TSTP Solution File: SWC307+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC307+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 22:03:12 EDT 2022
% Result : Theorem 60.13s 60.35s
% Output : Refutation 67.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWC307+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jun 12 08:12:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 60.13/60.35
% 60.13/60.35 SPASS V 3.9
% 60.13/60.35 SPASS beiseite: Proof found.
% 60.13/60.35 % SZS status Theorem
% 60.13/60.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.13/60.35 SPASS derived 24835 clauses, backtracked 11493 clauses, performed 43 splits and kept 17154 clauses.
% 60.13/60.35 SPASS allocated 135585 KBytes.
% 60.13/60.35 SPASS spent 0:0:59.96 on the problem.
% 60.13/60.35 0:00:00.04 for the input.
% 60.13/60.35 0:00:00.06 for the FLOTTER CNF translation.
% 60.13/60.35 0:00:00.37 for inferences.
% 60.13/60.35 0:00:02.15 for the backtracking.
% 60.13/60.35 0:0:56.99 for the reduction.
% 60.13/60.35
% 60.13/60.35
% 60.13/60.35 Here is a proof with depth 7, length 337 :
% 60.13/60.35 % SZS output start Refutation
% 60.13/60.35 1[0:Inp] || -> ssList(skc15)*.
% 60.13/60.35 2[0:Inp] || -> ssList(skc14)*.
% 60.13/60.35 3[0:Inp] || -> ssList(skc13)*.
% 60.13/60.35 4[0:Inp] || -> ssItem(skc12)*.
% 60.13/60.35 5[0:Inp] || -> ssItem(skc11)*.
% 60.13/60.35 6[0:Inp] || -> ssList(skc10)*.
% 60.13/60.35 7[0:Inp] || -> ssList(skc9)*.
% 60.13/60.35 8[0:Inp] || -> ssItem(skc17)*.
% 60.13/60.35 9[0:Inp] || -> ssItem(skc16)*.
% 60.13/60.35 10[0:Inp] || -> ssList(nil)*.
% 60.13/60.35 11[0:Inp] || -> cyclefreeP(nil)*.
% 60.13/60.35 12[0:Inp] || -> totalorderP(nil)*.
% 60.13/60.35 13[0:Inp] || -> strictorderP(nil)*.
% 60.13/60.35 14[0:Inp] || -> totalorderedP(nil)*.
% 60.13/60.35 15[0:Inp] || -> strictorderedP(nil)*.
% 60.13/60.35 16[0:Inp] || -> duplicatefreeP(nil)*.
% 60.13/60.35 17[0:Inp] || -> equalelemsP(nil)*.
% 60.13/60.35 18[0:Inp] || -> segmentP(skc10,skc9)*.
% 60.13/60.35 20[0:Inp] || -> ssItem(skf45(u))*.
% 60.13/60.35 26[0:Inp] || -> ssList(skf59(u))*.
% 60.13/60.35 27[0:Inp] || -> ssList(skf58(u))*.
% 60.13/60.35 28[0:Inp] || -> ssList(skf57(u))*.
% 60.13/60.35 29[0:Inp] || -> ssItem(skf56(u))*.
% 60.13/60.35 30[0:Inp] || -> ssItem(skf55(u))*.
% 60.13/60.35 31[0:Inp] || -> ssList(skf64(u))*.
% 60.13/60.35 32[0:Inp] || -> ssList(skf63(u))*.
% 60.13/60.35 33[0:Inp] || -> ssList(skf62(u))*.
% 60.13/60.35 34[0:Inp] || -> ssItem(skf61(u))*.
% 60.13/60.35 35[0:Inp] || -> ssItem(skf60(u))*.
% 60.13/60.35 36[0:Inp] || -> ssList(skf69(u))*.
% 60.13/60.35 37[0:Inp] || -> ssList(skf68(u))*.
% 60.13/60.35 38[0:Inp] || -> ssList(skf67(u))*.
% 60.13/60.35 39[0:Inp] || -> ssItem(skf66(u))*.
% 60.13/60.35 40[0:Inp] || -> ssItem(skf65(u))*.
% 60.13/60.35 58[0:Inp] || equal(skc17,skc16)** -> .
% 60.13/60.35 65[0:Inp] || neq(skc10,nil)* -> singletonP(skc9).
% 60.13/60.35 69[0:Inp] ssList(u) || -> rearsegP(u,u)*.
% 60.13/60.35 74[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 60.13/60.35 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 60.13/60.35 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 60.13/60.35 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 60.13/60.35 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 60.13/60.35 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 60.13/60.35 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 60.13/60.35 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 60.13/60.35 83[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 60.13/60.35 84[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 60.13/60.35 87[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 60.13/60.35 88[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 60.13/60.35 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 60.13/60.35 92[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 60.13/60.35 93[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 60.13/60.35 94[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 60.13/60.35 98[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 60.13/60.35 101[0:Inp] ssList(u) || leq(skf55(u),skf56(u))* -> totalorderP(u).
% 60.13/60.35 103[0:Inp] ssList(u) || lt(skf60(u),skf61(u))* -> strictorderP(u).
% 60.13/60.35 104[0:Inp] ssList(u) || leq(skf65(u),skf66(u))* -> totalorderedP(u).
% 60.13/60.35 108[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 60.13/60.35 109[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 60.13/60.35 110[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 60.13/60.35 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 60.13/60.35 113[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 60.13/60.35 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 60.13/60.35 120[0:Inp] ssItem(u) ssItem(v) || lt(v,u) -> leq(v,u)*.
% 60.13/60.35 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 60.13/60.35 129[0:Inp] || -> equal(app(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil)),skc15),skc9)**.
% 60.13/60.35 130[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 60.13/60.35 131[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 60.13/60.35 132[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 60.13/60.35 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 60.13/60.35 142[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(v,u).
% 60.13/60.35 145[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 60.13/60.35 146[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 60.13/60.35 153[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(w,v) -> rearsegP(app(u,w),v)*.
% 60.13/60.35 154[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 60.13/60.35 155[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 60.13/60.35 156[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 60.13/60.35 161[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 60.13/60.35 162[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,u),app(v,w))* -> equal(u,w).
% 60.13/60.35 163[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,v),app(w,v))* -> equal(u,w).
% 60.13/60.35 172[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 60.13/60.35 175[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 60.13/60.35 176[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 60.13/60.35 177[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 60.13/60.35 178[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 60.13/60.35 188[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 60.13/60.35 192[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).
% 60.13/60.35 193[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).
% 60.13/60.35 219[0:Res:7.0,178.0] || -> totalorderP(skc9) equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 60.13/60.35 220[0:Res:7.0,177.0] || -> strictorderP(skc9) equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 60.13/60.35 221[0:Res:7.0,176.0] || -> totalorderedP(skc9) equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 60.13/60.35 222[0:Res:7.0,175.0] || -> strictorderedP(skc9) equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 60.13/60.35 231[0:Res:7.0,162.0] ssList(u) ssList(v) || equal(app(v,u),app(v,skc9))* -> equal(u,skc9).
% 60.13/60.35 239[0:Res:7.0,156.0] ssList(u) || -> equal(skc9,nil) equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 60.13/60.35 245[0:Res:7.0,135.0] ssList(u) || -> equal(skc9,nil) equal(hd(app(skc9,u)),hd(skc9))**.
% 60.13/60.35 246[0:Res:7.0,130.0] ssItem(u) || -> equal(app(cons(u,nil),skc9),cons(u,skc9))**.
% 60.13/60.35 248[0:Res:7.0,132.0] ssList(u) || equal(app(skc9,u),nil)** -> equal(skc9,nil).
% 60.13/60.35 251[0:Res:7.0,119.0] || -> equal(skc9,nil) equal(cons(hd(skc9),tl(skc9)),skc9)**.
% 60.13/60.35 252[0:Res:7.0,108.1] singletonP(skc9) || -> equal(cons(skf45(skc9),nil),skc9)**.
% 60.13/60.35 254[0:Res:7.0,110.0] ssItem(u) || equal(cons(u,skc9),skc9)** -> .
% 60.13/60.35 256[0:Res:7.0,112.0] ssItem(u) || -> equal(hd(cons(u,skc9)),u)**.
% 60.13/60.35 265[0:Res:7.0,89.0] || -> cyclefreeP(skc9) leq(skf51(skc9),skf50(skc9))*.
% 60.13/60.35 268[0:Res:7.0,92.0] ssItem(u) || -> ssList(cons(u,skc9))*.
% 60.13/60.35 274[0:Res:7.0,98.0] || segmentP(nil,skc9)* -> equal(skc9,nil).
% 60.13/60.35 276[0:Res:7.0,87.0] || -> ssItem(hd(skc9))* equal(skc9,nil).
% 60.13/60.35 278[0:Res:7.0,83.0] || -> equal(app(nil,skc9),skc9)**.
% 60.13/60.35 309[0:Res:7.0,155.1] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)) equal(skc9,nil).
% 60.13/60.35 326[0:Res:7.0,93.1] ssList(u) || -> ssList(app(u,skc9))*.
% 60.13/60.35 348[0:Res:7.0,153.2] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(app(skc9,v),u)*.
% 60.13/60.35 424[0:Res:6.0,109.0] ssList(u) || -> neq(skc10,u)* equal(skc10,u).
% 60.13/60.35 479[0:Res:6.0,154.1] ssItem(u) || totalorderedP(cons(u,skc10))* -> leq(u,hd(skc10)) equal(skc10,nil).
% 60.13/60.35 545[1:Spt:245.0,245.2] ssList(u) || -> equal(hd(app(skc9,u)),hd(skc9))**.
% 60.13/60.35 547[2:Spt:239.0,239.2] ssList(u) || -> equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 60.13/60.35 553[3:Spt:309.3] || -> equal(skc9,nil)**.
% 60.13/60.35 554[3:Rew:553.0,545.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 60.13/60.35 572[3:Rew:553.0,268.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 60.13/60.35 573[3:Rew:553.0,256.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 60.13/60.35 727[3:Rew:83.1,554.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 60.13/60.35 1181[3:SpR:573.1,727.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 60.13/60.35 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))*.
% 60.13/60.35 1251[3:SpR:1184.1,1184.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 60.13/60.35 1293[3:EmS:1251.0,4.0] ssItem(u) || -> equal(u,skc12)*.
% 60.13/60.35 1316[3:EmS:1293.0,5.0] || -> equal(skc12,skc11)**.
% 60.13/60.35 1317[3:EmS:1293.0,8.0] || -> equal(skc17,skc12)**.
% 60.13/60.35 1318[3:EmS:1293.0,9.0] || -> equal(skc16,skc12)**.
% 60.13/60.35 1323[3:Rew:1316.0,1317.0] || -> equal(skc17,skc11)**.
% 60.13/60.35 1325[3:Rew:1323.0,58.0] || equal(skc16,skc11)** -> .
% 60.13/60.35 1327[3:Rew:1316.0,1318.0] || -> equal(skc16,skc11)**.
% 60.13/60.35 1448[3:Rew:1327.0,1325.0] || equal(skc11,skc11)* -> .
% 60.13/60.35 1449[3:Obv:1448.0] || -> .
% 60.13/60.35 1489[3:Spt:1449.0,309.3,553.0] || equal(skc9,nil)** -> .
% 60.13/60.35 1490[3:Spt:1449.0,309.0,309.1,309.2] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)).
% 60.13/60.35 1492[3:MRR:276.1,1489.0] || -> ssItem(hd(skc9))*.
% 60.13/60.35 1493[3:MRR:274.1,1489.0] || segmentP(nil,skc9)* -> .
% 60.13/60.35 1496[3:MRR:251.0,1489.0] || -> equal(cons(hd(skc9),tl(skc9)),skc9)**.
% 60.13/60.35 1499[3:MRR:248.2,1489.0] ssList(u) || equal(app(skc9,u),nil)** -> .
% 60.13/60.35 1504[4:Spt:479.3] || -> equal(skc10,nil)**.
% 60.13/60.35 1512[4:Rew:1504.0,18.0] || -> segmentP(nil,skc9)*.
% 60.13/60.35 1657[4:MRR:1512.0,1493.0] || -> .
% 60.13/60.35 1768[4:Spt:1657.0,479.3,1504.0] || equal(skc10,nil)** -> .
% 60.13/60.35 1769[4:Spt:1657.0,479.0,479.1,479.2] ssItem(u) || totalorderedP(cons(u,skc10))* -> leq(u,hd(skc10)).
% 60.13/60.35 1783[5:Spt:222.0] || -> strictorderedP(skc9)*.
% 60.13/60.35 1786[6:Spt:221.0] || -> totalorderedP(skc9)*.
% 60.13/60.35 1797[7:Spt:265.0] || -> cyclefreeP(skc9)*.
% 60.13/60.35 1801[8:Spt:220.0] || -> strictorderP(skc9)*.
% 60.13/60.35 1802[9:Spt:219.0] || -> totalorderP(skc9)*.
% 60.13/60.35 1810[10:Spt:65.0] || neq(skc10,nil)* -> .
% 60.13/60.35 1862[10:Res:424.1,1810.0] ssList(nil) || -> equal(skc10,nil)**.
% 60.13/60.35 1863[10:SSi:1862.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 60.13/60.35 1864[10:MRR:1863.0,1768.0] || -> .
% 60.13/60.35 1865[10:Spt:1864.0,65.0,1810.0] || -> neq(skc10,nil)*.
% 60.13/60.35 1866[10:Spt:1864.0,65.1] || -> singletonP(skc9)*.
% 60.13/60.35 1867[10:MRR:252.0,1866.0] || -> equal(cons(skf45(skc9),nil),skc9)**.
% 60.13/60.35 1868[10:SpR:1867.0,81.1] ssItem(skf45(skc9)) || -> equalelemsP(skc9)*.
% 60.13/60.35 1869[10:SpR:1867.0,80.1] ssItem(skf45(skc9)) || -> duplicatefreeP(skc9)*.
% 60.13/60.35 1877[10:SSi:1868.0,20.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0] || -> equalelemsP(skc9)*.
% 60.13/60.35 1879[10:SSi:1869.0,20.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0] || -> duplicatefreeP(skc9)*.
% 60.13/60.35 1947[10:SpR:1867.0,246.1] ssItem(skf45(skc9)) || -> equal(cons(skf45(skc9),skc9),app(skc9,skc9))**.
% 60.13/60.35 1949[10:SSi:1947.0,20.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || -> equal(cons(skf45(skc9),skc9),app(skc9,skc9))**.
% 60.13/60.35 1957[10:SpL:1949.0,254.1] ssItem(skf45(skc9)) || equal(app(skc9,skc9),skc9)** -> .
% 60.13/60.35 1964[10:SSi:1957.0,20.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || equal(app(skc9,skc9),skc9)** -> .
% 60.13/60.35 1972[0:SpR:108.2,75.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> cyclefreeP(u)*.
% 60.13/60.35 1973[0:SpR:108.2,79.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> strictorderedP(u)*.
% 60.13/60.35 1986[0:SSi:1972.2,20.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 60.13/60.35 1987[0:SSi:1973.2,20.0] ssList(u) singletonP(u) || -> strictorderedP(u)*.
% 60.13/60.35 2004[10:SpR:1867.0,113.2] ssItem(skf45(skc9)) ssList(nil) || -> equal(tl(skc9),nil)**.
% 60.13/60.35 2007[10:SSi:2004.1,2004.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,20.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || -> equal(tl(skc9),nil)**.
% 60.13/60.35 2009[10:Rew:2007.0,1496.0] || -> equal(cons(hd(skc9),nil),skc9)**.
% 60.13/60.35 2010[10:Rew:2007.0,547.1] ssList(u) || -> equal(tl(app(skc9,u)),app(nil,u))**.
% 60.13/60.35 2012[10:Rew:83.1,2010.1] ssList(u) || -> equal(tl(app(skc9,u)),u)**.
% 60.13/60.35 2034[10:SpR:2009.0,246.1] ssItem(hd(skc9)) || -> equal(cons(hd(skc9),skc9),app(skc9,skc9))**.
% 60.13/60.35 2040[10:SSi:2034.0,1492.0] || -> equal(cons(hd(skc9),skc9),app(skc9,skc9))**.
% 60.13/60.35 2049[0:SpR:108.2,112.2] ssList(u) singletonP(u) ssItem(skf45(u)) ssList(nil) || -> equal(skf45(u),hd(u))**.
% 60.13/60.35 2060[0:SSi:2049.3,2049.2,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,20.0] ssList(u) singletonP(u) || -> equal(skf45(u),hd(u))**.
% 60.13/60.35 2061[0:Rew:2060.2,108.2] ssList(u) singletonP(u) || -> equal(cons(hd(u),nil),u)**.
% 60.13/60.35 2181[10:SpR:2012.1,119.2] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(hd(app(skc9,u)),u),app(skc9,u))**.
% 60.13/60.35 2197[10:Rew:545.1,2181.3] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(hd(skc9),u),app(skc9,u))**.
% 60.13/60.35 2198[10:SSi:2197.1,93.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.2] ssList(u) || -> equal(app(skc9,u),nil) equal(cons(hd(skc9),u),app(skc9,u))**.
% 60.13/60.35 2199[10:MRR:2198.1,1499.1] ssList(u) || -> equal(cons(hd(skc9),u),app(skc9,u))**.
% 60.13/60.35 2367[0:SpR:2060.2,20.0] ssList(u) singletonP(u) || -> ssItem(hd(u))*.
% 60.13/60.35 2426[0:Res:120.3,104.1] ssItem(skf66(u)) ssItem(skf65(u)) ssList(u) || lt(skf65(u),skf66(u))* -> totalorderedP(u).
% 60.13/60.35 2429[0:SSi:2426.1,2426.0,40.0,39.0] ssList(u) || lt(skf65(u),skf66(u))* -> totalorderedP(u).
% 60.13/60.35 2582[0:EqR:122.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 60.13/60.35 2587[0:SSi:2582.0,92.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 60.13/60.35 3394[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).
% 60.13/60.35 3418[0:Obv:3394.0] ssList(u) ssList(v) ssList(tl(u)) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 60.13/60.35 3419[0:MRR:3418.2,88.1] ssList(u) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 60.13/60.35 3780[0:SpR:129.0,153.4] ssList(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil))) ssList(u) ssList(skc15) || rearsegP(skc15,u)* -> rearsegP(skc9,u).
% 60.13/60.35 3795[0:SSi:3780.2,3780.0,1.0,93.1,93.0,93.1,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.2,5.0,78.0,5.1,2587.0,5.1,2.0,92.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.0,4.0,77.0,4.0,76.0,4.0,75.0,4.0,79.2,4.0,78.2,4.2,2587.2,4.0] ssList(u) || rearsegP(skc15,u)* -> rearsegP(skc9,u).
% 60.13/60.35 3817[0:Res:69.1,3795.1] ssList(skc15) ssList(skc15) || -> rearsegP(skc9,skc15)*.
% 60.13/60.35 3818[0:Obv:3817.0] ssList(skc15) || -> rearsegP(skc9,skc15)*.
% 60.13/60.35 3819[0:SSi:3818.0,1.0] || -> rearsegP(skc9,skc15)*.
% 60.13/60.35 3820[0:Res:3819.0,142.2] ssList(skc9) ssList(skc15) || rearsegP(skc15,skc9)* -> equal(skc15,skc9).
% 60.13/60.35 3821[10:SSi:3820.1,3820.0,1.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || rearsegP(skc15,skc9)* -> equal(skc15,skc9).
% 60.13/60.35 3876[0:EqR:146.3] ssList(u) ssList(app(v,u)) ssList(v) || -> rearsegP(app(v,u),u)*.
% 60.13/60.35 3878[0:SpL:278.0,146.3] ssList(skc9) ssList(u) ssList(nil) || equal(skc9,u) -> rearsegP(u,skc9)*.
% 60.13/60.35 3891[0:SSi:3876.1,93.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 60.13/60.35 3892[10:SSi:3878.2,3878.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] ssList(u) || equal(skc9,u) -> rearsegP(u,skc9)*.
% 60.13/60.35 3932[0:EqR:145.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 60.13/60.35 3947[0:SSi:3932.1,93.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 60.13/60.35 4393[0:SpR:130.2,3891.2] ssItem(u) ssList(v) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 60.13/60.35 4402[0:Obv:4393.1] ssItem(u) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 60.13/60.35 4403[0:SSi:4402.2,92.1,17.1,16.1,13.1,12.1,11.1,15.1,14.1,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.0,2587.2] ssItem(u) ssList(v) || -> rearsegP(cons(u,v),v)*.
% 60.13/60.35 4429[0:SpR:161.3,129.0] ssList(skc14) ssList(cons(skc11,nil)) ssList(skc13) || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),cons(skc12,nil)),skc15),skc9)**.
% 60.13/60.35 4431[0:SpR:161.3,129.0] ssList(skc15) ssList(cons(skc12,nil)) ssList(app(app(skc13,cons(skc11,nil)),skc14)) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),app(cons(skc12,nil),skc15)),skc9)**.
% 60.13/60.35 4473[0:SSi:4429.2,4429.1,4429.0,3.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2587.0,5.2,2.0] || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),cons(skc12,nil)),skc15),skc9)**.
% 60.13/60.35 4502[0:SSi:4431.2,4431.1,4431.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2587.0,5.0,2.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.2,2587.0,4.2,1.2] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),app(cons(skc12,nil),skc15)),skc9)**.
% 60.13/60.35 4547[0:SpL:278.0,163.3] ssList(nil) ssList(skc9) ssList(u) || equal(app(u,skc9),skc9)** -> equal(nil,u).
% 60.13/60.35 4580[10:SSi:4547.1,4547.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(u) || equal(app(u,skc9),skc9)** -> equal(nil,u).
% 60.13/60.35 5210[0:SpR:119.2,4403.2] ssList(u) ssItem(hd(u)) ssList(tl(u)) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 60.13/60.35 5220[0:Res:4403.2,142.2] ssItem(u) ssList(v) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 60.13/60.35 5228[0:MRR:5210.1,5210.2,87.1,88.1] ssList(u) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 60.13/60.35 5229[0:Obv:5220.1] ssItem(u) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 60.13/60.35 5230[0:SSi:5229.1,92.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 60.13/60.35 5231[0:MRR:5230.3,110.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> .
% 60.13/60.35 5334[0:Res:5228.2,3795.1] ssList(skc15) ssList(tl(skc15)) || -> equal(skc15,nil) rearsegP(skc9,tl(skc15))*.
% 60.13/60.35 5337[0:SSi:5334.0,1.0] ssList(tl(skc15)) || -> equal(skc15,nil) rearsegP(skc9,tl(skc15))*.
% 60.13/60.35 5343[0:SoR:5337.0,88.1] ssList(skc15) || -> equal(skc15,nil) rearsegP(skc9,tl(skc15))* equal(skc15,nil).
% 60.13/60.35 5344[0:Obv:5343.1] ssList(skc15) || -> rearsegP(skc9,tl(skc15))* equal(skc15,nil).
% 60.13/60.35 5345[0:SSi:5344.0,1.0] || -> rearsegP(skc9,tl(skc15))* equal(skc15,nil).
% 60.13/60.35 5346[11:Spt:5345.1] || -> equal(skc15,nil)**.
% 60.13/60.35 5351[11:Rew:5346.0,129.0] || -> equal(app(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil)),nil),skc9)**.
% 60.13/60.35 5386[11:SpR:5351.0,84.1] ssList(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil))) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil)),skc9)**.
% 60.13/60.35 5412[11:SSi:5386.0,93.0,93.1,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.2,78.0,5.0,2587.1,5.0,2.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.0,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.2,78.0,4.2,2587.2,4.2] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,nil)),skc9)**.
% 60.13/60.35 6333[10:SpL:2009.0,172.3] ssList(nil) ssItem(hd(skc9)) ssItem(u) || memberP(skc9,u)* -> memberP(nil,u) equal(u,hd(skc9)).
% 60.13/60.35 6346[10:SSi:6333.1,6333.0,1492.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssItem(u) || memberP(skc9,u)* -> memberP(nil,u) equal(u,hd(skc9)).
% 60.13/60.35 6347[10:MRR:6346.2,74.1] ssItem(u) || memberP(skc9,u)* -> equal(u,hd(skc9)).
% 60.13/60.35 7580[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))*.
% 60.13/60.35 7597[0:SSi:7580.6,7580.5,7580.4,7580.3,7580.2,30.0,29.0,28.0,27.0,26.0] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)* -> totalorderP(u) leq(skf55(u),skf56(u))*.
% 60.13/60.35 7598[0:MRR:7597.5,101.1] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)*+ -> totalorderP(u)*.
% 60.13/60.35 7732[0:SpL:176.2,192.7] ssList(u) ssList(v) ssList(skf69(u)) ssList(skf68(u)) ssList(skf67(u)) ssItem(skf66(u)) ssItem(skf65(u)) strictorderedP(v) || equal(u,v)* -> totalorderedP(u) lt(skf65(u),skf66(u))*.
% 60.13/60.35 7733[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))*.
% 60.13/60.35 7754[0:SSi:7733.6,7733.5,7733.4,7733.3,7733.2,35.0,34.0,33.0,32.0,31.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skf60(u),skf61(u))*.
% 60.13/60.35 7755[0:MRR:7754.5,103.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> strictorderP(u)*.
% 60.13/60.35 7756[0:SSi:7732.6,7732.5,7732.4,7732.3,7732.2,40.0,39.0,38.0,37.0,36.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> totalorderedP(u) lt(skf65(u),skf66(u))*.
% 60.13/60.35 7757[0:MRR:7756.5,2429.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> totalorderedP(u)*.
% 60.13/60.35 8027[0:SpL:2061.2,5231.2] ssList(u) singletonP(u) ssItem(hd(u)) ssList(nil) || rearsegP(nil,u)* -> .
% 60.13/60.35 8041[0:SSi:8027.3,8027.2,17.2,16.0,13.0,12.0,11.0,15.0,14.0,10.0,2367.0] ssList(u) singletonP(u) || rearsegP(nil,u)* -> .
% 60.13/60.35 8428[11:SpL:5412.0,188.4] ssItem(skc12) ssList(u) ssList(nil) ssList(app(app(skc13,cons(skc11,nil)),skc14)) || equal(skc9,u) -> memberP(u,skc12)*.
% 60.13/60.35 8441[11:SSi:8428.3,8428.2,8428.0,93.0,93.0,3.0,92.0,5.0,17.0,16.0,13.0,12.0,11.0,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.1,5.0,76.1,5.0,75.1,5.0,79.1,5.0,78.1,5.0,2587.0,5.0,2.0,17.0,16.0,13.0,12.0,11.0,15.2,14.0,10.2,4.2] ssList(u) || equal(skc9,u) -> memberP(u,skc12)*.
% 60.13/60.35 8527[11:Res:8441.2,6347.1] ssList(skc9) ssItem(skc12) || equal(skc9,skc9) -> equal(hd(skc9),skc12)**.
% 60.13/60.35 8533[11:Obv:8527.2] ssList(skc9) ssItem(skc12) || -> equal(hd(skc9),skc12)**.
% 60.13/60.35 8534[11:SSi:8533.1,8533.0,4.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || -> equal(hd(skc9),skc12)**.
% 60.13/60.35 8539[11:Rew:8534.0,2009.0] || -> equal(cons(skc12,nil),skc9)**.
% 60.13/60.35 8694[11:Rew:8539.0,5412.0] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),skc9),skc9)**.
% 60.13/60.35 9155[11:SpL:8694.0,4580.1] ssList(app(app(skc13,cons(skc11,nil)),skc14)) || equal(skc9,skc9) -> equal(app(app(skc13,cons(skc11,nil)),skc14),nil)**.
% 60.13/60.35 9167[11:Obv:9155.1] ssList(app(app(skc13,cons(skc11,nil)),skc14)) || -> equal(app(app(skc13,cons(skc11,nil)),skc14),nil)**.
% 60.13/60.35 9168[11:SSi:9167.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2587.0,5.2,2.2] || -> equal(app(app(skc13,cons(skc11,nil)),skc14),nil)**.
% 60.13/60.35 9690[11:SpR:9168.0,3947.2] ssList(app(skc13,cons(skc11,nil))) ssList(skc14) || -> frontsegP(nil,app(skc13,cons(skc11,nil)))*.
% 60.13/60.35 9714[11:SSi:9690.1,9690.0,2.0,93.1,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.2,5.0,2587.2,5.0] || -> frontsegP(nil,app(skc13,cons(skc11,nil)))*.
% 60.13/60.35 9781[11:Res:9714.0,94.1] ssList(app(skc13,cons(skc11,nil))) || -> equal(app(skc13,cons(skc11,nil)),nil)**.
% 60.13/60.35 9784[11:SSi:9781.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2587.0,5.2] || -> equal(app(skc13,cons(skc11,nil)),nil)**.
% 60.13/60.35 9815[11:SpR:9784.0,3891.2] ssList(cons(skc11,nil)) ssList(skc13) || -> rearsegP(nil,cons(skc11,nil))*.
% 60.13/60.35 9838[11:SSi:9815.1,9815.0,3.0,92.1,5.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,5.0,80.1,5.0,77.1,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2587.2,5.0] || -> rearsegP(nil,cons(skc11,nil))*.
% 60.13/60.35 9891[11:Res:9838.0,8041.2] ssList(cons(skc11,nil)) singletonP(cons(skc11,nil)) || -> .
% 60.13/60.35 9900[11:SSi:9891.1,9891.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2587.0,5.2,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2587.0,5.2] || -> .
% 60.13/60.35 9916[11:Spt:9900.0,5345.1,5346.0] || equal(skc15,nil)** -> .
% 60.13/60.35 9917[11:Spt:9900.0,5345.0] || -> rearsegP(skc9,tl(skc15))*.
% 60.13/60.35 12303[0:SpR:4502.0,3891.2] ssList(app(cons(skc12,nil),skc15)) ssList(app(app(skc13,cons(skc11,nil)),skc14)) || -> rearsegP(skc9,app(cons(skc12,nil),skc15))*.
% 60.13/60.35 12311[0:SpR:130.2,4502.0] ssItem(skc12) ssList(skc15) || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,skc15)),skc9)**.
% 60.13/60.35 12327[0:SSi:12311.1,12311.0,1.0,4.0] || -> equal(app(app(app(skc13,cons(skc11,nil)),skc14),cons(skc12,skc15)),skc9)**.
% 60.13/60.35 12328[0:SSi:12303.1,12303.0,93.0,93.0,3.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2587.2,5.0,2.0,93.1,92.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.2,2587.0,4.2,1.2] || -> rearsegP(skc9,app(cons(skc12,nil),skc15))*.
% 60.13/60.35 12360[0:SpR:130.2,12328.0] ssItem(skc12) ssList(skc15) || -> rearsegP(skc9,cons(skc12,skc15))*.
% 60.13/60.35 12364[0:SSi:12360.1,12360.0,1.0,4.0] || -> rearsegP(skc9,cons(skc12,skc15))*.
% 60.13/60.35 12367[0:Res:12364.0,142.2] ssList(skc9) ssList(cons(skc12,skc15)) || rearsegP(cons(skc12,skc15),skc9)* -> equal(cons(skc12,skc15),skc9).
% 60.13/60.35 12369[10:SSi:12367.1,12367.0,92.0,4.0,1.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.2] || rearsegP(cons(skc12,skc15),skc9)* -> equal(cons(skc12,skc15),skc9).
% 67.81/67.97 16532[0:EqR:7598.3] ssList(u) ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 67.81/67.97 16533[0:Obv:16532.0] ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 67.81/67.97 16597[0:EqR:7755.3] ssList(u) ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 67.81/67.97 16598[0:Obv:16597.0] ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 67.81/67.97 16637[0:EqR:7757.3] ssList(u) ssList(u) strictorderedP(u) || -> totalorderedP(u)*.
% 67.81/67.97 16638[0:Obv:16637.0] ssList(u) strictorderedP(u) || -> totalorderedP(u)*.
% 67.81/67.97 18299[0:SpL:12327.0,188.4] ssItem(skc12) ssList(u) ssList(skc15) ssList(app(app(skc13,cons(skc11,nil)),skc14)) || equal(skc9,u) -> memberP(u,skc12)*.
% 67.81/67.97 18310[0:SSi:18299.3,18299.2,18299.0,93.0,93.0,3.0,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.1,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.0,2587.0,5.2,2.0,1.2,4.2] ssList(u) || equal(skc9,u) -> memberP(u,skc12)*.
% 67.81/67.97 18334[0:Res:18310.2,74.1] ssList(nil) ssItem(skc12) || equal(skc9,nil)** -> .
% 67.81/67.97 18339[10:Res:18310.2,6347.1] ssList(skc9) ssItem(skc12) || equal(skc9,skc9) -> equal(hd(skc9),skc12)**.
% 67.81/67.97 18351[10:Obv:18339.2] ssList(skc9) ssItem(skc12) || -> equal(hd(skc9),skc12)**.
% 67.81/67.97 18352[10:SSi:18351.1,18351.0,4.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || -> equal(hd(skc9),skc12)**.
% 67.81/67.97 18356[10:Rew:18352.0,2009.0] || -> equal(cons(skc12,nil),skc9)**.
% 67.81/67.97 18364[10:Rew:18352.0,2040.0] || -> equal(app(skc9,skc9),cons(skc12,skc9))**.
% 67.81/67.97 18384[10:Rew:18352.0,2199.1] ssList(u) || -> equal(app(skc9,u),cons(skc12,u))**.
% 67.81/67.97 18527[10:Rew:18356.0,4473.0] || -> equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),skc15),skc9)**.
% 67.81/67.97 18759[10:Rew:18364.0,1964.0] || equal(cons(skc12,skc9),skc9)** -> .
% 67.81/67.97 18878[10:Rew:18384.1,348.3] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(cons(skc12,v),u)*.
% 67.81/67.97 19945[10:Res:18878.3,12369.0] ssList(skc9) ssList(skc15) || rearsegP(skc15,skc9) -> equal(cons(skc12,skc15),skc9)**.
% 67.81/67.97 19947[10:Rew:3821.1,19945.3] ssList(skc9) ssList(skc15) || rearsegP(skc15,skc9) -> equal(cons(skc12,skc9),skc9)**.
% 67.81/67.97 19948[10:SSi:19947.1,19947.0,1.0,7.0,1783.0,1786.0,1797.0,1801.0,1802.0,1866.0,1877.0,1879.0] || rearsegP(skc15,skc9) -> equal(cons(skc12,skc9),skc9)**.
% 67.81/67.97 19949[10:MRR:19948.1,18759.0] || rearsegP(skc15,skc9)* -> .
% 67.81/67.97 19954[10:Res:3892.2,19949.0] ssList(skc15) || equal(skc15,skc9)** -> .
% 67.81/67.97 19955[10:SSi:19954.0,1.0] || equal(skc15,skc9)** -> .
% 67.81/67.97 22094[10:SpL:18527.0,231.2] ssList(skc15) ssList(app(app(skc13,app(cons(skc11,nil),skc14)),skc9)) || equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),skc9),skc9)** -> equal(skc15,skc9).
% 67.81/67.97 22170[10:SSi:22094.1,22094.0,326.0,93.0,3.0,93.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.1,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.0,78.0,5.2,2587.2,5.0,2.2,1.1] || equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),skc9),skc9)** -> equal(skc15,skc9).
% 67.81/67.97 22171[10:MRR:22170.1,19955.0] || equal(app(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),skc9),skc9)** -> .
% 67.81/67.97 32852[10:SpL:18527.0,3419.2] ssList(app(app(skc13,app(cons(skc11,nil),skc14)),skc9)) ssList(skc15) || equal(tl(skc9),nil) -> equal(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),nil)** equal(skc15,nil).
% 67.81/67.97 32970[10:Rew:2007.0,32852.2] ssList(app(app(skc13,app(cons(skc11,nil),skc14)),skc9)) ssList(skc15) || equal(nil,nil) -> equal(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),nil)** equal(skc15,nil).
% 67.81/67.97 32971[10:Obv:32970.2] ssList(app(app(skc13,app(cons(skc11,nil),skc14)),skc9)) ssList(skc15) || -> equal(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),nil)** equal(skc15,nil).
% 67.81/67.97 35241[10:SSi:32971.1,32971.0,1.0,326.0,93.1,3.0,93.1,92.0,5.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,5.1,80.0,5.0,77.0,5.0,76.0,5.0,75.0,5.0,79.0,5.2,78.2,5.0,2587.2,5.1,2.0] || -> equal(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),nil)** equal(skc15,nil).
% 67.81/67.97 35242[11:MRR:35241.1,9916.0] || -> equal(app(app(skc13,app(cons(skc11,nil),skc14)),skc9),nil)**.
% 67.81/67.97 35246[11:Rew:35242.0,22171.0] || equal(app(nil,skc9),skc9)** -> .
% 67.81/67.97 35260[11:Rew:278.0,35246.0] || equal(skc9,skc9)* -> .
% 67.81/67.97 35261[11:Obv:35260.0] || -> .
% 67.81/67.97 35454[9:Spt:35261.0,219.0,1802.0] || totalorderP(skc9)* -> .
% 67.81/67.97 35455[9:Spt:35261.0,219.1] || -> equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 67.81/67.97 36870[9:Res:16533.2,35454.0] ssList(skc9) totalorderedP(skc9) || -> .
% 67.81/67.97 36874[9:SSi:36870.1,36870.0,7.0,1783.0,1786.0,1797.0,1801.0,7.0,1783.0,1786.0,1797.0,1801.0] || -> .
% 67.81/67.97 36878[8:Spt:36874.0,220.0,1801.0] || strictorderP(skc9)* -> .
% 67.81/67.97 36879[8:Spt:36874.0,220.1] || -> equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 67.81/67.97 37344[8:Res:16598.2,36878.0] ssList(skc9) strictorderedP(skc9) || -> .
% 67.81/67.97 37346[8:SSi:37344.1,37344.0,7.0,1783.0,1786.0,1797.0,7.0,1783.0,1786.0,1797.0] || -> .
% 67.81/67.97 37350[7:Spt:37346.0,265.0,1797.0] || cyclefreeP(skc9)* -> .
% 67.81/67.97 37351[7:Spt:37346.0,265.1] || -> leq(skf51(skc9),skf50(skc9))*.
% 67.81/67.97 38222[7:Res:1986.2,37350.0] ssList(skc9) singletonP(skc9) || -> .
% 67.81/67.97 38226[7:SSi:38222.0,7.0,1783.0,1786.0] singletonP(skc9) || -> .
% 67.81/67.97 38227[7:MRR:65.1,38226.0] || neq(skc10,nil)* -> .
% 67.81/67.97 38241[7:Res:424.1,38227.0] ssList(nil) || -> equal(skc10,nil)**.
% 67.81/67.97 38244[7:SSi:38241.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 67.81/67.97 38245[7:MRR:38244.0,1768.0] || -> .
% 67.81/67.97 38249[6:Spt:38245.0,221.0,1786.0] || totalorderedP(skc9)* -> .
% 67.81/67.97 38250[6:Spt:38245.0,221.1] || -> equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 67.81/67.97 39211[6:Res:16638.2,38249.0] ssList(skc9) strictorderedP(skc9) || -> .
% 67.81/67.97 39213[6:SSi:39211.1,39211.0,7.0,1783.0,7.0,1783.0] || -> .
% 67.81/67.97 39217[5:Spt:39213.0,222.0,1783.0] || strictorderedP(skc9)* -> .
% 67.81/67.97 39218[5:Spt:39213.0,222.1] || -> equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 67.81/67.97 39721[5:Res:1987.2,39217.0] ssList(skc9) singletonP(skc9) || -> .
% 67.81/67.97 39722[5:SSi:39721.0,7.0] singletonP(skc9) || -> .
% 67.81/67.97 39723[5:MRR:65.1,39722.0] || neq(skc10,nil)* -> .
% 67.81/67.97 39739[5:Res:424.1,39723.0] ssList(nil) || -> equal(skc10,nil)**.
% 67.81/67.97 39742[5:SSi:39739.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 67.81/67.97 39743[5:MRR:39742.0,1768.0] || -> .
% 67.81/67.97 39747[2:Spt:39743.0,239.1] || -> equal(skc9,nil)**.
% 67.81/67.97 40720[2:Rew:39747.0,18334.2] ssList(nil) ssItem(skc12) || equal(nil,nil)* -> .
% 67.81/67.97 40721[2:Obv:40720.2] ssList(nil) ssItem(skc12) || -> .
% 67.81/67.97 40722[2:SSi:40721.1,40721.0,4.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> .
% 67.81/67.97 41939[1:Spt:40722.0,245.1] || -> equal(skc9,nil)**.
% 67.81/67.97 42055[1:Rew:41939.0,18334.2] ssList(nil) ssItem(skc12) || equal(nil,nil)* -> .
% 67.81/67.97 42056[1:Obv:42055.2] ssList(nil) ssItem(skc12) || -> .
% 67.81/67.97 42057[1:SSi:42056.1,42056.0,4.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> .
% 67.81/67.97 % SZS output end Refutation
% 67.81/67.97 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax9 ax10 ax11 ax49 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax75 ax76 ax8 ax16 ax26 ax46 ax58 ax15 ax18 ax23 ax25 ax78 ax93 ax81 ax83 ax85 ax48 ax5 ax6 ax50 ax67 ax70 ax86 ax82 ax80 ax79 ax37 ax12 ax3
% 67.81/67.97
%------------------------------------------------------------------------------