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  
%------------------------------------------------------------------------------