TSTP Solution File: SWC031+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC031+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 22:01:13 EDT 2022
% Result : Theorem 1.93s 2.10s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC031+1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n024.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 : Sun Jun 12 13:45:03 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.93/2.10
% 1.93/2.10 SPASS V 3.9
% 1.93/2.10 SPASS beiseite: Proof found.
% 1.93/2.10 % SZS status Theorem
% 1.93/2.10 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.93/2.10 SPASS derived 3918 clauses, backtracked 1212 clauses, performed 50 splits and kept 3044 clauses.
% 1.93/2.10 SPASS allocated 103302 KBytes.
% 1.93/2.10 SPASS spent 0:00:01.73 on the problem.
% 1.93/2.10 0:00:00.04 for the input.
% 1.93/2.10 0:00:00.07 for the FLOTTER CNF translation.
% 1.93/2.10 0:00:00.04 for inferences.
% 1.93/2.10 0:00:00.04 for the backtracking.
% 1.93/2.10 0:00:01.37 for the reduction.
% 1.93/2.10
% 1.93/2.10
% 1.93/2.10 Here is a proof with depth 6, length 181 :
% 1.93/2.10 % SZS output start Refutation
% 1.93/2.10 1[0:Inp] || -> ssList(skc5)*.
% 1.93/2.10 2[0:Inp] || -> ssList(skc4)*.
% 1.93/2.10 6[0:Inp] || -> ssList(nil)*.
% 1.93/2.10 7[0:Inp] || -> cyclefreeP(nil)*.
% 1.93/2.10 8[0:Inp] || -> totalorderP(nil)*.
% 1.93/2.10 9[0:Inp] || -> strictorderP(nil)*.
% 1.93/2.10 10[0:Inp] || -> totalorderedP(nil)*.
% 1.93/2.10 11[0:Inp] || -> strictorderedP(nil)*.
% 1.93/2.10 12[0:Inp] || -> duplicatefreeP(nil)*.
% 1.93/2.10 13[0:Inp] || -> equalelemsP(nil)*.
% 1.93/2.10 14[0:Inp] || -> frontsegP(skc5,skc4)*.
% 1.93/2.10 19[0:Inp] || -> ssItem(skf51(u))*.
% 1.93/2.10 20[0:Inp] || -> ssItem(skf50(u))*.
% 1.93/2.10 34[0:Inp] || -> ssItem(skf66(u))*.
% 1.93/2.10 35[0:Inp] || -> ssItem(skf65(u))*.
% 1.93/2.10 60[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 1.93/2.10 61[0:Inp] ssItem(u) || -> leq(u,u)*.
% 1.93/2.10 62[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 1.93/2.10 67[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 1.93/2.10 69[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 1.93/2.10 71[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 1.93/2.10 72[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 1.93/2.10 73[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 1.93/2.10 74[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 1.93/2.10 75[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 1.93/2.10 76[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 1.93/2.10 77[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 1.93/2.10 79[0:Inp] || SkP0(skc5,skc4)* SkP0(skc4,skc5) -> .
% 1.93/2.10 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 1.93/2.10 84[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 1.93/2.10 85[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 1.93/2.10 86[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 1.93/2.10 87[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf50(u),skf51(u))*.
% 1.93/2.10 89[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 1.93/2.10 90[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 1.93/2.10 91[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 1.93/2.10 101[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 1.93/2.10 106[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 1.93/2.10 108[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 1.93/2.10 109[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 1.93/2.10 116[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 1.93/2.10 119[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 1.93/2.10 126[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 1.93/2.10 131[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 1.93/2.10 141[0:Inp] totalorderedP(u) ssList(u) || segmentP(u,skc4) neq(skc4,u) frontsegP(skc5,u)* -> .
% 1.93/2.10 142[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 1.93/2.10 172[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 1.93/2.10 173[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 1.93/2.10 186[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).
% 1.93/2.10 246[0:Res:2.0,131.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 1.93/2.10 254[0:Res:2.0,106.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 1.93/2.10 256[0:Res:2.0,108.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 1.93/2.10 269[0:Res:2.0,89.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 1.93/2.10 271[0:Res:2.0,91.0] || frontsegP(nil,skc4)* -> equal(skc4,nil).
% 1.93/2.10 287[0:Res:2.0,186.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(skc4,nil).
% 1.93/2.10 393[0:Res:1.0,173.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 1.93/2.10 394[0:Res:1.0,172.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 1.93/2.10 406[0:Res:1.0,141.0] totalorderedP(skc5) || frontsegP(skc5,skc5)* segmentP(skc5,skc4) neq(skc4,skc5) -> .
% 1.93/2.10 424[0:Res:1.0,116.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 1.93/2.10 429[0:Res:1.0,109.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 1.93/2.10 435[0:Res:1.0,101.0] || leq(skf65(skc5),skf66(skc5))* -> totalorderedP(skc5).
% 1.93/2.10 438[0:Res:1.0,86.0] || -> cyclefreeP(skc5) leq(skf51(skc5),skf50(skc5))*.
% 1.93/2.10 439[0:Res:1.0,87.0] || -> cyclefreeP(skc5) leq(skf50(skc5),skf51(skc5))*.
% 1.93/2.10 441[0:Res:1.0,89.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 1.93/2.10 449[0:Res:1.0,84.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 1.93/2.10 450[0:Res:1.0,85.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 1.93/2.10 453[0:Res:1.0,62.0] || -> frontsegP(skc5,skc5)*.
% 1.93/2.10 458[0:Res:1.0,67.0] || -> segmentP(skc5,nil)*.
% 1.93/2.10 459[0:Res:1.0,186.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(skc5,nil).
% 1.93/2.10 498[0:Res:1.0,106.1] ssList(u) || -> neq(u,skc5)* equal(u,skc5).
% 1.93/2.10 549[0:MRR:406.1,453.0] totalorderedP(skc5) || neq(skc4,skc5) segmentP(skc5,skc4)* -> .
% 1.93/2.10 556[1:Spt:246.0,246.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 1.93/2.10 560[2:Spt:459.5] || -> equal(skc5,nil)**.
% 1.93/2.10 671[2:Rew:560.0,14.0] || -> frontsegP(nil,skc4)*.
% 1.93/2.10 674[2:Rew:560.0,79.0] || SkP0(nil,skc4) SkP0(skc4,skc5)* -> .
% 1.93/2.10 715[2:MRR:271.0,671.0] || -> equal(skc4,nil)**.
% 1.93/2.10 890[2:Rew:715.0,674.1,560.0,674.1,715.0,674.0] || SkP0(nil,nil)* SkP0(nil,nil)* -> .
% 1.93/2.10 891[2:Obv:890.0] || SkP0(nil,nil)* -> .
% 1.93/2.10 1066[2:Res:69.1,891.0] || equal(nil,nil)* -> .
% 1.93/2.10 1067[2:Obv:1066.0] || -> .
% 1.93/2.10 1068[2:Spt:1067.0,459.5,560.0] || equal(skc5,nil)** -> .
% 1.93/2.10 1069[2:Spt:1067.0,459.0,459.1,459.2,459.3,459.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 1.93/2.10 1071[2:MRR:449.1,1068.0] || -> ssItem(hd(skc5))*.
% 1.93/2.10 1084[3:Spt:287.5] || -> equal(skc4,nil)**.
% 1.93/2.10 1116[3:Rew:1084.0,556.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 1.93/2.10 1164[3:Rew:1084.0,549.1] totalorderedP(skc5) || neq(nil,skc5) segmentP(skc5,skc4)* -> .
% 1.93/2.10 1255[3:Rew:80.1,1116.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 1.93/2.10 1263[3:Rew:1084.0,1164.2] totalorderedP(skc5) || neq(nil,skc5) segmentP(skc5,nil)* -> .
% 1.93/2.10 1264[3:MRR:1263.2,458.0] totalorderedP(skc5) || neq(nil,skc5)* -> .
% 1.93/2.10 1344[4:Spt:393.0] || -> totalorderedP(skc5)*.
% 1.93/2.10 1347[4:MRR:1264.0,1344.0] || neq(nil,skc5)* -> .
% 1.93/2.10 1379[3:SpR:1255.1,1071.0] ssList(skc5) || -> ssItem(hd(nil))*.
% 1.93/2.10 1422[4:Res:498.1,1347.0] ssList(nil) || -> equal(skc5,nil)**.
% 1.93/2.10 1423[4:SSi:1422.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0] || -> equal(skc5,nil)**.
% 1.93/2.10 1424[4:MRR:1423.0,1068.0] || -> .
% 1.93/2.10 1425[4:Spt:1424.0,393.0,1344.0] || totalorderedP(skc5)* -> .
% 1.93/2.10 1426[4:Spt:1424.0,393.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 1.93/2.10 1427[3:SSi:1379.0,1.0] || -> ssItem(hd(nil))*.
% 1.93/2.10 1428[4:MRR:435.1,1425.0] || leq(skf65(skc5),skf66(skc5))* -> .
% 1.93/2.10 1433[5:Spt:394.0] || -> strictorderedP(skc5)*.
% 1.93/2.10 1436[6:Spt:439.0] || -> cyclefreeP(skc5)*.
% 1.93/2.10 1456[3:SpR:429.1,1255.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 1.93/2.10 1459[3:SSi:1456.1,441.1] ssItem(u) || -> equal(u,hd(nil))*.
% 1.93/2.10 1558[4:SpL:1459.1,1428.0] ssItem(skf65(skc5)) || leq(hd(nil),skf66(skc5))* -> .
% 1.93/2.10 1729[6:SSi:1558.0,35.0,1.0,1433.0,1436.0] || leq(hd(nil),skf66(skc5))* -> .
% 1.93/2.10 1763[6:SpL:1459.1,1729.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 1.93/2.10 1822[6:SSi:1763.0,34.0,1.0,1433.0,1436.0] || leq(hd(nil),hd(nil))* -> .
% 1.93/2.10 1877[6:SpL:1459.1,1822.0] ssItem(u) || leq(u,u)* -> .
% 1.93/2.10 1883[6:MRR:1877.1,61.1] ssItem(u) || -> .
% 1.93/2.10 1884[6:UnC:1883.0,1427.0] || -> .
% 1.93/2.10 1885[6:Spt:1884.0,439.0,1436.0] || cyclefreeP(skc5)* -> .
% 1.93/2.10 1886[6:Spt:1884.0,439.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 1.93/2.10 1888[5:SSi:1558.0,35.0,1.0,1433.0] || leq(hd(nil),skf66(skc5))* -> .
% 1.93/2.10 1895[6:SpR:1459.1,1886.0] ssItem(skf51(skc5)) || -> leq(skf50(skc5),hd(nil))*.
% 1.93/2.10 1897[6:SSi:1895.0,19.0,1.0,1433.0] || -> leq(skf50(skc5),hd(nil))*.
% 1.93/2.10 1910[6:SpR:1459.1,1897.0] ssItem(skf50(skc5)) || -> leq(hd(nil),hd(nil))*.
% 1.93/2.10 1943[5:SpL:1459.1,1888.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 1.93/2.10 1965[6:SSi:1910.0,20.0,1.0,1433.0] || -> leq(hd(nil),hd(nil))*.
% 1.93/2.10 1966[5:SSi:1943.0,34.0,1.0,1433.0] || leq(hd(nil),hd(nil))* -> .
% 1.93/2.10 1967[6:MRR:1966.0,1965.0] || -> .
% 1.97/2.21 1968[5:Spt:1967.0,394.0,1433.0] || strictorderedP(skc5)* -> .
% 1.97/2.21 1969[5:Spt:1967.0,394.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 1.97/2.21 1972[4:SSi:1558.0,35.0,1.0] || leq(hd(nil),skf66(skc5))* -> .
% 1.97/2.21 1991[6:Spt:438.0] || -> cyclefreeP(skc5)*.
% 1.97/2.21 2001[4:SpL:1459.1,1972.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 1.97/2.21 2087[6:SSi:2001.0,34.0,1.0,1991.0] || leq(hd(nil),hd(nil))* -> .
% 1.97/2.21 2155[6:SpL:1459.1,2087.0] ssItem(u) || leq(u,u)* -> .
% 1.97/2.21 2161[6:MRR:2155.1,61.1] ssItem(u) || -> .
% 1.97/2.21 2162[6:UnC:2161.0,1427.0] || -> .
% 1.97/2.21 2163[6:Spt:2162.0,438.0,1991.0] || cyclefreeP(skc5)* -> .
% 1.97/2.21 2164[6:Spt:2162.0,438.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 1.97/2.21 2168[4:SSi:2001.0,34.0,1.0] || leq(hd(nil),hd(nil))* -> .
% 1.97/2.21 2170[6:SpR:1459.1,2164.0] ssItem(skf50(skc5)) || -> leq(skf51(skc5),hd(nil))*.
% 1.97/2.21 2172[6:SSi:2170.0,20.0,1.0] || -> leq(skf51(skc5),hd(nil))*.
% 1.97/2.21 2186[6:SpR:1459.1,2172.0] ssItem(skf51(skc5)) || -> leq(hd(nil),hd(nil))*.
% 1.97/2.21 2203[6:SSi:2186.0,19.0,1.0] || -> leq(hd(nil),hd(nil))*.
% 1.97/2.21 2204[6:MRR:2203.0,2168.0] || -> .
% 1.97/2.21 2205[3:Spt:2204.0,287.5,1084.0] || equal(skc4,nil)** -> .
% 1.97/2.21 2206[3:Spt:2204.0,287.0,287.1,287.2,287.3,287.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 1.97/2.21 2248[0:Res:69.1,79.0] || equal(skc5,nil) SkP0(skc4,skc5)* -> .
% 1.97/2.21 2249[0:Res:60.0,79.0] || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 1.97/2.21 2250[3:MRR:2249.1,2205.0] || SkP0(skc4,skc5)* -> .
% 1.97/2.21 2253[3:Res:60.0,2250.0] || -> equal(skc5,nil)**.
% 1.97/2.21 2254[3:MRR:2253.0,1068.0] || -> .
% 1.97/2.21 2255[1:Spt:2254.0,246.1] || -> equal(skc4,nil)**.
% 1.97/2.21 2271[1:Rew:2255.0,269.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 1.97/2.21 2273[1:Rew:2255.0,256.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 1.97/2.21 2300[1:Rew:2255.0,141.3] totalorderedP(u) ssList(u) || segmentP(u,skc4) neq(nil,u) frontsegP(skc5,u)* -> .
% 1.97/2.21 2302[1:Rew:2255.0,254.1] ssList(u) || -> neq(nil,u)* equal(skc4,u).
% 1.97/2.21 2398[1:Rew:2255.0,2248.1] || equal(skc5,nil) SkP0(nil,skc5)* -> .
% 1.97/2.21 2402[1:Rew:2255.0,2302.2] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 1.97/2.21 2483[1:Rew:2255.0,2300.2] totalorderedP(u) ssList(u) || segmentP(u,nil) neq(nil,u) frontsegP(skc5,u)* -> .
% 1.97/2.21 2484[1:MRR:2483.2,67.1] totalorderedP(u) ssList(u) || neq(nil,u) frontsegP(skc5,u)* -> .
% 1.97/2.21 2508[2:Spt:459.5] || -> equal(skc5,nil)**.
% 1.97/2.21 2644[2:Rew:2508.0,2398.0] || equal(nil,nil) SkP0(nil,skc5)* -> .
% 1.97/2.21 2672[2:Obv:2644.0] || SkP0(nil,skc5)* -> .
% 1.97/2.21 2673[2:Rew:2508.0,2672.0] || SkP0(nil,nil)* -> .
% 1.97/2.21 2760[2:Res:69.1,2673.0] || equal(nil,nil)* -> .
% 1.97/2.21 2762[2:Obv:2760.0] || -> .
% 1.97/2.21 2763[2:Spt:2762.0,459.5,2508.0] || equal(skc5,nil)** -> .
% 1.97/2.21 2764[2:Spt:2762.0,459.0,459.1,459.2,459.3,459.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 1.97/2.21 2765[2:MRR:450.1,2763.0] || -> ssList(tl(skc5))*.
% 1.97/2.21 2766[2:MRR:449.1,2763.0] || -> ssItem(hd(skc5))*.
% 1.97/2.21 2770[2:MRR:424.0,2763.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 1.97/2.21 3182[0:EqR:119.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.97/2.21 3184[1:SSi:3182.0,77.1,76.1,72.1,73.1,71.1,74.1,75.1,2271.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.97/2.21 4569[0:EqR:142.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 1.97/2.21 4585[0:SSi:4569.1,90.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 1.97/2.21 4926[0:SpR:126.2,4585.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 1.97/2.21 4941[0:Obv:4926.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 1.97/2.21 4942[1:SSi:4941.1,77.1,76.1,72.1,73.1,71.1,74.1,75.1,2271.1,3184.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 1.97/2.21 5770[2:SpR:2770.0,4942.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 1.97/2.21 5958[2:SSi:5770.1,2765.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 1.97/2.21 5959[2:MRR:5958.0,2766.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 1.97/2.21 6193[2:Res:5959.0,2484.3] totalorderedP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 1.97/2.21 6195[2:SSi:6193.1,6193.0,77.0,2766.1,76.0,2766.1,72.0,2766.1,73.0,2766.1,71.0,2766.1,74.0,2766.1,75.0,2766.1,2271.0,2766.1,3184.0,2766.1,77.0,2766.1,76.0,2766.1,72.0,2766.1,73.0,2766.1,71.0,2766.1,74.0,2766.1,75.0,2766.1,2271.0,2766.1,3184.0,2766.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 1.97/2.21 6271[2:Res:2402.1,6195.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 1.97/2.21 6274[2:SSi:6271.0,77.0,2766.1,76.0,2766.1,72.0,2766.1,73.0,2766.1,71.0,2766.1,74.0,2766.1,75.0,2766.1,2271.0,2766.1,3184.0,2766.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 1.97/2.21 6309[2:SpL:6274.0,2273.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 1.97/2.21 6320[2:Obv:6309.1] ssItem(hd(skc5)) || -> .
% 1.97/2.21 6321[2:SSi:6320.0,2766.0] || -> .
% 1.97/2.21 % SZS output end Refutation
% 1.97/2.21 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax8 ax2 ax11 ax31 ax42 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax46 ax15 ax21 ax23 ax78 ax4 ax81 ax85 ax5 ax12 ax77
% 1.97/2.21
%------------------------------------------------------------------------------