TSTP Solution File: SWC109+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC109+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 22:01:47 EDT 2022
% Result : Theorem 20.66s 20.89s
% Output : Refutation 23.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC109+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 03:05:34 EDT 2022
% 0.14/0.34 % CPUTime :
% 20.66/20.89
% 20.66/20.89 SPASS V 3.9
% 20.66/20.89 SPASS beiseite: Proof found.
% 20.66/20.89 % SZS status Theorem
% 20.66/20.89 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.66/20.89 SPASS derived 16330 clauses, backtracked 4861 clauses, performed 55 splits and kept 9372 clauses.
% 20.66/20.89 SPASS allocated 121273 KBytes.
% 20.66/20.89 SPASS spent 0:0:20.52 on the problem.
% 20.66/20.89 0:00:00.04 for the input.
% 20.66/20.89 0:00:00.07 for the FLOTTER CNF translation.
% 20.66/20.89 0:00:00.25 for inferences.
% 20.66/20.89 0:00:00.84 for the backtracking.
% 20.66/20.89 0:0:19.02 for the reduction.
% 20.66/20.89
% 20.66/20.89
% 20.66/20.89 Here is a proof with depth 6, length 151 :
% 20.66/20.89 % SZS output start Refutation
% 20.66/20.89 1[0:Inp] || -> ssList(skc5)*.
% 20.66/20.89 2[0:Inp] || -> ssList(skc4)*.
% 20.66/20.89 3[0:Inp] || -> ssItem(skc7)*.
% 20.66/20.89 4[0:Inp] || -> ssItem(skc6)*.
% 20.66/20.89 5[0:Inp] || -> ssList(nil)*.
% 20.66/20.89 6[0:Inp] || -> cyclefreeP(nil)*.
% 20.66/20.89 7[0:Inp] || -> totalorderP(nil)*.
% 20.66/20.89 8[0:Inp] || -> strictorderP(nil)*.
% 20.66/20.89 9[0:Inp] || -> totalorderedP(nil)*.
% 20.66/20.89 10[0:Inp] || -> strictorderedP(nil)*.
% 20.66/20.89 11[0:Inp] || -> duplicatefreeP(nil)*.
% 20.66/20.89 12[0:Inp] || -> equalelemsP(nil)*.
% 20.66/20.89 51[0:Inp] || -> ssList(skf48(u,v))*.
% 20.66/20.89 52[0:Inp] || -> ssList(skf47(u,v))*.
% 20.66/20.89 53[0:Inp] || -> ssItem(skf46(u,v))*.
% 20.66/20.89 54[0:Inp] || equal(skc7,skc6)** -> .
% 20.66/20.89 61[0:Inp] || -> SkP1(u,v)* equal(nil,v).
% 20.66/20.89 67[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 20.66/20.89 70[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc5).
% 20.66/20.89 71[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc4).
% 20.66/20.89 72[0:Inp] || SkP1(skc4,skc5) -> neq(skc5,nil)*.
% 20.66/20.89 73[0:Inp] || equal(nil,u) -> SkP1(u,v)*.
% 20.66/20.89 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 20.66/20.89 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 20.66/20.89 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 20.66/20.89 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 20.66/20.89 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 20.66/20.89 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 20.66/20.89 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 20.66/20.89 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 20.66/20.89 88[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 20.66/20.89 89[0:Inp] || -> SkP0(u,v) equal(cons(skf46(u,v),nil),v)**.
% 20.66/20.89 93[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 20.66/20.89 94[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 20.66/20.89 99[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 20.66/20.89 108[0:Inp] || SkP1(skc4,skc5) segmentP(skc5,skc4)* neq(skc4,nil) -> .
% 20.66/20.89 111[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 20.66/20.89 112[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 20.66/20.89 114[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 20.66/20.89 123[0:Inp] || -> SkP0(u,v) equal(app(app(skf47(u,v),v),skf48(v,u)),u)**.
% 20.66/20.89 132[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 20.66/20.89 137[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 20.66/20.89 165[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 20.66/20.89 191[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(u,x),v),w)* -> segmentP(w,x)*.
% 20.66/20.89 193[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).
% 20.66/20.89 202[0:Rew:71.1,70.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4).
% 20.66/20.89 207[0:Rew:165.3,191.4] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(x,app(u,w)),v)*+ -> segmentP(v,u)*.
% 20.66/20.89 250[0:Res:2.0,137.0] ssList(u) || -> equal(nil,skc4) equal(hd(app(skc4,u)),hd(skc4))**.
% 20.66/20.89 258[0:Res:2.0,111.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 20.66/20.89 261[0:Res:2.0,114.0] ssItem(u) || -> equal(hd(cons(u,skc4)),u)**.
% 20.66/20.89 273[0:Res:2.0,93.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 20.66/20.89 279[0:Res:2.0,99.0] || segmentP(nil,skc4)* -> equal(nil,skc4).
% 20.66/20.89 282[0:Res:2.0,88.0] || -> ssList(tl(skc4))* equal(nil,skc4).
% 20.66/20.89 289[0:Res:2.0,67.0] || -> segmentP(skc4,skc4)*.
% 20.66/20.89 291[0:Res:2.0,193.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(nil,skc4).
% 20.66/20.89 421[0:Res:1.0,137.0] ssList(u) || -> equal(nil,skc5) equal(hd(app(skc5,u)),hd(skc5))**.
% 20.66/20.89 422[0:Res:1.0,132.0] ssItem(u) || -> equal(app(cons(u,nil),skc5),cons(u,skc5))**.
% 20.66/20.89 430[0:Res:1.0,112.0] ssItem(u) || equal(cons(u,skc5),skc5)** -> .
% 20.66/20.89 454[0:Res:1.0,83.0] || -> equal(app(nil,skc5),skc5)**.
% 20.66/20.89 462[0:Res:1.0,193.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 20.66/20.89 554[1:Spt:421.0,421.2] ssList(u) || -> equal(hd(app(skc5,u)),hd(skc5))**.
% 20.66/20.89 556[2:Spt:250.0,250.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 20.66/20.89 562[3:Spt:462.5] || -> equal(nil,skc5)**.
% 20.66/20.89 662[3:Rew:562.0,83.1] ssList(u) || -> equal(app(skc5,u),u)**.
% 20.66/20.89 721[3:Rew:662.1,554.1] ssList(u) || -> equal(hd(u),hd(skc5))*.
% 20.66/20.89 1244[3:SpR:261.1,721.1] ssItem(u) ssList(cons(u,skc4)) || -> equal(u,hd(skc5))*.
% 20.66/20.89 1247[3:SSi:1244.1,273.1] ssItem(u) || -> equal(u,hd(skc5))*.
% 20.66/20.89 1330[3:SpR:1247.1,1247.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 20.66/20.89 1415[3:EmS:1330.0,3.0] ssItem(u) || -> equal(u,skc7)*.
% 20.66/20.89 1438[3:EmS:1415.0,4.0] || -> equal(skc7,skc6)**.
% 20.66/20.89 1439[3:MRR:1438.0,54.0] || -> .
% 20.66/20.89 1620[3:Spt:1439.0,462.5,562.0] || equal(nil,skc5)** -> .
% 20.66/20.89 1621[3:Spt:1439.0,462.0,462.1,462.2,462.3,462.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 20.66/20.89 1645[4:Spt:291.5] || -> equal(nil,skc4)**.
% 20.66/20.89 1688[4:Rew:1645.0,75.1] ssItem(u) || -> cyclefreeP(cons(u,skc4))*.
% 20.66/20.89 1689[4:Rew:1645.0,76.1] ssItem(u) || -> totalorderP(cons(u,skc4))*.
% 20.66/20.89 1690[4:Rew:1645.0,77.1] ssItem(u) || -> strictorderP(cons(u,skc4))*.
% 20.66/20.89 1691[4:Rew:1645.0,78.1] ssItem(u) || -> totalorderedP(cons(u,skc4))*.
% 20.66/20.89 1692[4:Rew:1645.0,79.1] ssItem(u) || -> strictorderedP(cons(u,skc4))*.
% 20.66/20.89 1693[4:Rew:1645.0,80.1] ssItem(u) || -> duplicatefreeP(cons(u,skc4))*.
% 20.66/20.89 1694[4:Rew:1645.0,81.1] ssItem(u) || -> equalelemsP(cons(u,skc4))*.
% 20.66/20.89 1722[4:Rew:1645.0,83.1] ssList(u) || -> equal(app(skc4,u),u)**.
% 20.66/20.89 1782[4:Rew:1722.1,556.1] ssList(u) || -> equal(hd(u),hd(skc4))*.
% 20.66/20.89 1851[4:SpR:1782.1,261.1] ssList(cons(u,skc4)) ssItem(u) || -> equal(hd(skc4),u)*.
% 20.66/20.89 1861[4:SSi:1851.0,273.1,1688.1,1689.1,1690.1,1691.1,1692.1,1693.1,1694.1] ssItem(u) || -> equal(hd(skc4),u)*.
% 20.66/20.89 1881[4:SpR:1861.1,1861.1] ssItem(u) ssItem(v) || -> equal(u,v)*.
% 20.66/20.89 2059[4:EmS:1881.0,3.0] ssItem(u) || -> equal(skc7,u)*.
% 20.66/20.89 2082[4:EmS:2059.0,4.0] || -> equal(skc7,skc6)**.
% 20.66/20.89 2083[4:MRR:2082.0,54.0] || -> .
% 20.66/20.89 2270[4:Spt:2083.0,291.5,1645.0] || equal(nil,skc4)** -> .
% 20.66/20.89 2271[4:Spt:2083.0,291.0,291.1,291.2,291.3,291.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 20.66/20.89 2277[4:MRR:71.1,2270.0] || SkP0(skc5,skc4)* -> .
% 20.66/20.89 2392[0:SpR:89.1,93.2] ssItem(skf46(u,v)) ssList(nil) || -> SkP0(u,v)* ssList(v).
% 20.66/20.89 2408[0:SSi:2392.1,2392.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0,53.0] || -> SkP0(u,v)* ssList(v).
% 20.66/20.89 2552[0:SpR:89.1,114.2] ssItem(skf46(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 20.66/20.89 2556[0:SSi:2552.1,2552.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0,53.0] || -> SkP0(u,v) equal(skf46(u,v),hd(v))**.
% 20.66/20.89 2557[0:Rew:2556.1,89.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 20.66/20.89 2641[0:SpR:2556.1,53.0] || -> SkP0(u,v)* ssItem(hd(v)).
% 20.66/20.89 2699[0:SpR:2557.1,422.1] ssItem(hd(u)) || -> SkP0(v,u)* equal(cons(hd(u),skc5),app(u,skc5))**.
% 20.66/20.89 2703[0:MRR:2699.0,2641.1] || -> SkP0(u,v)* equal(cons(hd(v),skc5),app(v,skc5))**.
% 20.66/20.89 2936[0:SpL:2703.1,430.1] ssItem(hd(u)) || equal(app(u,skc5),skc5)** -> SkP0(v,u)*.
% 20.66/20.89 2942[0:MRR:2936.0,2641.1] || equal(app(u,skc5),skc5)** -> SkP0(v,u)*.
% 20.66/20.89 2973[0:SpL:454.0,2942.0] || equal(skc5,skc5) -> SkP0(u,nil)*.
% 20.66/20.89 2975[0:Obv:2973.0] || -> SkP0(u,nil)*.
% 20.66/20.89 5248[0:SpR:165.3,123.1] ssList(skf48(u,v)) ssList(u) ssList(skf47(v,u)) || -> SkP0(v,u) equal(app(skf47(v,u),app(u,skf48(u,v))),v)**.
% 20.66/20.89 5306[0:SSi:5248.2,5248.0,52.0,51.0] ssList(u) || -> SkP0(v,u) equal(app(skf47(v,u),app(u,skf48(u,v))),v)**.
% 20.66/20.89 5307[0:MRR:5306.0,2408.1] || -> SkP0(u,v) equal(app(skf47(u,v),app(v,skf48(v,u))),u)**.
% 20.66/20.89 7512[0:EqR:207.4] ssList(u) ssList(app(v,app(u,w))) ssList(w) ssList(v) || -> segmentP(app(v,app(u,w)),u)*.
% 20.66/20.89 7549[0:SSi:7512.1,94.2,94.2] ssList(u) ssList(v) ssList(w) || -> segmentP(app(w,app(u,v)),u)*.
% 20.66/20.89 21146[0:SpR:5307.1,7549.3] ssList(u) ssList(skf48(u,v)) ssList(skf47(v,u)) || -> SkP0(v,u)* segmentP(v,u).
% 20.66/20.89 21171[0:SSi:21146.2,21146.1,52.0,51.0] ssList(u) || -> SkP0(v,u)* segmentP(v,u).
% 20.66/20.89 21172[0:MRR:21171.0,2408.1] || -> SkP0(u,v)* segmentP(u,v).
% 20.66/20.89 21246[4:Res:21172.0,2277.0] || -> segmentP(skc5,skc4)*.
% 20.66/20.89 21247[4:MRR:108.1,21246.0] || SkP1(skc4,skc5) neq(skc4,nil)* -> .
% 20.66/20.89 21254[4:Res:258.1,21247.1] ssList(nil) || SkP1(skc4,skc5)* -> equal(nil,skc4).
% 20.66/20.89 21257[4:SSi:21254.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0] || SkP1(skc4,skc5)* -> equal(nil,skc4).
% 23.28/23.44 21258[4:MRR:21257.1,2270.0] || SkP1(skc4,skc5)* -> .
% 23.28/23.44 21261[4:Res:61.0,21258.0] || -> equal(nil,skc5)**.
% 23.28/23.44 21262[4:MRR:21261.0,1620.0] || -> .
% 23.28/23.44 21263[2:Spt:21262.0,250.1] || -> equal(nil,skc4)**.
% 23.28/23.44 21298[2:Rew:21263.0,73.0] || equal(skc4,u) -> SkP1(u,v)*.
% 23.28/23.44 21806[2:Rew:21263.0,2975.0] || -> SkP0(u,skc4)*.
% 23.28/23.44 21843[2:MRR:202.0,21806.0] || -> equal(skc5,skc4)**.
% 23.28/23.44 22035[2:Rew:21843.0,72.1,21263.0,72.1,21843.0,72.0] || SkP1(skc4,skc4) -> neq(skc4,skc4)*.
% 23.28/23.44 22171[2:Rew:21263.0,108.2,21843.0,108.1,21843.0,108.0] || SkP1(skc4,skc4) segmentP(skc4,skc4)* neq(skc4,skc4) -> .
% 23.28/23.44 22172[2:MRR:22171.1,289.0] || SkP1(skc4,skc4) neq(skc4,skc4)* -> .
% 23.28/23.44 22173[2:MRR:22172.1,22035.1] || SkP1(skc4,skc4)* -> .
% 23.28/23.44 23513[2:Res:21298.1,22173.0] || equal(skc4,skc4)* -> .
% 23.28/23.44 23514[2:Obv:23513.0] || -> .
% 23.28/23.44 23515[1:Spt:23514.0,421.1] || -> equal(nil,skc5)**.
% 23.28/23.44 23544[1:Rew:23515.0,282.1] || -> ssList(tl(skc4))* equal(skc5,skc4).
% 23.28/23.44 23561[1:Rew:23515.0,73.0] || equal(skc5,u) -> SkP1(u,v)*.
% 23.28/23.44 23562[1:Rew:23515.0,279.1,23515.0,279.0] || segmentP(skc5,skc4)* -> equal(skc5,skc4).
% 23.28/23.44 23565[1:Rew:23515.0,71.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4).
% 23.28/23.44 23570[1:Rew:23515.0,72.1] || SkP1(skc4,skc5) -> neq(skc5,skc5)*.
% 23.28/23.44 23681[1:Rew:23562.1,108.2,23515.0,108.2,23562.1,108.0] || SkP1(skc4,skc4) segmentP(skc5,skc4)* neq(skc4,skc4) -> .
% 23.28/23.44 25177[2:Spt:23544.1] || -> equal(skc5,skc4)**.
% 23.28/23.44 25552[2:Rew:25177.0,23561.0] || equal(skc4,u) -> SkP1(u,v)*.
% 23.28/23.44 25553[2:Rew:25177.0,23681.1] || SkP1(skc4,skc4) segmentP(skc4,skc4)* neq(skc4,skc4) -> .
% 23.28/23.44 25562[2:Rew:25177.0,23570.0] || SkP1(skc4,skc4) -> neq(skc5,skc5)*.
% 23.28/23.44 25925[2:Rew:25177.0,25562.1] || SkP1(skc4,skc4) -> neq(skc4,skc4)*.
% 23.28/23.44 26032[2:MRR:25553.1,289.0] || SkP1(skc4,skc4) neq(skc4,skc4)* -> .
% 23.28/23.44 26033[2:MRR:26032.1,25925.1] || SkP1(skc4,skc4)* -> .
% 23.28/23.44 26415[2:Res:25552.1,26033.0] || equal(skc4,skc4)* -> .
% 23.28/23.44 26416[2:Obv:26415.0] || -> .
% 23.28/23.44 26417[2:Spt:26416.0,23544.1,25177.0] || equal(skc5,skc4)** -> .
% 23.28/23.44 26418[2:Spt:26416.0,23544.0] || -> ssList(tl(skc4))*.
% 23.28/23.44 26420[2:MRR:23562.1,26417.0] || segmentP(skc5,skc4)* -> .
% 23.28/23.44 26423[2:MRR:23565.1,26417.0] || SkP0(skc5,skc4)* -> .
% 23.28/23.44 26457[2:Res:21172.0,26423.0] || -> segmentP(skc5,skc4)*.
% 23.28/23.44 26472[2:MRR:26457.0,26420.0] || -> .
% 23.28/23.44 % SZS output end Refutation
% 23.28/23.44 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax55 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax76 ax16 ax26 ax58 ax15 ax18 ax23 ax81 ax85 ax82 ax7 ax77
% 23.28/23.44
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