TSTP Solution File: SWC284+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC284+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 22:03:03 EDT 2022
% Result : Theorem 3.44s 3.68s
% Output : Refutation 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC284+1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 07:02:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.44/3.68
% 3.44/3.68 SPASS V 3.9
% 3.44/3.68 SPASS beiseite: Proof found.
% 3.44/3.68 % SZS status Theorem
% 3.44/3.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/3.68 SPASS derived 5437 clauses, backtracked 2852 clauses, performed 33 splits and kept 4010 clauses.
% 3.44/3.68 SPASS allocated 105499 KBytes.
% 3.44/3.68 SPASS spent 0:00:03.33 on the problem.
% 3.44/3.68 0:00:00.04 for the input.
% 3.44/3.68 0:00:00.07 for the FLOTTER CNF translation.
% 3.44/3.68 0:00:00.05 for inferences.
% 3.44/3.68 0:00:00.06 for the backtracking.
% 3.44/3.68 0:00:02.94 for the reduction.
% 3.44/3.68
% 3.44/3.68
% 3.44/3.68 Here is a proof with depth 6, length 301 :
% 3.44/3.68 % SZS output start Refutation
% 3.44/3.68 1[0:Inp] || -> ssItem(skc15)*.
% 3.44/3.68 2[0:Inp] || -> ssList(skc14)*.
% 3.44/3.68 3[0:Inp] || -> ssList(skc13)*.
% 3.44/3.68 4[0:Inp] || -> ssItem(skc12)*.
% 3.44/3.68 5[0:Inp] || -> ssItem(skc11)*.
% 3.44/3.68 6[0:Inp] || -> ssList(skc10)*.
% 3.44/3.68 7[0:Inp] || -> ssList(skc9)*.
% 3.44/3.68 8[0:Inp] || -> ssItem(skc17)*.
% 3.44/3.68 9[0:Inp] || -> ssItem(skc16)*.
% 3.44/3.68 10[0:Inp] || -> ssList(nil)*.
% 3.44/3.68 11[0:Inp] || -> cyclefreeP(nil)*.
% 3.44/3.68 12[0:Inp] || -> totalorderP(nil)*.
% 3.44/3.68 13[0:Inp] || -> strictorderP(nil)*.
% 3.44/3.68 14[0:Inp] || -> totalorderedP(nil)*.
% 3.44/3.68 15[0:Inp] || -> strictorderedP(nil)*.
% 3.44/3.68 16[0:Inp] || -> duplicatefreeP(nil)*.
% 3.44/3.68 17[0:Inp] || -> equalelemsP(nil)*.
% 3.44/3.68 18[0:Inp] || -> ssItem(skf45(u))*.
% 3.44/3.68 56[0:Inp] || equal(skc17,skc16)** -> .
% 3.44/3.68 64[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 3.44/3.68 71[0:Inp] || equal(skc10,nil)** -> equal(skc9,nil).
% 3.44/3.68 73[0:Inp] || -> memberP(u,v) SkP0(w,v,u)*.
% 3.44/3.68 74[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 3.44/3.68 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.44/3.68 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.44/3.68 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.44/3.68 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.44/3.68 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.44/3.68 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.44/3.68 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.44/3.68 83[0:Inp] || SkP0(skc12,skc15,skc13)* -> memberP(skc14,skc15).
% 3.44/3.68 85[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.44/3.68 87[0:Inp] || neq(skc10,nil) -> equal(cons(skc11,nil),skc9)**.
% 3.44/3.68 88[0:Inp] || -> equal(app(app(skc13,cons(skc12,nil)),skc14),skc9)**.
% 3.44/3.68 93[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 3.44/3.68 94[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 3.44/3.68 97[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 3.44/3.68 98[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 3.44/3.68 99[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 3.44/3.68 101[0:Inp] ssList(u) || rearsegP(nil,u)* -> equal(nil,u).
% 3.44/3.68 113[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 3.44/3.68 114[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 3.44/3.68 116[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 3.44/3.68 117[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 3.44/3.68 118[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 3.44/3.68 124[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 3.44/3.68 127[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 3.44/3.68 134[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 3.44/3.68 136[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 3.44/3.68 139[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 3.44/3.68 145[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(v,u).
% 3.44/3.68 149[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 3.44/3.68 150[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 3.44/3.68 156[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(w,v) -> frontsegP(app(w,u),v)*.
% 3.44/3.68 159[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 3.44/3.68 160[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 3.44/3.68 165[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 3.44/3.68 179[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 3.44/3.68 180[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 3.44/3.68 181[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 3.44/3.68 182[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 3.44/3.68 223[0:Res:7.0,182.0] || -> totalorderP(skc9) equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 3.44/3.68 224[0:Res:7.0,181.0] || -> strictorderP(skc9) equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 3.44/3.68 225[0:Res:7.0,180.0] || -> totalorderedP(skc9) equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 3.44/3.68 226[0:Res:7.0,179.0] || -> strictorderedP(skc9) equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 3.44/3.68 243[0:Res:7.0,160.0] ssList(u) || -> equal(skc9,nil) equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 3.44/3.68 249[0:Res:7.0,139.0] ssList(u) || -> equal(skc9,nil) equal(hd(app(skc9,u)),hd(skc9))**.
% 3.44/3.68 252[0:Res:7.0,136.0] ssList(u) || equal(app(skc9,u),nil)** -> equal(skc9,nil).
% 3.44/3.68 256[0:Res:7.0,113.1] singletonP(skc9) || -> equal(cons(skf45(skc9),nil),skc9)**.
% 3.44/3.68 259[0:Res:7.0,116.0] ssItem(u) || equal(cons(u,skc9),nil)** -> .
% 3.44/3.68 269[0:Res:7.0,94.0] || -> cyclefreeP(skc9) leq(skf51(skc9),skf50(skc9))*.
% 3.44/3.68 313[0:Res:7.0,159.1] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)) equal(skc9,nil).
% 3.44/3.68 325[0:Res:7.0,127.1] ssItem(u) || equal(cons(u,nil),skc9)** -> singletonP(skc9).
% 3.44/3.68 420[0:Res:6.0,139.0] ssList(u) || -> equal(skc10,nil) equal(hd(app(skc10,u)),hd(skc10))**.
% 3.44/3.68 428[0:Res:6.0,114.0] ssList(u) || -> neq(skc10,u)* equal(skc10,u).
% 3.44/3.68 431[0:Res:6.0,117.0] ssItem(u) || -> equal(hd(cons(u,skc10)),u)**.
% 3.44/3.68 443[0:Res:6.0,97.0] ssItem(u) || -> ssList(cons(u,skc10))*.
% 3.44/3.68 484[0:Res:6.0,159.1] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)) equal(skc10,nil).
% 3.44/3.68 549[1:Spt:420.0,420.2] ssList(u) || -> equal(hd(app(skc10,u)),hd(skc10))**.
% 3.44/3.68 551[2:Spt:249.0,249.2] ssList(u) || -> equal(hd(app(skc9,u)),hd(skc9))**.
% 3.44/3.68 555[3:Spt:243.0,243.2] ssList(u) || -> equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 3.44/3.68 557[4:Spt:484.3] || -> equal(skc10,nil)**.
% 3.44/3.68 558[4:Rew:557.0,549.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 3.44/3.68 577[4:Rew:557.0,443.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 3.44/3.68 578[4:Rew:557.0,431.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 3.44/3.68 903[4:Rew:85.1,558.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 3.44/3.68 1064[0:Res:73.1,83.0] || -> memberP(skc13,skc15) memberP(skc14,skc15)*.
% 3.44/3.68 1202[4:SpR:578.1,903.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 3.44/3.68 1205[4:SSi:1202.1,81.1,80.1,77.1,76.1,75.1,79.1,78.1,577.1] ssItem(u) || -> equal(u,hd(nil))*.
% 3.44/3.68 1274[4:SpR:1205.1,1205.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 3.44/3.68 1314[4:EmS:1274.0,1.0] ssItem(u) || -> equal(u,skc15)*.
% 3.44/3.68 1338[4:EmS:1314.0,4.0] || -> equal(skc15,skc12)**.
% 3.44/3.68 1339[4:EmS:1314.0,5.0] || -> equal(skc15,skc11)**.
% 3.44/3.68 1340[4:EmS:1314.0,8.0] || -> equal(skc17,skc15)**.
% 3.44/3.68 1341[4:EmS:1314.0,9.0] || -> equal(skc16,skc15)**.
% 3.44/3.68 1347[4:Rew:1338.0,1339.0] || -> equal(skc12,skc11)**.
% 3.44/3.68 1351[4:Rew:1347.0,1338.0] || -> equal(skc15,skc11)**.
% 3.44/3.68 1353[4:Rew:1340.0,56.0] || equal(skc16,skc15)** -> .
% 3.44/3.68 1360[4:Rew:1351.0,1341.0] || -> equal(skc16,skc11)**.
% 3.44/3.68 1481[4:Rew:1360.0,1353.0,1351.0,1353.0] || equal(skc11,skc11)* -> .
% 3.44/3.68 1482[4:Obv:1481.0] || -> .
% 3.44/3.68 1519[4:Spt:1482.0,484.3,557.0] || equal(skc10,nil)** -> .
% 3.44/3.68 1520[4:Spt:1482.0,484.0,484.1,484.2] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)).
% 3.44/3.68 1534[5:Spt:313.3] || -> equal(skc9,nil)**.
% 3.44/3.68 1573[5:Rew:1534.0,259.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 3.44/3.68 1598[5:Rew:1534.0,87.1] || neq(skc10,nil) -> equal(cons(skc11,nil),nil)**.
% 3.44/3.68 1878[5:SpL:1598.1,1573.1] ssItem(skc11) || neq(skc10,nil)* equal(nil,nil) -> .
% 3.44/3.68 1879[5:Obv:1878.2] ssItem(skc11) || neq(skc10,nil)* -> .
% 3.44/3.68 1880[5:SSi:1879.0,5.0] || neq(skc10,nil)* -> .
% 3.44/3.68 1883[5:Res:428.1,1880.0] ssList(nil) || -> equal(skc10,nil)**.
% 3.44/3.68 1884[5:SSi:1883.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 3.44/3.68 1885[5:MRR:1884.0,1519.0] || -> .
% 3.44/3.68 1886[5:Spt:1885.0,313.3,1534.0] || equal(skc9,nil)** -> .
% 3.44/3.68 1887[5:Spt:1885.0,313.0,313.1,313.2] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)).
% 3.44/3.68 1896[5:MRR:252.2,1886.0] ssList(u) || equal(app(skc9,u),nil)** -> .
% 3.44/3.68 1908[6:Spt:225.0] || -> totalorderedP(skc9)*.
% 3.44/3.68 1912[7:Spt:226.0] || -> strictorderedP(skc9)*.
% 3.44/3.68 1917[8:Spt:269.0] || -> cyclefreeP(skc9)*.
% 3.44/3.68 1921[9:Spt:223.0] || -> totalorderP(skc9)*.
% 3.44/3.68 1922[10:Spt:224.0] || -> strictorderP(skc9)*.
% 3.44/3.68 1923[11:Spt:83.0] || SkP0(skc12,skc15,skc13)* -> .
% 3.44/3.68 1924[11:Res:73.1,1923.0] || -> memberP(skc13,skc15)*.
% 3.44/3.68 1939[0:SpR:87.1,81.1] ssItem(skc11) || neq(skc10,nil)* -> equalelemsP(skc9).
% 3.44/3.68 1940[0:SpR:87.1,80.1] ssItem(skc11) || neq(skc10,nil)* -> duplicatefreeP(skc9).
% 3.44/3.68 1948[0:SSi:1939.0,5.0] || neq(skc10,nil)* -> equalelemsP(skc9).
% 3.44/3.68 1949[0:SSi:1940.0,5.0] || neq(skc10,nil)* -> duplicatefreeP(skc9).
% 3.44/3.68 1950[0:Res:428.1,1948.0] ssList(nil) || -> equal(skc10,nil) equalelemsP(skc9)*.
% 3.44/3.68 1951[0:SSi:1950.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) equalelemsP(skc9)*.
% 3.44/3.68 1952[4:MRR:1951.0,1519.0] || -> equalelemsP(skc9)*.
% 3.44/3.68 1954[0:Res:428.1,1949.0] ssList(nil) || -> equal(skc10,nil) duplicatefreeP(skc9)*.
% 3.44/3.68 1955[0:SSi:1954.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) duplicatefreeP(skc9)*.
% 3.44/3.68 1956[4:MRR:1955.0,1519.0] || -> duplicatefreeP(skc9)*.
% 3.44/3.68 2005[0:SpL:87.1,325.1] ssItem(skc11) || neq(skc10,nil)* equal(skc9,skc9) -> singletonP(skc9).
% 3.44/3.68 2006[0:Obv:2005.2] ssItem(skc11) || neq(skc10,nil)* -> singletonP(skc9).
% 3.44/3.68 2007[0:SSi:2006.0,5.0] || neq(skc10,nil)* -> singletonP(skc9).
% 3.44/3.68 2010[0:Res:428.1,2007.0] ssList(nil) || -> equal(skc10,nil) singletonP(skc9)*.
% 3.44/3.68 2011[0:SSi:2010.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) singletonP(skc9)*.
% 3.44/3.68 2012[4:MRR:2011.0,1519.0] || -> singletonP(skc9)*.
% 3.44/3.68 2013[4:MRR:256.0,2012.0] || -> equal(cons(skf45(skc9),nil),skc9)**.
% 3.44/3.68 2016[4:SpR:2013.0,77.1] ssItem(skf45(skc9)) || -> strictorderP(skc9)*.
% 3.44/3.68 2017[4:SpR:2013.0,76.1] ssItem(skf45(skc9)) || -> totalorderP(skc9)*.
% 3.44/3.68 2018[4:SpR:2013.0,75.1] ssItem(skf45(skc9)) || -> cyclefreeP(skc9)*.
% 3.44/3.68 2019[4:SpR:2013.0,79.1] ssItem(skf45(skc9)) || -> strictorderedP(skc9)*.
% 3.44/3.68 2020[4:SpR:2013.0,78.1] ssItem(skf45(skc9)) || -> totalorderedP(skc9)*.
% 3.44/3.68 2086[4:SpR:2013.0,118.2] ssItem(skf45(skc9)) ssList(nil) || -> equal(tl(skc9),nil)**.
% 3.44/3.68 2093[10:SSi:2086.1,2086.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,18.0,7.0,1908.0,1912.0,1917.0,1921.0,1922.0,1952.0,1956.0,2012.0] || -> equal(tl(skc9),nil)**.
% 3.44/3.68 2096[10:Rew:2093.0,555.1] ssList(u) || -> equal(tl(app(skc9,u)),app(nil,u))**.
% 3.44/3.68 2098[10:Rew:85.1,2096.1] ssList(u) || -> equal(tl(app(skc9,u)),u)**.
% 3.44/3.68 2131[0:SpR:87.1,117.2] ssItem(skc11) ssList(nil) || neq(skc10,nil)* -> equal(hd(skc9),skc11).
% 3.44/3.68 2136[0:SSi:2131.1,2131.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,5.0] || neq(skc10,nil)* -> equal(hd(skc9),skc11).
% 3.44/3.68 2200[0:Res:428.1,2136.0] ssList(nil) || -> equal(skc10,nil) equal(hd(skc9),skc11)**.
% 3.44/3.68 2201[0:SSi:2200.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) equal(hd(skc9),skc11)**.
% 3.44/3.68 2202[4:MRR:2201.0,1519.0] || -> equal(hd(skc9),skc11)**.
% 3.44/3.68 2205[4:Rew:2202.0,551.1] ssList(u) || -> equal(hd(app(skc9,u)),skc11)**.
% 3.44/3.68 2275[4:SpR:2205.1,124.2] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(skc11,tl(app(skc9,u))),app(skc9,u))**.
% 3.44/3.68 2283[10:Rew:2098.1,2275.3] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(app(skc9,u),cons(skc11,u))**.
% 3.44/3.68 2284[10:SSi:2283.1,98.0,7.0,1908.0,1912.0,1917.0,1921.0,1922.0,1952.0,1956.0,2012.2] ssList(u) || -> equal(app(skc9,u),nil) equal(app(skc9,u),cons(skc11,u))**.
% 3.44/3.68 2285[10:MRR:2284.1,1896.1] ssList(u) || -> equal(app(skc9,u),cons(skc11,u))**.
% 3.44/3.68 2289[10:Rew:2285.1,2098.1] ssList(u) || -> equal(tl(cons(skc11,u)),u)**.
% 3.44/3.68 2643[0:EqR:127.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 3.44/3.68 2647[0:SSi:2643.0,97.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 3.44/3.68 4021[0:SpL:88.0,150.3] ssList(skc14) ssList(u) ssList(app(skc13,cons(skc12,nil))) || equal(skc9,u) -> rearsegP(u,skc14)*.
% 3.44/3.68 4034[0:SSi:4021.2,4021.0,98.0,3.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2647.2,4.0,2.2] ssList(u) || equal(skc9,u) -> rearsegP(u,skc14)*.
% 3.44/3.68 4064[0:Res:4034.2,101.1] ssList(nil) ssList(skc14) || equal(skc9,nil) -> equal(skc14,nil)**.
% 3.44/3.68 4070[0:EqR:149.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 3.44/3.68 4088[0:SSi:4070.1,98.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 3.44/3.68 4477[0:SpR:165.3,88.0] ssList(skc14) ssList(cons(skc12,nil)) ssList(skc13) || -> equal(app(skc13,app(cons(skc12,nil),skc14)),skc9)**.
% 3.44/3.68 4510[0:SSi:4477.2,4477.1,4477.0,3.0,97.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.1,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2647.0,4.2,2.0] || -> equal(app(skc13,app(cons(skc12,nil),skc14)),skc9)**.
% 3.44/3.68 4685[0:SpR:4510.0,139.3] ssList(app(cons(skc12,nil),skc14)) ssList(skc13) || -> equal(skc13,nil) equal(hd(skc13),hd(skc9))**.
% 3.44/3.68 4689[0:SpR:4510.0,156.4] ssList(app(cons(skc12,nil),skc14)) ssList(u) ssList(skc13) || frontsegP(skc13,u)* -> frontsegP(skc9,u).
% 3.44/3.68 4693[0:SpR:134.2,4510.0] ssItem(skc12) ssList(skc14) || -> equal(app(skc13,cons(skc12,skc14)),skc9)**.
% 3.44/3.68 4695[0:SpL:4510.0,149.3] ssList(skc13) ssList(u) ssList(app(cons(skc12,nil),skc14)) || equal(skc9,u) -> frontsegP(u,skc13)*.
% 3.44/3.68 4701[0:SSi:4693.1,4693.0,2.0,4.0] || -> equal(app(skc13,cons(skc12,skc14)),skc9)**.
% 3.44/3.68 4703[4:Rew:2202.0,4685.3] ssList(app(cons(skc12,nil),skc14)) ssList(skc13) || -> equal(skc13,nil) equal(hd(skc13),skc11)**.
% 3.44/3.68 4704[4:SSi:4703.1,4703.0,3.0,98.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2647.2,4.2,2.0] || -> equal(skc13,nil) equal(hd(skc13),skc11)**.
% 3.44/3.68 4706[0:SSi:4695.2,4695.0,98.0,97.0,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.1,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2647.0,4.0,2.2,3.2] ssList(u) || equal(skc9,u) -> frontsegP(u,skc13)*.
% 3.44/3.68 4707[0:SSi:4689.2,4689.0,3.0,98.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2647.2,4.2,2.0] ssList(u) || frontsegP(skc13,u)* -> frontsegP(skc9,u).
% 3.44/3.68 4859[12:Spt:4704.0] || -> equal(skc13,nil)**.
% 3.44/3.68 4862[12:Rew:4859.0,1924.0] || -> memberP(nil,skc15)*.
% 3.44/3.68 4903[12:Res:4862.0,74.1] ssItem(skc15) || -> .
% 3.44/3.68 4904[12:SSi:4903.0,1.0] || -> .
% 3.44/3.68 4905[12:Spt:4904.0,4704.0,4859.0] || equal(skc13,nil)** -> .
% 3.44/3.68 4906[12:Spt:4904.0,4704.1] || -> equal(hd(skc13),skc11)**.
% 3.44/3.68 4910[12:SpR:4906.0,124.2] ssList(skc13) || -> equal(skc13,nil) equal(cons(skc11,tl(skc13)),skc13)**.
% 3.44/3.68 4914[12:MRR:4910.0,4910.1,3.0,4905.0] || -> equal(cons(skc11,tl(skc13)),skc13)**.
% 3.44/3.68 5224[0:Res:64.1,4707.1] ssList(skc13) ssList(skc13) || -> frontsegP(skc9,skc13)*.
% 3.44/3.68 5227[0:Obv:5224.0] ssList(skc13) || -> frontsegP(skc9,skc13)*.
% 3.44/3.68 5228[0:SSi:5227.0,3.0] || -> frontsegP(skc9,skc13)*.
% 3.44/3.68 5230[0:Res:5228.0,145.2] ssList(skc9) ssList(skc13) || frontsegP(skc13,skc9)* -> equal(skc13,skc9).
% 3.44/3.68 5231[10:SSi:5230.1,5230.0,3.0,7.0,1908.0,1912.0,1917.0,1921.0,1922.0,1952.0,1956.0,2012.0] || frontsegP(skc13,skc9)* -> equal(skc13,skc9).
% 3.44/3.68 5270[0:Res:4706.2,99.1] ssList(nil) ssList(skc13) || equal(skc9,nil) -> equal(skc13,nil)**.
% 3.44/3.68 5329[10:SpR:2285.1,4088.2] ssList(u) ssList(skc9) ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.44/3.68 5352[10:Obv:5329.0] ssList(skc9) ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.44/3.68 5353[10:SSi:5352.0,7.0,1908.0,1912.0,1917.0,1921.0,1922.0,1952.0,1956.0,2012.0] ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.44/3.68 5423[12:SpR:4914.0,5353.1] ssList(tl(skc13)) || -> frontsegP(skc13,skc9)*.
% 3.44/3.68 5427[12:SoR:5423.0,93.1] ssList(skc13) || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.44/3.68 5428[12:SSi:5427.0,3.0] || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.44/3.68 5429[12:MRR:5428.1,4905.0] || -> frontsegP(skc13,skc9)*.
% 3.44/3.68 5430[12:MRR:5231.0,5429.0] || -> equal(skc13,skc9)**.
% 3.44/3.68 5441[12:Rew:5430.0,4701.0] || -> equal(app(skc9,cons(skc12,skc14)),skc9)**.
% 3.44/3.68 5548[12:SpR:5441.0,2285.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.44/3.68 5560[12:SSi:5548.0,97.0,4.0,2.2] || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.44/3.68 5612[12:SpR:5560.0,2289.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),tl(skc9))**.
% 3.44/3.68 5633[12:Rew:2093.0,5612.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),nil)**.
% 3.44/3.68 5634[12:SSi:5633.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),nil)**.
% 3.74/3.91 5667[12:SpL:5634.0,116.2] ssItem(skc12) ssList(skc14) || equal(nil,nil)* -> .
% 3.74/3.91 5675[12:Obv:5667.2] ssItem(skc12) ssList(skc14) || -> .
% 3.74/3.91 5676[12:SSi:5675.1,5675.0,2.0,4.0] || -> .
% 3.74/3.91 5696[11:Spt:5676.0,83.0,1923.0] || -> SkP0(skc12,skc15,skc13)*.
% 3.74/3.91 5697[11:Spt:5676.0,83.1] || -> memberP(skc14,skc15)*.
% 3.74/3.91 5885[12:Spt:4704.0] || -> equal(skc13,nil)**.
% 3.74/3.91 5892[12:Rew:5885.0,4701.0] || -> equal(app(nil,cons(skc12,skc14)),skc9)**.
% 3.74/3.91 6319[12:SpR:5892.0,85.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),skc9)**.
% 3.74/3.91 6340[12:SSi:6319.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),skc9)**.
% 3.74/3.91 6367[12:SpR:6340.0,118.2] ssItem(skc12) ssList(skc14) || -> equal(tl(skc9),skc14)**.
% 3.74/3.91 6383[12:Rew:2093.0,6367.2] ssItem(skc12) ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 6384[12:SSi:6383.1,6383.0,2.0,4.0] || -> equal(skc14,nil)**.
% 3.74/3.91 6390[12:Rew:6384.0,5697.0] || -> memberP(nil,skc15)*.
% 3.74/3.91 6502[12:Res:6390.0,74.1] ssItem(skc15) || -> .
% 3.74/3.91 6503[12:SSi:6502.0,1.0] || -> .
% 3.74/3.91 6504[12:Spt:6503.0,4704.0,5885.0] || equal(skc13,nil)** -> .
% 3.74/3.91 6505[12:Spt:6503.0,4704.1] || -> equal(hd(skc13),skc11)**.
% 3.74/3.91 6511[12:SpR:6505.0,124.2] ssList(skc13) || -> equal(skc13,nil) equal(cons(skc11,tl(skc13)),skc13)**.
% 3.74/3.91 6515[12:MRR:6511.0,6511.1,3.0,6504.0] || -> equal(cons(skc11,tl(skc13)),skc13)**.
% 3.74/3.91 6616[12:SpR:6515.0,5353.1] ssList(tl(skc13)) || -> frontsegP(skc13,skc9)*.
% 3.74/3.91 7096[12:SoR:6616.0,93.1] ssList(skc13) || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.74/3.91 7097[12:SSi:7096.0,3.0] || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.74/3.91 7098[12:MRR:7097.1,6504.0] || -> frontsegP(skc13,skc9)*.
% 3.74/3.91 7099[12:MRR:5231.0,7098.0] || -> equal(skc13,skc9)**.
% 3.74/3.91 7108[12:Rew:7099.0,4701.0] || -> equal(app(skc9,cons(skc12,skc14)),skc9)**.
% 3.74/3.91 7221[12:SpR:7108.0,2285.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.74/3.91 7237[12:SSi:7221.0,97.0,4.0,2.2] || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.74/3.91 7251[12:SpR:7237.0,2289.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),tl(skc9))**.
% 3.74/3.91 7273[12:Rew:2093.0,7251.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),nil)**.
% 3.74/3.91 7274[12:SSi:7273.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),nil)**.
% 3.74/3.91 7322[12:SpL:7274.0,116.2] ssItem(skc12) ssList(skc14) || equal(nil,nil)* -> .
% 3.74/3.91 7334[12:Obv:7322.2] ssItem(skc12) ssList(skc14) || -> .
% 3.74/3.91 7335[12:SSi:7334.1,7334.0,2.0,4.0] || -> .
% 3.74/3.91 7360[10:Spt:7335.0,224.0,1922.0] || strictorderP(skc9)* -> .
% 3.74/3.91 7361[10:Spt:7335.0,224.1] || -> equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 3.74/3.91 7362[9:SSi:2016.0,18.0,7.0,1908.0,1912.0,1917.0,1921.0,1952.0,1956.0,2012.0] || -> strictorderP(skc9)*.
% 3.74/3.91 7363[10:MRR:7362.0,7360.0] || -> .
% 3.74/3.91 7446[9:Spt:7363.0,223.0,1921.0] || totalorderP(skc9)* -> .
% 3.74/3.91 7447[9:Spt:7363.0,223.1] || -> equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 3.74/3.91 7449[8:SSi:2017.0,18.0,7.0,1908.0,1912.0,1917.0,1952.0,1956.0,2012.0] || -> totalorderP(skc9)*.
% 3.74/3.91 7450[9:MRR:7449.0,7446.0] || -> .
% 3.74/3.91 7526[8:Spt:7450.0,269.0,1917.0] || cyclefreeP(skc9)* -> .
% 3.74/3.91 7527[8:Spt:7450.0,269.1] || -> leq(skf51(skc9),skf50(skc9))*.
% 3.74/3.91 7529[7:SSi:2018.0,18.0,7.0,1908.0,1912.0,1952.0,1956.0,2012.0] || -> cyclefreeP(skc9)*.
% 3.74/3.91 7530[8:MRR:7529.0,7526.0] || -> .
% 3.74/3.91 7629[7:Spt:7530.0,226.0,1912.0] || strictorderedP(skc9)* -> .
% 3.74/3.91 7630[7:Spt:7530.0,226.1] || -> equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 3.74/3.91 7632[6:SSi:2019.0,18.0,7.0,1908.0,1952.0,1956.0,2012.0] || -> strictorderedP(skc9)*.
% 3.74/3.91 7633[7:MRR:7632.0,7629.0] || -> .
% 3.74/3.91 7740[6:Spt:7633.0,225.0,1908.0] || totalorderedP(skc9)* -> .
% 3.74/3.91 7741[6:Spt:7633.0,225.1] || -> equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 3.74/3.91 7743[4:SSi:2020.0,18.0,7.0,1952.0,1956.0,2012.0] || -> totalorderedP(skc9)*.
% 3.74/3.91 7744[6:MRR:7743.0,7740.0] || -> .
% 3.74/3.91 7837[3:Spt:7744.0,243.1] || -> equal(skc9,nil)**.
% 3.74/3.91 8205[3:Rew:7837.0,4064.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.74/3.91 8206[3:Obv:8205.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 8207[3:SSi:8206.1,8206.0,2.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc14,nil)**.
% 3.74/3.91 8211[3:Rew:8207.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.74/3.91 8227[3:Rew:7837.0,5270.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.74/3.91 8228[3:Obv:8227.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 8229[3:SSi:8228.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 8230[3:MRR:8229.0,3.0] || -> equal(skc13,nil)**.
% 3.74/3.91 8232[3:Rew:8230.0,8211.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.74/3.91 8243[3:Obv:8232.0] || -> memberP(nil,skc15)*.
% 3.74/3.91 8576[3:Res:8243.0,74.1] ssItem(skc15) || -> .
% 3.74/3.91 8577[3:SSi:8576.0,1.0] || -> .
% 3.74/3.91 8578[2:Spt:8577.0,249.1] || -> equal(skc9,nil)**.
% 3.74/3.91 8728[2:Rew:8578.0,4064.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.74/3.91 8729[2:Obv:8728.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 8730[2:SSi:8729.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 8731[2:MRR:8730.0,2.0] || -> equal(skc14,nil)**.
% 3.74/3.91 8741[2:Rew:8731.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.74/3.91 8752[2:Rew:8578.0,5270.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.74/3.91 8753[2:Obv:8752.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 8754[2:SSi:8753.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 8755[2:MRR:8754.0,3.0] || -> equal(skc13,nil)**.
% 3.74/3.91 8758[2:Rew:8755.0,8741.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.74/3.91 8767[2:Obv:8758.0] || -> memberP(nil,skc15)*.
% 3.74/3.91 9185[2:Res:8767.0,74.1] ssItem(skc15) || -> .
% 3.74/3.91 9186[2:SSi:9185.0,1.0] || -> .
% 3.74/3.91 9187[1:Spt:9186.0,420.1] || -> equal(skc10,nil)**.
% 3.74/3.91 9220[1:Rew:9187.0,71.0] || equal(nil,nil) -> equal(skc9,nil)**.
% 3.74/3.91 9221[1:Obv:9220.0] || -> equal(skc9,nil)**.
% 3.74/3.91 9344[1:Rew:9221.0,4064.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.74/3.91 9345[1:Obv:9344.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 9346[1:SSi:9345.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc14) || -> equal(skc14,nil)**.
% 3.74/3.91 9347[1:MRR:9346.0,2.0] || -> equal(skc14,nil)**.
% 3.74/3.91 9351[1:Rew:9347.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.74/3.91 9368[1:Rew:9221.0,5270.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.74/3.91 9369[1:Obv:9368.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 9370[1:SSi:9369.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.74/3.91 9371[1:MRR:9370.0,3.0] || -> equal(skc13,nil)**.
% 3.74/3.91 9373[1:Rew:9371.0,9351.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.74/3.91 9383[1:Obv:9373.0] || -> memberP(nil,skc15)*.
% 3.74/3.91 9784[1:Res:9383.0,74.1] ssItem(skc15) || -> .
% 3.74/3.91 9785[1:SSi:9784.0,1.0] || -> .
% 3.74/3.91 % SZS output end Refutation
% 3.74/3.91 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax42 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax76 ax8 ax16 ax26 ax46 ax52 ax15 ax21 ax23 ax25 ax78 ax81 ax83 ax85 ax41 ax5 ax6 ax43 ax70 ax86 ax82 ax12 ax11 ax10 ax9
% 3.74/3.91
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