TSTP Solution File: SWC162+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC162+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:02:09 EDT 2022
% Result : Theorem 66.57s 66.76s
% Output : Refutation 74.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC162+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 14:27:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 66.57/66.76
% 66.57/66.76 SPASS V 3.9
% 66.57/66.76 SPASS beiseite: Proof found.
% 66.57/66.76 % SZS status Theorem
% 66.57/66.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.57/66.76 SPASS derived 24907 clauses, backtracked 11007 clauses, performed 46 splits and kept 16950 clauses.
% 66.57/66.76 SPASS allocated 135228 KBytes.
% 66.57/66.76 SPASS spent 0:01:06.34 on the problem.
% 66.57/66.76 0:00:00.04 for the input.
% 66.57/66.76 0:00:00.07 for the FLOTTER CNF translation.
% 66.57/66.76 0:00:00.43 for inferences.
% 66.57/66.76 0:00:02.21 for the backtracking.
% 66.57/66.76 0:01:03.19 for the reduction.
% 66.57/66.76
% 66.57/66.76
% 66.57/66.76 Here is a proof with depth 7, length 329 :
% 66.57/66.76 % SZS output start Refutation
% 66.57/66.76 1[0:Inp] || -> ssItem(skc17)*.
% 66.57/66.76 2[0:Inp] || -> ssList(skc16)*.
% 66.57/66.76 3[0:Inp] || -> ssList(skc15)*.
% 66.57/66.76 4[0:Inp] || -> ssList(skc14)*.
% 66.57/66.76 5[0:Inp] || -> ssItem(skc13)*.
% 66.57/66.76 6[0:Inp] || -> ssItem(skc12)*.
% 66.57/66.76 7[0:Inp] || -> ssList(skc11)*.
% 66.57/66.76 8[0:Inp] || -> ssList(skc10)*.
% 66.57/66.76 11[0:Inp] || -> ssList(nil)*.
% 66.57/66.76 12[0:Inp] || -> cyclefreeP(nil)*.
% 66.57/66.76 13[0:Inp] || -> totalorderP(nil)*.
% 66.57/66.76 14[0:Inp] || -> strictorderP(nil)*.
% 66.57/66.76 15[0:Inp] || -> totalorderedP(nil)*.
% 66.57/66.76 16[0:Inp] || -> strictorderedP(nil)*.
% 66.57/66.76 17[0:Inp] || -> duplicatefreeP(nil)*.
% 66.57/66.76 18[0:Inp] || -> equalelemsP(nil)*.
% 66.57/66.76 19[0:Inp] || -> segmentP(skc11,skc10)*.
% 66.57/66.76 20[0:Inp] || -> leq(skc13,skc12)*.
% 66.57/66.76 21[0:Inp] || -> ssItem(skf45(u))*.
% 66.57/66.76 27[0:Inp] || -> ssList(skf59(u))*.
% 66.57/66.76 28[0:Inp] || -> ssList(skf58(u))*.
% 66.57/66.76 29[0:Inp] || -> ssList(skf57(u))*.
% 66.57/66.76 30[0:Inp] || -> ssItem(skf56(u))*.
% 66.57/66.76 31[0:Inp] || -> ssItem(skf55(u))*.
% 66.57/66.76 32[0:Inp] || -> ssList(skf64(u))*.
% 66.57/66.76 33[0:Inp] || -> ssList(skf63(u))*.
% 66.57/66.76 34[0:Inp] || -> ssList(skf62(u))*.
% 66.57/66.76 35[0:Inp] || -> ssItem(skf61(u))*.
% 66.57/66.76 36[0:Inp] || -> ssItem(skf60(u))*.
% 66.57/66.76 66[0:Inp] || neq(skc11,nil)* -> singletonP(skc10).
% 66.57/66.76 70[0:Inp] ssList(u) || -> rearsegP(u,u)*.
% 66.57/66.76 76[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 66.57/66.76 77[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 66.57/66.76 78[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 66.57/66.76 79[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 66.57/66.76 80[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 66.57/66.76 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 66.57/66.76 82[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 66.57/66.76 83[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 66.57/66.76 85[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 66.57/66.76 86[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 66.57/66.76 89[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 66.57/66.76 90[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 66.57/66.76 91[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 66.57/66.76 94[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 66.57/66.76 95[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 66.57/66.76 96[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 66.57/66.76 100[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 66.57/66.76 103[0:Inp] ssList(u) || leq(skf55(u),skf56(u))* -> totalorderP(u).
% 66.57/66.76 105[0:Inp] ssList(u) || lt(skf60(u),skf61(u))* -> strictorderP(u).
% 66.57/66.76 109[0:Inp] || leq(skc12,skc13) leq(skc17,skc13)* leq(skc12,skc17) -> .
% 66.57/66.76 111[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 66.57/66.76 112[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 66.57/66.76 113[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 66.57/66.76 115[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 66.57/66.76 116[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 66.57/66.76 122[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 66.57/66.76 125[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 66.57/66.76 132[0:Inp] || -> equal(app(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil)),skc16),skc10)**.
% 66.57/66.76 133[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 66.57/66.76 134[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 66.57/66.76 135[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 66.57/66.76 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 66.57/66.76 145[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(v,u).
% 66.57/66.76 148[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 66.57/66.76 149[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 66.57/66.76 156[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(w,v) -> rearsegP(app(u,w),v)*.
% 66.57/66.76 157[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 66.57/66.76 158[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 66.57/66.76 159[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 66.57/66.76 164[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 66.57/66.76 165[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,u),app(v,w))* -> equal(u,w).
% 66.57/66.76 166[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,v),app(w,v))* -> equal(u,w).
% 66.57/66.76 175[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 66.57/66.76 178[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 66.57/66.76 179[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 66.57/66.76 180[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 66.57/66.76 181[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 66.57/66.76 191[0:Inp] ssItem(u) ssList(v) ssList(w) ssList(x) || equal(app(x,cons(u,w)),v)*+ -> memberP(v,u)*.
% 66.57/66.76 195[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).
% 66.57/66.76 196[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).
% 66.57/66.76 222[0:Res:8.0,181.0] || -> totalorderP(skc10) equal(app(app(skf57(skc10),cons(skf55(skc10),skf58(skc10))),cons(skf56(skc10),skf59(skc10))),skc10)**.
% 66.57/66.76 223[0:Res:8.0,180.0] || -> strictorderP(skc10) equal(app(app(skf62(skc10),cons(skf60(skc10),skf63(skc10))),cons(skf61(skc10),skf64(skc10))),skc10)**.
% 66.57/66.76 224[0:Res:8.0,179.0] || -> totalorderedP(skc10) equal(app(app(skf67(skc10),cons(skf65(skc10),skf68(skc10))),cons(skf66(skc10),skf69(skc10))),skc10)**.
% 66.57/66.76 225[0:Res:8.0,178.0] || -> strictorderedP(skc10) equal(app(app(skf72(skc10),cons(skf70(skc10),skf73(skc10))),cons(skf71(skc10),skf74(skc10))),skc10)**.
% 66.57/66.76 234[0:Res:8.0,165.0] ssList(u) ssList(v) || equal(app(v,u),app(v,skc10))* -> equal(u,skc10).
% 66.57/66.76 242[0:Res:8.0,159.0] ssList(u) || -> equal(skc10,nil) equal(app(tl(skc10),u),tl(app(skc10,u)))**.
% 66.57/66.76 248[0:Res:8.0,138.0] ssList(u) || -> equal(skc10,nil) equal(hd(app(skc10,u)),hd(skc10))**.
% 66.57/66.76 249[0:Res:8.0,133.0] ssItem(u) || -> equal(app(cons(u,nil),skc10),cons(u,skc10))**.
% 66.57/66.76 251[0:Res:8.0,135.0] ssList(u) || equal(app(skc10,u),nil)** -> equal(skc10,nil).
% 66.57/66.76 254[0:Res:8.0,122.0] || -> equal(skc10,nil) equal(cons(hd(skc10),tl(skc10)),skc10)**.
% 66.57/66.76 255[0:Res:8.0,111.1] singletonP(skc10) || -> equal(cons(skf45(skc10),nil),skc10)**.
% 66.57/66.76 257[0:Res:8.0,113.0] ssItem(u) || equal(cons(u,skc10),skc10)** -> .
% 66.57/66.76 259[0:Res:8.0,115.0] ssItem(u) || -> equal(hd(cons(u,skc10)),u)**.
% 66.57/66.76 268[0:Res:8.0,91.0] || -> cyclefreeP(skc10) leq(skf51(skc10),skf50(skc10))*.
% 66.57/66.76 271[0:Res:8.0,94.0] ssItem(u) || -> ssList(cons(u,skc10))*.
% 66.57/66.76 272[0:Res:8.0,95.0] ssList(u) || -> ssList(app(skc10,u))*.
% 66.57/66.76 277[0:Res:8.0,100.0] || segmentP(nil,skc10)* -> equal(skc10,nil).
% 66.57/66.76 279[0:Res:8.0,89.0] || -> ssItem(hd(skc10))* equal(skc10,nil).
% 66.57/66.76 281[0:Res:8.0,85.0] || -> equal(app(nil,skc10),skc10)**.
% 66.57/66.76 312[0:Res:8.0,158.1] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)) equal(skc10,nil).
% 66.57/66.76 329[0:Res:8.0,95.1] ssList(u) || -> ssList(app(u,skc10))*.
% 66.57/66.76 351[0:Res:8.0,156.2] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(app(skc10,v),u)*.
% 66.57/66.76 427[0:Res:7.0,112.0] ssList(u) || -> neq(skc11,u)* equal(skc11,u).
% 66.57/66.76 482[0:Res:7.0,157.1] ssItem(u) || totalorderedP(cons(u,skc11))* -> leq(u,hd(skc11)) equal(skc11,nil).
% 66.57/66.76 548[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc10,u)),hd(skc10))**.
% 66.57/66.76 550[2:Spt:242.0,242.2] ssList(u) || -> equal(app(tl(skc10),u),tl(app(skc10,u)))**.
% 66.57/66.76 556[3:Spt:312.3] || -> equal(skc10,nil)**.
% 66.57/66.76 557[3:Rew:556.0,548.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 66.57/66.76 575[3:Rew:556.0,271.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 66.57/66.76 576[3:Rew:556.0,259.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 66.57/66.76 730[3:Rew:85.1,557.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 66.57/66.76 1185[3:SpR:576.1,730.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 66.57/66.76 1188[3:SSi:1185.1,83.1,82.1,79.1,78.1,77.1,81.1,80.1,575.1] ssItem(u) || -> equal(u,hd(nil))*.
% 66.57/66.76 1256[3:SpR:1188.1,1188.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 66.57/66.76 1294[3:EmS:1256.0,1.0] ssItem(u) || -> equal(u,skc17)*.
% 66.57/66.76 1322[3:EmS:1294.0,5.0] || -> equal(skc17,skc13)**.
% 66.57/66.76 1323[3:EmS:1294.0,6.0] || -> equal(skc17,skc12)**.
% 66.57/66.76 1329[3:Rew:1322.0,109.1] || leq(skc12,skc13) leq(skc13,skc13)* leq(skc12,skc17) -> .
% 66.57/66.76 1330[3:Rew:1322.0,1323.0] || -> equal(skc13,skc12)**.
% 66.57/66.76 1332[3:Rew:1330.0,20.0] || -> leq(skc12,skc12)*.
% 66.57/66.76 1335[3:Rew:1330.0,1322.0] || -> equal(skc17,skc12)**.
% 66.57/66.76 1502[3:Rew:1335.0,1329.2,1330.0,1329.1,1330.0,1329.0] || leq(skc12,skc12)* leq(skc12,skc12)* leq(skc12,skc12)* -> .
% 66.57/66.76 1503[3:Obv:1502.1] || leq(skc12,skc12)* -> .
% 66.57/66.76 1504[3:MRR:1503.0,1332.0] || -> .
% 66.57/66.76 1515[3:Spt:1504.0,312.3,556.0] || equal(skc10,nil)** -> .
% 66.57/66.76 1516[3:Spt:1504.0,312.0,312.1,312.2] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)).
% 66.57/66.76 1518[3:MRR:279.1,1515.0] || -> ssItem(hd(skc10))*.
% 66.57/66.76 1519[3:MRR:277.1,1515.0] || segmentP(nil,skc10)* -> .
% 66.57/66.76 1522[3:MRR:254.0,1515.0] || -> equal(cons(hd(skc10),tl(skc10)),skc10)**.
% 66.57/66.76 1525[3:MRR:251.2,1515.0] ssList(u) || equal(app(skc10,u),nil)** -> .
% 66.57/66.76 1530[4:Spt:482.3] || -> equal(skc11,nil)**.
% 66.57/66.76 1538[4:Rew:1530.0,19.0] || -> segmentP(nil,skc10)*.
% 66.57/66.76 1683[4:MRR:1538.0,1519.0] || -> .
% 66.57/66.76 1794[4:Spt:1683.0,482.3,1530.0] || equal(skc11,nil)** -> .
% 66.57/66.76 1795[4:Spt:1683.0,482.0,482.1,482.2] ssItem(u) || totalorderedP(cons(u,skc11))* -> leq(u,hd(skc11)).
% 66.57/66.76 1809[5:Spt:225.0] || -> strictorderedP(skc10)*.
% 66.57/66.76 1812[6:Spt:224.0] || -> totalorderedP(skc10)*.
% 66.57/66.76 1823[7:Spt:268.0] || -> cyclefreeP(skc10)*.
% 66.57/66.76 1827[8:Spt:223.0] || -> strictorderP(skc10)*.
% 66.57/66.76 1828[9:Spt:222.0] || -> totalorderP(skc10)*.
% 66.57/66.76 1836[10:Spt:66.0] || neq(skc11,nil)* -> .
% 66.57/66.76 1888[10:Res:427.1,1836.0] ssList(nil) || -> equal(skc11,nil)**.
% 66.57/66.76 1889[10:SSi:1888.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> equal(skc11,nil)**.
% 66.57/66.76 1890[10:MRR:1889.0,1794.0] || -> .
% 66.57/66.76 1891[10:Spt:1890.0,66.0,1836.0] || -> neq(skc11,nil)*.
% 66.57/66.76 1892[10:Spt:1890.0,66.1] || -> singletonP(skc10)*.
% 66.57/66.76 1893[10:MRR:255.0,1892.0] || -> equal(cons(skf45(skc10),nil),skc10)**.
% 66.57/66.76 1894[10:SpR:1893.0,83.1] ssItem(skf45(skc10)) || -> equalelemsP(skc10)*.
% 66.57/66.76 1895[10:SpR:1893.0,82.1] ssItem(skf45(skc10)) || -> duplicatefreeP(skc10)*.
% 66.57/66.76 1903[10:SSi:1894.0,21.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0] || -> equalelemsP(skc10)*.
% 66.57/66.76 1905[10:SSi:1895.0,21.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0] || -> duplicatefreeP(skc10)*.
% 66.57/66.76 1973[0:SpR:111.2,77.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> cyclefreeP(u)*.
% 66.57/66.76 1974[0:SpR:111.2,81.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> strictorderedP(u)*.
% 66.57/66.76 1975[0:SpR:111.2,80.1] ssList(u) singletonP(u) ssItem(skf45(u)) || -> totalorderedP(u)*.
% 66.57/66.76 1986[0:SSi:1973.2,21.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 66.57/66.76 1987[0:SSi:1974.2,21.0] ssList(u) singletonP(u) || -> strictorderedP(u)*.
% 66.57/66.76 1988[0:SSi:1975.2,21.0] ssList(u) singletonP(u) || -> totalorderedP(u)*.
% 66.57/66.76 2000[10:SpR:1893.0,116.2] ssItem(skf45(skc10)) ssList(nil) || -> equal(tl(skc10),nil)**.
% 66.57/66.76 2002[10:SSi:2000.1,2000.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0,21.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || -> equal(tl(skc10),nil)**.
% 66.57/66.76 2004[10:Rew:2002.0,1522.0] || -> equal(cons(hd(skc10),nil),skc10)**.
% 66.57/66.76 2005[10:Rew:2002.0,550.1] ssList(u) || -> equal(tl(app(skc10,u)),app(nil,u))**.
% 66.57/66.76 2007[10:Rew:85.1,2005.1] ssList(u) || -> equal(tl(app(skc10,u)),u)**.
% 66.57/66.76 2041[0:SpR:111.2,115.2] ssList(u) singletonP(u) ssItem(skf45(u)) ssList(nil) || -> equal(skf45(u),hd(u))**.
% 66.57/66.76 2047[0:SSi:2041.3,2041.2,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0,21.0] ssList(u) singletonP(u) || -> equal(skf45(u),hd(u))**.
% 66.57/66.76 2048[0:Rew:2047.2,111.2] ssList(u) singletonP(u) || -> equal(cons(hd(u),nil),u)**.
% 66.57/66.76 2187[10:SpR:2007.1,122.2] ssList(u) ssList(app(skc10,u)) || -> equal(app(skc10,u),nil) equal(cons(hd(app(skc10,u)),u),app(skc10,u))**.
% 66.57/66.76 2201[10:Rew:548.1,2187.3] ssList(u) ssList(app(skc10,u)) || -> equal(app(skc10,u),nil) equal(cons(hd(skc10),u),app(skc10,u))**.
% 66.57/66.76 2202[10:SSi:2201.1,272.1] ssList(u) || -> equal(app(skc10,u),nil) equal(cons(hd(skc10),u),app(skc10,u))**.
% 66.57/66.76 2203[10:MRR:2202.1,1525.1] ssList(u) || -> equal(cons(hd(skc10),u),app(skc10,u))**.
% 66.57/66.76 2278[10:SpL:2203.1,257.1] ssList(skc10) ssItem(hd(skc10)) || equal(app(skc10,skc10),skc10)** -> .
% 66.57/66.76 2292[10:SSi:2278.1,2278.0,1518.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || equal(app(skc10,skc10),skc10)** -> .
% 66.57/66.76 2328[0:SpR:2047.2,21.0] ssList(u) singletonP(u) || -> ssItem(hd(u))*.
% 66.57/66.76 2356[10:SpR:2004.0,249.1] ssItem(hd(skc10)) || -> equal(cons(hd(skc10),skc10),app(skc10,skc10))**.
% 66.57/66.76 2360[10:SSi:2356.0,1518.0] || -> equal(cons(hd(skc10),skc10),app(skc10,skc10))**.
% 66.57/66.76 2604[0:EqR:125.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 66.57/66.76 2609[0:SSi:2604.0,94.1,18.1,17.1,14.1,13.1,12.1,16.1,15.0,11.0,83.0,82.0,79.0,78.0,77.0,81.0,80.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 66.57/66.76 3445[0:SpL:159.3,134.2] ssList(u) ssList(v) ssList(u) ssList(tl(v)) || equal(tl(app(v,u)),nil)** -> equal(nil,v) equal(nil,u).
% 66.57/66.76 3469[0:Obv:3445.0] ssList(u) ssList(v) ssList(tl(u)) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 66.57/66.76 3470[0:MRR:3469.2,90.1] ssList(u) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 66.57/66.76 3822[0:SpR:132.0,156.4] ssList(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil))) ssList(u) ssList(skc16) || rearsegP(skc16,u)* -> rearsegP(skc10,u).
% 66.57/66.76 3833[0:SSi:3822.2,3822.0,2.0,95.1,95.0,95.1,4.0,94.1,6.0,18.1,17.0,14.1,13.0,12.1,16.0,15.1,11.0,83.1,6.0,82.0,6.0,79.0,6.0,78.0,6.0,77.0,6.0,81.2,6.0,80.0,6.1,2609.0,6.1,3.0,94.1,5.0,18.1,17.0,14.1,13.0,12.1,16.0,15.1,11.0,83.1,5.0,82.0,5.0,79.0,5.0,78.0,5.0,77.0,5.0,81.2,5.0,80.2,5.2,2609.2,5.0] ssList(u) || rearsegP(skc16,u)* -> rearsegP(skc10,u).
% 66.57/66.76 3849[0:Res:70.1,3833.1] ssList(skc16) ssList(skc16) || -> rearsegP(skc10,skc16)*.
% 66.57/66.76 3850[0:Obv:3849.0] ssList(skc16) || -> rearsegP(skc10,skc16)*.
% 66.57/66.76 3851[0:SSi:3850.0,2.0] || -> rearsegP(skc10,skc16)*.
% 66.57/66.76 3852[0:Res:3851.0,145.2] ssList(skc10) ssList(skc16) || rearsegP(skc16,skc10)* -> equal(skc16,skc10).
% 66.57/66.76 3853[10:SSi:3852.1,3852.0,2.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || rearsegP(skc16,skc10)* -> equal(skc16,skc10).
% 66.57/66.76 3902[0:EqR:149.3] ssList(u) ssList(app(v,u)) ssList(v) || -> rearsegP(app(v,u),u)*.
% 66.57/66.76 3904[0:SpL:281.0,149.3] ssList(skc10) ssList(u) ssList(nil) || equal(skc10,u) -> rearsegP(u,skc10)*.
% 66.57/66.76 3917[0:SSi:3902.1,95.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 66.57/66.76 3918[10:SSi:3904.2,3904.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] ssList(u) || equal(skc10,u) -> rearsegP(u,skc10)*.
% 66.57/66.76 3953[0:EqR:148.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 66.57/66.76 3968[0:SSi:3953.1,95.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 66.57/66.76 4348[0:SpR:164.3,132.0] ssList(skc15) ssList(cons(skc12,nil)) ssList(skc14) || -> equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),cons(skc13,nil)),skc16),skc10)**.
% 66.57/66.76 4350[0:SpR:164.3,132.0] ssList(skc16) ssList(cons(skc13,nil)) ssList(app(app(skc14,cons(skc12,nil)),skc15)) || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),app(cons(skc13,nil),skc16)),skc10)**.
% 66.57/66.76 4390[0:SSi:4348.2,4348.1,4348.0,4.0,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.1,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.0,2609.0,6.2,3.0] || -> equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),cons(skc13,nil)),skc16),skc10)**.
% 66.57/66.76 4419[0:SSi:4350.2,4350.1,4350.0,95.0,95.0,4.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.2,2609.0,6.0,3.1,94.0,5.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,5.1,82.0,5.1,79.0,5.0,78.0,5.0,77.0,5.0,81.0,5.0,80.0,5.2,2609.0,5.2,2.2] || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),app(cons(skc13,nil),skc16)),skc10)**.
% 66.57/66.76 4561[0:SpR:133.2,3917.2] ssItem(u) ssList(v) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 66.57/66.76 4570[0:Obv:4561.1] ssItem(u) ssList(v) ssList(cons(u,nil)) || -> rearsegP(cons(u,v),v)*.
% 66.57/66.76 4571[0:SSi:4570.2,94.1,18.1,17.1,14.1,13.1,12.1,16.1,15.1,11.0,83.0,82.0,79.0,78.0,77.0,81.0,80.0,2609.2] ssItem(u) ssList(v) || -> rearsegP(cons(u,v),v)*.
% 66.57/66.76 4587[0:SpL:281.0,166.3] ssList(nil) ssList(skc10) ssList(u) || equal(app(u,skc10),skc10)** -> equal(nil,u).
% 66.57/66.76 4620[10:SSi:4587.1,4587.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] ssList(u) || equal(app(u,skc10),skc10)** -> equal(nil,u).
% 66.57/66.76 5342[0:SpR:122.2,4571.2] ssList(u) ssItem(hd(u)) ssList(tl(u)) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 66.57/66.76 5353[0:Res:4571.2,145.2] ssItem(u) ssList(v) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 66.57/66.76 5360[0:MRR:5342.1,5342.2,89.1,90.1] ssList(u) || -> equal(nil,u) rearsegP(u,tl(u))*.
% 66.57/66.76 5361[0:Obv:5353.1] ssItem(u) ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 66.57/66.76 5362[0:SSi:5361.1,94.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 66.57/66.76 5363[0:MRR:5362.3,113.2] ssItem(u) ssList(v) || rearsegP(v,cons(u,v))* -> .
% 66.57/66.76 5504[0:Res:5360.2,3833.1] ssList(skc16) ssList(tl(skc16)) || -> equal(skc16,nil) rearsegP(skc10,tl(skc16))*.
% 66.57/66.76 5507[0:SSi:5504.0,2.0] ssList(tl(skc16)) || -> equal(skc16,nil) rearsegP(skc10,tl(skc16))*.
% 66.57/66.76 5513[0:SoR:5507.0,90.1] ssList(skc16) || -> equal(skc16,nil) rearsegP(skc10,tl(skc16))* equal(skc16,nil).
% 66.57/66.76 5514[0:Obv:5513.1] ssList(skc16) || -> rearsegP(skc10,tl(skc16))* equal(skc16,nil).
% 66.57/66.76 5515[0:SSi:5514.0,2.0] || -> rearsegP(skc10,tl(skc16))* equal(skc16,nil).
% 66.57/66.76 5516[11:Spt:5515.1] || -> equal(skc16,nil)**.
% 66.57/66.76 5521[11:Rew:5516.0,132.0] || -> equal(app(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil)),nil),skc10)**.
% 66.57/66.76 5572[11:SpR:5521.0,86.1] ssList(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil))) || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil)),skc10)**.
% 66.57/66.76 5598[11:SSi:5572.0,95.0,95.1,95.0,4.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.0,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.2,80.0,6.0,2609.1,6.0,3.1,94.0,5.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,5.1,82.0,5.0,79.0,5.0,78.0,5.0,77.0,5.0,81.0,5.2,80.0,5.2,2609.2,5.2] || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,nil)),skc10)**.
% 66.57/66.76 6333[10:SpL:2004.0,175.3] ssList(nil) ssItem(hd(skc10)) ssItem(u) || memberP(skc10,u)* -> memberP(nil,u) equal(u,hd(skc10)).
% 66.57/66.76 6340[10:SSi:6333.1,6333.0,1518.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] ssItem(u) || memberP(skc10,u)* -> memberP(nil,u) equal(u,hd(skc10)).
% 66.57/66.76 6341[10:MRR:6340.2,76.1] ssItem(u) || memberP(skc10,u)* -> equal(u,hd(skc10)).
% 66.57/66.76 7575[0:SpL:180.2,195.7] 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))*.
% 66.57/66.76 7595[0:SSi:7575.6,7575.5,7575.4,7575.3,7575.2,36.0,35.0,34.0,33.0,32.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skf60(u),skf61(u))*.
% 66.57/66.76 7596[0:MRR:7595.5,105.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> strictorderP(u)*.
% 66.57/66.76 7745[0:SpL:181.2,196.7] 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))*.
% 66.57/66.76 7762[0:SSi:7745.6,7745.5,7745.4,7745.3,7745.2,31.0,30.0,29.0,28.0,27.0] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)* -> totalorderP(u) leq(skf55(u),skf56(u))*.
% 66.57/66.76 7763[0:MRR:7762.5,103.1] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)*+ -> totalorderP(u)*.
% 66.57/66.76 8343[0:SpL:2048.2,5363.2] ssList(u) singletonP(u) ssItem(hd(u)) ssList(nil) || rearsegP(nil,u)* -> .
% 66.57/66.76 8351[0:SSi:8343.3,8343.2,18.2,17.0,14.0,13.0,12.0,16.0,15.0,11.0,2328.0] ssList(u) singletonP(u) || rearsegP(nil,u)* -> .
% 66.57/66.76 8507[11:SpL:5598.0,191.4] ssItem(skc13) ssList(u) ssList(nil) ssList(app(app(skc14,cons(skc12,nil)),skc15)) || equal(skc10,u) -> memberP(u,skc13)*.
% 66.57/66.76 8520[11:SSi:8507.3,8507.2,8507.0,95.0,95.0,4.0,94.0,6.0,18.0,17.0,14.0,13.0,12.0,16.0,15.1,11.0,83.1,6.0,82.1,6.0,79.1,6.0,78.1,6.0,77.1,6.0,81.1,6.0,80.1,6.0,2609.0,6.0,3.0,18.0,17.0,14.0,13.0,12.0,16.2,15.0,11.2,5.2] ssList(u) || equal(skc10,u) -> memberP(u,skc13)*.
% 66.57/66.76 8606[11:Res:8520.2,6341.1] ssList(skc10) ssItem(skc13) || equal(skc10,skc10) -> equal(hd(skc10),skc13)**.
% 66.57/66.76 8612[11:Obv:8606.2] ssList(skc10) ssItem(skc13) || -> equal(hd(skc10),skc13)**.
% 66.57/66.76 8613[11:SSi:8612.1,8612.0,5.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || -> equal(hd(skc10),skc13)**.
% 66.57/66.76 8618[11:Rew:8613.0,2004.0] || -> equal(cons(skc13,nil),skc10)**.
% 66.57/66.76 8778[11:Rew:8618.0,5598.0] || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),skc10),skc10)**.
% 66.57/66.76 9246[11:SpL:8778.0,4620.1] ssList(app(app(skc14,cons(skc12,nil)),skc15)) || equal(skc10,skc10) -> equal(app(app(skc14,cons(skc12,nil)),skc15),nil)**.
% 66.57/66.76 9258[11:Obv:9246.1] ssList(app(app(skc14,cons(skc12,nil)),skc15)) || -> equal(app(app(skc14,cons(skc12,nil)),skc15),nil)**.
% 66.57/66.76 9259[11:SSi:9258.0,95.0,95.0,4.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.2,2609.0,6.2,3.2] || -> equal(app(app(skc14,cons(skc12,nil)),skc15),nil)**.
% 66.57/66.76 9767[11:SpR:9259.0,3968.2] ssList(app(skc14,cons(skc12,nil))) ssList(skc15) || -> frontsegP(nil,app(skc14,cons(skc12,nil)))*.
% 66.57/66.76 9791[11:SSi:9767.1,9767.0,3.0,95.1,4.0,94.1,6.0,18.1,17.0,14.1,13.0,12.1,16.0,15.1,11.0,83.1,6.0,82.1,6.0,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.2,6.0,2609.2,6.0] || -> frontsegP(nil,app(skc14,cons(skc12,nil)))*.
% 66.57/66.76 9859[11:Res:9791.0,96.1] ssList(app(skc14,cons(skc12,nil))) || -> equal(app(skc14,cons(skc12,nil)),nil)**.
% 66.57/66.76 9862[11:SSi:9859.0,95.0,4.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.2,2609.0,6.2] || -> equal(app(skc14,cons(skc12,nil)),nil)**.
% 66.57/66.76 9896[11:SpR:9862.0,3917.2] ssList(cons(skc12,nil)) ssList(skc14) || -> rearsegP(nil,cons(skc12,nil))*.
% 66.57/66.76 9919[11:SSi:9896.1,9896.0,4.0,94.1,6.0,18.1,17.0,14.1,13.0,12.1,16.0,15.1,11.0,83.1,6.0,82.1,6.0,79.1,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.0,2609.2,6.0] || -> rearsegP(nil,cons(skc12,nil))*.
% 66.57/66.76 9972[11:Res:9919.0,8351.2] ssList(cons(skc12,nil)) singletonP(cons(skc12,nil)) || -> .
% 66.57/66.76 9981[11:SSi:9972.1,9972.0,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.1,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.0,2609.0,6.2,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.1,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.0,2609.0,6.2] || -> .
% 66.57/66.76 9997[11:Spt:9981.0,5515.1,5516.0] || equal(skc16,nil)** -> .
% 66.57/66.76 9998[11:Spt:9981.0,5515.0] || -> rearsegP(skc10,tl(skc16))*.
% 66.57/66.76 12422[0:SpR:4419.0,3917.2] ssList(app(cons(skc13,nil),skc16)) ssList(app(app(skc14,cons(skc12,nil)),skc15)) || -> rearsegP(skc10,app(cons(skc13,nil),skc16))*.
% 66.57/66.76 12430[0:SpR:133.2,4419.0] ssItem(skc13) ssList(skc16) || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,skc16)),skc10)**.
% 66.57/66.76 12446[0:SSi:12430.1,12430.0,2.0,5.0] || -> equal(app(app(app(skc14,cons(skc12,nil)),skc15),cons(skc13,skc16)),skc10)**.
% 66.57/66.76 12447[0:SSi:12422.1,12422.0,95.0,95.0,4.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.2,2609.2,6.0,3.0,95.1,94.0,5.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,5.1,82.0,5.1,79.0,5.0,78.0,5.0,77.0,5.0,81.0,5.0,80.0,5.2,2609.0,5.2,2.2] || -> rearsegP(skc10,app(cons(skc13,nil),skc16))*.
% 66.57/66.76 12473[0:SpR:133.2,12447.0] ssItem(skc13) ssList(skc16) || -> rearsegP(skc10,cons(skc13,skc16))*.
% 66.57/66.76 12477[0:SSi:12473.1,12473.0,2.0,5.0] || -> rearsegP(skc10,cons(skc13,skc16))*.
% 66.57/66.76 12480[0:Res:12477.0,145.2] ssList(skc10) ssList(cons(skc13,skc16)) || rearsegP(cons(skc13,skc16),skc10)* -> equal(cons(skc13,skc16),skc10).
% 66.57/66.76 12482[10:SSi:12480.1,12480.0,94.0,5.0,2.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.2] || rearsegP(cons(skc13,skc16),skc10)* -> equal(cons(skc13,skc16),skc10).
% 66.57/66.76 16625[0:EqR:7596.3] ssList(u) ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 66.57/66.76 16626[0:Obv:16625.0] ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 66.57/66.76 16698[0:EqR:7763.3] ssList(u) ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 66.57/66.76 16699[0:Obv:16698.0] ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 66.57/66.76 18385[0:SpL:12446.0,191.4] ssItem(skc13) ssList(u) ssList(skc16) ssList(app(app(skc14,cons(skc12,nil)),skc15)) || equal(skc10,u) -> memberP(u,skc13)*.
% 66.57/66.76 18396[0:SSi:18385.3,18385.2,18385.0,95.0,95.0,4.0,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.1,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.0,2609.0,6.2,3.0,2.2,5.2] ssList(u) || equal(skc10,u) -> memberP(u,skc13)*.
% 74.49/74.66 18418[0:Res:18396.2,76.1] ssList(nil) ssItem(skc13) || equal(skc10,nil)** -> .
% 74.49/74.66 18423[10:Res:18396.2,6341.1] ssList(skc10) ssItem(skc13) || equal(skc10,skc10) -> equal(hd(skc10),skc13)**.
% 74.49/74.66 18434[10:Obv:18423.2] ssList(skc10) ssItem(skc13) || -> equal(hd(skc10),skc13)**.
% 74.49/74.66 18435[10:SSi:18434.1,18434.0,5.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || -> equal(hd(skc10),skc13)**.
% 74.49/74.66 18439[10:Rew:18435.0,2004.0] || -> equal(cons(skc13,nil),skc10)**.
% 74.49/74.66 18445[10:Rew:18435.0,2360.0] || -> equal(app(skc10,skc10),cons(skc13,skc10))**.
% 74.49/74.66 18467[10:Rew:18435.0,2203.1] ssList(u) || -> equal(app(skc10,u),cons(skc13,u))**.
% 74.49/74.66 18611[10:Rew:18439.0,4390.0] || -> equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),skc16),skc10)**.
% 74.49/74.66 18847[10:Rew:18445.0,2292.0] || equal(cons(skc13,skc10),skc10)** -> .
% 74.49/74.66 18966[10:Rew:18467.1,351.3] ssList(u) ssList(v) || rearsegP(v,u) -> rearsegP(cons(skc13,v),u)*.
% 74.49/74.66 20028[10:Res:18966.3,12482.0] ssList(skc10) ssList(skc16) || rearsegP(skc16,skc10) -> equal(cons(skc13,skc16),skc10)**.
% 74.49/74.66 20032[10:Rew:3853.1,20028.3] ssList(skc10) ssList(skc16) || rearsegP(skc16,skc10) -> equal(cons(skc13,skc10),skc10)**.
% 74.49/74.66 20033[10:SSi:20032.1,20032.0,2.0,8.0,1809.0,1812.0,1823.0,1827.0,1828.0,1892.0,1903.0,1905.0] || rearsegP(skc16,skc10) -> equal(cons(skc13,skc10),skc10)**.
% 74.49/74.66 20034[10:MRR:20033.1,18847.0] || rearsegP(skc16,skc10)* -> .
% 74.49/74.66 20039[10:Res:3918.2,20034.0] ssList(skc16) || equal(skc16,skc10)** -> .
% 74.49/74.66 20040[10:SSi:20039.0,2.0] || equal(skc16,skc10)** -> .
% 74.49/74.66 22232[10:SpL:18611.0,234.2] ssList(skc16) ssList(app(app(skc14,app(cons(skc12,nil),skc15)),skc10)) || equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),skc10),skc10)** -> equal(skc16,skc10).
% 74.49/74.66 22308[10:SSi:22232.1,22232.0,329.0,95.0,4.0,95.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.1,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.0,80.0,6.2,2609.2,6.0,3.2,2.1] || equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),skc10),skc10)** -> equal(skc16,skc10).
% 74.49/74.66 22309[10:MRR:22308.1,20040.0] || equal(app(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),skc10),skc10)** -> .
% 74.49/74.66 32905[10:SpL:18611.0,3470.2] ssList(app(app(skc14,app(cons(skc12,nil),skc15)),skc10)) ssList(skc16) || equal(tl(skc10),nil) -> equal(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),nil)** equal(skc16,nil).
% 74.49/74.66 33023[10:Rew:2002.0,32905.2] ssList(app(app(skc14,app(cons(skc12,nil),skc15)),skc10)) ssList(skc16) || equal(nil,nil) -> equal(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),nil)** equal(skc16,nil).
% 74.49/74.66 33024[10:Obv:33023.2] ssList(app(app(skc14,app(cons(skc12,nil),skc15)),skc10)) ssList(skc16) || -> equal(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),nil)** equal(skc16,nil).
% 74.49/74.66 35294[10:SSi:33024.1,33024.0,2.0,329.0,95.1,4.0,95.1,94.0,6.1,18.0,17.1,14.0,13.1,12.0,16.1,15.0,11.1,83.0,6.1,82.0,6.0,79.0,6.0,78.0,6.0,77.0,6.0,81.0,6.2,80.2,6.0,2609.2,6.1,3.0] || -> equal(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),nil)** equal(skc16,nil).
% 74.49/74.66 35295[11:MRR:35294.1,9997.0] || -> equal(app(app(skc14,app(cons(skc12,nil),skc15)),skc10),nil)**.
% 74.49/74.66 35299[11:Rew:35295.0,22309.0] || equal(app(nil,skc10),skc10)** -> .
% 74.49/74.66 35313[11:Rew:281.0,35299.0] || equal(skc10,skc10)* -> .
% 74.49/74.66 35314[11:Obv:35313.0] || -> .
% 74.49/74.66 35507[9:Spt:35314.0,222.0,1828.0] || totalorderP(skc10)* -> .
% 74.49/74.66 35508[9:Spt:35314.0,222.1] || -> equal(app(app(skf57(skc10),cons(skf55(skc10),skf58(skc10))),cons(skf56(skc10),skf59(skc10))),skc10)**.
% 74.49/74.66 36762[9:Res:16699.2,35507.0] ssList(skc10) totalorderedP(skc10) || -> .
% 74.49/74.66 36764[9:SSi:36762.1,36762.0,8.0,1809.0,1812.0,1823.0,1827.0,8.0,1809.0,1812.0,1823.0,1827.0] || -> .
% 74.49/74.66 36768[8:Spt:36764.0,223.0,1827.0] || strictorderP(skc10)* -> .
% 74.49/74.66 36769[8:Spt:36764.0,223.1] || -> equal(app(app(skf62(skc10),cons(skf60(skc10),skf63(skc10))),cons(skf61(skc10),skf64(skc10))),skc10)**.
% 74.49/74.66 37234[8:Res:16626.2,36768.0] ssList(skc10) strictorderedP(skc10) || -> .
% 74.49/74.66 37236[8:SSi:37234.1,37234.0,8.0,1809.0,1812.0,1823.0,8.0,1809.0,1812.0,1823.0] || -> .
% 74.49/74.66 37240[7:Spt:37236.0,268.0,1823.0] || cyclefreeP(skc10)* -> .
% 74.49/74.66 37241[7:Spt:37236.0,268.1] || -> leq(skf51(skc10),skf50(skc10))*.
% 74.49/74.66 38003[7:Res:1986.2,37240.0] ssList(skc10) singletonP(skc10) || -> .
% 74.49/74.66 38007[7:SSi:38003.0,8.0,1809.0,1812.0] singletonP(skc10) || -> .
% 74.49/74.66 38008[7:MRR:66.1,38007.0] || neq(skc11,nil)* -> .
% 74.49/74.66 38022[7:Res:427.1,38008.0] ssList(nil) || -> equal(skc11,nil)**.
% 74.49/74.66 38025[7:SSi:38022.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> equal(skc11,nil)**.
% 74.49/74.66 38026[7:MRR:38025.0,1794.0] || -> .
% 74.49/74.66 38030[6:Spt:38026.0,224.0,1812.0] || totalorderedP(skc10)* -> .
% 74.49/74.66 38031[6:Spt:38026.0,224.1] || -> equal(app(app(skf67(skc10),cons(skf65(skc10),skf68(skc10))),cons(skf66(skc10),skf69(skc10))),skc10)**.
% 74.49/74.66 38884[6:Res:1988.2,38030.0] ssList(skc10) singletonP(skc10) || -> .
% 74.49/74.66 38885[6:SSi:38884.0,8.0,1809.0] singletonP(skc10) || -> .
% 74.49/74.66 38886[6:MRR:66.1,38885.0] || neq(skc11,nil)* -> .
% 74.49/74.66 38902[6:Res:427.1,38886.0] ssList(nil) || -> equal(skc11,nil)**.
% 74.49/74.66 38905[6:SSi:38902.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> equal(skc11,nil)**.
% 74.49/74.66 38906[6:MRR:38905.0,1794.0] || -> .
% 74.49/74.66 38910[5:Spt:38906.0,225.0,1809.0] || strictorderedP(skc10)* -> .
% 74.49/74.66 38911[5:Spt:38906.0,225.1] || -> equal(app(app(skf72(skc10),cons(skf70(skc10),skf73(skc10))),cons(skf71(skc10),skf74(skc10))),skc10)**.
% 74.49/74.66 39414[5:Res:1987.2,38910.0] ssList(skc10) singletonP(skc10) || -> .
% 74.49/74.66 39415[5:SSi:39414.0,8.0] singletonP(skc10) || -> .
% 74.49/74.66 39416[5:MRR:66.1,39415.0] || neq(skc11,nil)* -> .
% 74.49/74.66 39422[5:Res:427.1,39416.0] ssList(nil) || -> equal(skc11,nil)**.
% 74.49/74.66 39425[5:SSi:39422.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> equal(skc11,nil)**.
% 74.49/74.66 39426[5:MRR:39425.0,1794.0] || -> .
% 74.49/74.66 39430[2:Spt:39426.0,242.1] || -> equal(skc10,nil)**.
% 74.49/74.66 40409[2:Rew:39430.0,18418.2] ssList(nil) ssItem(skc13) || equal(nil,nil)* -> .
% 74.49/74.66 40410[2:Obv:40409.2] ssList(nil) ssItem(skc13) || -> .
% 74.49/74.66 40411[2:SSi:40410.1,40410.0,5.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> .
% 74.49/74.66 41622[1:Spt:40411.0,248.1] || -> equal(skc10,nil)**.
% 74.49/74.66 41738[1:Rew:41622.0,18418.2] ssList(nil) ssItem(skc13) || equal(nil,nil)* -> .
% 74.49/74.66 41739[1:Obv:41738.2] ssList(nil) ssItem(skc13) || -> .
% 74.49/74.66 41740[1:SSi:41739.1,41739.0,5.0,18.0,17.0,14.0,13.0,12.0,16.0,15.0,11.0] || -> .
% 74.49/74.66 % SZS output end Refutation
% 74.49/74.66 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
% 74.49/74.66
%------------------------------------------------------------------------------