TSTP Solution File: SWC066+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC066+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 22:01:29 EDT 2022
% Result : Theorem 41.65s 41.84s
% Output : Refutation 48.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWC066+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.10 % Command : run_spass %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sun Jun 12 16:59:41 EDT 2022
% 0.09/0.28 % CPUTime :
% 41.65/41.84
% 41.65/41.84 SPASS V 3.9
% 41.65/41.84 SPASS beiseite: Proof found.
% 41.65/41.84 % SZS status Theorem
% 41.65/41.84 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.65/41.84 SPASS derived 21659 clauses, backtracked 8398 clauses, performed 89 splits and kept 12082 clauses.
% 41.65/41.84 SPASS allocated 130169 KBytes.
% 41.65/41.84 SPASS spent 0:0:41.51 on the problem.
% 41.65/41.84 0:00:00.03 for the input.
% 41.65/41.84 0:00:00.04 for the FLOTTER CNF translation.
% 41.65/41.84 0:00:00.34 for inferences.
% 41.65/41.84 0:00:01.65 for the backtracking.
% 41.65/41.84 0:0:39.11 for the reduction.
% 41.65/41.84
% 41.65/41.84
% 41.65/41.84 Here is a proof with depth 7, length 205 :
% 41.65/41.84 % SZS output start Refutation
% 41.65/41.84 1[0:Inp] || -> ssList(skc5)*.
% 41.65/41.84 2[0:Inp] || -> ssList(skc4)*.
% 41.65/41.84 3[0:Inp] || -> totalorderedP(skc4)*.
% 41.65/41.84 6[0:Inp] || -> ssList(nil)*.
% 41.65/41.84 7[0:Inp] || -> cyclefreeP(nil)*.
% 41.65/41.84 8[0:Inp] || -> totalorderP(nil)*.
% 41.65/41.84 9[0:Inp] || -> strictorderP(nil)*.
% 41.65/41.84 10[0:Inp] || -> totalorderedP(nil)*.
% 41.65/41.84 11[0:Inp] || -> strictorderedP(nil)*.
% 41.65/41.84 12[0:Inp] || -> duplicatefreeP(nil)*.
% 41.65/41.84 13[0:Inp] || -> equalelemsP(nil)*.
% 41.65/41.84 14[0:Inp] || -> segmentP(skc5,skc4)*.
% 41.65/41.84 19[0:Inp] || -> ssItem(skf51(u))*.
% 41.65/41.84 20[0:Inp] || -> ssItem(skf50(u))*.
% 41.65/41.84 34[0:Inp] || -> ssItem(skf66(u))*.
% 41.65/41.84 35[0:Inp] || -> ssItem(skf65(u))*.
% 41.65/41.84 56[0:Inp] || -> ssList(skf46(u,v))*.
% 41.65/41.84 60[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 41.65/41.84 61[0:Inp] ssItem(u) || -> leq(u,u)*.
% 41.65/41.84 66[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 41.65/41.84 67[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 41.65/41.84 69[0:Inp] || SkP0(skc4,skc5) -> neq(skc5,nil)*.
% 41.65/41.84 70[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 41.65/41.84 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 41.65/41.84 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 41.65/41.84 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 41.65/41.84 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 41.65/41.84 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 41.65/41.84 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 41.65/41.84 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 41.65/41.84 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 41.65/41.84 84[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 41.65/41.84 85[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 41.65/41.84 86[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 41.65/41.84 87[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf50(u),skf51(u))*.
% 41.65/41.84 89[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 41.65/41.84 90[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 41.65/41.84 95[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 41.65/41.84 101[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 41.65/41.84 106[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 41.65/41.84 108[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 41.65/41.84 109[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 41.65/41.84 116[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 41.65/41.84 119[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 41.65/41.84 126[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 41.65/41.84 131[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 41.65/41.84 134[0:Inp] ssList(u) ssList(v) || frontsegP(v,u) -> equal(app(u,skf46(v,u)),v)**.
% 41.65/41.84 141[0:Inp] totalorderedP(u) ssList(u) || segmentP(u,skc4)* neq(skc4,u) segmentP(skc5,u)* -> .
% 41.65/41.84 142[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 41.65/41.84 154[0:Inp] ssList(u) || neq(u,nil) segmentP(skc4,u) segmentP(skc5,u)* SkP0(skc4,skc5) -> .
% 41.65/41.84 159[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 41.65/41.84 173[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 41.65/41.84 174[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 41.65/41.84 185[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(u,x),v),w)* -> segmentP(w,x)*.
% 41.65/41.84 187[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).
% 41.65/41.84 200[0:Rew:159.3,185.4] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(x,app(u,w)),v)*+ -> segmentP(v,u)*.
% 41.65/41.84 203[0:Res:3.0,141.1] ssList(skc4) || segmentP(skc5,skc4)* segmentP(skc4,skc4) neq(skc4,skc4) -> .
% 41.65/41.84 248[0:Res:2.0,131.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 41.65/41.84 256[0:Res:2.0,106.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 41.65/41.84 258[0:Res:2.0,108.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 41.65/41.84 271[0:Res:2.0,89.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 41.65/41.84 277[0:Res:2.0,95.0] || segmentP(nil,skc4)* -> equal(skc4,nil).
% 41.65/41.84 287[0:Res:2.0,66.0] || -> segmentP(skc4,skc4)*.
% 41.65/41.84 289[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).
% 41.65/41.84 395[0:Res:1.0,174.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 41.65/41.84 396[0:Res:1.0,173.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 41.65/41.84 409[0:Res:1.0,141.0] totalorderedP(skc5) || segmentP(skc5,skc5)* segmentP(skc5,skc4) neq(skc4,skc5) -> .
% 41.65/41.84 416[0:Res:1.0,134.0] ssList(u) || frontsegP(skc5,u) -> equal(app(u,skf46(skc5,u)),skc5)**.
% 41.65/41.84 427[0:Res:1.0,116.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 41.65/41.84 432[0:Res:1.0,109.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 41.65/41.84 438[0:Res:1.0,101.0] || leq(skf65(skc5),skf66(skc5))* -> totalorderedP(skc5).
% 41.65/41.84 441[0:Res:1.0,86.0] || -> cyclefreeP(skc5) leq(skf51(skc5),skf50(skc5))*.
% 41.65/41.84 442[0:Res:1.0,87.0] || -> cyclefreeP(skc5) leq(skf50(skc5),skf51(skc5))*.
% 41.65/41.84 444[0:Res:1.0,89.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 41.65/41.84 452[0:Res:1.0,84.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 41.65/41.84 453[0:Res:1.0,85.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 41.65/41.84 460[0:Res:1.0,66.0] || -> segmentP(skc5,skc5)*.
% 41.65/41.84 462[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).
% 41.65/41.84 501[0:Res:1.0,106.1] ssList(u) || -> neq(u,skc5)* equal(u,skc5).
% 41.65/41.84 551[0:MRR:203.0,203.1,203.2,2.0,14.0,287.0] || neq(skc4,skc4)* -> .
% 41.65/41.84 552[0:MRR:409.1,409.2,460.0,14.0] totalorderedP(skc5) || neq(skc4,skc5)* -> .
% 41.65/41.84 561[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 41.65/41.84 565[2:Spt:462.5] || -> equal(skc5,nil)**.
% 41.65/41.84 571[2:Rew:565.0,69.0] || SkP0(skc4,nil) -> neq(skc5,nil)*.
% 41.65/41.84 680[2:Rew:565.0,14.0] || -> segmentP(nil,skc4)*.
% 41.65/41.84 723[2:MRR:277.0,680.0] || -> equal(skc4,nil)**.
% 41.65/41.84 831[2:Rew:723.0,551.0] || neq(nil,nil)* -> .
% 41.65/41.84 873[2:Rew:565.0,571.1,723.0,571.0] || SkP0(nil,nil) -> neq(nil,nil)*.
% 41.65/41.84 874[2:MRR:873.1,831.0] || SkP0(nil,nil)* -> .
% 41.65/41.84 1078[2:Res:70.1,874.0] || equal(nil,nil)* -> .
% 41.65/41.84 1079[2:Obv:1078.0] || -> .
% 41.65/41.84 1080[2:Spt:1079.0,462.5,565.0] || equal(skc5,nil)** -> .
% 41.65/41.84 1081[2:Spt:1079.0,462.0,462.1,462.2,462.3,462.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 41.65/41.84 1083[2:MRR:452.1,1080.0] || -> ssItem(hd(skc5))*.
% 41.65/41.84 1096[3:Spt:289.5] || -> equal(skc4,nil)**.
% 41.65/41.84 1118[3:Rew:1096.0,552.1] totalorderedP(skc5) || neq(nil,skc5)* -> .
% 41.65/41.84 1133[3:Rew:1096.0,561.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 41.65/41.84 1271[3:Rew:80.1,1133.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 41.65/41.84 1359[4:Spt:395.0] || -> totalorderedP(skc5)*.
% 41.65/41.84 1362[4:MRR:1118.0,1359.0] || neq(nil,skc5)* -> .
% 41.65/41.84 1392[3:SpR:1271.1,1083.0] ssList(skc5) || -> ssItem(hd(nil))*.
% 41.65/41.84 1435[4:Res:501.1,1362.0] ssList(nil) || -> equal(skc5,nil)**.
% 41.65/41.84 1436[4:SSi:1435.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0] || -> equal(skc5,nil)**.
% 41.65/41.84 1437[4:MRR:1436.0,1080.0] || -> .
% 41.65/41.84 1438[4:Spt:1437.0,395.0,1359.0] || totalorderedP(skc5)* -> .
% 41.65/41.84 1439[4:Spt:1437.0,395.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 41.65/41.84 1440[3:SSi:1392.0,1.0] || -> ssItem(hd(nil))*.
% 41.65/41.84 1441[4:MRR:438.1,1438.0] || leq(skf65(skc5),skf66(skc5))* -> .
% 41.65/41.84 1446[5:Spt:396.0] || -> strictorderedP(skc5)*.
% 41.65/41.84 1449[6:Spt:442.0] || -> cyclefreeP(skc5)*.
% 41.65/41.84 1469[3:SpR:432.1,1271.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 41.65/41.84 1472[3:SSi:1469.1,444.1] ssItem(u) || -> equal(u,hd(nil))*.
% 41.65/41.84 1571[4:SpL:1472.1,1441.0] ssItem(skf65(skc5)) || leq(hd(nil),skf66(skc5))* -> .
% 41.65/41.84 1742[6:SSi:1571.0,35.0,1.0,1446.0,1449.0] || leq(hd(nil),skf66(skc5))* -> .
% 41.65/41.84 1776[6:SpL:1472.1,1742.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 41.65/41.84 1835[6:SSi:1776.0,34.0,1.0,1446.0,1449.0] || leq(hd(nil),hd(nil))* -> .
% 41.65/41.84 1890[6:SpL:1472.1,1835.0] ssItem(u) || leq(u,u)* -> .
% 41.65/41.84 1896[6:MRR:1890.1,61.1] ssItem(u) || -> .
% 41.65/41.84 1897[6:UnC:1896.0,1440.0] || -> .
% 48.25/48.50 1898[6:Spt:1897.0,442.0,1449.0] || cyclefreeP(skc5)* -> .
% 48.25/48.50 1899[6:Spt:1897.0,442.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 48.25/48.50 1901[5:SSi:1571.0,35.0,1.0,1446.0] || leq(hd(nil),skf66(skc5))* -> .
% 48.25/48.50 1908[6:SpR:1472.1,1899.0] ssItem(skf51(skc5)) || -> leq(skf50(skc5),hd(nil))*.
% 48.25/48.50 1910[6:SSi:1908.0,19.0,1.0,1446.0] || -> leq(skf50(skc5),hd(nil))*.
% 48.25/48.50 1923[6:SpR:1472.1,1910.0] ssItem(skf50(skc5)) || -> leq(hd(nil),hd(nil))*.
% 48.25/48.50 1956[5:SpL:1472.1,1901.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 48.25/48.50 1978[6:SSi:1923.0,20.0,1.0,1446.0] || -> leq(hd(nil),hd(nil))*.
% 48.25/48.50 1979[5:SSi:1956.0,34.0,1.0,1446.0] || leq(hd(nil),hd(nil))* -> .
% 48.25/48.50 1980[6:MRR:1979.0,1978.0] || -> .
% 48.25/48.50 1981[5:Spt:1980.0,396.0,1446.0] || strictorderedP(skc5)* -> .
% 48.25/48.50 1982[5:Spt:1980.0,396.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 48.25/48.50 1985[4:SSi:1571.0,35.0,1.0] || leq(hd(nil),skf66(skc5))* -> .
% 48.25/48.50 2004[6:Spt:441.0] || -> cyclefreeP(skc5)*.
% 48.25/48.50 2014[4:SpL:1472.1,1985.0] ssItem(skf66(skc5)) || leq(hd(nil),hd(nil))* -> .
% 48.25/48.50 2100[6:SSi:2014.0,34.0,1.0,2004.0] || leq(hd(nil),hd(nil))* -> .
% 48.25/48.50 2168[6:SpL:1472.1,2100.0] ssItem(u) || leq(u,u)* -> .
% 48.25/48.50 2174[6:MRR:2168.1,61.1] ssItem(u) || -> .
% 48.25/48.50 2175[6:UnC:2174.0,1440.0] || -> .
% 48.25/48.50 2176[6:Spt:2175.0,441.0,2004.0] || cyclefreeP(skc5)* -> .
% 48.25/48.50 2177[6:Spt:2175.0,441.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 48.25/48.50 2181[4:SSi:2014.0,34.0,1.0] || leq(hd(nil),hd(nil))* -> .
% 48.25/48.50 2183[6:SpR:1472.1,2177.0] ssItem(skf50(skc5)) || -> leq(skf51(skc5),hd(nil))*.
% 48.25/48.50 2185[6:SSi:2183.0,20.0,1.0] || -> leq(skf51(skc5),hd(nil))*.
% 48.25/48.50 2199[6:SpR:1472.1,2185.0] ssItem(skf51(skc5)) || -> leq(hd(nil),hd(nil))*.
% 48.25/48.50 2216[6:SSi:2199.0,19.0,1.0] || -> leq(hd(nil),hd(nil))*.
% 48.25/48.50 2217[6:MRR:2216.0,2181.0] || -> .
% 48.25/48.50 2218[3:Spt:2217.0,289.5,1096.0] || equal(skc4,nil)** -> .
% 48.25/48.50 2219[3:Spt:2217.0,289.0,289.1,289.2,289.3,289.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 48.25/48.50 2241[4:Spt:154.0,154.1,154.2,154.3] ssList(u) || neq(u,nil) segmentP(skc4,u) segmentP(skc5,u)* -> .
% 48.25/48.50 2273[4:Res:14.0,2241.3] ssList(skc4) || neq(skc4,nil) segmentP(skc4,skc4)* -> .
% 48.25/48.50 3036[4:SSi:2273.0,3.0,2.0] || neq(skc4,nil) segmentP(skc4,skc4)* -> .
% 48.25/48.50 3037[4:MRR:3036.1,287.0] || neq(skc4,nil)* -> .
% 48.25/48.50 3138[4:Res:106.2,3037.0] ssList(nil) ssList(skc4) || -> equal(skc4,nil)**.
% 48.25/48.50 3179[4:SSi:3138.1,3138.0,3.0,2.0,13.0,12.0,8.0,9.0,7.0,10.0,11.0,6.0] || -> equal(skc4,nil)**.
% 48.25/48.50 3180[4:MRR:3179.0,2218.0] || -> .
% 48.25/48.50 3193[4:Spt:3180.0,154.4] || SkP0(skc4,skc5)* -> .
% 48.25/48.50 3195[4:Res:60.0,3193.0] || -> equal(skc5,nil)**.
% 48.25/48.50 3196[4:MRR:3195.0,1080.0] || -> .
% 48.25/48.50 3197[1:Spt:3196.0,248.1] || -> equal(skc4,nil)**.
% 48.25/48.50 3206[1:Rew:3197.0,551.0] || neq(nil,nil)* -> .
% 48.25/48.50 3213[1:Rew:3197.0,271.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 48.25/48.50 3215[1:Rew:3197.0,258.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 48.25/48.50 3239[1:Rew:3197.0,141.3] totalorderedP(u) ssList(u) || segmentP(u,skc4)* neq(nil,u) segmentP(skc5,u)* -> .
% 48.25/48.50 3241[1:Rew:3197.0,256.1] ssList(u) || -> neq(nil,u)* equal(skc4,u).
% 48.25/48.50 3339[1:Rew:3197.0,69.0] || SkP0(nil,skc5) -> neq(skc5,nil)*.
% 48.25/48.50 3355[1:Rew:3197.0,3241.2] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 48.25/48.50 3431[1:Rew:3197.0,3239.2] totalorderedP(u) ssList(u) || segmentP(u,nil)* neq(nil,u) segmentP(skc5,u)* -> .
% 48.25/48.50 3432[1:MRR:3431.2,67.1] totalorderedP(u) ssList(u) || neq(nil,u) segmentP(skc5,u)* -> .
% 48.25/48.50 3454[2:Spt:462.5] || -> equal(skc5,nil)**.
% 48.25/48.50 3608[2:Rew:3454.0,3339.0] || SkP0(nil,nil) -> neq(skc5,nil)*.
% 48.25/48.50 3618[2:Rew:3454.0,3608.1] || SkP0(nil,nil) -> neq(nil,nil)*.
% 48.25/48.50 3619[2:MRR:3618.1,3206.0] || SkP0(nil,nil)* -> .
% 48.25/48.50 3709[2:Res:70.1,3619.0] || equal(nil,nil)* -> .
% 48.25/48.50 3711[2:Obv:3709.0] || -> .
% 48.25/48.50 3712[2:Spt:3711.0,462.5,3454.0] || equal(skc5,nil)** -> .
% 48.25/48.50 3713[2:Spt:3711.0,462.0,462.1,462.2,462.3,462.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 48.25/48.50 3714[2:MRR:453.1,3712.0] || -> ssList(tl(skc5))*.
% 48.25/48.50 3715[2:MRR:452.1,3712.0] || -> ssItem(hd(skc5))*.
% 48.25/48.50 3719[2:MRR:427.0,3712.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 48.25/48.50 3892[0:EqR:119.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 48.25/48.50 3894[1:SSi:3892.0,78.1,77.1,73.1,74.1,72.1,75.1,76.1,3213.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 48.25/48.50 5381[0:EqR:142.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 48.25/48.50 5397[0:SSi:5381.1,90.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 48.25/48.50 5628[0:SpR:126.2,5397.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 48.25/48.50 5641[0:Obv:5628.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 48.25/48.50 5642[1:SSi:5641.1,78.1,77.1,73.1,74.1,72.1,75.1,76.1,3213.1,3894.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 48.25/48.50 6381[2:SpR:3719.0,5642.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 48.25/48.50 7722[0:EqR:200.4] ssList(u) ssList(app(v,app(u,w))) ssList(w) ssList(v) || -> segmentP(app(v,app(u,w)),u)*.
% 48.25/48.50 7759[0:SSi:7722.1,90.2,90.2] ssList(u) ssList(v) ssList(w) || -> segmentP(app(w,app(u,v)),u)*.
% 48.25/48.50 17097[0:SpR:80.1,7759.3] ssList(app(u,v)) ssList(u) ssList(v) ssList(nil) || -> segmentP(app(u,v),u)*.
% 48.25/48.50 17115[0:SSi:17097.3,17097.0,13.2,12.0,8.0,9.0,7.0,10.0,11.0,6.0,90.0] ssList(u) ssList(v) || -> segmentP(app(u,v),u)*.
% 48.25/48.50 21500[0:SpR:416.2,17115.2] ssList(u) ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 48.25/48.50 21530[0:Obv:21500.0] ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 48.25/48.50 33931[2:SSi:6381.1,3714.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 48.25/48.50 33932[2:MRR:33931.0,3715.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 48.25/48.50 33938[0:SSi:21530.1,56.0,1.0] ssList(u) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 48.25/48.50 36226[2:Res:33932.0,33938.1] ssList(cons(hd(skc5),nil)) || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 48.25/48.50 36229[2:SSi:36226.0,78.0,3715.1,77.0,3715.1,73.0,3715.1,74.0,3715.1,72.0,3715.1,75.0,3715.1,76.0,3715.1,3213.0,3715.1,3894.0,3715.1] || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 48.25/48.50 36288[2:Res:36229.0,3432.3] totalorderedP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 48.25/48.50 36293[2:SSi:36288.1,36288.0,78.0,3715.1,77.0,3715.1,73.0,3715.1,74.0,3715.1,72.0,3715.1,75.0,3715.1,76.0,3715.1,3213.0,3715.1,3894.0,3715.1,78.0,3715.1,77.0,3715.1,73.0,3715.1,74.0,3715.1,72.0,3715.1,75.0,3715.1,76.0,3715.1,3213.0,3715.1,3894.0,3715.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 48.25/48.50 36300[2:Res:3355.1,36293.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 48.25/48.50 36301[2:SSi:36300.0,78.0,3715.1,77.0,3715.1,73.0,3715.1,74.0,3715.1,72.0,3715.1,75.0,3715.1,76.0,3715.1,3213.0,3715.1,3894.0,3715.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 48.25/48.50 36354[2:SpL:36301.0,3215.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 48.25/48.50 36395[2:Obv:36354.1] ssItem(hd(skc5)) || -> .
% 48.25/48.50 36396[2:SSi:36395.0,3715.0] || -> .
% 48.25/48.50 % SZS output end Refutation
% 48.25/48.50 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
% 48.25/48.50
%------------------------------------------------------------------------------