TSTP Solution File: SWC099+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC099+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 22:01:43 EDT 2022
% Result : Theorem 4.49s 4.68s
% Output : Refutation 4.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC099+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 20:59:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.49/4.68
% 4.49/4.68 SPASS V 3.9
% 4.49/4.68 SPASS beiseite: Proof found.
% 4.49/4.68 % SZS status Theorem
% 4.49/4.68 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.49/4.68 SPASS derived 6057 clauses, backtracked 1967 clauses, performed 93 splits and kept 4576 clauses.
% 4.49/4.68 SPASS allocated 106615 KBytes.
% 4.49/4.68 SPASS spent 0:00:04.33 on the problem.
% 4.49/4.68 0:00:00.04 for the input.
% 4.49/4.68 0:00:00.07 for the FLOTTER CNF translation.
% 4.49/4.68 0:00:00.07 for inferences.
% 4.49/4.68 0:00:00.09 for the backtracking.
% 4.49/4.68 0:00:03.87 for the reduction.
% 4.49/4.68
% 4.49/4.68
% 4.49/4.68 Here is a proof with depth 6, length 276 :
% 4.49/4.68 % SZS output start Refutation
% 4.49/4.68 1[0:Inp] || -> ssList(skc5)*.
% 4.49/4.68 2[0:Inp] || -> ssList(skc4)*.
% 4.49/4.68 3[0:Inp] || -> equalelemsP(skc4)*.
% 4.49/4.68 6[0:Inp] || -> ssList(nil)*.
% 4.49/4.68 7[0:Inp] || -> cyclefreeP(nil)*.
% 4.49/4.68 8[0:Inp] || -> totalorderP(nil)*.
% 4.49/4.68 9[0:Inp] || -> strictorderP(nil)*.
% 4.49/4.68 10[0:Inp] || -> totalorderedP(nil)*.
% 4.49/4.68 11[0:Inp] || -> strictorderedP(nil)*.
% 4.49/4.68 12[0:Inp] || -> duplicatefreeP(nil)*.
% 4.49/4.68 13[0:Inp] || -> equalelemsP(nil)*.
% 4.49/4.68 14[0:Inp] || -> frontsegP(skc5,skc4)*.
% 4.49/4.68 19[0:Inp] || -> ssItem(skf51(u))*.
% 4.49/4.68 20[0:Inp] || -> ssItem(skf50(u))*.
% 4.49/4.68 34[0:Inp] || -> ssItem(skf66(u))*.
% 4.49/4.68 35[0:Inp] || -> ssItem(skf65(u))*.
% 4.49/4.68 48[0:Inp] || -> ssItem(skf81(u))*.
% 4.49/4.68 49[0:Inp] || -> ssItem(skf80(u))*.
% 4.49/4.68 60[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 4.49/4.68 62[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 4.49/4.68 66[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 4.49/4.68 67[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 4.49/4.68 69[0:Inp] || SkP0(skc4,skc5) -> neq(skc5,nil)*.
% 4.49/4.68 70[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 4.49/4.68 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 4.49/4.68 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 4.49/4.68 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 4.49/4.68 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 4.49/4.68 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 4.49/4.68 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 4.49/4.68 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 4.49/4.68 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 4.49/4.68 84[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 4.49/4.68 85[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 4.49/4.68 86[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 4.49/4.68 87[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf50(u),skf51(u))*.
% 4.49/4.68 89[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 4.49/4.68 90[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 4.49/4.68 91[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 4.49/4.68 101[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 4.49/4.68 103[0:Inp] ssList(u) || equal(skf81(u),skf80(u))** -> equalelemsP(u).
% 4.49/4.68 104[0:Inp] || neq(skc4,nil) frontsegP(skc5,skc4)* SkP0(skc4,skc5) -> .
% 4.49/4.68 107[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 4.49/4.68 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 4.49/4.68 110[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 4.49/4.68 117[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 4.49/4.68 120[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 4.49/4.68 127[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 4.49/4.68 132[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 4.49/4.68 142[0:Inp] equalelemsP(u) ssList(u) || segmentP(u,skc4) neq(skc4,u) frontsegP(skc5,u)* -> .
% 4.49/4.68 143[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 4.49/4.68 145[0:Inp] ssList(u) || -> equalelemsP(u) equal(app(skf82(u),cons(skf80(u),cons(skf81(u),skf83(u)))),u)**.
% 4.49/4.68 154[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 4.49/4.68 173[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 4.49/4.68 174[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 4.49/4.68 187[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).
% 4.49/4.68 196[0:MRR:104.1,14.0] || SkP0(skc4,skc5) neq(skc4,nil)* -> .
% 4.49/4.68 203[0:Res:3.0,142.1] ssList(skc4) || frontsegP(skc5,skc4)* segmentP(skc4,skc4) neq(skc4,skc4) -> .
% 4.49/4.68 247[0:Res:2.0,132.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 4.49/4.68 255[0:Res:2.0,107.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 4.49/4.68 257[0:Res:2.0,109.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 4.49/4.68 258[0:Res:2.0,110.0] ssItem(u) || -> equal(hd(cons(u,skc4)),u)**.
% 4.49/4.68 270[0:Res:2.0,89.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 4.49/4.68 272[0:Res:2.0,91.0] || frontsegP(nil,skc4)* -> equal(skc4,nil).
% 4.49/4.68 286[0:Res:2.0,66.0] || -> segmentP(skc4,skc4)*.
% 4.49/4.68 288[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).
% 4.49/4.68 394[0:Res:1.0,174.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 4.49/4.68 395[0:Res:1.0,173.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 4.49/4.68 407[0:Res:1.0,142.0] equalelemsP(skc5) || frontsegP(skc5,skc5)* segmentP(skc5,skc4) neq(skc4,skc5) -> .
% 4.49/4.68 410[0:Res:1.0,145.0] || -> equalelemsP(skc5) equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 413[0:Res:1.0,154.0] ssList(u) || -> equal(skc5,nil) equal(app(tl(skc5),u),tl(app(skc5,u)))**.
% 4.49/4.68 425[0:Res:1.0,117.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 4.49/4.68 436[0:Res:1.0,101.0] || leq(skf65(skc5),skf66(skc5))* -> totalorderedP(skc5).
% 4.49/4.68 438[0:Res:1.0,103.0] || equal(skf81(skc5),skf80(skc5))** -> equalelemsP(skc5).
% 4.49/4.68 439[0:Res:1.0,86.0] || -> cyclefreeP(skc5) leq(skf51(skc5),skf50(skc5))*.
% 4.49/4.68 440[0:Res:1.0,87.0] || -> cyclefreeP(skc5) leq(skf50(skc5),skf51(skc5))*.
% 4.49/4.68 450[0:Res:1.0,84.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 4.49/4.68 451[0:Res:1.0,85.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 4.49/4.68 454[0:Res:1.0,62.0] || -> frontsegP(skc5,skc5)*.
% 4.49/4.68 459[0:Res:1.0,67.0] || -> segmentP(skc5,nil)*.
% 4.49/4.68 460[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).
% 4.49/4.68 548[0:MRR:203.0,203.1,203.2,2.0,14.0,286.0] || neq(skc4,skc4)* -> .
% 4.49/4.68 549[0:MRR:407.1,454.0] equalelemsP(skc5) || neq(skc4,skc5) segmentP(skc5,skc4)* -> .
% 4.49/4.68 553[1:Spt:247.0,247.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 4.49/4.68 559[2:Spt:288.5] || -> equal(skc4,nil)**.
% 4.49/4.68 560[2:Rew:559.0,553.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 4.49/4.68 563[2:Rew:559.0,69.0] || SkP0(nil,skc5) -> neq(skc5,nil)*.
% 4.49/4.68 570[2:Rew:559.0,255.1] ssList(u) || -> neq(nil,u)* equal(skc4,u).
% 4.49/4.68 585[2:Rew:559.0,270.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 4.49/4.68 586[2:Rew:559.0,258.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 4.49/4.68 672[2:Rew:559.0,548.0] || neq(nil,nil)* -> .
% 4.49/4.68 678[2:Rew:559.0,549.1] equalelemsP(skc5) || neq(nil,skc5) segmentP(skc5,skc4)* -> .
% 4.49/4.68 732[2:Rew:559.0,570.2] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 4.49/4.68 734[2:Rew:80.1,560.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 4.49/4.68 742[2:Rew:559.0,678.2] equalelemsP(skc5) || neq(nil,skc5) segmentP(skc5,nil)* -> .
% 4.49/4.68 743[2:MRR:742.2,459.0] equalelemsP(skc5) || neq(nil,skc5)* -> .
% 4.49/4.68 823[3:Spt:460.5] || -> equal(skc5,nil)**.
% 4.49/4.68 975[3:Rew:823.0,563.0] || SkP0(nil,nil) -> neq(skc5,nil)*.
% 4.49/4.68 987[3:Rew:823.0,975.1] || SkP0(nil,nil) -> neq(nil,nil)*.
% 4.49/4.68 988[3:MRR:987.1,672.0] || SkP0(nil,nil)* -> .
% 4.49/4.68 1073[3:Res:70.1,988.0] || equal(nil,nil)* -> .
% 4.49/4.68 1074[3:Obv:1073.0] || -> .
% 4.49/4.68 1075[3:Spt:1074.0,460.5,823.0] || equal(skc5,nil)** -> .
% 4.49/4.68 1076[3:Spt:1074.0,460.0,460.1,460.2,460.3,460.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 4.49/4.68 1091[4:Spt:395.0] || -> strictorderedP(skc5)*.
% 4.49/4.68 1094[5:Spt:394.0] || -> totalorderedP(skc5)*.
% 4.49/4.68 1098[6:Spt:439.0] || -> cyclefreeP(skc5)*.
% 4.49/4.68 1100[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 1101[7:MRR:743.0,1100.0] || neq(nil,skc5)* -> .
% 4.49/4.68 1163[7:Res:732.1,1101.0] ssList(skc5) || -> equal(skc5,nil)**.
% 4.49/4.68 1184[7:SSi:1163.0,1091.0,1.0,1094.0,1098.0,1100.0] || -> equal(skc5,nil)**.
% 4.49/4.68 1185[7:MRR:1184.0,1075.0] || -> .
% 4.49/4.68 1189[7:Spt:1185.0,410.0,1100.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 1190[7:Spt:1185.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 1192[7:MRR:438.1,1189.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 1211[2:SpR:586.1,734.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 4.49/4.68 1214[2:SSi:1211.1,78.1,77.1,74.1,73.1,72.1,76.1,75.1,585.1] ssItem(u) || -> equal(u,hd(nil))*.
% 4.49/4.68 1310[7:SpL:1214.1,1192.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1374[7:SSi:1310.0,48.0,1091.0,1.0,1094.0,1098.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1402[7:SpL:1214.1,1374.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 1414[7:Obv:1402.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 1415[7:SSi:1414.0,49.0,1091.0,1.0,1094.0,1098.0] || -> .
% 4.49/4.68 1416[6:Spt:1415.0,439.0,1098.0] || cyclefreeP(skc5)* -> .
% 4.49/4.68 1417[6:Spt:1415.0,439.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 4.49/4.68 1427[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 1428[7:MRR:743.0,1427.0] || neq(nil,skc5)* -> .
% 4.49/4.68 1441[7:Res:732.1,1428.0] ssList(skc5) || -> equal(skc5,nil)**.
% 4.49/4.68 1452[7:SSi:1441.0,1091.0,1.0,1094.0,1427.0] || -> equal(skc5,nil)**.
% 4.49/4.68 1453[7:MRR:1452.0,1075.0] || -> .
% 4.49/4.68 1456[7:Spt:1453.0,410.0,1427.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 1457[7:Spt:1453.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 1458[7:MRR:438.1,1456.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 1509[7:SpL:1214.1,1458.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1576[7:SSi:1509.0,48.0,1091.0,1.0,1094.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1625[7:SpL:1214.1,1576.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 1637[7:Obv:1625.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 1638[7:SSi:1637.0,49.0,1091.0,1.0,1094.0] || -> .
% 4.49/4.68 1639[5:Spt:1638.0,394.0,1094.0] || totalorderedP(skc5)* -> .
% 4.49/4.68 1640[5:Spt:1638.0,394.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 4.49/4.68 1642[5:MRR:436.1,1639.0] || leq(skf65(skc5),skf66(skc5))* -> .
% 4.49/4.68 1659[6:Spt:440.0] || -> cyclefreeP(skc5)*.
% 4.49/4.68 1661[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 1662[7:MRR:743.0,1661.0] || neq(nil,skc5)* -> .
% 4.49/4.68 1668[7:Res:732.1,1662.0] ssList(skc5) || -> equal(skc5,nil)**.
% 4.49/4.68 1673[7:SSi:1668.0,1091.0,1.0,1659.0,1661.0] || -> equal(skc5,nil)**.
% 4.49/4.68 1674[7:MRR:1673.0,1075.0] || -> .
% 4.49/4.68 1677[7:Spt:1674.0,410.0,1661.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 1678[7:Spt:1674.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 1679[7:MRR:438.1,1677.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 1693[5:SpL:1214.1,1642.0] ssItem(skf66(skc5)) || leq(skf65(skc5),hd(nil))* -> .
% 4.49/4.68 1697[7:SpL:1214.1,1679.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1768[7:SSi:1697.0,48.0,1091.0,1.0,1659.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 1809[7:SpL:1214.1,1768.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 1822[7:Obv:1809.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 1823[7:SSi:1822.0,49.0,1091.0,1.0,1659.0] || -> .
% 4.49/4.68 1824[6:Spt:1823.0,440.0,1659.0] || cyclefreeP(skc5)* -> .
% 4.49/4.68 1825[6:Spt:1823.0,440.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 4.49/4.68 1827[5:SSi:1693.0,34.0,1091.0,1.0] || leq(skf65(skc5),hd(nil))* -> .
% 4.49/4.68 1830[6:SpR:1214.1,1825.0] ssItem(skf51(skc5)) || -> leq(skf50(skc5),hd(nil))*.
% 4.49/4.68 1832[6:SSi:1830.0,19.0,1091.0,1.0] || -> leq(skf50(skc5),hd(nil))*.
% 4.49/4.68 1874[6:SpR:1214.1,1832.0] ssItem(skf50(skc5)) || -> leq(hd(nil),hd(nil))*.
% 4.49/4.68 1907[5:SpL:1214.1,1827.0] ssItem(skf65(skc5)) || leq(hd(nil),hd(nil))* -> .
% 4.49/4.68 1925[6:SSi:1874.0,20.0,1091.0,1.0] || -> leq(hd(nil),hd(nil))*.
% 4.49/4.68 1926[5:SSi:1907.0,35.0,1091.0,1.0] || leq(hd(nil),hd(nil))* -> .
% 4.49/4.68 1927[6:MRR:1926.0,1925.0] || -> .
% 4.49/4.68 1928[4:Spt:1927.0,395.0,1091.0] || strictorderedP(skc5)* -> .
% 4.49/4.68 1929[4:Spt:1927.0,395.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 4.49/4.68 1948[5:Spt:394.0] || -> totalorderedP(skc5)*.
% 4.49/4.68 1952[6:Spt:439.0] || -> cyclefreeP(skc5)*.
% 4.49/4.68 1960[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 1961[7:MRR:743.0,1960.0] || neq(nil,skc5)* -> .
% 4.49/4.68 1968[7:Res:732.1,1961.0] ssList(skc5) || -> equal(skc5,nil)**.
% 4.49/4.68 1973[7:SSi:1968.0,1.0,1948.0,1952.0,1960.0] || -> equal(skc5,nil)**.
% 4.49/4.68 1974[7:MRR:1973.0,1075.0] || -> .
% 4.49/4.68 1977[7:Spt:1974.0,410.0,1960.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 1978[7:Spt:1974.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 1979[7:MRR:438.1,1977.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 2021[7:SpL:1214.1,1979.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2088[7:SSi:2021.0,48.0,1.0,1948.0,1952.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2139[7:SpL:1214.1,2088.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 2152[7:Obv:2139.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 2153[7:SSi:2152.0,49.0,1.0,1948.0,1952.0] || -> .
% 4.49/4.68 2157[6:Spt:2153.0,439.0,1952.0] || cyclefreeP(skc5)* -> .
% 4.49/4.68 2158[6:Spt:2153.0,439.1] || -> leq(skf51(skc5),skf50(skc5))*.
% 4.49/4.68 2170[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 2171[7:MRR:743.0,2170.0] || neq(nil,skc5)* -> .
% 4.49/4.68 2174[7:Res:732.1,2171.0] ssList(skc5) || -> equal(skc5,nil)**.
% 4.49/4.68 2179[7:SSi:2174.0,1.0,1948.0,2170.0] || -> equal(skc5,nil)**.
% 4.49/4.68 2180[7:MRR:2179.0,1075.0] || -> .
% 4.49/4.68 2183[7:Spt:2180.0,410.0,2170.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 2184[7:Spt:2180.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 2185[7:MRR:438.1,2183.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 2257[7:SpL:1214.1,2185.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2377[7:SSi:2257.0,48.0,1.0,1948.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2443[7:SpL:1214.1,2377.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 2455[7:Obv:2443.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 2456[7:SSi:2455.0,49.0,1.0,1948.0] || -> .
% 4.49/4.68 2457[5:Spt:2456.0,394.0,1948.0] || totalorderedP(skc5)* -> .
% 4.49/4.68 2458[5:Spt:2456.0,394.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 4.49/4.68 2459[5:MRR:436.1,2457.0] || leq(skf65(skc5),skf66(skc5))* -> .
% 4.49/4.68 2479[6:Spt:440.0] || -> cyclefreeP(skc5)*.
% 4.49/4.68 2481[7:Spt:410.0] || -> equalelemsP(skc5)*.
% 4.49/4.68 2482[7:MRR:743.0,2481.0] || neq(nil,skc5)* -> .
% 4.49/4.68 2486[7:Res:107.2,2482.0] ssList(skc5) ssList(nil) || -> equal(skc5,nil)**.
% 4.49/4.68 2497[7:SSi:2486.1,2486.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0,1.0,2479.0,2481.0] || -> equal(skc5,nil)**.
% 4.49/4.68 2498[7:MRR:2497.0,1075.0] || -> .
% 4.49/4.68 2499[7:Spt:2498.0,410.0,2481.0] || equalelemsP(skc5)* -> .
% 4.49/4.68 2500[7:Spt:2498.0,410.1] || -> equal(app(skf82(skc5),cons(skf80(skc5),cons(skf81(skc5),skf83(skc5)))),skc5)**.
% 4.49/4.68 2501[7:MRR:438.1,2499.0] || equal(skf81(skc5),skf80(skc5))** -> .
% 4.49/4.68 2518[5:SpL:1214.1,2459.0] ssItem(skf66(skc5)) || leq(skf65(skc5),hd(nil))* -> .
% 4.49/4.68 2534[7:SpL:1214.1,2501.0] ssItem(skf81(skc5)) || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2623[7:SSi:2534.0,48.0,1.0,2479.0] || equal(skf80(skc5),hd(nil))** -> .
% 4.49/4.68 2684[7:SpL:1214.1,2623.0] ssItem(skf80(skc5)) || equal(hd(nil),hd(nil))* -> .
% 4.49/4.68 2697[7:Obv:2684.1] ssItem(skf80(skc5)) || -> .
% 4.49/4.68 2698[7:SSi:2697.0,49.0,1.0,2479.0] || -> .
% 4.49/4.68 2699[6:Spt:2698.0,440.0,2479.0] || cyclefreeP(skc5)* -> .
% 4.49/4.68 2700[6:Spt:2698.0,440.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 4.49/4.68 2702[5:SSi:2518.0,34.0,1.0] || leq(skf65(skc5),hd(nil))* -> .
% 4.49/4.68 2706[6:SpR:1214.1,2700.0] ssItem(skf51(skc5)) || -> leq(skf50(skc5),hd(nil))*.
% 4.49/4.68 2708[6:SSi:2706.0,19.0,1.0] || -> leq(skf50(skc5),hd(nil))*.
% 4.49/4.68 2753[6:SpR:1214.1,2708.0] ssItem(skf50(skc5)) || -> leq(hd(nil),hd(nil))*.
% 4.49/4.68 2767[0:EqR:120.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 4.49/4.68 2791[5:SpL:1214.1,2702.0] ssItem(skf65(skc5)) || leq(hd(nil),hd(nil))* -> .
% 4.49/4.68 2810[6:SSi:2753.0,20.0,1.0] || -> leq(hd(nil),hd(nil))*.
% 4.49/4.68 2811[5:SSi:2791.0,35.0,1.0] || leq(hd(nil),hd(nil))* -> .
% 4.49/4.68 2812[6:MRR:2811.0,2810.0] || -> .
% 4.49/4.68 2814[2:Spt:2812.0,288.5,559.0] || equal(skc4,nil)** -> .
% 4.49/4.68 2815[2:Spt:2812.0,288.0,288.1,288.2,288.3,288.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 4.49/4.68 2820[2:MRR:272.1,2814.0] || frontsegP(nil,skc4)* -> .
% 4.49/4.68 2825[0:SSi:2767.0,89.1,13.1,12.1,9.1,8.1,7.1,11.1,10.0,6.0,78.0,77.0,74.0,73.0,72.0,76.0,75.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 4.49/4.68 2849[3:Spt:460.5] || -> equal(skc5,nil)**.
% 4.49/4.68 2997[3:Rew:2849.0,14.0] || -> frontsegP(nil,skc4)*.
% 4.49/4.68 3008[3:MRR:2997.0,2820.0] || -> .
% 4.49/4.68 3108[3:Spt:3008.0,460.5,2849.0] || equal(skc5,nil)** -> .
% 4.49/4.68 3109[3:Spt:3008.0,460.0,460.1,460.2,460.3,460.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 4.49/4.68 3156[0:Res:107.2,196.1] ssList(nil) ssList(skc4) || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 4.49/4.68 3254[0:SSi:3156.1,3156.0,2.0,3.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || SkP0(skc4,skc5)* -> equal(skc4,nil).
% 4.49/4.68 3255[2:MRR:3254.1,2814.0] || SkP0(skc4,skc5)* -> .
% 4.49/4.68 3267[2:Res:60.0,3255.0] || -> equal(skc5,nil)**.
% 4.49/4.68 3268[3:MRR:3267.0,3108.0] || -> .
% 4.49/4.68 3269[1:Spt:3268.0,247.1] || -> equal(skc4,nil)**.
% 4.76/4.96 3279[1:Rew:3269.0,548.0] || neq(nil,nil)* -> .
% 4.76/4.96 3298[1:Rew:3269.0,270.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 4.76/4.96 3299[1:Rew:3269.0,257.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 4.76/4.96 3317[1:Rew:3269.0,142.3] equalelemsP(u) ssList(u) || segmentP(u,skc4) neq(nil,u) frontsegP(skc5,u)* -> .
% 4.76/4.96 3319[1:Rew:3269.0,255.1] ssList(u) || -> neq(nil,u)* equal(skc4,u).
% 4.76/4.96 3415[1:Rew:3269.0,69.0] || SkP0(nil,skc5) -> neq(skc5,nil)*.
% 4.76/4.96 3425[1:Rew:3269.0,3319.2] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 4.76/4.96 3503[1:Rew:3269.0,3317.2] equalelemsP(u) ssList(u) || segmentP(u,nil) neq(nil,u) frontsegP(skc5,u)* -> .
% 4.76/4.96 3504[1:MRR:3503.2,67.1] equalelemsP(u) ssList(u) || neq(nil,u) frontsegP(skc5,u)* -> .
% 4.76/4.96 3525[2:Spt:413.1] || -> equal(skc5,nil)**.
% 4.76/4.96 3674[2:Rew:3525.0,3415.0] || SkP0(nil,nil) -> neq(skc5,nil)*.
% 4.76/4.96 3688[2:Rew:3525.0,3674.1] || SkP0(nil,nil) -> neq(nil,nil)*.
% 4.76/4.96 3689[2:MRR:3688.1,3279.0] || SkP0(nil,nil)* -> .
% 4.76/4.96 3774[2:Res:70.1,3689.0] || equal(nil,nil)* -> .
% 4.76/4.96 3776[2:Obv:3774.0] || -> .
% 4.76/4.96 3777[2:Spt:3776.0,413.1,3525.0] || equal(skc5,nil)** -> .
% 4.76/4.96 3778[2:Spt:3776.0,413.0,413.2] ssList(u) || -> equal(app(tl(skc5),u),tl(app(skc5,u)))**.
% 4.76/4.96 3779[2:MRR:451.1,3777.0] || -> ssList(tl(skc5))*.
% 4.76/4.96 3780[2:MRR:450.1,3777.0] || -> ssItem(hd(skc5))*.
% 4.76/4.96 3784[2:MRR:425.0,3777.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 4.76/4.96 5242[0:EqR:143.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 4.76/4.96 5258[0:SSi:5242.1,90.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 4.76/4.96 6169[0:SpR:127.2,5258.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 4.76/4.96 6186[0:Obv:6169.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 4.76/4.96 6187[1:SSi:6186.1,78.1,77.1,74.1,73.1,72.1,76.1,75.1,2825.1,3298.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 4.76/4.96 8758[2:SpR:3784.0,6187.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 4.76/4.96 9404[2:SSi:8758.1,3779.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 4.76/4.96 9405[2:MRR:9404.0,3780.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 4.76/4.96 9571[2:Res:9405.0,3504.3] equalelemsP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 4.76/4.96 9574[2:SSi:9571.1,9571.0,78.0,3780.1,77.0,3780.1,74.0,3780.1,73.0,3780.1,72.0,3780.1,76.0,3780.1,75.0,3780.1,2825.0,3780.1,3298.0,3780.1,78.0,3780.1,77.0,3780.1,74.0,3780.1,73.0,3780.1,72.0,3780.1,76.0,3780.1,75.0,3780.1,2825.0,3780.1,3298.0,3780.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 4.76/4.96 9820[2:Res:3425.1,9574.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 4.76/4.96 9821[2:SSi:9820.0,78.0,3780.1,77.0,3780.1,74.0,3780.1,73.0,3780.1,72.0,3780.1,76.0,3780.1,75.0,3780.1,2825.0,3780.1,3298.0,3780.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 4.76/4.96 9861[2:SpL:9821.0,3299.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 4.76/4.96 9897[2:Obv:9861.1] ssItem(hd(skc5)) || -> .
% 4.76/4.96 9898[2:SSi:9897.0,3780.0] || -> .
% 4.76/4.96 % SZS output end Refutation
% 4.76/4.96 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax8 ax2 ax11 ax14 ax42 ax55 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax46 ax15 ax21 ax23 ax78 ax4 ax81 ax85 ax5 ax86 ax12 ax77
% 4.76/4.96
%------------------------------------------------------------------------------