TSTP Solution File: SWC197+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC197+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 22:02:24 EDT 2022
% Result : Theorem 63.83s 64.03s
% Output : Refutation 71.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC197+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 12 10:44:44 EDT 2022
% 0.14/0.35 % CPUTime :
% 63.83/64.03
% 63.83/64.03 SPASS V 3.9
% 63.83/64.03 SPASS beiseite: Proof found.
% 63.83/64.03 % SZS status Theorem
% 63.83/64.03 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.83/64.03 SPASS derived 24842 clauses, backtracked 11492 clauses, performed 44 splits and kept 17143 clauses.
% 63.83/64.03 SPASS allocated 135496 KBytes.
% 63.83/64.03 SPASS spent 0:01:03.63 on the problem.
% 63.83/64.03 0:00:00.04 for the input.
% 63.83/64.03 0:00:00.07 for the FLOTTER CNF translation.
% 63.83/64.03 0:00:00.43 for inferences.
% 63.83/64.03 0:00:02.12 for the backtracking.
% 63.83/64.03 0:01:00.56 for the reduction.
% 63.83/64.03
% 63.83/64.03
% 63.83/64.03 Here is a proof with depth 7, length 325 :
% 63.83/64.03 % SZS output start Refutation
% 63.83/64.03 1[0:Inp] || -> ssList(skc15)*.
% 63.83/64.03 2[0:Inp] || -> ssList(skc14)*.
% 63.83/64.03 3[0:Inp] || -> ssList(skc13)*.
% 63.83/64.03 4[0:Inp] || -> ssItem(skc12)*.
% 63.83/64.03 5[0:Inp] || -> ssItem(skc11)*.
% 63.83/64.03 6[0:Inp] || -> ssList(skc10)*.
% 63.83/64.03 7[0:Inp] || -> ssList(skc9)*.
% 63.83/64.03 8[0:Inp] || -> ssItem(skc17)*.
% 63.83/64.03 9[0:Inp] || -> ssItem(skc16)*.
% 63.83/64.03 10[0:Inp] || -> ssList(nil)*.
% 63.83/64.03 11[0:Inp] || -> cyclefreeP(nil)*.
% 63.83/64.03 12[0:Inp] || -> totalorderP(nil)*.
% 63.83/64.03 13[0:Inp] || -> strictorderP(nil)*.
% 63.83/64.03 14[0:Inp] || -> totalorderedP(nil)*.
% 63.83/64.03 15[0:Inp] || -> strictorderedP(nil)*.
% 63.83/64.03 16[0:Inp] || -> duplicatefreeP(nil)*.
% 63.83/64.03 17[0:Inp] || -> equalelemsP(nil)*.
% 63.83/64.03 18[0:Inp] || -> segmentP(skc10,skc9)*.
% 63.83/64.03 19[0:Inp] || -> ssItem(skf45(u))*.
% 63.83/64.03 25[0:Inp] || -> ssList(skf59(u))*.
% 63.83/64.03 26[0:Inp] || -> ssList(skf58(u))*.
% 63.83/64.03 27[0:Inp] || -> ssList(skf57(u))*.
% 63.83/64.03 28[0:Inp] || -> ssItem(skf56(u))*.
% 63.83/64.03 29[0:Inp] || -> ssItem(skf55(u))*.
% 63.83/64.03 30[0:Inp] || -> ssList(skf64(u))*.
% 63.83/64.03 31[0:Inp] || -> ssList(skf63(u))*.
% 63.83/64.03 32[0:Inp] || -> ssList(skf62(u))*.
% 63.83/64.03 33[0:Inp] || -> ssItem(skf61(u))*.
% 63.83/64.03 34[0:Inp] || -> ssItem(skf60(u))*.
% 63.83/64.03 58[0:Inp] || equal(skc17,skc16)** -> .
% 63.83/64.03 65[0:Inp] || neq(skc10,nil)* -> singletonP(skc9).
% 63.83/64.03 69[0:Inp] ssList(u) || -> rearsegP(u,u)*.
% 63.83/64.03 74[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 63.83/64.03 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 63.83/64.03 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 63.83/64.03 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 63.83/64.03 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 63.83/64.03 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 63.83/64.03 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 63.83/64.03 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 63.83/64.03 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 63.83/64.03 84[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 63.83/64.03 87[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 63.83/64.03 88[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 63.83/64.03 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 63.83/64.03 92[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 63.83/64.03 93[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 63.83/64.03 94[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 63.83/64.03 98[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 63.83/64.03 101[0:Inp] ssList(u) || leq(skf55(u),skf56(u))* -> totalorderP(u).
% 63.83/64.03 103[0:Inp] ssList(u) || lt(skf60(u),skf61(u))* -> strictorderP(u).
% 63.83/64.03 108[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 63.83/64.03 109[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 63.83/64.03 110[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 63.83/64.03 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 63.83/64.03 113[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 63.83/64.03 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 63.83/64.03 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 63.83/64.03 129[0:Inp] || -> equal(app(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil)),skc14),skc9)**.
% 63.83/64.03 130[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 63.83/64.03 131[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 63.83/64.03 132[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 63.83/64.03 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 63.83/64.03 142[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(v,u).
% 63.83/64.03 145[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 63.83/64.03 146[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 63.83/64.03 153[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(w,v) -> rearsegP(app(u,w),v)*.
% 63.83/64.03 154[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 63.83/64.03 155[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 63.83/64.03 156[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 63.83/64.03 161[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 63.83/64.03 162[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,u),app(v,w))* -> equal(u,w).
% 63.83/64.03 163[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,v),app(w,v))* -> equal(u,w).
% 63.83/64.03 172[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 63.83/64.03 175[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 63.83/64.03 176[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 63.83/64.03 177[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 63.83/64.03 178[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 63.83/64.03 188[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 63.83/64.03 192[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) ssItem(y) ssItem(z) strictorderedP(u) || equal(app(app(x,cons(z,w)),cons(y,v)),u)* -> lt(z,y).
% 63.83/64.03 193[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) ssItem(y) ssItem(z) totalorderedP(u) || equal(app(app(x,cons(z,w)),cons(y,v)),u)* -> leq(z,y).
% 63.83/64.03 219[0:Res:7.0,178.0] || -> totalorderP(skc9) equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 63.83/64.03 220[0:Res:7.0,177.0] || -> strictorderP(skc9) equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 63.83/64.03 221[0:Res:7.0,176.0] || -> totalorderedP(skc9) equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 63.83/64.03 222[0:Res:7.0,175.0] || -> strictorderedP(skc9) equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 63.83/64.03 231[0:Res:7.0,162.0] ssList(u) ssList(v) || equal(app(v,u),app(v,skc9))* -> equal(u,skc9).
% 63.83/64.03 239[0:Res:7.0,156.0] ssList(u) || -> equal(skc9,nil) equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 63.83/64.03 245[0:Res:7.0,135.0] ssList(u) || -> equal(skc9,nil) equal(hd(app(skc9,u)),hd(skc9))**.
% 63.83/64.03 246[0:Res:7.0,130.0] ssItem(u) || -> equal(app(cons(u,nil),skc9),cons(u,skc9))**.
% 63.83/64.03 248[0:Res:7.0,132.0] ssList(u) || equal(app(skc9,u),nil)** -> equal(skc9,nil).
% 63.83/64.03 251[0:Res:7.0,119.0] || -> equal(skc9,nil) equal(cons(hd(skc9),tl(skc9)),skc9)**.
% 63.83/64.03 252[0:Res:7.0,108.1] singletonP(skc9) || -> equal(cons(skf45(skc9),nil),skc9)**.
% 63.83/64.03 254[0:Res:7.0,110.0] ssItem(u) || equal(cons(u,skc9),skc9)** -> .
% 63.83/64.03 256[0:Res:7.0,112.0] ssItem(u) || -> equal(hd(cons(u,skc9)),u)**.
% 63.83/64.03 265[0:Res:7.0,89.0] || -> cyclefreeP(skc9) leq(skf51(skc9),skf50(skc9))*.
% 63.83/64.03 268[0:Res:7.0,92.0] ssItem(u) || -> ssList(cons(u,skc9))*.
% 63.83/64.03 269[0:Res:7.0,93.0] ssList(u) || -> ssList(app(skc9,u))*.
% 63.83/64.03 274[0:Res:7.0,98.0] || segmentP(nil,skc9)* -> equal(skc9,nil).
% 63.83/64.03 276[0:Res:7.0,87.0] || -> ssItem(hd(skc9))* equal(skc9,nil).
% 63.83/64.03 278[0:Res:7.0,83.0] || -> equal(app(nil,skc9),skc9)**.
% 63.83/64.03 309[0:Res:7.0,155.1] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)) equal(skc9,nil).
% 63.83/64.03 326[0:Res:7.0,93.1] ssList(u) || -> ssList(app(u,skc9))*.
% 63.83/64.03 348[0:Res:7.0,153.2] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(app(skc9,v),u)*.
% 63.83/64.03 424[0:Res:6.0,109.0] ssList(u) || -> neq(skc10,u)* equal(skc10,u).
% 63.83/64.03 479[0:Res:6.0,154.1] ssItem(u) || totalorderedP(cons(u,skc10))* -> leq(u,hd(skc10)) equal(skc10,nil).
% 63.83/64.03 545[1:Spt:245.0,245.2] ssList(u) || -> equal(hd(app(skc9,u)),hd(skc9))**.
% 63.83/64.03 547[2:Spt:239.0,239.2] ssList(u) || -> equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 63.83/64.03 553[3:Spt:309.3] || -> equal(skc9,nil)**.
% 63.83/64.03 554[3:Rew:553.0,545.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 63.83/64.03 572[3:Rew:553.0,268.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 63.83/64.03 573[3:Rew:553.0,256.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 63.83/64.03 727[3:Rew:83.1,554.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 63.83/64.03 1181[3:SpR:573.1,727.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 63.83/64.03 1184[3:SSi:1181.1,81.1,80.1,77.1,76.1,75.1,79.1,78.1,572.1] ssItem(u) || -> equal(u,hd(nil))*.
% 63.83/64.03 1251[3:SpR:1184.1,1184.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 63.83/64.03 1293[3:EmS:1251.0,4.0] ssItem(u) || -> equal(u,skc12)*.
% 63.83/64.03 1317[3:EmS:1293.0,8.0] || -> equal(skc17,skc12)**.
% 63.83/64.03 1318[3:EmS:1293.0,9.0] || -> equal(skc16,skc12)**.
% 63.83/64.03 1321[3:Rew:1317.0,58.0] || equal(skc16,skc12)** -> .
% 63.83/64.03 1426[3:Rew:1318.0,1321.0] || equal(skc12,skc12)* -> .
% 63.83/64.03 1427[3:Obv:1426.0] || -> .
% 63.83/64.03 1458[3:Spt:1427.0,309.3,553.0] || equal(skc9,nil)** -> .
% 63.83/64.03 1459[3:Spt:1427.0,309.0,309.1,309.2] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)).
% 63.83/64.03 1461[3:MRR:276.1,1458.0] || -> ssItem(hd(skc9))*.
% 63.83/64.03 1462[3:MRR:274.1,1458.0] || segmentP(nil,skc9)* -> .
% 63.83/64.03 1465[3:MRR:251.0,1458.0] || -> equal(cons(hd(skc9),tl(skc9)),skc9)**.
% 63.83/64.03 1468[3:MRR:248.2,1458.0] ssList(u) || equal(app(skc9,u),nil)** -> .
% 63.83/64.03 1473[4:Spt:479.3] || -> equal(skc10,nil)**.
% 63.83/64.03 1481[4:Rew:1473.0,18.0] || -> segmentP(nil,skc9)*.
% 63.83/64.03 1626[4:MRR:1481.0,1462.0] || -> .
% 63.83/64.03 1737[4:Spt:1626.0,479.3,1473.0] || equal(skc10,nil)** -> .
% 63.83/64.03 1738[4:Spt:1626.0,479.0,479.1,479.2] ssItem(u) || totalorderedP(cons(u,skc10))* -> leq(u,hd(skc10)).
% 63.83/64.03 1752[5:Spt:222.0] || -> strictorderedP(skc9)*.
% 63.83/64.03 1755[6:Spt:221.0] || -> totalorderedP(skc9)*.
% 63.83/64.03 1766[7:Spt:265.0] || -> cyclefreeP(skc9)*.
% 63.83/64.03 1770[8:Spt:220.0] || -> strictorderP(skc9)*.
% 63.83/64.03 1771[9:Spt:219.0] || -> totalorderP(skc9)*.
% 63.83/64.03 1782[10:Spt:65.0] || neq(skc10,nil)* -> .
% 63.83/64.03 1831[10:Res:424.1,1782.0] ssList(nil) || -> equal(skc10,nil)**.
% 63.83/64.03 1832[10:SSi:1831.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 63.83/64.03 1833[10:MRR:1832.0,1737.0] || -> .
% 63.83/64.03 1834[10:Spt:1833.0,65.0,1782.0] || -> neq(skc10,nil)*.
% 63.83/64.03 1835[10:Spt:1833.0,65.1] || -> singletonP(skc9)*.
% 63.83/64.03 1836[10:MRR:252.0,1835.0] || -> equal(cons(skf45(skc9),nil),skc9)**.
% 63.83/64.03 1837[10:SpR:1836.0,81.1] ssItem(skf45(skc9)) || -> equalelemsP(skc9)*.
% 63.83/64.03 1838[10:SpR:1836.0,80.1] ssItem(skf45(skc9)) || -> duplicatefreeP(skc9)*.
% 63.83/64.03 1846[10:SSi:1837.0,19.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0] || -> equalelemsP(skc9)*.
% 63.83/64.03 1848[10:SSi:1838.0,19.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0] || -> duplicatefreeP(skc9)*.
% 63.83/64.03 1914[0:SpR:108.2,75.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> cyclefreeP(u)*.
% 63.83/64.03 1915[0:SpR:108.2,79.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> strictorderedP(u)*.
% 63.83/64.03 1916[0:SpR:108.2,78.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> totalorderedP(u)*.
% 63.83/64.03 1927[0:SSi:1914.2,19.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 63.83/64.03 1928[0:SSi:1915.2,19.0] ssList(u) singletonP(u) || -> strictorderedP(u)*.
% 63.83/64.03 1929[0:SSi:1916.2,19.0] ssList(u) singletonP(u) || -> totalorderedP(u)*.
% 63.83/64.03 1943[10:SpR:1836.0,113.2] ssItem(skf45(skc9)) ssList(nil) || -> equal(tl(skc9),nil)**.
% 63.83/64.03 1945[10:SSi:1943.1,1943.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,19.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || -> equal(tl(skc9),nil)**.
% 63.83/64.03 1947[10:Rew:1945.0,1465.0] || -> equal(cons(hd(skc9),nil),skc9)**.
% 63.83/64.03 1948[10:Rew:1945.0,547.1] ssList(u) || -> equal(tl(app(skc9,u)),app(nil,u))**.
% 63.83/64.03 1950[10:Rew:83.1,1948.1] ssList(u) || -> equal(tl(app(skc9,u)),u)**.
% 63.83/64.03 1984[0:SpR:108.2,112.2] ssList(u) singletonP(u) ssItem(skf45(u)) ssList(nil) || -> equal(skf45(u),hd(u))**.
% 63.83/64.03 1990[0:SSi:1984.3,1984.2,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,19.0] ssList(u) singletonP(u) || -> equal(skf45(u),hd(u))**.
% 63.83/64.03 1991[0:Rew:1990.2,108.2] ssList(u) singletonP(u) || -> equal(cons(hd(u),nil),u)**.
% 63.83/64.03 2130[10:SpR:1950.1,119.2] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(hd(app(skc9,u)),u),app(skc9,u))**.
% 63.83/64.03 2144[10:Rew:545.1,2130.3] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(hd(skc9),u),app(skc9,u))**.
% 63.83/64.03 2145[10:SSi:2144.1,269.1] ssList(u) || -> equal(app(skc9,u),nil) equal(cons(hd(skc9),u),app(skc9,u))**.
% 63.83/64.03 2146[10:MRR:2145.1,1468.1] ssList(u) || -> equal(cons(hd(skc9),u),app(skc9,u))**.
% 63.83/64.03 2221[10:SpL:2146.1,254.1] ssList(skc9) ssItem(hd(skc9)) || equal(app(skc9,skc9),skc9)** -> .
% 63.83/64.03 2235[10:SSi:2221.1,2221.0,1461.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || equal(app(skc9,skc9),skc9)** -> .
% 63.83/64.03 2271[0:SpR:1990.2,19.0] ssList(u) singletonP(u) || -> ssItem(hd(u))*.
% 63.83/64.03 2299[10:SpR:1947.0,246.1] ssItem(hd(skc9)) || -> equal(cons(hd(skc9),skc9),app(skc9,skc9))**.
% 63.83/64.03 2303[10:SSi:2299.0,1461.0] || -> equal(cons(hd(skc9),skc9),app(skc9,skc9))**.
% 63.83/64.03 2528[0:EqR:122.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 63.83/64.03 2533[0:SSi:2528.0,92.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 63.83/64.03 3344[0:SpL:156.3,131.2] ssList(u) ssList(v) ssList(u) ssList(tl(v)) || equal(tl(app(v,u)),nil)** -> equal(nil,v) equal(nil,u).
% 63.83/64.03 3368[0:Obv:3344.0] ssList(u) ssList(v) ssList(tl(u)) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 63.83/64.03 3369[0:MRR:3368.2,88.1] ssList(u) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 63.83/64.03 3722[0:SpR:129.0,153.4] ssList(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil))) ssList(u) ssList(skc14) || rearsegP(skc14,u)* -> rearsegP(skc9,u).
% 63.83/64.03 3733[0:SSi:3722.2,3722.0,2.0,93.1,93.0,93.1,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.2,5.0,78.0,5.1,2533.0,5.1,1.0,92.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.0,4.0,77.0,4.0,76.0,4.0,75.0,4.0,79.2,4.0,78.2,4.2,2533.2,4.0] ssList(u) || rearsegP(skc14,u)* -> rearsegP(skc9,u).
% 63.83/64.03 3749[0:Res:69.1,3733.1] ssList(skc14) ssList(skc14) || -> rearsegP(skc9,skc14)*.
% 63.83/64.03 3750[0:Obv:3749.0] ssList(skc14) || -> rearsegP(skc9,skc14)*.
% 63.83/64.03 3751[0:SSi:3750.0,2.0] || -> rearsegP(skc9,skc14)*.
% 63.83/64.03 3752[0:Res:3751.0,142.2] ssList(skc9) ssList(skc14) || rearsegP(skc14,skc9)* -> equal(skc14,skc9).
% 63.83/64.03 3753[10:SSi:3752.1,3752.0,2.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || rearsegP(skc14,skc9)* -> equal(skc14,skc9).
% 63.83/64.03 3802[0:EqR:146.3] ssList(u) ssList(app(v,u)) ssList(v) || -> rearsegP(app(v,u),u)*.
% 63.83/64.03 3804[0:SpL:278.0,146.3] ssList(skc9) ssList(u) ssList(nil) || equal(skc9,u) -> rearsegP(u,skc9)*.
% 63.83/64.03 3817[0:SSi:3802.1,93.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 63.83/64.03 3818[10:SSi:3804.2,3804.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] ssList(u) || equal(skc9,u) -> rearsegP(u,skc9)*.
% 63.83/64.03 3853[0:EqR:145.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 63.83/64.03 3868[0:SSi:3853.1,93.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 63.83/64.03 4248[0:SpR:161.3,129.0] ssList(skc15) ssList(cons(skc11,nil)) ssList(skc13) || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),cons(skc12,nil)),skc14),skc9)**.
% 63.83/64.03 4250[0:SpR:161.3,129.0] ssList(skc14) ssList(cons(skc12,nil)) ssList(app(app(skc13,cons(skc11,nil)),skc15)) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),app(cons(skc12,nil),skc14)),skc9)**.
% 63.83/64.03 4290[0:SSi:4248.2,4248.1,4248.0,3.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2533.0,5.2,1.0] || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),cons(skc12,nil)),skc14),skc9)**.
% 63.83/64.03 4319[0:SSi:4250.2,4250.1,4250.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2533.0,5.0,1.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.2,2533.0,4.2,2.2] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),app(cons(skc12,nil),skc14)),skc9)**.
% 63.83/64.03 4461[0:SpR:130.2,3817.2] ssItem(u) ssList(v) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 63.83/64.03 4470[0:Obv:4461.1] ssItem(u) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 63.83/64.03 4471[0:SSi:4470.2,92.1,17.1,16.1,13.1,12.1,11.1,15.1,14.1,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.0,2533.2] ssItem(u) ssList(v) || -> rearsegP(cons(u,v),v)*.
% 63.83/64.03 4487[0:SpL:278.0,163.3] ssList(nil) ssList(skc9) ssList(u) || equal(app(u,skc9),skc9)** -> equal(nil,u).
% 63.83/64.03 4520[10:SSi:4487.1,4487.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(u) || equal(app(u,skc9),skc9)** -> equal(nil,u).
% 63.83/64.03 5166[0:SpR:119.2,4471.2] ssList(u) ssItem(hd(u)) ssList(tl(u)) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 63.83/64.03 5177[0:Res:4471.2,142.2] ssItem(u) ssList(v) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 63.83/64.03 5184[0:MRR:5166.1,5166.2,87.1,88.1] ssList(u) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 63.83/64.03 5185[0:Obv:5177.1] ssItem(u) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 63.83/64.03 5186[0:SSi:5185.1,92.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 63.83/64.03 5187[0:MRR:5186.3,110.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> .
% 63.83/64.03 5290[0:Res:5184.2,3733.1] ssList(skc14) ssList(tl(skc14)) || -> equal(skc14,nil) rearsegP(skc9,tl(skc14))*.
% 63.83/64.03 5293[0:SSi:5290.0,2.0] ssList(tl(skc14)) || -> equal(skc14,nil) rearsegP(skc9,tl(skc14))*.
% 63.83/64.03 5299[0:SoR:5293.0,88.1] ssList(skc14) || -> equal(skc14,nil) rearsegP(skc9,tl(skc14))* equal(skc14,nil).
% 63.83/64.03 5300[0:Obv:5299.1] ssList(skc14) || -> rearsegP(skc9,tl(skc14))* equal(skc14,nil).
% 63.83/64.03 5301[0:SSi:5300.0,2.0] || -> rearsegP(skc9,tl(skc14))* equal(skc14,nil).
% 63.83/64.03 5340[11:Spt:5301.1] || -> equal(skc14,nil)**.
% 63.83/64.03 5345[11:Rew:5340.0,129.0] || -> equal(app(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil)),nil),skc9)**.
% 63.83/64.03 5412[11:SpR:5345.0,84.1] ssList(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil))) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil)),skc9)**.
% 63.83/64.03 5438[11:SSi:5412.0,93.0,93.1,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.2,78.0,5.0,2533.1,5.0,1.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.0,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.2,78.0,4.2,2533.2,4.2] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,nil)),skc9)**.
% 63.83/64.03 6306[10:SpL:1947.0,172.3] ssList(nil) ssItem(hd(skc9)) ssItem(u) || memberP(skc9,u)* -> memberP(nil,u) equal(u,hd(skc9)).
% 63.83/64.03 6313[10:SSi:6306.1,6306.0,1461.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssItem(u) || memberP(skc9,u)* -> memberP(nil,u) equal(u,hd(skc9)).
% 63.83/64.03 6314[10:MRR:6313.2,74.1] ssItem(u) || memberP(skc9,u)* -> equal(u,hd(skc9)).
% 63.83/64.03 7544[0:SpL:177.2,192.7] ssList(u) ssList(v) ssList(skf64(u)) ssList(skf63(u)) ssList(skf62(u)) ssItem(skf61(u)) ssItem(skf60(u)) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skf60(u),skf61(u))*.
% 63.83/64.03 7564[0:SSi:7544.6,7544.5,7544.4,7544.3,7544.2,34.0,33.0,32.0,31.0,30.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skf60(u),skf61(u))*.
% 63.83/64.03 7565[0:MRR:7564.5,103.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> strictorderP(u)*.
% 63.83/64.03 7700[0:SpL:178.2,193.7] ssList(u) ssList(v) ssList(skf59(u)) ssList(skf58(u)) ssList(skf57(u)) ssItem(skf56(u)) ssItem(skf55(u)) totalorderedP(v) || equal(u,v)* -> totalorderP(u) leq(skf55(u),skf56(u))*.
% 63.83/64.03 7717[0:SSi:7700.6,7700.5,7700.4,7700.3,7700.2,29.0,28.0,27.0,26.0,25.0] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)* -> totalorderP(u) leq(skf55(u),skf56(u))*.
% 63.83/64.03 7718[0:MRR:7717.5,101.1] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)*+ -> totalorderP(u)*.
% 63.83/64.03 8107[0:SpL:1991.2,5187.2] ssList(u) singletonP(u) ssItem(hd(u)) ssList(nil) || rearsegP(nil,u)* -> .
% 63.83/64.03 8115[0:SSi:8107.3,8107.2,17.2,16.0,13.0,12.0,11.0,15.0,14.0,10.0,2271.0] ssList(u) singletonP(u) || rearsegP(nil,u)* -> .
% 63.83/64.03 8403[11:SpL:5438.0,188.4] ssItem(skc12) ssList(u) ssList(nil) ssList(app(app(skc13,cons(skc11,nil)),skc15)) || equal(skc9,u) -> memberP(u,skc12)*.
% 63.83/64.03 8416[11:SSi:8403.3,8403.2,8403.0,93.0,93.0,3.0,92.0,5.0,17.0,16.0,13.0,12.0,11.0,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.1,5.0,76.1,5.0,75.1,5.0,79.1,5.0,78.1,5.0,2533.0,5.0,1.0,17.0,16.0,13.0,12.0,11.0,15.2,14.0,10.2,4.2] ssList(u) || equal(skc9,u) -> memberP(u,skc12)*.
% 63.83/64.03 8502[11:Res:8416.2,6314.1] ssList(skc9) ssItem(skc12) || equal(skc9,skc9) -> equal(hd(skc9),skc12)**.
% 63.83/64.03 8508[11:Obv:8502.2] ssList(skc9) ssItem(skc12) || -> equal(hd(skc9),skc12)**.
% 63.83/64.03 8509[11:SSi:8508.1,8508.0,4.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || -> equal(hd(skc9),skc12)**.
% 63.83/64.03 8514[11:Rew:8509.0,1947.0] || -> equal(cons(skc12,nil),skc9)**.
% 63.83/64.03 8675[11:Rew:8514.0,5438.0] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),skc9),skc9)**.
% 63.83/64.03 9124[11:SpL:8675.0,4520.1] ssList(app(app(skc13,cons(skc11,nil)),skc15)) || equal(skc9,skc9) -> equal(app(app(skc13,cons(skc11,nil)),skc15),nil)**.
% 63.83/64.03 9136[11:Obv:9124.1] ssList(app(app(skc13,cons(skc11,nil)),skc15)) || -> equal(app(app(skc13,cons(skc11,nil)),skc15),nil)**.
% 63.83/64.03 9137[11:SSi:9136.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2533.0,5.2,1.2] || -> equal(app(app(skc13,cons(skc11,nil)),skc15),nil)**.
% 63.83/64.03 9682[11:SpR:9137.0,3868.2] ssList(app(skc13,cons(skc11,nil))) ssList(skc15) || -> frontsegP(nil,app(skc13,cons(skc11,nil)))*.
% 63.83/64.03 9706[11:SSi:9682.1,9682.0,1.0,93.1,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.2,5.0,2533.2,5.0] || -> frontsegP(nil,app(skc13,cons(skc11,nil)))*.
% 63.83/64.03 9785[11:Res:9706.0,94.1] ssList(app(skc13,cons(skc11,nil))) || -> equal(app(skc13,cons(skc11,nil)),nil)**.
% 63.83/64.03 9789[11:SSi:9785.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2533.0,5.2] || -> equal(app(skc13,cons(skc11,nil)),nil)**.
% 63.83/64.03 9809[11:SpR:9789.0,3817.2] ssList(cons(skc11,nil)) ssList(skc13) || -> rearsegP(nil,cons(skc11,nil))*.
% 63.83/64.03 9832[11:SSi:9809.1,9809.0,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.1,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2533.2,5.0] || -> rearsegP(nil,cons(skc11,nil))*.
% 63.83/64.03 9892[11:Res:9832.0,8115.2] ssList(cons(skc11,nil)) singletonP(cons(skc11,nil)) || -> .
% 63.83/64.03 9901[11:SSi:9892.1,9892.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2533.0,5.2,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2533.0,5.2] || -> .
% 63.83/64.03 9917[11:Spt:9901.0,5301.1,5340.0] || equal(skc14,nil)** -> .
% 63.83/64.03 9918[11:Spt:9901.0,5301.0] || -> rearsegP(skc9,tl(skc14))*.
% 63.83/64.03 12074[0:SpR:4319.0,3817.2] ssList(app(cons(skc12,nil),skc14)) ssList(app(app(skc13,cons(skc11,nil)),skc15)) || -> rearsegP(skc9,app(cons(skc12,nil),skc14))*.
% 63.83/64.03 12082[0:SpR:130.2,4319.0] ssItem(skc12) ssList(skc14) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,skc14)),skc9)**.
% 63.83/64.03 12098[0:SSi:12082.1,12082.0,2.0,4.0] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc15),cons(skc12,skc14)),skc9)**.
% 63.83/64.03 12099[0:SSi:12074.1,12074.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2533.2,5.0,1.0,93.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.2,2533.0,4.2,2.2] || -> rearsegP(skc9,app(cons(skc12,nil),skc14))*.
% 63.83/64.03 12125[0:SpR:130.2,12099.0] ssItem(skc12) ssList(skc14) || -> rearsegP(skc9,cons(skc12,skc14))*.
% 63.83/64.03 12129[0:SSi:12125.1,12125.0,2.0,4.0] || -> rearsegP(skc9,cons(skc12,skc14))*.
% 63.83/64.03 12132[0:Res:12129.0,142.2] ssList(skc9) ssList(cons(skc12,skc14)) || rearsegP(cons(skc12,skc14),skc9)* -> equal(cons(skc12,skc14),skc9).
% 63.83/64.03 12134[10:SSi:12132.1,12132.0,92.0,4.0,2.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.2] || rearsegP(cons(skc12,skc14),skc9)* -> equal(cons(skc12,skc14),skc9).
% 63.83/64.03 16416[0:EqR:7565.3] ssList(u) ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 63.83/64.03 16417[0:Obv:16416.0] ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 63.83/64.03 16530[0:EqR:7718.3] ssList(u) ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 63.83/64.03 16531[0:Obv:16530.0] ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 63.83/64.03 18272[0:SpL:12098.0,188.4] ssItem(skc12) ssList(u) ssList(skc14) ssList(app(app(skc13,cons(skc11,nil)),skc15)) || equal(skc9,u) -> memberP(u,skc12)*.
% 63.83/64.03 18283[0:SSi:18272.3,18272.2,18272.0,93.0,93.0,3.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2533.0,5.2,1.0,2.2,4.2] ssList(u) || equal(skc9,u) -> memberP(u,skc12)*.
% 63.83/64.03 18305[0:Res:18283.2,74.1] ssList(nil) ssItem(skc12) || equal(skc9,nil)** -> .
% 63.83/64.03 18310[10:Res:18283.2,6314.1] ssList(skc9) ssItem(skc12) || equal(skc9,skc9) -> equal(hd(skc9),skc12)**.
% 63.83/64.03 18322[10:Obv:18310.2] ssList(skc9) ssItem(skc12) || -> equal(hd(skc9),skc12)**.
% 63.83/64.03 18323[10:SSi:18322.1,18322.0,4.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || -> equal(hd(skc9),skc12)**.
% 71.61/71.80 18327[10:Rew:18323.0,1947.0] || -> equal(cons(skc12,nil),skc9)**.
% 71.61/71.80 18333[10:Rew:18323.0,2303.0] || -> equal(app(skc9,skc9),cons(skc12,skc9))**.
% 71.61/71.80 18355[10:Rew:18323.0,2146.1] ssList(u) || -> equal(app(skc9,u),cons(skc12,u))**.
% 71.61/71.80 18500[10:Rew:18327.0,4290.0] || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),skc14),skc9)**.
% 71.61/71.80 18736[10:Rew:18333.0,2235.0] || equal(cons(skc12,skc9),skc9)** -> .
% 71.61/71.80 18855[10:Rew:18355.1,348.3] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(cons(skc12,v),u)*.
% 71.61/71.80 19925[10:Res:18855.3,12134.0] ssList(skc9) ssList(skc14) || rearsegP(skc14,skc9) -> equal(cons(skc12,skc14),skc9)**.
% 71.61/71.80 19929[10:Rew:3753.1,19925.3] ssList(skc9) ssList(skc14) || rearsegP(skc14,skc9) -> equal(cons(skc12,skc9),skc9)**.
% 71.61/71.80 19930[10:SSi:19929.1,19929.0,2.0,7.0,1752.0,1755.0,1766.0,1770.0,1771.0,1835.0,1846.0,1848.0] || rearsegP(skc14,skc9) -> equal(cons(skc12,skc9),skc9)**.
% 71.61/71.80 19931[10:MRR:19930.1,18736.0] || rearsegP(skc14,skc9)* -> .
% 71.61/71.80 19936[10:Res:3818.2,19931.0] ssList(skc14) || equal(skc14,skc9)** -> .
% 71.61/71.80 19937[10:SSi:19936.0,2.0] || equal(skc14,skc9)** -> .
% 71.61/71.80 22086[10:SpL:18500.0,231.2] ssList(skc14) ssList(app(app(skc13,app(cons(skc11,nil),skc15)),skc9)) || equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),skc9),skc9)** -> equal(skc14,skc9).
% 71.61/71.80 22162[10:SSi:22086.1,22086.0,326.0,93.0,3.0,93.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2533.2,5.0,1.2,2.1] || equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),skc9),skc9)** -> equal(skc14,skc9).
% 71.61/71.80 22163[10:MRR:22162.1,19937.0] || equal(app(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),skc9),skc9)** -> .
% 71.61/71.80 32780[10:SpL:18500.0,3369.2] ssList(app(app(skc13,app(cons(skc11,nil),skc15)),skc9)) ssList(skc14) || equal(tl(skc9),nil) -> equal(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),nil)** equal(skc14,nil).
% 71.61/71.80 32898[10:Rew:1945.0,32780.2] ssList(app(app(skc13,app(cons(skc11,nil),skc15)),skc9)) ssList(skc14) || equal(nil,nil) -> equal(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),nil)** equal(skc14,nil).
% 71.61/71.80 32899[10:Obv:32898.2] ssList(app(app(skc13,app(cons(skc11,nil),skc15)),skc9)) ssList(skc14) || -> equal(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),nil)** equal(skc14,nil).
% 71.61/71.80 35169[10:SSi:32899.1,32899.0,2.0,326.0,93.1,3.0,93.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.2,78.2,5.0,2533.2,5.1,1.0] || -> equal(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),nil)** equal(skc14,nil).
% 71.61/71.80 35170[11:MRR:35169.1,9917.0] || -> equal(app(app(skc13,app(cons(skc11,nil),skc15)),skc9),nil)**.
% 71.61/71.80 35174[11:Rew:35170.0,22163.0] || equal(app(nil,skc9),skc9)** -> .
% 71.61/71.80 35188[11:Rew:278.0,35174.0] || equal(skc9,skc9)* -> .
% 71.61/71.80 35189[11:Obv:35188.0] || -> .
% 71.61/71.80 35382[9:Spt:35189.0,219.0,1771.0] || totalorderP(skc9)* -> .
% 71.61/71.80 35383[9:Spt:35189.0,219.1] || -> equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 71.61/71.80 36793[9:Res:16531.2,35382.0] ssList(skc9) totalorderedP(skc9) || -> .
% 71.61/71.80 36795[9:SSi:36793.1,36793.0,7.0,1752.0,1755.0,1766.0,1770.0,7.0,1752.0,1755.0,1766.0,1770.0] || -> .
% 71.61/71.80 36799[8:Spt:36795.0,220.0,1770.0] || strictorderP(skc9)* -> .
% 71.61/71.80 36800[8:Spt:36795.0,220.1] || -> equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 71.61/71.80 37263[8:Res:16417.2,36799.0] ssList(skc9) strictorderedP(skc9) || -> .
% 71.61/71.80 37265[8:SSi:37263.1,37263.0,7.0,1752.0,1755.0,1766.0,7.0,1752.0,1755.0,1766.0] || -> .
% 71.61/71.80 37269[7:Spt:37265.0,265.0,1766.0] || cyclefreeP(skc9)* -> .
% 71.61/71.80 37270[7:Spt:37265.0,265.1] || -> leq(skf51(skc9),skf50(skc9))*.
% 71.61/71.80 38135[7:Res:1927.2,37269.0] ssList(skc9) singletonP(skc9) || -> .
% 71.61/71.80 38139[7:SSi:38135.0,7.0,1752.0,1755.0] singletonP(skc9) || -> .
% 71.61/71.80 38140[7:MRR:65.1,38139.0] || neq(skc10,nil)* -> .
% 71.61/71.80 38154[7:Res:424.1,38140.0] ssList(nil) || -> equal(skc10,nil)**.
% 71.61/71.80 38157[7:SSi:38154.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 71.61/71.80 38158[7:MRR:38157.0,1737.0] || -> .
% 71.61/71.80 38162[6:Spt:38158.0,221.0,1755.0] || totalorderedP(skc9)* -> .
% 71.61/71.80 38163[6:Spt:38158.0,221.1] || -> equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 71.61/71.80 39115[6:Res:1929.2,38162.0] ssList(skc9) singletonP(skc9) || -> .
% 71.61/71.80 39116[6:SSi:39115.0,7.0,1752.0] singletonP(skc9) || -> .
% 71.61/71.80 39117[6:MRR:65.1,39116.0] || neq(skc10,nil)* -> .
% 71.61/71.80 39132[6:Res:424.1,39117.0] ssList(nil) || -> equal(skc10,nil)**.
% 71.61/71.80 39135[6:SSi:39132.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 71.61/71.80 39136[6:MRR:39135.0,1737.0] || -> .
% 71.61/71.80 39140[5:Spt:39136.0,222.0,1752.0] || strictorderedP(skc9)* -> .
% 71.61/71.80 39141[5:Spt:39136.0,222.1] || -> equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 71.61/71.80 39641[5:Res:1928.2,39140.0] ssList(skc9) singletonP(skc9) || -> .
% 71.61/71.80 39642[5:SSi:39641.0,7.0] singletonP(skc9) || -> .
% 71.61/71.80 39643[5:MRR:65.1,39642.0] || neq(skc10,nil)* -> .
% 71.61/71.80 39649[5:Res:424.1,39643.0] ssList(nil) || -> equal(skc10,nil)**.
% 71.61/71.80 39652[5:SSi:39649.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 71.61/71.80 39653[5:MRR:39652.0,1737.0] || -> .
% 71.61/71.80 39657[2:Spt:39653.0,239.1] || -> equal(skc9,nil)**.
% 71.61/71.80 40635[2:Rew:39657.0,18305.2] ssList(nil) ssItem(skc12) || equal(nil,nil)* -> .
% 71.61/71.80 40636[2:Obv:40635.2] ssList(nil) ssItem(skc12) || -> .
% 71.61/71.80 40637[2:SSi:40636.1,40636.0,4.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> .
% 71.61/71.80 41845[1:Spt:40637.0,245.1] || -> equal(skc9,nil)**.
% 71.61/71.80 41961[1:Rew:41845.0,18305.2] ssList(nil) ssItem(skc12) || equal(nil,nil)* -> .
% 71.61/71.80 41962[1:Obv:41961.2] ssList(nil) ssItem(skc12) || -> .
% 71.61/71.80 41963[1:SSi:41962.1,41962.0,4.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> .
% 71.61/71.80 % SZS output end Refutation
% 71.61/71.80 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax9 ax10 ax49 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax75 ax76 ax8 ax16 ax26 ax46 ax58 ax15 ax18 ax23 ax25 ax78 ax81 ax83 ax85 ax48 ax5 ax6 ax50 ax67 ax70 ax86 ax82 ax80 ax79 ax37 ax12 ax11 ax3
% 71.61/71.80
%------------------------------------------------------------------------------