TSTP Solution File: SWC018+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC018+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 22:01:07 EDT 2022
% Result : Theorem 16.65s 16.82s
% Output : Refutation 18.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC018+1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n014.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 18:27:22 EDT 2022
% 0.13/0.35 % CPUTime :
% 16.65/16.82
% 16.65/16.82 SPASS V 3.9
% 16.65/16.82 SPASS beiseite: Proof found.
% 16.65/16.82 % SZS status Theorem
% 16.65/16.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.65/16.82 SPASS derived 14310 clauses, backtracked 6885 clauses, performed 303 splits and kept 10638 clauses.
% 16.65/16.82 SPASS allocated 116966 KBytes.
% 16.65/16.82 SPASS spent 0:0:16.44 on the problem.
% 16.65/16.82 0:00:00.04 for the input.
% 16.65/16.82 0:00:00.07 for the FLOTTER CNF translation.
% 16.65/16.82 0:00:00.23 for inferences.
% 16.65/16.82 0:00:00.30 for the backtracking.
% 16.65/16.82 0:0:15.50 for the reduction.
% 16.65/16.82
% 16.65/16.82
% 16.65/16.82 Here is a proof with depth 3, length 366 :
% 16.65/16.82 % SZS output start Refutation
% 16.65/16.82 1[0:Inp] || -> ssList(skc7)*.
% 16.65/16.82 2[0:Inp] || -> ssList(skc6)*.
% 16.65/16.82 3[0:Inp] || -> ssList(skc5)*.
% 16.65/16.82 4[0:Inp] || -> equalelemsP(skc5)*.
% 16.65/16.82 7[0:Inp] || -> ssList(nil)*.
% 16.65/16.82 8[0:Inp] || -> cyclefreeP(nil)*.
% 16.65/16.82 9[0:Inp] || -> totalorderP(nil)*.
% 16.65/16.82 10[0:Inp] || -> strictorderP(nil)*.
% 16.65/16.82 11[0:Inp] || -> totalorderedP(nil)*.
% 16.65/16.82 12[0:Inp] || -> strictorderedP(nil)*.
% 16.65/16.82 13[0:Inp] || -> duplicatefreeP(nil)*.
% 16.65/16.82 14[0:Inp] || -> equalelemsP(nil)*.
% 16.65/16.82 60[0:Inp] || -> equal(app(skc5,skc7),skc6)**.
% 16.65/16.82 61[0:Inp] || -> SkP0(u,v)* equal(nil,v).
% 16.65/16.82 63[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 16.65/16.82 64[0:Inp] ssList(u) || -> frontsegP(u,nil)*.
% 16.65/16.82 70[0:Inp] || equal(skc5,nil) -> equal(skc6,nil)**.
% 16.65/16.82 71[0:Inp] || SkP0(skc5,skc6) -> neq(skc6,nil)*.
% 16.65/16.82 72[0:Inp] || equal(nil,u) -> SkP0(u,v)*.
% 16.65/16.82 88[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 16.65/16.82 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf50(u),skf51(u))*.
% 16.65/16.82 108[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 16.65/16.82 130[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 16.65/16.82 143[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 16.65/16.82 153[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 16.65/16.82 155[0:Inp] ssList(u) || neq(u,nil) frontsegP(skc5,u) frontsegP(skc6,u)* SkP0(skc5,skc6) -> .
% 16.65/16.82 174[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 16.65/16.82 175[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 16.65/16.82 223[0:Res:3.0,175.0] || -> totalorderedP(skc5) equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 16.65/16.82 224[0:Res:3.0,174.0] || -> strictorderedP(skc5) equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 16.65/16.82 235[0:Res:3.0,155.0] || neq(skc5,nil) frontsegP(skc6,skc5)* frontsegP(skc5,skc5) SkP0(skc5,skc6) -> .
% 16.65/16.82 251[0:Res:3.0,130.0] ssList(u) || equal(app(skc5,u),nil)** -> equal(skc5,nil).
% 16.65/16.82 256[0:Res:3.0,108.0] ssList(u) || -> neq(skc5,u)* equal(skc5,u).
% 16.65/16.82 269[0:Res:3.0,89.0] || -> cyclefreeP(skc5) leq(skf50(skc5),skf51(skc5))*.
% 16.65/16.82 283[0:Res:3.0,63.0] || -> frontsegP(skc5,skc5)*.
% 16.65/16.82 284[0:Res:3.0,64.0] || -> frontsegP(skc5,nil)*.
% 16.65/16.82 313[0:Res:3.0,153.1] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)) equal(skc5,nil).
% 16.65/16.82 397[0:Res:2.0,175.0] || -> totalorderedP(skc6) equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 16.65/16.82 398[0:Res:2.0,174.0] || -> strictorderedP(skc6) equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 16.65/16.82 409[0:Res:2.0,155.0] || neq(skc6,nil) frontsegP(skc6,skc6)* frontsegP(skc5,skc6) SkP0(skc5,skc6) -> .
% 16.65/16.82 442[0:Res:2.0,88.0] || -> cyclefreeP(skc6) leq(skf51(skc6),skf50(skc6))*.
% 16.65/16.82 457[0:Res:2.0,63.0] || -> frontsegP(skc6,skc6)*.
% 16.65/16.82 487[0:Res:2.0,153.1] ssItem(u) || strictorderedP(cons(u,skc6))* -> lt(u,hd(skc6)) equal(skc6,nil).
% 16.65/16.82 553[0:MRR:235.2,283.0] || SkP0(skc5,skc6) frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 554[0:MRR:409.0,409.1,71.1,457.0] || SkP0(skc5,skc6) frontsegP(skc5,skc6)* -> .
% 16.65/16.82 564[1:Spt:313.3] || -> equal(skc5,nil)**.
% 16.65/16.82 569[1:Rew:564.0,554.0] || SkP0(nil,skc6) frontsegP(skc5,skc6)* -> .
% 16.65/16.82 575[1:Rew:564.0,70.0] || equal(nil,nil) -> equal(skc6,nil)**.
% 16.65/16.82 677[1:Rew:564.0,284.0] || -> frontsegP(nil,nil)*.
% 16.65/16.82 725[1:Obv:575.0] || -> equal(skc6,nil)**.
% 16.65/16.82 899[1:Rew:564.0,569.1,725.0,569.1,725.0,569.0] || SkP0(nil,nil) frontsegP(nil,nil)* -> .
% 16.65/16.82 900[1:MRR:899.1,677.0] || SkP0(nil,nil)* -> .
% 16.65/16.82 1085[1:Res:72.1,900.0] || equal(nil,nil)* -> .
% 16.65/16.82 1086[1:Obv:1085.0] || -> .
% 16.65/16.82 1087[1:Spt:1086.0,313.3,564.0] || equal(skc5,nil)** -> .
% 16.65/16.82 1088[1:Spt:1086.0,313.0,313.1,313.2] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)).
% 16.65/16.82 1097[1:MRR:251.2,1087.0] ssList(u) || equal(app(skc5,u),nil)** -> .
% 16.65/16.82 1102[2:Spt:487.3] || -> equal(skc6,nil)**.
% 16.65/16.82 1110[2:Rew:1102.0,60.0] || -> equal(app(skc5,skc7),nil)**.
% 16.65/16.82 1423[2:SpL:1110.0,1097.1] ssList(skc7) || equal(nil,nil)* -> .
% 16.65/16.82 1426[2:Obv:1423.1] ssList(skc7) || -> .
% 16.65/16.82 1427[2:SSi:1426.0,1.0] || -> .
% 16.65/16.82 1428[2:Spt:1427.0,487.3,1102.0] || equal(skc6,nil)** -> .
% 16.65/16.82 1429[2:Spt:1427.0,487.0,487.1,487.2] ssItem(u) || strictorderedP(cons(u,skc6))* -> lt(u,hd(skc6)).
% 16.65/16.82 1451[3:Spt:223.0] || -> totalorderedP(skc5)*.
% 16.65/16.82 1455[4:Spt:224.0] || -> strictorderedP(skc5)*.
% 16.65/16.82 1458[5:Spt:397.0] || -> totalorderedP(skc6)*.
% 16.65/16.82 1462[6:Spt:398.0] || -> strictorderedP(skc6)*.
% 16.65/16.82 1465[7:Spt:269.0] || -> cyclefreeP(skc5)*.
% 16.65/16.82 1467[8:Spt:442.0] || -> cyclefreeP(skc6)*.
% 16.65/16.82 1470[9:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 1472[9:Res:61.0,1470.0] || -> equal(skc6,nil)**.
% 16.65/16.82 1473[9:MRR:1472.0,1428.0] || -> .
% 16.65/16.82 1474[9:Spt:1473.0,71.0,1470.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 1475[9:Spt:1473.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 1477[9:MRR:553.0,1474.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 3697[0:SpL:60.0,143.3] ssList(skc5) ssList(u) ssList(skc7) || equal(skc6,u) -> frontsegP(u,skc5)*.
% 16.65/16.82 9832[7:SSi:3697.2,3697.0,1.0,3.0,4.0,1451.0,1455.0,1465.0] ssList(u) || equal(skc6,u) -> frontsegP(u,skc5)*.
% 16.65/16.82 10865[9:Res:9832.2,1477.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 10866[9:Obv:10865.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 11048[9:SSi:10866.0,2.0,1458.0,1462.0,1467.0] || neq(skc5,nil)* -> .
% 16.65/16.82 11132[9:Res:256.1,11048.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 11135[9:SSi:11132.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 11136[9:MRR:11135.0,1087.0] || -> .
% 16.65/16.82 11140[8:Spt:11136.0,442.0,1467.0] || cyclefreeP(skc6)* -> .
% 16.65/16.82 11141[8:Spt:11136.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 16.65/16.82 11179[9:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 11181[9:Res:61.0,11179.0] || -> equal(skc6,nil)**.
% 16.65/16.82 11182[9:MRR:11181.0,1428.0] || -> .
% 16.65/16.82 11183[9:Spt:11182.0,71.0,11179.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 11184[9:Spt:11182.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 11186[9:MRR:553.0,11183.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 12485[9:Res:9832.2,11186.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 12486[9:Obv:12485.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 12716[9:SSi:12486.0,2.0,1462.0,1458.0] || neq(skc5,nil)* -> .
% 16.65/16.82 12826[9:Res:256.1,12716.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 12829[9:SSi:12826.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 12830[9:MRR:12829.0,1087.0] || -> .
% 16.65/16.82 12834[7:Spt:12830.0,269.0,1465.0] || cyclefreeP(skc5)* -> .
% 16.65/16.82 12835[7:Spt:12830.0,269.1] || -> leq(skf50(skc5),skf51(skc5))*.
% 16.65/16.82 12850[4:SSi:3697.2,3697.0,1.0,3.0,4.0,1451.0,1455.0] ssList(u) || equal(skc6,u) -> frontsegP(u,skc5)*.
% 16.65/16.82 12878[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 12880[8:Res:61.0,12878.0] || -> equal(skc6,nil)**.
% 16.65/16.82 12881[8:MRR:12880.0,1428.0] || -> .
% 16.65/16.82 12882[8:Spt:12881.0,71.0,12878.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 12883[8:Spt:12881.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 12885[8:MRR:553.0,12882.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 14526[8:Res:12850.2,12885.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 14527[8:Obv:14526.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 14819[8:SSi:14527.0,2.0,1458.0,1462.0] || neq(skc5,nil)* -> .
% 16.65/16.82 14875[8:Res:256.1,14819.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 14878[8:SSi:14875.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 14879[8:MRR:14878.0,1087.0] || -> .
% 16.65/16.82 14883[6:Spt:14879.0,398.0,1462.0] || strictorderedP(skc6)* -> .
% 16.65/16.82 14884[6:Spt:14879.0,398.1] || -> equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 16.65/16.82 14992[7:Spt:442.0] || -> cyclefreeP(skc6)*.
% 16.65/16.82 14998[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 15000[8:Res:61.0,14998.0] || -> equal(skc6,nil)**.
% 16.65/16.82 15001[8:MRR:15000.0,1428.0] || -> .
% 16.65/16.82 15002[8:Spt:15001.0,71.0,14998.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 15003[8:Spt:15001.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 15005[8:MRR:553.0,15002.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 15318[8:Res:12850.2,15005.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 15320[8:Obv:15318.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 15496[8:SSi:15320.0,2.0,1458.0,14992.0] || neq(skc5,nil)* -> .
% 16.65/16.82 15600[8:Res:256.1,15496.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 15603[8:SSi:15600.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 15604[8:MRR:15603.0,1087.0] || -> .
% 16.65/16.82 15608[7:Spt:15604.0,442.0,14992.0] || cyclefreeP(skc6)* -> .
% 16.65/16.82 15609[7:Spt:15604.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 16.65/16.82 15660[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 15662[8:Res:61.0,15660.0] || -> equal(skc6,nil)**.
% 16.65/16.82 15663[8:MRR:15662.0,1428.0] || -> .
% 16.65/16.82 15664[8:Spt:15663.0,71.0,15660.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 15665[8:Spt:15663.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 15667[8:MRR:553.0,15664.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 15940[8:Res:12850.2,15667.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 15942[8:Obv:15940.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 16059[8:SSi:15942.0,2.0,1458.0] || neq(skc5,nil)* -> .
% 16.65/16.82 16134[8:Res:256.1,16059.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 16137[8:SSi:16134.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 16138[8:MRR:16137.0,1087.0] || -> .
% 16.65/16.82 16142[5:Spt:16138.0,397.0,1458.0] || totalorderedP(skc6)* -> .
% 16.65/16.82 16143[5:Spt:16138.0,397.1] || -> equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 16.65/16.82 16250[6:Spt:398.0] || -> strictorderedP(skc6)*.
% 16.65/16.82 16259[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 16261[7:Res:61.0,16259.0] || -> equal(skc6,nil)**.
% 16.65/16.82 16262[7:MRR:16261.0,1428.0] || -> .
% 16.65/16.82 16263[7:Spt:16262.0,71.0,16259.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 16264[7:Spt:16262.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 16266[7:MRR:553.0,16263.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 16570[7:Res:12850.2,16266.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 16572[7:Obv:16570.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 16853[7:SSi:16572.0,2.0,16250.0] || neq(skc5,nil)* -> .
% 16.65/16.82 16943[7:Res:256.1,16853.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 16946[7:SSi:16943.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 16947[7:MRR:16946.0,1087.0] || -> .
% 16.65/16.82 16951[6:Spt:16947.0,398.0,16250.0] || strictorderedP(skc6)* -> .
% 16.65/16.82 16952[6:Spt:16947.0,398.1] || -> equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 16.65/16.82 17056[7:Spt:442.0] || -> cyclefreeP(skc6)*.
% 16.65/16.82 17062[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 17064[8:Res:61.0,17062.0] || -> equal(skc6,nil)**.
% 16.65/16.82 17065[8:MRR:17064.0,1428.0] || -> .
% 16.65/16.82 17066[8:Spt:17065.0,71.0,17062.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 17067[8:Spt:17065.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 17069[8:MRR:553.0,17066.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 17299[8:Res:12850.2,17069.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 17301[8:Obv:17299.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 17419[8:SSi:17301.0,2.0,17056.0] || neq(skc5,nil)* -> .
% 16.65/16.82 17492[8:Res:256.1,17419.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 17495[8:SSi:17492.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 17496[8:MRR:17495.0,1087.0] || -> .
% 16.65/16.82 17500[7:Spt:17496.0,442.0,17056.0] || cyclefreeP(skc6)* -> .
% 16.65/16.82 17501[7:Spt:17496.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 16.65/16.82 17518[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 17520[8:Res:61.0,17518.0] || -> equal(skc6,nil)**.
% 16.65/16.82 17521[8:MRR:17520.0,1428.0] || -> .
% 16.65/16.82 17522[8:Spt:17521.0,71.0,17518.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 17523[8:Spt:17521.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 17525[8:MRR:553.0,17522.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 17793[8:Res:12850.2,17525.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 17795[8:Obv:17793.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 17909[8:SSi:17795.0,2.0] || neq(skc5,nil)* -> .
% 16.65/16.82 17984[8:Res:256.1,17909.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 17987[8:SSi:17984.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 17988[8:MRR:17987.0,1087.0] || -> .
% 16.65/16.82 17992[4:Spt:17988.0,224.0,1455.0] || strictorderedP(skc5)* -> .
% 16.65/16.82 17993[4:Spt:17988.0,224.1] || -> equal(app(app(skf72(skc5),cons(skf70(skc5),skf73(skc5))),cons(skf71(skc5),skf74(skc5))),skc5)**.
% 16.65/16.82 18017[3:SSi:3697.2,3697.0,1.0,3.0,4.0,1451.0] ssList(u) || equal(skc6,u) -> frontsegP(u,skc5)*.
% 16.65/16.82 18106[5:Spt:398.0] || -> strictorderedP(skc6)*.
% 16.65/16.82 18115[6:Spt:397.0] || -> totalorderedP(skc6)*.
% 16.65/16.82 18121[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 18123[7:Res:61.0,18121.0] || -> equal(skc6,nil)**.
% 16.65/16.82 18124[7:MRR:18123.0,1428.0] || -> .
% 16.65/16.82 18125[7:Spt:18124.0,71.0,18121.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 18126[7:Spt:18124.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 18128[7:MRR:553.0,18125.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 18976[7:Res:18017.2,18128.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 18977[7:Obv:18976.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 19283[7:SSi:18977.0,2.0,18106.0,18115.0] || neq(skc5,nil)* -> .
% 16.65/16.82 19341[7:Res:256.1,19283.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 19344[7:SSi:19341.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 19345[7:MRR:19344.0,1087.0] || -> .
% 16.65/16.82 19349[6:Spt:19345.0,397.0,18115.0] || totalorderedP(skc6)* -> .
% 16.65/16.82 19350[6:Spt:19345.0,397.1] || -> equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 16.65/16.82 19461[7:Spt:442.0] || -> cyclefreeP(skc6)*.
% 16.65/16.82 19470[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 19472[8:Res:61.0,19470.0] || -> equal(skc6,nil)**.
% 16.65/16.82 19473[8:MRR:19472.0,1428.0] || -> .
% 16.65/16.82 19474[8:Spt:19473.0,71.0,19470.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 19475[8:Spt:19473.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 19477[8:MRR:553.0,19474.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 19508[8:Res:18017.2,19477.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 19510[8:Obv:19508.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 19626[8:SSi:19510.0,2.0,18106.0,19461.0] || neq(skc5,nil)* -> .
% 16.65/16.82 19699[8:Res:256.1,19626.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 19702[8:SSi:19699.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 19703[8:MRR:19702.0,1087.0] || -> .
% 16.65/16.82 19707[7:Spt:19703.0,442.0,19461.0] || cyclefreeP(skc6)* -> .
% 16.65/16.82 19708[7:Spt:19703.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 16.65/16.82 19726[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 19728[8:Res:61.0,19726.0] || -> equal(skc6,nil)**.
% 16.65/16.82 19729[8:MRR:19728.0,1428.0] || -> .
% 16.65/16.82 19730[8:Spt:19729.0,71.0,19726.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 19731[8:Spt:19729.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 19733[8:MRR:553.0,19730.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 19755[8:Res:18017.2,19733.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 19757[8:Obv:19755.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 19868[8:SSi:19757.0,2.0,18106.0] || neq(skc5,nil)* -> .
% 16.65/16.82 19948[8:Res:256.1,19868.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 19951[8:SSi:19948.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 19952[8:MRR:19951.0,1087.0] || -> .
% 16.65/16.82 19956[5:Spt:19952.0,398.0,18106.0] || strictorderedP(skc6)* -> .
% 16.65/16.82 19957[5:Spt:19952.0,398.1] || -> equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 16.65/16.82 20040[6:Spt:397.0] || -> totalorderedP(skc6)*.
% 16.65/16.82 20050[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 20052[7:Res:61.0,20050.0] || -> equal(skc6,nil)**.
% 16.65/16.82 20053[7:MRR:20052.0,1428.0] || -> .
% 16.65/16.82 20054[7:Spt:20053.0,71.0,20050.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 20055[7:Spt:20053.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 20057[7:MRR:553.0,20054.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 16.65/16.82 20085[7:Res:18017.2,20057.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 16.65/16.82 20087[7:Obv:20085.1] ssList(skc6) || neq(skc5,nil)* -> .
% 16.65/16.82 20286[7:SSi:20087.0,2.0,20040.0] || neq(skc5,nil)* -> .
% 16.65/16.82 20306[7:Res:256.1,20286.0] ssList(nil) || -> equal(skc5,nil)**.
% 16.65/16.82 20309[7:SSi:20306.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 16.65/16.82 20310[7:MRR:20309.0,1087.0] || -> .
% 16.65/16.82 20314[6:Spt:20310.0,397.0,20040.0] || totalorderedP(skc6)* -> .
% 16.65/16.82 20315[6:Spt:20310.0,397.1] || -> equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 16.65/16.82 20390[7:Spt:442.0] || -> cyclefreeP(skc6)*.
% 16.65/16.82 20393[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 16.65/16.82 20395[8:Res:61.0,20393.0] || -> equal(skc6,nil)**.
% 16.65/16.82 20396[8:MRR:20395.0,1428.0] || -> .
% 16.65/16.82 20397[8:Spt:20396.0,71.0,20393.0] || -> SkP0(skc5,skc6)*.
% 16.65/16.82 20398[8:Spt:20396.0,71.1] || -> neq(skc6,nil)*.
% 16.65/16.82 20400[8:MRR:553.0,20397.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 20416[8:Res:18017.2,20400.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 20418[8:Obv:20416.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 20534[8:SSi:20418.0,2.0,20390.0] || neq(skc5,nil)* -> .
% 18.46/18.68 20607[8:Res:256.1,20534.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 20610[8:SSi:20607.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 20611[8:MRR:20610.0,1087.0] || -> .
% 18.46/18.68 20615[7:Spt:20611.0,442.0,20390.0] || cyclefreeP(skc6)* -> .
% 18.46/18.68 20616[7:Spt:20611.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 18.46/18.68 20632[8:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 20634[8:Res:61.0,20632.0] || -> equal(skc6,nil)**.
% 18.46/18.68 20635[8:MRR:20634.0,1428.0] || -> .
% 18.46/18.68 20636[8:Spt:20635.0,71.0,20632.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 20637[8:Spt:20635.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 20639[8:MRR:553.0,20636.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 20658[8:Res:18017.2,20639.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 20660[8:Obv:20658.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 20768[8:SSi:20660.0,2.0] || neq(skc5,nil)* -> .
% 18.46/18.68 20842[8:Res:256.1,20768.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 20845[8:SSi:20842.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 20846[8:MRR:20845.0,1087.0] || -> .
% 18.46/18.68 20850[3:Spt:20846.0,223.0,1451.0] || totalorderedP(skc5)* -> .
% 18.46/18.68 20851[3:Spt:20846.0,223.1] || -> equal(app(app(skf67(skc5),cons(skf65(skc5),skf68(skc5))),cons(skf66(skc5),skf69(skc5))),skc5)**.
% 18.46/18.68 20873[0:SSi:3697.2,3697.0,1.0,3.0,4.0] ssList(u) || equal(skc6,u) -> frontsegP(u,skc5)*.
% 18.46/18.68 20959[4:Spt:397.0] || -> totalorderedP(skc6)*.
% 18.46/18.68 20969[5:Spt:398.0] || -> strictorderedP(skc6)*.
% 18.46/18.68 20974[6:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 20976[6:Res:61.0,20974.0] || -> equal(skc6,nil)**.
% 18.46/18.68 20977[6:MRR:20976.0,1428.0] || -> .
% 18.46/18.68 20978[6:Spt:20977.0,71.0,20974.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 20979[6:Spt:20977.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 20981[6:MRR:553.0,20978.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 21751[6:Res:20873.2,20981.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 21752[6:Obv:21751.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 22027[6:SSi:21752.0,2.0,20959.0,20969.0] || neq(skc5,nil)* -> .
% 18.46/18.68 22085[6:Res:256.1,22027.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 22088[6:SSi:22085.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 22089[6:MRR:22088.0,1087.0] || -> .
% 18.46/18.68 22093[5:Spt:22089.0,398.0,20969.0] || strictorderedP(skc6)* -> .
% 18.46/18.68 22094[5:Spt:22089.0,398.1] || -> equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 18.46/18.68 22215[6:Spt:442.0] || -> cyclefreeP(skc6)*.
% 18.46/18.68 22221[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 22223[7:Res:61.0,22221.0] || -> equal(skc6,nil)**.
% 18.46/18.68 22224[7:MRR:22223.0,1428.0] || -> .
% 18.46/18.68 22225[7:Spt:22224.0,71.0,22221.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 22226[7:Spt:22224.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 22228[7:MRR:553.0,22225.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 22269[7:Res:20873.2,22228.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 22271[7:Obv:22269.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 22385[7:SSi:22271.0,2.0,20959.0,22215.0] || neq(skc5,nil)* -> .
% 18.46/18.68 22464[7:Res:256.1,22385.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 22467[7:SSi:22464.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 22468[7:MRR:22467.0,1087.0] || -> .
% 18.46/18.68 22472[6:Spt:22468.0,442.0,22215.0] || cyclefreeP(skc6)* -> .
% 18.46/18.68 22473[6:Spt:22468.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 18.46/18.68 22490[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 22492[7:Res:61.0,22490.0] || -> equal(skc6,nil)**.
% 18.46/18.68 22493[7:MRR:22492.0,1428.0] || -> .
% 18.46/18.68 22494[7:Spt:22493.0,71.0,22490.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 22495[7:Spt:22493.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 22497[7:MRR:553.0,22494.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 22518[7:Res:20873.2,22497.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 22520[7:Obv:22518.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 22631[7:SSi:22520.0,2.0,20959.0] || neq(skc5,nil)* -> .
% 18.46/18.68 22704[7:Res:256.1,22631.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 22707[7:SSi:22704.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 22708[7:MRR:22707.0,1087.0] || -> .
% 18.46/18.68 22712[4:Spt:22708.0,397.0,20959.0] || totalorderedP(skc6)* -> .
% 18.46/18.68 22713[4:Spt:22708.0,397.1] || -> equal(app(app(skf67(skc6),cons(skf65(skc6),skf68(skc6))),cons(skf66(skc6),skf69(skc6))),skc6)**.
% 18.46/18.68 22803[5:Spt:398.0] || -> strictorderedP(skc6)*.
% 18.46/18.68 22808[6:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 22810[6:Res:61.0,22808.0] || -> equal(skc6,nil)**.
% 18.46/18.68 22811[6:MRR:22810.0,1428.0] || -> .
% 18.46/18.68 22812[6:Spt:22811.0,71.0,22808.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 22813[6:Spt:22811.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 22815[6:MRR:553.0,22812.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 22855[6:Res:20873.2,22815.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 22857[6:Obv:22855.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 23057[6:SSi:22857.0,2.0,22803.0] || neq(skc5,nil)* -> .
% 18.46/18.68 23073[6:Res:256.1,23057.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 23076[6:SSi:23073.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 23077[6:MRR:23076.0,1087.0] || -> .
% 18.46/18.68 23081[5:Spt:23077.0,398.0,22803.0] || strictorderedP(skc6)* -> .
% 18.46/18.68 23082[5:Spt:23077.0,398.1] || -> equal(app(app(skf72(skc6),cons(skf70(skc6),skf73(skc6))),cons(skf71(skc6),skf74(skc6))),skc6)**.
% 18.46/18.68 23156[6:Spt:442.0] || -> cyclefreeP(skc6)*.
% 18.46/18.68 23161[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 23163[7:Res:61.0,23161.0] || -> equal(skc6,nil)**.
% 18.46/18.68 23164[7:MRR:23163.0,1428.0] || -> .
% 18.46/18.68 23165[7:Spt:23164.0,71.0,23161.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 23166[7:Spt:23164.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 23168[7:MRR:553.0,23165.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 23185[7:Res:20873.2,23168.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 23187[7:Obv:23185.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 23299[7:SSi:23187.0,2.0,23156.0] || neq(skc5,nil)* -> .
% 18.46/18.68 23373[7:Res:256.1,23299.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 23376[7:SSi:23373.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 23377[7:MRR:23376.0,1087.0] || -> .
% 18.46/18.68 23381[6:Spt:23377.0,442.0,23156.0] || cyclefreeP(skc6)* -> .
% 18.46/18.68 23382[6:Spt:23377.0,442.1] || -> leq(skf51(skc6),skf50(skc6))*.
% 18.46/18.68 23397[7:Spt:71.0] || SkP0(skc5,skc6)* -> .
% 18.46/18.68 23399[7:Res:61.0,23397.0] || -> equal(skc6,nil)**.
% 18.46/18.68 23400[7:MRR:23399.0,1428.0] || -> .
% 18.46/18.68 23401[7:Spt:23400.0,71.0,23397.0] || -> SkP0(skc5,skc6)*.
% 18.46/18.68 23402[7:Spt:23400.0,71.1] || -> neq(skc6,nil)*.
% 18.46/18.68 23404[7:MRR:553.0,23401.0] || frontsegP(skc6,skc5)* neq(skc5,nil) -> .
% 18.46/18.68 23426[7:Res:20873.2,23404.0] ssList(skc6) || equal(skc6,skc6) neq(skc5,nil)* -> .
% 18.46/18.68 23428[7:Obv:23426.1] ssList(skc6) || neq(skc5,nil)* -> .
% 18.46/18.68 23538[7:SSi:23428.0,2.0] || neq(skc5,nil)* -> .
% 18.46/18.68 23612[7:Res:256.1,23538.0] ssList(nil) || -> equal(skc5,nil)**.
% 18.46/18.68 23615[7:SSi:23612.0,14.0,13.0,10.0,9.0,8.0,12.0,11.0,7.0] || -> equal(skc5,nil)**.
% 18.46/18.68 23616[7:MRR:23615.0,1087.0] || -> .
% 18.46/18.68 % SZS output end Refutation
% 18.46/18.68 Formulae used in the proof : co1 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax42 ax45 ax8 ax2 ax15 ax83 ax5 ax70 ax12 ax11
% 18.46/18.68
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