TSTP Solution File: SWC193+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC193+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 22:02:23 EDT 2022
% Result : Theorem 9.14s 9.34s
% Output : Refutation 9.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC193+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.14/0.33 % Computer : n019.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sun Jun 12 06:58:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 9.14/9.34
% 9.14/9.34 SPASS V 3.9
% 9.14/9.34 SPASS beiseite: Proof found.
% 9.14/9.34 % SZS status Theorem
% 9.14/9.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.14/9.34 SPASS derived 9222 clauses, backtracked 2738 clauses, performed 38 splits and kept 5914 clauses.
% 9.14/9.34 SPASS allocated 110907 KBytes.
% 9.14/9.34 SPASS spent 0:00:08.98 on the problem.
% 9.14/9.34 0:00:00.04 for the input.
% 9.14/9.34 0:00:00.07 for the FLOTTER CNF translation.
% 9.14/9.34 0:00:00.11 for inferences.
% 9.14/9.34 0:00:00.21 for the backtracking.
% 9.14/9.34 0:00:08.37 for the reduction.
% 9.14/9.34
% 9.14/9.34
% 9.14/9.34 Here is a proof with depth 8, length 327 :
% 9.14/9.34 % SZS output start Refutation
% 9.14/9.34 1[0:Inp] || -> ssList(skc13)*.
% 9.14/9.34 2[0:Inp] || -> ssList(skc12)*.
% 9.14/9.34 3[0:Inp] || -> ssItem(skc11)*.
% 9.14/9.34 4[0:Inp] || -> ssItem(skc10)*.
% 9.14/9.34 5[0:Inp] || -> ssList(skc9)*.
% 9.14/9.34 6[0:Inp] || -> ssList(skc8)*.
% 9.14/9.34 7[0:Inp] || -> ssItem(skc15)*.
% 9.14/9.34 8[0:Inp] || -> ssItem(skc14)*.
% 9.14/9.34 9[0:Inp] || -> ssList(nil)*.
% 9.14/9.34 10[0:Inp] || -> cyclefreeP(nil)*.
% 9.14/9.34 11[0:Inp] || -> totalorderP(nil)*.
% 9.14/9.34 12[0:Inp] || -> strictorderP(nil)*.
% 9.14/9.34 13[0:Inp] || -> totalorderedP(nil)*.
% 9.14/9.34 14[0:Inp] || -> strictorderedP(nil)*.
% 9.14/9.34 15[0:Inp] || -> duplicatefreeP(nil)*.
% 9.14/9.34 16[0:Inp] || -> equalelemsP(nil)*.
% 9.14/9.34 17[0:Inp] || -> segmentP(skc9,skc8)*.
% 9.14/9.34 18[0:Inp] || -> ssItem(skf45(u))*.
% 9.14/9.34 56[0:Inp] || equal(skc11,skc10)** -> .
% 9.14/9.34 57[0:Inp] || equal(skc15,skc14)** -> .
% 9.14/9.34 64[0:Inp] || neq(skc9,nil)* -> singletonP(skc8).
% 9.14/9.34 73[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 9.14/9.34 74[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 9.14/9.34 75[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 9.14/9.34 76[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 9.14/9.34 77[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 9.14/9.34 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 9.14/9.34 79[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 9.14/9.34 80[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 9.14/9.34 82[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 9.14/9.34 83[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 9.14/9.34 86[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 9.14/9.34 87[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 9.14/9.34 88[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 9.14/9.34 91[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 9.14/9.34 92[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 9.14/9.34 97[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 9.14/9.34 107[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 9.14/9.34 108[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 9.14/9.34 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 9.14/9.34 111[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 9.14/9.34 112[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 9.14/9.34 113[0:Inp] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8)**.
% 9.14/9.34 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 9.14/9.34 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 9.14/9.34 129[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 9.14/9.34 130[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 9.14/9.34 131[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 9.14/9.34 134[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 9.14/9.34 140[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(v,u).
% 9.14/9.34 144[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 9.14/9.34 145[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 9.14/9.34 152[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(w,v) -> rearsegP(app(u,w),v)*.
% 9.14/9.34 153[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 9.14/9.34 154[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 9.14/9.34 155[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 9.14/9.34 160[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 9.14/9.34 168[0:Inp] ssItem(u) ssList(v) ssList(w) || -> equal(app(cons(u,v),w),cons(u,app(v,w)))**.
% 9.14/9.34 171[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 9.14/9.34 174[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 9.14/9.34 175[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 9.14/9.34 176[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 9.14/9.34 177[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 9.14/9.34 187[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 9.14/9.34 190[0:Inp] ssList(u) ssList(v) ssList(w) ssItem(x) ssItem(y) equalelemsP(u) || equal(app(w,cons(y,cons(x,v))),u)* -> equal(y,x).
% 9.14/9.34 218[0:Res:6.0,177.0] || -> totalorderP(skc8) equal(app(app(skf57(skc8),cons(skf55(skc8),skf58(skc8))),cons(skf56(skc8),skf59(skc8))),skc8)**.
% 9.14/9.34 219[0:Res:6.0,176.0] || -> strictorderP(skc8) equal(app(app(skf62(skc8),cons(skf60(skc8),skf63(skc8))),cons(skf61(skc8),skf64(skc8))),skc8)**.
% 9.14/9.34 220[0:Res:6.0,175.0] || -> totalorderedP(skc8) equal(app(app(skf67(skc8),cons(skf65(skc8),skf68(skc8))),cons(skf66(skc8),skf69(skc8))),skc8)**.
% 9.14/9.34 221[0:Res:6.0,174.0] || -> strictorderedP(skc8) equal(app(app(skf72(skc8),cons(skf70(skc8),skf73(skc8))),cons(skf71(skc8),skf74(skc8))),skc8)**.
% 9.14/9.34 238[0:Res:6.0,155.0] ssList(u) || -> equal(skc8,nil) equal(app(tl(skc8),u),tl(app(skc8,u)))**.
% 9.14/9.34 244[0:Res:6.0,134.0] ssList(u) || -> equal(skc8,nil) equal(hd(app(skc8,u)),hd(skc8))**.
% 9.14/9.34 245[0:Res:6.0,129.0] ssItem(u) || -> equal(app(cons(u,nil),skc8),cons(u,skc8))**.
% 9.14/9.34 247[0:Res:6.0,131.0] ssList(u) || equal(app(skc8,u),nil)** -> equal(skc8,nil).
% 9.14/9.34 250[0:Res:6.0,119.0] || -> equal(skc8,nil) equal(cons(hd(skc8),tl(skc8)),skc8)**.
% 9.14/9.34 251[0:Res:6.0,107.1] singletonP(skc8) || -> equal(cons(skf45(skc8),nil),skc8)**.
% 9.14/9.34 253[0:Res:6.0,109.0] ssItem(u) || equal(cons(u,skc8),skc8)** -> .
% 9.14/9.34 255[0:Res:6.0,111.0] ssItem(u) || -> equal(hd(cons(u,skc8)),u)**.
% 9.14/9.34 264[0:Res:6.0,88.0] || -> cyclefreeP(skc8) leq(skf51(skc8),skf50(skc8))*.
% 9.14/9.34 267[0:Res:6.0,91.0] ssItem(u) || -> ssList(cons(u,skc8))*.
% 9.14/9.34 273[0:Res:6.0,97.0] || segmentP(nil,skc8)* -> equal(skc8,nil).
% 9.14/9.34 275[0:Res:6.0,86.0] || -> ssItem(hd(skc8))* equal(skc8,nil).
% 9.14/9.34 277[0:Res:6.0,82.0] || -> equal(app(nil,skc8),skc8)**.
% 9.14/9.34 308[0:Res:6.0,154.1] ssItem(u) || strictorderedP(cons(u,skc8))* -> lt(u,hd(skc8)) equal(skc8,nil).
% 9.14/9.34 423[0:Res:5.0,108.0] ssList(u) || -> neq(skc9,u)* equal(skc9,u).
% 9.14/9.34 478[0:Res:5.0,153.1] ssItem(u) || totalorderedP(cons(u,skc9))* -> leq(u,hd(skc9)) equal(skc9,nil).
% 9.14/9.34 544[1:Spt:244.0,244.2] ssList(u) || -> equal(hd(app(skc8,u)),hd(skc8))**.
% 9.14/9.34 546[2:Spt:238.0,238.2] ssList(u) || -> equal(app(tl(skc8),u),tl(app(skc8,u)))**.
% 9.14/9.34 552[3:Spt:308.3] || -> equal(skc8,nil)**.
% 9.14/9.34 553[3:Rew:552.0,544.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 9.14/9.34 571[3:Rew:552.0,267.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 9.14/9.34 572[3:Rew:552.0,255.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 9.14/9.34 726[3:Rew:82.1,553.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 9.14/9.34 1177[3:SpR:572.1,726.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 9.14/9.34 1180[3:SSi:1177.1,80.1,79.1,76.1,75.1,74.1,78.1,77.1,571.1] ssItem(u) || -> equal(u,hd(nil))*.
% 9.14/9.34 1246[3:SpR:1180.1,1180.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 9.14/9.34 1286[3:EmS:1246.0,3.0] ssItem(u) || -> equal(u,skc11)*.
% 9.14/9.34 1310[3:EmS:1286.0,7.0] || -> equal(skc15,skc11)**.
% 9.14/9.34 1311[3:EmS:1286.0,8.0] || -> equal(skc14,skc11)**.
% 9.14/9.34 1314[3:Rew:1310.0,57.0] || equal(skc14,skc11)** -> .
% 9.14/9.34 1417[3:Rew:1311.0,1314.0] || equal(skc11,skc11)* -> .
% 9.14/9.34 1418[3:Obv:1417.0] || -> .
% 9.14/9.34 1447[3:Spt:1418.0,308.3,552.0] || equal(skc8,nil)** -> .
% 9.14/9.34 1448[3:Spt:1418.0,308.0,308.1,308.2] ssItem(u) || strictorderedP(cons(u,skc8))* -> lt(u,hd(skc8)).
% 9.14/9.34 1450[3:MRR:275.1,1447.0] || -> ssItem(hd(skc8))*.
% 9.14/9.34 1451[3:MRR:273.1,1447.0] || segmentP(nil,skc8)* -> .
% 9.14/9.34 1454[3:MRR:250.0,1447.0] || -> equal(cons(hd(skc8),tl(skc8)),skc8)**.
% 9.14/9.34 1457[3:MRR:247.2,1447.0] ssList(u) || equal(app(skc8,u),nil)** -> .
% 9.14/9.34 1462[4:Spt:478.3] || -> equal(skc9,nil)**.
% 9.14/9.34 1470[4:Rew:1462.0,17.0] || -> segmentP(nil,skc8)*.
% 9.14/9.34 1615[4:MRR:1470.0,1451.0] || -> .
% 9.14/9.34 1726[4:Spt:1615.0,478.3,1462.0] || equal(skc9,nil)** -> .
% 9.14/9.34 1727[4:Spt:1615.0,478.0,478.1,478.2] ssItem(u) || totalorderedP(cons(u,skc9))* -> leq(u,hd(skc9)).
% 9.14/9.34 1741[5:Spt:221.0] || -> strictorderedP(skc8)*.
% 9.14/9.34 1744[6:Spt:220.0] || -> totalorderedP(skc8)*.
% 9.14/9.34 1755[7:Spt:264.0] || -> cyclefreeP(skc8)*.
% 9.14/9.34 1759[8:Spt:219.0] || -> strictorderP(skc8)*.
% 9.14/9.34 1760[9:Spt:218.0] || -> totalorderP(skc8)*.
% 9.14/9.34 1768[10:Spt:64.0] || neq(skc9,nil)* -> .
% 9.14/9.34 1820[10:Res:423.1,1768.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.14/9.34 1821[10:SSi:1820.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.14/9.34 1822[10:MRR:1821.0,1726.0] || -> .
% 9.14/9.34 1823[10:Spt:1822.0,64.0,1768.0] || -> neq(skc9,nil)*.
% 9.14/9.34 1824[10:Spt:1822.0,64.1] || -> singletonP(skc8)*.
% 9.14/9.34 1825[10:MRR:251.0,1824.0] || -> equal(cons(skf45(skc8),nil),skc8)**.
% 9.14/9.34 1826[10:SpR:1825.0,80.1] ssItem(skf45(skc8)) || -> equalelemsP(skc8)*.
% 9.14/9.34 1827[10:SpR:1825.0,79.1] ssItem(skf45(skc8)) || -> duplicatefreeP(skc8)*.
% 9.14/9.34 1835[10:SSi:1826.0,18.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0] || -> equalelemsP(skc8)*.
% 9.14/9.34 1837[10:SSi:1827.0,18.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0] || -> duplicatefreeP(skc8)*.
% 9.14/9.34 1905[10:SpR:1825.0,245.1] ssItem(skf45(skc8)) || -> equal(cons(skf45(skc8),skc8),app(skc8,skc8))**.
% 9.14/9.34 1907[10:SSi:1905.0,18.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || -> equal(cons(skf45(skc8),skc8),app(skc8,skc8))**.
% 9.14/9.34 1915[10:SpL:1907.0,253.1] ssItem(skf45(skc8)) || equal(app(skc8,skc8),skc8)** -> .
% 9.14/9.34 1922[10:SSi:1915.0,18.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || equal(app(skc8,skc8),skc8)** -> .
% 9.14/9.34 1926[0:SpR:107.2,80.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> equalelemsP(u)*.
% 9.14/9.34 1928[0:SpR:107.2,76.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> strictorderP(u)*.
% 9.14/9.34 1929[0:SpR:107.2,75.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> totalorderP(u)*.
% 9.14/9.34 1930[0:SpR:107.2,74.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> cyclefreeP(u)*.
% 9.14/9.34 1931[0:SpR:107.2,78.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> strictorderedP(u)*.
% 9.14/9.34 1932[0:SpR:107.2,77.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> totalorderedP(u)*.
% 9.14/9.34 1940[0:SSi:1926.2,18.0] ssList(u) singletonP(u) || -> equalelemsP(u)*.
% 9.14/9.34 1942[0:SSi:1928.2,18.0] ssList(u) singletonP(u) || -> strictorderP(u)*.
% 9.14/9.34 1943[0:SSi:1929.2,18.0] ssList(u) singletonP(u) || -> totalorderP(u)*.
% 9.14/9.34 1944[0:SSi:1930.2,18.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 9.14/9.34 1945[0:SSi:1931.2,18.0] ssList(u) singletonP(u) || -> strictorderedP(u)*.
% 9.14/9.34 1946[0:SSi:1932.2,18.0] ssList(u) singletonP(u) || -> totalorderedP(u)*.
% 9.14/9.34 1962[10:SpR:1825.0,112.2] ssItem(skf45(skc8)) ssList(nil) || -> equal(tl(skc8),nil)**.
% 9.14/9.34 1965[10:SSi:1962.1,1962.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0,18.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || -> equal(tl(skc8),nil)**.
% 9.14/9.34 1967[10:Rew:1965.0,1454.0] || -> equal(cons(hd(skc8),nil),skc8)**.
% 9.14/9.34 1968[10:Rew:1965.0,546.1] ssList(u) || -> equal(tl(app(skc8,u)),app(nil,u))**.
% 9.14/9.34 1970[10:Rew:82.1,1968.1] ssList(u) || -> equal(tl(app(skc8,u)),u)**.
% 9.14/9.34 1992[10:SpR:1967.0,245.1] ssItem(hd(skc8)) || -> equal(cons(hd(skc8),skc8),app(skc8,skc8))**.
% 9.14/9.34 1998[10:SSi:1992.0,1450.0] || -> equal(cons(hd(skc8),skc8),app(skc8,skc8))**.
% 9.14/9.34 2007[0:SpR:107.2,111.2] ssList(u) singletonP(u) ssItem(skf45(u)) ssList(nil) || -> equal(skf45(u),hd(u))**.
% 9.14/9.34 2018[0:SSi:2007.3,2007.2,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0,18.0] ssList(u) singletonP(u) || -> equal(skf45(u),hd(u))**.
% 9.14/9.34 2185[10:SpR:1970.1,119.2] ssList(u) ssList(app(skc8,u)) || -> equal(app(skc8,u),nil) equal(cons(hd(app(skc8,u)),u),app(skc8,u))**.
% 9.14/9.34 2202[10:Rew:544.1,2185.3] ssList(u) ssList(app(skc8,u)) || -> equal(app(skc8,u),nil) equal(cons(hd(skc8),u),app(skc8,u))**.
% 9.14/9.34 2203[10:SSi:2202.1,92.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.2] ssList(u) || -> equal(app(skc8,u),nil) equal(cons(hd(skc8),u),app(skc8,u))**.
% 9.14/9.34 2204[10:MRR:2203.1,1457.1] ssList(u) || -> equal(cons(hd(skc8),u),app(skc8,u))**.
% 9.14/9.34 2326[0:SpR:2018.2,18.0] ssList(u) singletonP(u) || -> ssItem(hd(u))*.
% 9.14/9.34 2571[0:EqR:122.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 9.14/9.34 2576[0:SSi:2571.0,91.1,16.1,15.1,12.1,11.1,10.1,14.1,13.0,9.0,80.0,79.0,76.0,75.0,74.0,78.0,77.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 9.14/9.34 3680[0:SpR:113.0,152.4] ssList(app(app(skc12,cons(skc10,nil)),cons(skc11,nil))) ssList(u) ssList(skc13) || rearsegP(skc13,u)* -> rearsegP(skc8,u).
% 9.14/9.34 3690[0:SSi:3680.2,3680.0,1.0,92.1,92.0,2.1,91.0,4.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,4.1,79.0,4.0,76.0,4.0,75.0,4.0,74.0,4.0,78.0,4.2,77.0,4.1,2576.0,4.1,91.0,3.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,3.1,79.0,3.0,76.0,3.0,75.0,3.0,74.0,3.0,78.0,3.2,77.0,3.2,2576.2,3.0] ssList(u) || rearsegP(skc13,u)* -> rearsegP(skc8,u).
% 9.14/9.34 3846[0:EqR:145.3] ssList(u) ssList(app(v,u)) ssList(v) || -> rearsegP(app(v,u),u)*.
% 9.14/9.34 3861[0:SSi:3846.1,92.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 9.14/9.34 3897[0:EqR:144.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 9.14/9.34 3912[0:SSi:3897.1,92.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 9.14/9.34 4287[0:SpR:160.3,113.0] ssList(cons(skc11,nil)) ssList(cons(skc10,nil)) ssList(skc12) || -> equal(app(app(skc12,app(cons(skc10,nil),cons(skc11,nil))),skc13),skc8)**.
% 9.14/9.34 4288[0:SpR:160.3,113.0] ssList(skc13) ssList(cons(skc11,nil)) ssList(app(skc12,cons(skc10,nil))) || -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8)**.
% 9.14/9.34 4327[0:SSi:4287.2,4287.1,4287.0,2.0,91.1,4.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,4.0,79.1,4.0,76.1,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2576.2,4.0,91.1,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.1,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2576.2,3.0] || -> equal(app(app(skc12,app(cons(skc10,nil),cons(skc11,nil))),skc13),skc8)**.
% 9.14/9.34 4336[0:SSi:4288.2,4288.1,4288.0,92.0,2.0,91.1,4.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,4.0,79.1,4.0,76.1,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2576.2,4.0,91.1,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.1,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2576.2,3.0,1.2] || -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc11,nil),skc13)),skc8)**.
% 9.14/9.34 4678[0:SpR:129.2,3861.2] ssItem(u) ssList(v) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 9.14/9.34 4687[0:Obv:4678.1] ssItem(u) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 9.14/9.34 4688[0:SSi:4687.2,91.1,16.1,15.1,12.1,11.1,10.1,14.1,13.1,9.0,80.0,79.0,76.0,75.0,74.0,78.0,77.0,2576.2] ssItem(u) ssList(v) || -> rearsegP(cons(u,v),v)*.
% 9.14/9.34 4903[0:SpR:245.1,3912.2] ssItem(u) ssList(cons(u,nil)) ssList(skc8) || -> frontsegP(cons(u,skc8),cons(u,nil))*.
% 9.14/9.34 4905[0:SpR:113.0,3912.2] ssList(app(app(skc12,cons(skc10,nil)),cons(skc11,nil))) ssList(skc13) || -> frontsegP(skc8,app(app(skc12,cons(skc10,nil)),cons(skc11,nil)))*.
% 9.14/9.34 4914[10:SSi:4903.2,4903.1,6.1,1741.1,1744.1,1755.1,1759.1,1760.1,1824.1,1835.1,1837.0,91.0,16.0,15.0,12.0,11.0,10.0,14.0,13.2,9.0,80.0,79.0,76.0,75.0,74.0,78.0,77.0,2576.0] ssItem(u) || -> frontsegP(cons(u,skc8),cons(u,nil))*.
% 9.14/9.34 4927[0:SSi:4905.1,4905.0,1.0,92.1,92.0,2.1,91.0,4.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,4.1,79.0,4.0,76.0,4.0,75.0,4.0,74.0,4.0,78.0,4.2,77.0,4.1,2576.0,4.1,91.0,3.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,3.1,79.0,3.0,76.0,3.0,75.0,3.0,74.0,3.0,78.0,3.2,77.0,3.2,2576.2,3.0] || -> frontsegP(skc8,app(app(skc12,cons(skc10,nil)),cons(skc11,nil)))*.
% 9.14/9.34 4936[10:SpR:1967.0,4914.1] ssItem(hd(skc8)) || -> frontsegP(cons(hd(skc8),skc8),skc8)*.
% 9.14/9.34 4946[10:Rew:1998.0,4936.1] ssItem(hd(skc8)) || -> frontsegP(app(skc8,skc8),skc8)*.
% 9.14/9.34 4947[10:SSi:4946.0,1450.0] || -> frontsegP(app(skc8,skc8),skc8)*.
% 9.14/9.34 5181[0:Res:4927.0,140.2] ssList(skc8) ssList(app(app(skc12,cons(skc10,nil)),cons(skc11,nil))) || frontsegP(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8)* -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8).
% 9.14/9.34 5185[10:SSi:5181.1,5181.0,92.0,92.0,2.0,91.0,4.0,16.0,15.0,12.0,11.0,10.0,14.1,13.0,9.1,80.0,4.1,79.0,4.1,76.0,4.1,75.0,4.1,74.0,4.1,78.0,4.1,77.0,4.0,2576.0,4.0,91.0,3.0,16.0,15.0,12.0,11.2,10.0,14.1,13.0,9.1,80.0,3.1,79.0,3.1,76.0,3.1,75.0,3.1,74.0,3.1,78.0,3.1,77.0,3.0,2576.0,3.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.2,1824.0,1835.2,1837.2] || frontsegP(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8)* -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8).
% 9.14/9.34 5274[0:SpR:119.2,4688.2] ssList(u) ssItem(hd(u)) ssList(tl(u)) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 9.14/9.34 5292[0:MRR:5274.1,5274.2,86.1,87.1] ssList(u) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 9.14/9.34 5398[0:Res:5292.2,3690.1] ssList(skc13) ssList(tl(skc13)) || -> equal(skc13,nil) rearsegP(skc8,tl(skc13))*.
% 9.14/9.34 5401[0:SSi:5398.0,1.0] ssList(tl(skc13)) || -> equal(skc13,nil) rearsegP(skc8,tl(skc13))*.
% 9.14/9.34 5407[0:SoR:5401.0,87.1] ssList(skc13) || -> equal(skc13,nil) rearsegP(skc8,tl(skc13))* equal(skc13,nil).
% 9.14/9.34 5408[0:Obv:5407.1] ssList(skc13) || -> rearsegP(skc8,tl(skc13))* equal(skc13,nil).
% 9.14/9.34 5409[0:SSi:5408.0,1.0] || -> rearsegP(skc8,tl(skc13))* equal(skc13,nil).
% 9.14/9.34 5448[11:Spt:5409.1] || -> equal(skc13,nil)**.
% 9.14/9.34 5450[11:Rew:5448.0,113.0] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),nil),skc8)**.
% 9.14/9.34 5518[11:SpR:5450.0,83.1] ssList(app(app(skc12,cons(skc10,nil)),cons(skc11,nil))) || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8)**.
% 9.14/9.34 5542[11:SSi:5518.0,92.0,92.1,2.0,91.1,4.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,4.0,79.1,4.0,76.0,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.2,4.0,2576.1,4.0,91.1,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.0,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.2,3.0,2576.2,3.2] || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8)**.
% 9.14/9.34 5579[11:SpR:5542.0,160.3] ssList(cons(skc11,nil)) ssList(cons(skc10,nil)) ssList(skc12) || -> equal(app(skc12,app(cons(skc10,nil),cons(skc11,nil))),skc8)**.
% 9.14/9.34 5594[11:SSi:5579.2,5579.1,5579.0,2.0,91.1,4.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,4.0,79.1,4.0,76.1,4.0,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2576.2,4.0,91.1,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.1,3.0,75.0,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2576.2,3.0] || -> equal(app(skc12,app(cons(skc10,nil),cons(skc11,nil))),skc8)**.
% 9.14/9.34 5669[11:SpR:129.2,5594.0] ssItem(skc10) ssList(cons(skc11,nil)) || -> equal(app(skc12,cons(skc10,cons(skc11,nil))),skc8)**.
% 9.14/9.34 5680[11:SSi:5669.1,5669.0,91.0,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.1,3.0,75.1,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2576.0,3.0,4.2] || -> equal(app(skc12,cons(skc10,cons(skc11,nil))),skc8)**.
% 9.14/9.34 6487[10:SpL:1967.0,171.3] ssList(nil) ssItem(hd(skc8)) ssItem(u) || memberP(skc8,u)* -> memberP(nil,u) equal(u,hd(skc8)).
% 9.14/9.34 6491[10:SSi:6487.1,6487.0,2326.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.2] ssItem(u) || memberP(skc8,u)* -> memberP(nil,u) equal(u,hd(skc8)).
% 9.14/9.34 6492[10:MRR:6491.2,73.1] ssItem(u) || memberP(skc8,u)* -> equal(u,hd(skc8)).
% 9.14/9.34 7542[11:SpL:5680.0,190.6] ssList(u) ssList(nil) ssList(skc12) ssItem(skc11) ssItem(skc10) equalelemsP(u) || equal(skc8,u)* -> equal(skc11,skc10)**.
% 9.14/9.34 7545[11:SSi:7542.4,7542.3,7542.2,7542.1,4.0,3.0,2.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] ssList(u) equalelemsP(u) || equal(skc8,u)* -> equal(skc11,skc10)**.
% 9.14/9.34 7546[11:MRR:7545.3,56.0] ssList(u) equalelemsP(u) || equal(skc8,u)* -> .
% 9.14/9.34 7899[11:EmS:7546.0,7546.1,6.0,1940.2] singletonP(skc8) ssList(skc8) || equal(skc8,skc8)* -> .
% 9.14/9.34 7940[11:Obv:7899.2] singletonP(skc8) ssList(skc8) || -> .
% 9.14/9.34 7941[11:SSi:7940.1,7940.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || -> .
% 9.14/9.34 7982[11:Spt:7941.0,5409.1,5448.0] || equal(skc13,nil)** -> .
% 9.14/9.34 7983[11:Spt:7941.0,5409.0] || -> rearsegP(skc8,tl(skc13))*.
% 9.14/9.34 9266[0:SpR:129.2,4336.0] ssItem(skc11) ssList(skc13) || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8)**.
% 9.14/9.34 9280[0:SSi:9266.1,9266.0,1.0,3.0] || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,skc13)),skc8)**.
% 9.14/9.34 9368[0:SpR:129.2,4327.0] ssItem(skc10) ssList(cons(skc11,nil)) || -> equal(app(app(skc12,cons(skc10,cons(skc11,nil))),skc13),skc8)**.
% 9.14/9.34 9381[0:SSi:9368.1,9368.0,91.0,3.0,16.1,15.0,12.1,11.0,10.1,14.0,13.1,9.0,80.1,3.0,79.1,3.0,76.1,3.0,75.1,3.0,74.0,3.0,78.0,3.0,77.0,3.0,2576.0,3.0,4.2] || -> equal(app(app(skc12,cons(skc10,cons(skc11,nil))),skc13),skc8)**.
% 9.14/9.34 9436[0:SpL:9280.0,187.4] ssItem(skc11) ssList(u) ssList(skc13) ssList(app(skc12,cons(skc10,nil))) || equal(skc8,u) -> memberP(u,skc11)*.
% 9.14/9.34 9445[0:SSi:9436.3,9436.2,9436.0,92.0,2.0,91.0,4.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,4.1,79.0,4.1,76.0,4.1,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2576.0,4.2,1.0,3.2] ssList(u) || equal(skc8,u) -> memberP(u,skc11)*.
% 9.14/9.34 9467[0:Res:9445.2,73.1] ssList(nil) ssItem(skc11) || equal(skc8,nil)** -> .
% 9.14/9.34 9470[10:Res:9445.2,6492.1] ssList(skc8) ssItem(skc11) || equal(skc8,skc8) -> equal(hd(skc8),skc11)**.
% 9.14/9.34 9477[10:Obv:9470.2] ssList(skc8) ssItem(skc11) || -> equal(hd(skc8),skc11)**.
% 9.14/9.34 9478[10:SSi:9477.1,9477.0,3.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || -> equal(hd(skc8),skc11)**.
% 9.14/9.34 9482[10:Rew:9478.0,1967.0] || -> equal(cons(skc11,nil),skc8)**.
% 9.14/9.34 9486[10:Rew:9478.0,1998.0] || -> equal(app(skc8,skc8),cons(skc11,skc8))**.
% 9.14/9.34 9506[10:Rew:9478.0,2204.1] ssList(u) || -> equal(app(skc8,u),cons(skc11,u))**.
% 9.14/9.34 9624[10:Rew:9482.0,113.0] || -> equal(app(app(app(skc12,cons(skc10,nil)),skc8),skc13),skc8)**.
% 9.14/9.34 9633[10:Rew:9482.0,9381.0] || -> equal(app(app(skc12,cons(skc10,skc8)),skc13),skc8)**.
% 9.14/9.34 9641[10:Rew:9482.0,5185.0] || frontsegP(app(app(skc12,cons(skc10,nil)),skc8),skc8) -> equal(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc8)**.
% 9.14/9.34 9698[10:Rew:9486.0,4947.0] || -> frontsegP(cons(skc11,skc8),skc8)*.
% 9.14/9.34 9707[10:Rew:9486.0,1922.0] || equal(cons(skc11,skc8),skc8)** -> .
% 9.14/9.34 9730[10:Rew:9506.1,1970.1] ssList(u) || -> equal(tl(cons(skc11,u)),u)**.
% 9.14/9.34 9816[10:Rew:9482.0,9641.1] || frontsegP(app(app(skc12,cons(skc10,nil)),skc8),skc8)* -> equal(app(app(skc12,cons(skc10,nil)),skc8),skc8).
% 9.14/9.34 10411[10:SpR:9633.0,160.3] ssList(skc13) ssList(cons(skc10,skc8)) ssList(skc12) || -> equal(app(skc12,app(cons(skc10,skc8),skc13)),skc8)**.
% 9.14/9.34 10426[10:SSi:10411.2,10411.1,10411.0,2.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.2,1.0] || -> equal(app(skc12,app(cons(skc10,skc8),skc13)),skc8)**.
% 9.14/9.34 10515[10:SpR:10426.0,3912.2] ssList(skc12) ssList(app(cons(skc10,skc8),skc13)) || -> frontsegP(skc8,skc12)*.
% 9.14/9.34 10518[10:SpR:10426.0,134.3] ssList(app(cons(skc10,skc8),skc13)) ssList(skc12) || -> equal(skc12,nil) equal(hd(skc12),hd(skc8))**.
% 9.14/9.34 10540[10:SSi:10515.1,10515.0,92.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0,1.2,2.2] || -> frontsegP(skc8,skc12)*.
% 9.14/9.34 10542[10:Rew:9478.0,10518.3] ssList(app(cons(skc10,skc8),skc13)) ssList(skc12) || -> equal(skc12,nil) equal(hd(skc12),skc11)**.
% 9.14/9.34 10543[10:SSi:10542.1,10542.0,2.0,92.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.2,1837.2,1.0] || -> equal(skc12,nil) equal(hd(skc12),skc11)**.
% 9.14/9.34 10628[10:Res:10540.0,140.2] ssList(skc8) ssList(skc12) || frontsegP(skc12,skc8)* -> equal(skc12,skc8).
% 9.14/9.34 10630[10:SSi:10628.1,10628.0,2.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] || frontsegP(skc12,skc8)* -> equal(skc12,skc8).
% 9.14/9.34 10638[12:Spt:10543.0] || -> equal(skc12,nil)**.
% 9.14/9.34 10642[12:Rew:10638.0,9624.0] || -> equal(app(app(app(nil,cons(skc10,nil)),skc8),skc13),skc8)**.
% 9.14/9.34 10681[12:Rew:10638.0,9816.0] || frontsegP(app(app(nil,cons(skc10,nil)),skc8),skc8)* -> equal(app(app(skc12,cons(skc10,nil)),skc8),skc8).
% 9.14/9.34 10740[12:Rew:10638.0,10681.1] || frontsegP(app(app(nil,cons(skc10,nil)),skc8),skc8)* -> equal(app(app(nil,cons(skc10,nil)),skc8),skc8).
% 9.14/9.34 10760[12:SpR:82.1,10642.0] ssList(cons(skc10,nil)) || -> equal(app(app(cons(skc10,nil),skc8),skc13),skc8)**.
% 9.14/9.34 10774[12:SSi:10760.0,91.0,4.1,16.0,15.1,12.0,11.1,10.0,14.1,13.0,9.1,80.0,4.1,79.0,4.1,76.0,4.1,75.0,4.0,74.0,4.0,78.0,4.0,77.0,4.0,2576.0,4.2] || -> equal(app(app(cons(skc10,nil),skc8),skc13),skc8)**.
% 9.14/9.34 10814[12:SpR:245.1,10774.0] ssItem(skc10) || -> equal(app(cons(skc10,skc8),skc13),skc8)**.
% 9.14/9.34 10827[12:SSi:10814.0,4.0] || -> equal(app(cons(skc10,skc8),skc13),skc8)**.
% 9.14/9.34 10871[12:SpR:10827.0,168.3] ssItem(skc10) ssList(skc8) ssList(skc13) || -> equal(cons(skc10,app(skc8,skc13)),skc8)**.
% 9.14/9.34 10883[12:Rew:9506.1,10871.3] ssItem(skc10) ssList(skc8) ssList(skc13) || -> equal(cons(skc10,cons(skc11,skc13)),skc8)**.
% 9.14/9.34 10884[12:SSi:10883.2,10883.1,10883.0,1.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0,4.0] || -> equal(cons(skc10,cons(skc11,skc13)),skc8)**.
% 9.14/9.34 10908[12:SpR:10884.0,112.2] ssItem(skc10) ssList(cons(skc11,skc13)) || -> equal(cons(skc11,skc13),tl(skc8))**.
% 9.14/9.34 10954[12:Rew:1965.0,10908.2] ssItem(skc10) ssList(cons(skc11,skc13)) || -> equal(cons(skc11,skc13),nil)**.
% 9.83/10.03 10955[12:SSi:10954.1,10954.0,91.0,3.0,1.0,4.2] || -> equal(cons(skc11,skc13),nil)**.
% 9.83/10.03 10957[12:Rew:10955.0,10884.0] || -> equal(cons(skc10,nil),skc8)**.
% 9.83/10.03 10983[12:Rew:10957.0,10740.0] || frontsegP(app(app(nil,skc8),skc8),skc8) -> equal(app(app(nil,cons(skc10,nil)),skc8),skc8)**.
% 9.83/10.03 11100[12:Rew:9486.0,10983.0,277.0,10983.0] || frontsegP(cons(skc11,skc8),skc8) -> equal(app(app(nil,cons(skc10,nil)),skc8),skc8)**.
% 9.83/10.03 11101[12:Rew:10957.0,11100.1] || frontsegP(cons(skc11,skc8),skc8) -> equal(app(app(nil,skc8),skc8),skc8)**.
% 9.83/10.03 11102[12:Rew:9486.0,11101.1,277.0,11101.1] || frontsegP(cons(skc11,skc8),skc8)* -> equal(cons(skc11,skc8),skc8).
% 9.83/10.03 11103[12:MRR:11102.0,11102.1,9698.0,9707.0] || -> .
% 9.83/10.03 11235[12:Spt:11103.0,10543.0,10638.0] || equal(skc12,nil)** -> .
% 9.83/10.03 11236[12:Spt:11103.0,10543.1] || -> equal(hd(skc12),skc11)**.
% 9.83/10.03 11240[12:SpR:11236.0,119.2] ssList(skc12) || -> equal(skc12,nil) equal(cons(skc11,tl(skc12)),skc12)**.
% 9.83/10.03 11244[12:MRR:11240.0,11240.1,2.0,11235.0] || -> equal(cons(skc11,tl(skc12)),skc12)**.
% 9.83/10.03 12019[10:SpR:9506.1,3912.2] ssList(u) ssList(skc8) ssList(u) || -> frontsegP(cons(skc11,u),skc8)*.
% 9.83/10.03 12066[10:Obv:12019.0] ssList(skc8) ssList(u) || -> frontsegP(cons(skc11,u),skc8)*.
% 9.83/10.03 12067[10:SSi:12066.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0] ssList(u) || -> frontsegP(cons(skc11,u),skc8)*.
% 9.83/10.03 12106[12:SpR:11244.0,12067.1] ssList(tl(skc12)) || -> frontsegP(skc12,skc8)*.
% 9.83/10.03 12218[12:SoR:12106.0,87.1] ssList(skc12) || -> frontsegP(skc12,skc8)* equal(skc12,nil).
% 9.83/10.03 12219[12:SSi:12218.0,2.0] || -> frontsegP(skc12,skc8)* equal(skc12,nil).
% 9.83/10.03 12220[12:MRR:12219.1,11235.0] || -> frontsegP(skc12,skc8)*.
% 9.83/10.03 12221[12:MRR:10630.0,12220.0] || -> equal(skc12,skc8)**.
% 9.83/10.03 12236[12:Rew:12221.0,10426.0] || -> equal(app(skc8,app(cons(skc10,skc8),skc13)),skc8)**.
% 9.83/10.03 12561[12:SpR:12236.0,9506.1] ssList(app(cons(skc10,skc8),skc13)) || -> equal(cons(skc11,app(cons(skc10,skc8),skc13)),skc8)**.
% 9.83/10.03 12580[12:SSi:12561.0,92.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.2,1.2] || -> equal(cons(skc11,app(cons(skc10,skc8),skc13)),skc8)**.
% 9.83/10.03 12695[12:SpR:12580.0,9730.1] ssList(app(cons(skc10,skc8),skc13)) || -> equal(app(cons(skc10,skc8),skc13),tl(skc8))**.
% 9.83/10.03 12732[12:Rew:1965.0,12695.1] ssList(app(cons(skc10,skc8),skc13)) || -> equal(app(cons(skc10,skc8),skc13),nil)**.
% 9.83/10.03 12733[12:SSi:12732.0,92.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.2,1.2] || -> equal(app(cons(skc10,skc8),skc13),nil)**.
% 9.83/10.03 12778[12:SpL:12733.0,130.2] ssList(skc13) ssList(cons(skc10,skc8)) || equal(nil,nil) -> equal(skc13,nil)**.
% 9.83/10.03 12786[12:Obv:12778.2] ssList(skc13) ssList(cons(skc10,skc8)) || -> equal(skc13,nil)**.
% 9.83/10.03 12787[12:SSi:12786.1,12786.0,91.0,4.0,6.0,1741.0,1744.0,1755.0,1759.0,1760.0,1824.0,1835.0,1837.0,1.2] || -> equal(skc13,nil)**.
% 9.83/10.03 12788[12:MRR:12787.0,7982.0] || -> .
% 9.83/10.03 12933[9:Spt:12788.0,218.0,1760.0] || totalorderP(skc8)* -> .
% 9.83/10.03 12934[9:Spt:12788.0,218.1] || -> equal(app(app(skf57(skc8),cons(skf55(skc8),skf58(skc8))),cons(skf56(skc8),skf59(skc8))),skc8)**.
% 9.83/10.03 13184[9:Res:1943.2,12933.0] ssList(skc8) singletonP(skc8) || -> .
% 9.83/10.03 13185[9:SSi:13184.0,6.0,1741.0,1744.0,1755.0,1759.0] singletonP(skc8) || -> .
% 9.83/10.03 13186[9:MRR:64.1,13185.0] || neq(skc9,nil)* -> .
% 9.83/10.03 13196[9:Res:423.1,13186.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.83/10.03 13199[9:SSi:13196.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.83/10.03 13200[9:MRR:13199.0,1726.0] || -> .
% 9.83/10.03 13204[8:Spt:13200.0,219.0,1759.0] || strictorderP(skc8)* -> .
% 9.83/10.03 13205[8:Spt:13200.0,219.1] || -> equal(app(app(skf62(skc8),cons(skf60(skc8),skf63(skc8))),cons(skf61(skc8),skf64(skc8))),skc8)**.
% 9.83/10.03 13371[8:Res:1942.2,13204.0] ssList(skc8) singletonP(skc8) || -> .
% 9.83/10.03 13372[8:SSi:13371.0,6.0,1741.0,1744.0,1755.0] singletonP(skc8) || -> .
% 9.83/10.03 13373[8:MRR:64.1,13372.0] || neq(skc9,nil)* -> .
% 9.83/10.03 13378[8:Res:423.1,13373.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.83/10.03 13381[8:SSi:13378.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.83/10.03 13382[8:MRR:13381.0,1726.0] || -> .
% 9.83/10.03 13386[7:Spt:13382.0,264.0,1755.0] || cyclefreeP(skc8)* -> .
% 9.83/10.03 13387[7:Spt:13382.0,264.1] || -> leq(skf51(skc8),skf50(skc8))*.
% 9.83/10.03 13521[7:Res:1944.2,13386.0] ssList(skc8) singletonP(skc8) || -> .
% 9.83/10.03 13522[7:SSi:13521.0,6.0,1741.0,1744.0] singletonP(skc8) || -> .
% 9.83/10.03 13523[7:MRR:64.1,13522.0] || neq(skc9,nil)* -> .
% 9.83/10.03 13526[7:Res:423.1,13523.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.83/10.03 13529[7:SSi:13526.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.83/10.03 13530[7:MRR:13529.0,1726.0] || -> .
% 9.83/10.03 13534[6:Spt:13530.0,220.0,1744.0] || totalorderedP(skc8)* -> .
% 9.83/10.03 13535[6:Spt:13530.0,220.1] || -> equal(app(app(skf67(skc8),cons(skf65(skc8),skf68(skc8))),cons(skf66(skc8),skf69(skc8))),skc8)**.
% 9.83/10.03 13734[6:Res:1946.2,13534.0] ssList(skc8) singletonP(skc8) || -> .
% 9.83/10.03 13735[6:SSi:13734.0,6.0,1741.0] singletonP(skc8) || -> .
% 9.83/10.03 13736[6:MRR:64.1,13735.0] || neq(skc9,nil)* -> .
% 9.83/10.03 13746[6:Res:423.1,13736.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.83/10.03 13749[6:SSi:13746.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.83/10.03 13750[6:MRR:13749.0,1726.0] || -> .
% 9.83/10.03 13754[5:Spt:13750.0,221.0,1741.0] || strictorderedP(skc8)* -> .
% 9.83/10.03 13755[5:Spt:13750.0,221.1] || -> equal(app(app(skf72(skc8),cons(skf70(skc8),skf73(skc8))),cons(skf71(skc8),skf74(skc8))),skc8)**.
% 9.83/10.03 13926[5:Res:1945.2,13754.0] ssList(skc8) singletonP(skc8) || -> .
% 9.83/10.03 13927[5:SSi:13926.0,6.0] singletonP(skc8) || -> .
% 9.83/10.03 13928[5:MRR:64.1,13927.0] || neq(skc9,nil)* -> .
% 9.83/10.03 13934[5:Res:423.1,13928.0] ssList(nil) || -> equal(skc9,nil)**.
% 9.83/10.03 13937[5:SSi:13934.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> equal(skc9,nil)**.
% 9.83/10.03 13938[5:MRR:13937.0,1726.0] || -> .
% 9.83/10.03 13942[2:Spt:13938.0,238.1] || -> equal(skc8,nil)**.
% 9.83/10.03 14254[2:Rew:13942.0,9467.2] ssList(nil) ssItem(skc11) || equal(nil,nil)* -> .
% 9.83/10.03 14255[2:Obv:14254.2] ssList(nil) ssItem(skc11) || -> .
% 9.83/10.03 14256[2:SSi:14255.1,14255.0,3.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> .
% 9.83/10.03 14590[1:Spt:14256.0,244.1] || -> equal(skc8,nil)**.
% 9.83/10.03 14653[1:Rew:14590.0,9467.2] ssList(nil) ssItem(skc11) || equal(nil,nil)* -> .
% 9.83/10.03 14654[1:Obv:14653.2] ssList(nil) ssItem(skc11) || -> .
% 9.83/10.03 14655[1:SSi:14654.1,14654.0,3.0,16.0,15.0,12.0,11.0,10.0,14.0,13.0,9.0] || -> .
% 9.83/10.03 % SZS output end Refutation
% 9.83/10.03 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax75 ax76 ax8 ax16 ax26 ax58 ax15 ax18 ax23 ax25 ax78 ax81 ax83 ax85 ax41 ax5 ax6 ax50 ax67 ax70 ax86 ax82 ax27 ax37 ax12 ax11 ax10 ax9 ax3 ax14
% 9.83/10.03
%------------------------------------------------------------------------------