP(skc5) || neq(nil,skc5)* -> .
% 40.83/41.05 1123[3:Rew:1088.0,558.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 40.83/41.05 1260[3:Rew:80.1,1123.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 40.83/41.05 1347[4:Spt:395.0] || -> totalorderedP(skc5)*.
% 40.83/41.05 1350[4:MRR:1110.0,1347.0] || neq(nil,skc5)* -> .
% 40.83/41.05 1380[3:SpR:1260.1,1075.0] ssList(skc5) || -> ssItem(hd(nil))*.
% 40.83/41.05 1423[4:Res:500.1,1350.0] ssList(nil) || -> equal(skc5,nil)**.
% 40.83/41.05 1424[4:SSi:1423.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0] || -> equal(skc5,nil)**.
% 40.83/41.05 1425[4:MRR:1424.0,1072.0] || -> .
% 40.83/41.05 1426[4:Spt:1425.0,395.0,1347.0] || totalorderedP(skc5)* -> .
% 40.83/41.05 1427[4:Spt:1425.0,395.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 40.83/41.05 1428[3:SSi:1380.0,1.0] || -> ssItem(hd(nil))*.
% 40.83/41.05 1429[4:MRR:437.1,1426.0] || leq(skf65(skc5),skf66(skc5))* -> .
% 40.83/41.05 1434[5:Spt:396.0] || -> strictorderedP(skc5)*.
% 40.83/41.05 1437[6:Spt:441.0] || -> cyclefreeP(skc5)*.
% 40.83/41.05 1457[3:SpR:431.1,1260.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 40.83/41.05 1460[3:SSi:1457.1,443.1] ssItem(u) || -> equal(u,hd(nil))*.
% 40.83/41.05 1559[4:SpL:1460.1,1429.0] ssItem(skf65(skc5)) || leq(hd(nil),skf66(skc5))* -> .
% 40.83/41.05 1730[6:SSi:1559.0,35.0,1.0,1434.0,1437.0] || leq(hd(nil),skf66(skc5))* -> .
% 40.83/41.05 1764[6:SpL:1460.1,1730.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 40.83/41.05 1823[6:SSi:1764.0,34.0,1.0,1434.0,1437.0] || leq(hd(nil),hd(nil))* -> .
% 40.83/41.05 1878[6:SpL:1460.1,1823.0] ssItem(u) || leq(u,u)* -> .
% 40.83/41.05 1884[6:MRR:1878.1,61.1] ssItem(u) || -> .
% 47.34/47.56 1885[6:UnC:1884.0,1428.0] || -> .
% 47.34/47.56 1886[6:Spt:1885.0,441.0,1437.0] || cyclefreeP(skc5)* -> .
% 47.34/47.56 1887[6:Spt:1885.0,441.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 47.34/47.56 1889[5:SSi:1559.0,35.0,1.0,1434.0] || leq(hd(nil),skf66(skc5))* -> .
% 47.34/47.56 1896[6:SpR:1460.1,1887.0] ssItem(skf51(skc5)) || -> leq(skf50(skc5),hd(nil))*.
% 47.34/47.56 1898[6:SSi:1896.0,19.0,1.0,1434.0] || -> leq(skf50(skc5),hd(nil))*.
% 47.34/47.56 1911[6:SpR:1460.1,1898.0] ssItem(skf50(skc5)) || -> leq(hd(nil),hd(nil))*.
% 47.34/47.56 1944[5:SpL:1460.1,1889.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 47.34/47.56 1966[6:SSi:1911.0,20.0,1.0,1434.0] || -> leq(hd(nil),hd(nil))*.
% 47.34/47.56 1967[5:SSi:1944.0,34.0,1.0,1434.0] || leq(hd(nil),hd(nil))* -> .
% 47.34/47.56 1968[6:MRR:1967.0,1966.0] || -> .
% 47.34/47.56 1969[5:Spt:1968.0,396.0,1434.0] || strictorderedP(skc5)* -> .
% 47.34/47.56 1970[5:Spt:1968.0,396.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 47.34/47.56 1973[4:SSi:1559.0,35.0,1.0] || leq(hd(nil),skf66(skc5))* -> .
% 47.34/47.56 1992[6:Spt:440.0] || -> cyclefreeP(skc5)*.
% 47.34/47.56 2002[4:SpL:1460.1,1973.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 47.34/47.56 2088[6:SSi:2002.0,34.0,1.0,1992.0] || leq(hd(nil),hd(nil))* -> .
% 47.34/47.56 2156[6:SpL:1460.1,2088.0] ssItem(u) || leq(u,u)* -> .
% 47.34/47.56 2162[6:MRR:2156.1,61.1] ssItem(u) || -> .
% 47.34/47.56 2163[6:UnC:2162.0,1428.0] || -> .
% 47.34/47.56 2164[6:Spt:2163.0,440.0,1992.0] || cyclefreeP(skc5)* -> .
% 47.34/47.56 2165[6:Spt:2163.0,440.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 47.34/47.56 2169[4:SSi:2002.0,34.0,1.0] || leq(hd(nil),hd(nil))* -> .
% 47.34/47.56 2171[6:SpR:1460.1,2165.0] ssItem(skf50(skc5)) || -> leq(skf51(skc5),hd(nil))*.
% 47.34/47.56 2173[6:SSi:2171.0,20.0,1.0] || -> leq(skf51(skc5),hd(nil))*.
% 47.34/47.56 2187[6:SpR:1460.1,2173.0] ssItem(skf51(skc5)) || -> leq(hd(nil),hd(nil))*.
% 47.34/47.56 2204[6:SSi:2187.0,19.0,1.0] || -> leq(hd(nil),hd(nil))*.
% 47.34/47.56 2205[6:MRR:2204.0,2169.0] || -> .
% 47.34/47.56 2206[3:Spt:2205.0,289.5,1088.0] || equal(skc4,nil)** -> .
% 47.34/47.56 2207[3:Spt:2205.0,289.0,289.1,289.2,289.3,289.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 47.34/47.56 3124[0:Res:107.2,196.1] ssList(nil) ssList(skc4) || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 47.34/47.56 3179[0:SSi:3124.1,3124.0,3.0,2.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0] || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 47.34/47.56 3180[3:MRR:3179.1,2206.0] || SkP0(skc4,skc5)* -> .
% 47.34/47.56 3206[3:Res:60.0,3180.0] || -> equal(skc5,nil)**.
% 47.34/47.56 3207[3:MRR:3206.0,1072.0] || -> .
% 47.34/47.56 3208[1:Spt:3207.0,248.1] || -> equal(skc4,nil)**.
% 47.34/47.56 3217[1:Rew:3208.0,550.0] || neq(nil,nil)* -> .
% 47.34/47.56 3222[1:Rew:3208.0,271.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 47.34/47.56 3227[1:Rew:3208.0,258.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 47.34/47.56 3249[1:Rew:3208.0,142.3] totalorderedP(u) ssList(u) || segmentP(u,skc4)* neq(nil,u) segmentP(skc5,u)* -> .
% 47.34/47.56 3251[1:Rew:3208.0,256.1] ssList(u) || -> neq(nil,u)* equal(skc4,u).
% 47.34/47.56 3347[1:Rew:3208.0,69.0] || SkP0(nil,skc5) -> neq(skc5,nil)*.
% 47.34/47.56 3357[1:Rew:3208.0,3251.2] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 47.34/47.56 3436[1:Rew:3208.0,3249.2] totalorderedP(u) ssList(u) || segmentP(u,nil)* neq(nil,u) segmentP(skc5,u)* -> .
% 47.34/47.56 3437[1:MRR:3436.2,67.1] totalorderedP(u) ssList(u) || neq(nil,u) segmentP(skc5,u)* -> .
% 47.34/47.56 3460[2:Spt:461.5] || -> equal(skc5,nil)**.
% 47.34/47.56 3610[2:Rew:3460.0,3347.0] || SkP0(nil,nil) -> neq(skc5,nil)*.
% 47.34/47.56 3622[2:Rew:3460.0,3610.1] || SkP0(nil,nil) -> neq(nil,nil)*.
% 47.34/47.56 3623[2:MRR:3622.1,3217.0] || SkP0(nil,nil)* -> .
% 47.34/47.56 3710[2:Res:70.1,3623.0] || equal(nil,nil)* -> .
% 47.34/47.56 3712[2:Obv:3710.0] || -> .
% 47.34/47.56 3713[2:Spt:3712.0,461.5,3460.0] || equal(skc5,nil)** -> .
% 47.34/47.56 3714[2:Spt:3712.0,461.0,461.1,461.2,461.3,461.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 47.34/47.56 3715[2:MRR:452.1,3713.0] || -> ssList(tl(skc5))*.
% 47.34/47.56 3716[2:MRR:451.1,3713.0] || -> ssItem(hd(skc5))*.
% 47.34/47.56 3720[2:MRR:426.0,3713.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 47.34/47.56 3853[0:EqR:120.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 47.34/47.56 3855[1:SSi:3853.0,78.1,77.1,73.1,74.1,72.1,75.1,76.1,3222.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 47.34/47.56 5152[0:EqR:143.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 47.34/47.56 5168[0:SSi:5152.1,90.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 47.34/47.56 5349[0:SpR:127.2,5168.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 47.34/47.56 5362[0:Obv:5349.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 47.34/47.56 5363[1:SSi:5362.1,78.1,77.1,73.1,74.1,72.1,75.1,76.1,3222.1,3855.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 47.34/47.56 5984[2:SpR:3720.0,5363.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 47.34/47.56 7514[0:EqR:201.4] ssList(u) ssList(app(v,app(u,w))) ssList(w) ssList(v) || -> segmentP(app(v,app(u,w)),u)*.
% 47.34/47.56 7551[0:SSi:7514.1,90.2,90.2] ssList(u) ssList(v) ssList(w) || -> segmentP(app(w,app(u,v)),u)*.
% 47.34/47.56 17048[0:SpR:80.1,7551.3] ssList(app(u,v)) ssList(u) ssList(v) ssList(nil) || -> segmentP(app(u,v),u)*.
% 47.34/47.56 17066[0:SSi:17048.3,17048.0,13.2,12.0,8.0,9.0,7.0,10.0,11.0,6.0,90.0] ssList(u) ssList(v) || -> segmentP(app(u,v),u)*.
% 47.34/47.56 21429[0:SpR:415.2,17066.2] ssList(u) ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 47.34/47.56 21452[0:Obv:21429.0] ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 47.34/47.56 33753[2:SSi:5984.1,3715.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 47.34/47.56 33754[2:MRR:33753.0,3716.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 47.34/47.56 33760[0:SSi:21452.1,56.0,1.0] ssList(u) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 47.34/47.56 36140[2:Res:33754.0,33760.1] ssList(cons(hd(skc5),nil)) || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 47.34/47.56 36143[2:SSi:36140.0,78.0,3716.1,77.0,3716.1,73.0,3716.1,74.0,3716.1,72.0,3716.1,75.0,3716.1,76.0,3716.1,3222.0,3716.1,3855.0,3716.1] || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 47.34/47.56 36156[2:Res:36143.0,3437.3] totalorderedP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 47.34/47.56 36161[2:SSi:36156.1,36156.0,78.0,3716.1,77.0,3716.1,73.0,3716.1,74.0,3716.1,72.0,3716.1,75.0,3716.1,76.0,3716.1,3222.0,3716.1,3855.0,3716.1,78.0,3716.1,77.0,3716.1,73.0,3716.1,74.0,3716.1,72.0,3716.1,75.0,3716.1,76.0,3716.1,3222.0,3716.1,3855.0,3716.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 47.34/47.56 36214[2:Res:3357.1,36161.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 47.34/47.56 36215[2:SSi:36214.0,78.0,3716.1,77.0,3716.1,73.0,3716.1,74.0,3716.1,72.0,3716.1,75.0,3716.1,76.0,3716.1,3222.0,3716.1,3855.0,3716.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 47.34/47.56 36268[2:SpL:36215.0,3227.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 47.34/47.56 36309[2:Obv:36268.1] ssItem(hd(skc5)) || -> .
% 47.34/47.56 36310[2:SSi:36309.0,3716.0] || -> .
% 47.34/47.56 % SZS output end Refutation
% 47.34/47.56 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax8 ax2 ax11 ax5 ax31 ax55 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax58 ax15 ax21 ax23 ax78 ax4 ax81 ax85 ax82 ax12 ax7 ax77
% 47.34/47.56
%------------------------------------------------------------------------------