TSTP Solution File: SWC297+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC297+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 22:03:08 EDT 2022
% Result : Theorem 3.45s 3.62s
% Output : Refutation 3.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC297+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 12 11:51:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.45/3.62
% 3.45/3.62 SPASS V 3.9
% 3.45/3.62 SPASS beiseite: Proof found.
% 3.45/3.62 % SZS status Theorem
% 3.45/3.62 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.45/3.62 SPASS derived 5407 clauses, backtracked 2851 clauses, performed 33 splits and kept 4001 clauses.
% 3.45/3.62 SPASS allocated 105477 KBytes.
% 3.45/3.62 SPASS spent 0:00:03.28 on the problem.
% 3.45/3.62 0:00:00.04 for the input.
% 3.45/3.62 0:00:00.07 for the FLOTTER CNF translation.
% 3.45/3.62 0:00:00.05 for inferences.
% 3.45/3.62 0:00:00.06 for the backtracking.
% 3.45/3.62 0:00:02.88 for the reduction.
% 3.45/3.62
% 3.45/3.62
% 3.45/3.62 Here is a proof with depth 6, length 301 :
% 3.45/3.62 % SZS output start Refutation
% 3.45/3.62 1[0:Inp] || -> ssItem(skc15)*.
% 3.45/3.62 2[0:Inp] || -> ssList(skc14)*.
% 3.45/3.62 3[0:Inp] || -> ssList(skc13)*.
% 3.45/3.62 4[0:Inp] || -> ssItem(skc12)*.
% 3.45/3.62 5[0:Inp] || -> ssItem(skc11)*.
% 3.45/3.62 6[0:Inp] || -> ssList(skc10)*.
% 3.45/3.62 7[0:Inp] || -> ssList(skc9)*.
% 3.45/3.62 8[0:Inp] || -> ssItem(skc17)*.
% 3.45/3.62 9[0:Inp] || -> ssItem(skc16)*.
% 3.45/3.62 10[0:Inp] || -> ssList(nil)*.
% 3.45/3.62 11[0:Inp] || -> cyclefreeP(nil)*.
% 3.45/3.62 12[0:Inp] || -> totalorderP(nil)*.
% 3.45/3.62 13[0:Inp] || -> strictorderP(nil)*.
% 3.45/3.62 14[0:Inp] || -> totalorderedP(nil)*.
% 3.45/3.62 15[0:Inp] || -> strictorderedP(nil)*.
% 3.45/3.62 16[0:Inp] || -> duplicatefreeP(nil)*.
% 3.45/3.62 17[0:Inp] || -> equalelemsP(nil)*.
% 3.45/3.62 18[0:Inp] || -> ssItem(skf45(u))*.
% 3.45/3.62 56[0:Inp] || equal(skc17,skc16)** -> .
% 3.45/3.62 64[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 3.45/3.62 71[0:Inp] || equal(skc10,nil)** -> equal(skc9,nil).
% 3.45/3.62 73[0:Inp] || -> memberP(u,v) SkP0(w,v,u)*.
% 3.45/3.62 74[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 3.45/3.62 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.45/3.62 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.45/3.62 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.45/3.62 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.45/3.62 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.45/3.62 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.45/3.62 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.45/3.62 83[0:Inp] || SkP0(skc12,skc15,skc13)* -> memberP(skc14,skc15).
% 3.45/3.62 85[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.45/3.62 87[0:Inp] || neq(skc10,nil) -> equal(cons(skc11,nil),skc9)**.
% 3.45/3.62 88[0:Inp] || -> equal(app(app(skc13,cons(skc12,nil)),skc14),skc9)**.
% 3.45/3.62 93[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 3.45/3.62 94[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf51(u),skf50(u))*.
% 3.45/3.62 97[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 3.45/3.62 98[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 3.45/3.62 99[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 3.45/3.62 101[0:Inp] ssList(u) || rearsegP(nil,u)* -> equal(nil,u).
% 3.45/3.62 113[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf45(u),nil),u)**.
% 3.45/3.62 114[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 3.45/3.62 116[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 3.45/3.62 117[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 3.45/3.62 118[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 3.45/3.62 124[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 3.45/3.62 127[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 3.45/3.62 134[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 3.45/3.62 136[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 3.45/3.62 139[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 3.45/3.62 145[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(v,u).
% 3.45/3.62 149[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 3.45/3.62 150[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,u),v)*+ -> rearsegP(v,u)*.
% 3.45/3.62 156[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(w,v) -> frontsegP(app(w,u),v)*.
% 3.45/3.62 159[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 3.45/3.62 160[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**.
% 3.45/3.62 165[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 3.45/3.62 179[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf72(u),cons(skf70(u),skf73(u))),cons(skf71(u),skf74(u))),u)**.
% 3.45/3.62 180[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf67(u),cons(skf65(u),skf68(u))),cons(skf66(u),skf69(u))),u)**.
% 3.45/3.62 181[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf62(u),cons(skf60(u),skf63(u))),cons(skf61(u),skf64(u))),u)**.
% 3.45/3.62 182[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf57(u),cons(skf55(u),skf58(u))),cons(skf56(u),skf59(u))),u)**.
% 3.45/3.62 223[0:Res:7.0,182.0] || -> totalorderP(skc9) equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 3.45/3.62 224[0:Res:7.0,181.0] || -> strictorderP(skc9) equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 3.45/3.62 225[0:Res:7.0,180.0] || -> totalorderedP(skc9) equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 3.45/3.62 226[0:Res:7.0,179.0] || -> strictorderedP(skc9) equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 3.45/3.62 243[0:Res:7.0,160.0] ssList(u) || -> equal(skc9,nil) equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 3.45/3.62 249[0:Res:7.0,139.0] ssList(u) || -> equal(skc9,nil) equal(hd(app(skc9,u)),hd(skc9))**.
% 3.45/3.62 252[0:Res:7.0,136.0] ssList(u) || equal(app(skc9,u),nil)** -> equal(skc9,nil).
% 3.45/3.62 256[0:Res:7.0,113.1] singletonP(skc9) || -> equal(cons(skf45(skc9),nil),skc9)**.
% 3.45/3.62 259[0:Res:7.0,116.0] ssItem(u) || equal(cons(u,skc9),nil)** -> .
% 3.45/3.62 269[0:Res:7.0,94.0] || -> cyclefreeP(skc9) leq(skf51(skc9),skf50(skc9))*.
% 3.45/3.62 313[0:Res:7.0,159.1] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)) equal(skc9,nil).
% 3.45/3.62 325[0:Res:7.0,127.1] ssItem(u) || equal(cons(u,nil),skc9)** -> singletonP(skc9).
% 3.45/3.62 420[0:Res:6.0,139.0] ssList(u) || -> equal(skc10,nil) equal(hd(app(skc10,u)),hd(skc10))**.
% 3.45/3.62 428[0:Res:6.0,114.0] ssList(u) || -> neq(skc10,u)* equal(skc10,u).
% 3.45/3.62 431[0:Res:6.0,117.0] ssItem(u) || -> equal(hd(cons(u,skc10)),u)**.
% 3.45/3.62 443[0:Res:6.0,97.0] ssItem(u) || -> ssList(cons(u,skc10))*.
% 3.45/3.62 484[0:Res:6.0,159.1] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)) equal(skc10,nil).
% 3.45/3.62 549[1:Spt:420.0,420.2] ssList(u) || -> equal(hd(app(skc10,u)),hd(skc10))**.
% 3.45/3.62 551[2:Spt:249.0,249.2] ssList(u) || -> equal(hd(app(skc9,u)),hd(skc9))**.
% 3.45/3.62 555[3:Spt:243.0,243.2] ssList(u) || -> equal(app(tl(skc9),u),tl(app(skc9,u)))**.
% 3.45/3.62 557[4:Spt:484.3] || -> equal(skc10,nil)**.
% 3.45/3.62 558[4:Rew:557.0,549.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 3.45/3.62 577[4:Rew:557.0,443.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 3.45/3.62 578[4:Rew:557.0,431.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 3.45/3.62 903[4:Rew:85.1,558.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 3.45/3.62 1064[0:Res:73.1,83.0] || -> memberP(skc13,skc15) memberP(skc14,skc15)*.
% 3.45/3.62 1202[4:SpR:578.1,903.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 3.45/3.62 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))*.
% 3.45/3.62 1274[4:SpR:1205.1,1205.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 3.45/3.62 1314[4:EmS:1274.0,1.0] ssItem(u) || -> equal(u,skc15)*.
% 3.45/3.62 1338[4:EmS:1314.0,4.0] || -> equal(skc15,skc12)**.
% 3.45/3.62 1339[4:EmS:1314.0,5.0] || -> equal(skc15,skc11)**.
% 3.45/3.62 1340[4:EmS:1314.0,8.0] || -> equal(skc17,skc15)**.
% 3.45/3.62 1341[4:EmS:1314.0,9.0] || -> equal(skc16,skc15)**.
% 3.45/3.62 1347[4:Rew:1338.0,1339.0] || -> equal(skc12,skc11)**.
% 3.45/3.62 1351[4:Rew:1347.0,1338.0] || -> equal(skc15,skc11)**.
% 3.45/3.62 1353[4:Rew:1340.0,56.0] || equal(skc16,skc15)** -> .
% 3.45/3.62 1360[4:Rew:1351.0,1341.0] || -> equal(skc16,skc11)**.
% 3.45/3.62 1481[4:Rew:1360.0,1353.0,1351.0,1353.0] || equal(skc11,skc11)* -> .
% 3.45/3.62 1482[4:Obv:1481.0] || -> .
% 3.45/3.62 1516[4:Spt:1482.0,484.3,557.0] || equal(skc10,nil)** -> .
% 3.45/3.62 1517[4:Spt:1482.0,484.0,484.1,484.2] ssItem(u) || strictorderedP(cons(u,skc10))* -> lt(u,hd(skc10)).
% 3.45/3.62 1531[5:Spt:313.3] || -> equal(skc9,nil)**.
% 3.45/3.62 1570[5:Rew:1531.0,259.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 3.45/3.62 1595[5:Rew:1531.0,87.1] || neq(skc10,nil) -> equal(cons(skc11,nil),nil)**.
% 3.45/3.62 1875[5:SpL:1595.1,1570.1] ssItem(skc11) || neq(skc10,nil)* equal(nil,nil) -> .
% 3.45/3.62 1876[5:Obv:1875.2] ssItem(skc11) || neq(skc10,nil)* -> .
% 3.45/3.62 1877[5:SSi:1876.0,5.0] || neq(skc10,nil)* -> .
% 3.45/3.62 1880[5:Res:428.1,1877.0] ssList(nil) || -> equal(skc10,nil)**.
% 3.45/3.62 1881[5:SSi:1880.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil)**.
% 3.45/3.62 1882[5:MRR:1881.0,1516.0] || -> .
% 3.45/3.62 1883[5:Spt:1882.0,313.3,1531.0] || equal(skc9,nil)** -> .
% 3.45/3.62 1884[5:Spt:1882.0,313.0,313.1,313.2] ssItem(u) || strictorderedP(cons(u,skc9))* -> lt(u,hd(skc9)).
% 3.45/3.62 1893[5:MRR:252.2,1883.0] ssList(u) || equal(app(skc9,u),nil)** -> .
% 3.45/3.62 1905[6:Spt:225.0] || -> totalorderedP(skc9)*.
% 3.45/3.62 1909[7:Spt:226.0] || -> strictorderedP(skc9)*.
% 3.45/3.62 1914[8:Spt:269.0] || -> cyclefreeP(skc9)*.
% 3.45/3.62 1918[9:Spt:223.0] || -> totalorderP(skc9)*.
% 3.45/3.62 1919[10:Spt:224.0] || -> strictorderP(skc9)*.
% 3.45/3.62 1920[11:Spt:83.0] || SkP0(skc12,skc15,skc13)* -> .
% 3.45/3.62 1921[11:Res:73.1,1920.0] || -> memberP(skc13,skc15)*.
% 3.45/3.62 1936[0:SpR:87.1,81.1] ssItem(skc11) || neq(skc10,nil)* -> equalelemsP(skc9).
% 3.45/3.62 1937[0:SpR:87.1,80.1] ssItem(skc11) || neq(skc10,nil)* -> duplicatefreeP(skc9).
% 3.45/3.62 1945[0:SSi:1936.0,5.0] || neq(skc10,nil)* -> equalelemsP(skc9).
% 3.45/3.62 1946[0:SSi:1937.0,5.0] || neq(skc10,nil)* -> duplicatefreeP(skc9).
% 3.45/3.62 1947[0:Res:428.1,1945.0] ssList(nil) || -> equal(skc10,nil) equalelemsP(skc9)*.
% 3.45/3.62 1948[0:SSi:1947.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) equalelemsP(skc9)*.
% 3.45/3.62 1949[4:MRR:1948.0,1516.0] || -> equalelemsP(skc9)*.
% 3.45/3.62 1951[0:Res:428.1,1946.0] ssList(nil) || -> equal(skc10,nil) duplicatefreeP(skc9)*.
% 3.45/3.62 1952[0:SSi:1951.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) duplicatefreeP(skc9)*.
% 3.45/3.62 1953[4:MRR:1952.0,1516.0] || -> duplicatefreeP(skc9)*.
% 3.45/3.62 2002[0:SpL:87.1,325.1] ssItem(skc11) || neq(skc10,nil)* equal(skc9,skc9) -> singletonP(skc9).
% 3.45/3.62 2003[0:Obv:2002.2] ssItem(skc11) || neq(skc10,nil)* -> singletonP(skc9).
% 3.45/3.62 2004[0:SSi:2003.0,5.0] || neq(skc10,nil)* -> singletonP(skc9).
% 3.45/3.62 2007[0:Res:428.1,2004.0] ssList(nil) || -> equal(skc10,nil) singletonP(skc9)*.
% 3.45/3.62 2008[0:SSi:2007.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) singletonP(skc9)*.
% 3.45/3.62 2009[4:MRR:2008.0,1516.0] || -> singletonP(skc9)*.
% 3.45/3.62 2010[4:MRR:256.0,2009.0] || -> equal(cons(skf45(skc9),nil),skc9)**.
% 3.45/3.62 2013[4:SpR:2010.0,77.1] ssItem(skf45(skc9)) || -> strictorderP(skc9)*.
% 3.45/3.62 2014[4:SpR:2010.0,76.1] ssItem(skf45(skc9)) || -> totalorderP(skc9)*.
% 3.45/3.62 2015[4:SpR:2010.0,75.1] ssItem(skf45(skc9)) || -> cyclefreeP(skc9)*.
% 3.45/3.62 2016[4:SpR:2010.0,79.1] ssItem(skf45(skc9)) || -> strictorderedP(skc9)*.
% 3.45/3.62 2017[4:SpR:2010.0,78.1] ssItem(skf45(skc9)) || -> totalorderedP(skc9)*.
% 3.45/3.62 2083[4:SpR:2010.0,118.2] ssItem(skf45(skc9)) ssList(nil) || -> equal(tl(skc9),nil)**.
% 3.45/3.62 2090[10:SSi:2083.1,2083.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,18.0,7.0,1905.0,1909.0,1914.0,1918.0,1919.0,1949.0,1953.0,2009.0] || -> equal(tl(skc9),nil)**.
% 3.45/3.62 2093[10:Rew:2090.0,555.1] ssList(u) || -> equal(tl(app(skc9,u)),app(nil,u))**.
% 3.45/3.62 2095[10:Rew:85.1,2093.1] ssList(u) || -> equal(tl(app(skc9,u)),u)**.
% 3.45/3.62 2128[0:SpR:87.1,117.2] ssItem(skc11) ssList(nil) || neq(skc10,nil)* -> equal(hd(skc9),skc11).
% 3.45/3.62 2133[0:SSi:2128.1,2128.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0,5.0] || neq(skc10,nil)* -> equal(hd(skc9),skc11).
% 3.45/3.62 2197[0:Res:428.1,2133.0] ssList(nil) || -> equal(skc10,nil) equal(hd(skc9),skc11)**.
% 3.45/3.62 2198[0:SSi:2197.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc10,nil) equal(hd(skc9),skc11)**.
% 3.45/3.62 2199[4:MRR:2198.0,1516.0] || -> equal(hd(skc9),skc11)**.
% 3.45/3.62 2202[4:Rew:2199.0,551.1] ssList(u) || -> equal(hd(app(skc9,u)),skc11)**.
% 3.45/3.62 2272[4:SpR:2202.1,124.2] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(cons(skc11,tl(app(skc9,u))),app(skc9,u))**.
% 3.45/3.62 2280[10:Rew:2095.1,2272.3] ssList(u) ssList(app(skc9,u)) || -> equal(app(skc9,u),nil) equal(app(skc9,u),cons(skc11,u))**.
% 3.45/3.62 2281[10:SSi:2280.1,98.0,7.0,1905.0,1909.0,1914.0,1918.0,1919.0,1949.0,1953.0,2009.2] ssList(u) || -> equal(app(skc9,u),nil) equal(app(skc9,u),cons(skc11,u))**.
% 3.45/3.62 2282[10:MRR:2281.1,1893.1] ssList(u) || -> equal(app(skc9,u),cons(skc11,u))**.
% 3.45/3.62 2286[10:Rew:2282.1,2095.1] ssList(u) || -> equal(tl(cons(skc11,u)),u)**.
% 3.45/3.62 2625[0:EqR:127.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 3.45/3.62 2629[0:SSi:2625.0,97.1,17.1,16.1,13.1,12.1,11.1,15.1,14.0,10.0,81.0,80.0,77.0,76.0,75.0,79.0,78.2] ssItem(u) || -> singletonP(cons(u,nil))*.
% 3.45/3.62 3984[0:SpL:88.0,150.3] ssList(skc14) ssList(u) ssList(app(skc13,cons(skc12,nil))) || equal(skc9,u) -> rearsegP(u,skc14)*.
% 3.45/3.62 3997[0:SSi:3984.2,3984.0,98.0,3.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2629.2,4.0,2.2] ssList(u) || equal(skc9,u) -> rearsegP(u,skc14)*.
% 3.45/3.62 4027[0:Res:3997.2,101.1] ssList(nil) ssList(skc14) || equal(skc9,nil) -> equal(skc14,nil)**.
% 3.45/3.62 4033[0:EqR:149.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 3.45/3.62 4051[0:SSi:4033.1,98.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 3.45/3.62 4440[0:SpR:165.3,88.0] ssList(skc14) ssList(cons(skc12,nil)) ssList(skc13) || -> equal(app(skc13,app(cons(skc12,nil),skc14)),skc9)**.
% 3.45/3.62 4473[0:SSi:4440.2,4440.1,4440.0,3.0,97.0,4.1,17.0,16.1,13.0,12.1,11.0,15.1,14.0,10.1,81.0,4.1,80.0,4.1,77.0,4.1,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2629.0,4.2,2.0] || -> equal(app(skc13,app(cons(skc12,nil),skc14)),skc9)**.
% 3.45/3.62 4648[0:SpR:4473.0,139.3] ssList(app(cons(skc12,nil),skc14)) ssList(skc13) || -> equal(skc13,nil) equal(hd(skc13),hd(skc9))**.
% 3.45/3.62 4652[0:SpR:4473.0,156.4] ssList(app(cons(skc12,nil),skc14)) ssList(u) ssList(skc13) || frontsegP(skc13,u)* -> frontsegP(skc9,u).
% 3.45/3.62 4656[0:SpR:134.2,4473.0] ssItem(skc12) ssList(skc14) || -> equal(app(skc13,cons(skc12,skc14)),skc9)**.
% 3.45/3.62 4658[0:SpL:4473.0,149.3] ssList(skc13) ssList(u) ssList(app(cons(skc12,nil),skc14)) || equal(skc9,u) -> frontsegP(u,skc13)*.
% 3.45/3.62 4664[0:SSi:4656.1,4656.0,2.0,4.0] || -> equal(app(skc13,cons(skc12,skc14)),skc9)**.
% 3.45/3.62 4666[4:Rew:2199.0,4648.3] ssList(app(cons(skc12,nil),skc14)) ssList(skc13) || -> equal(skc13,nil) equal(hd(skc13),skc11)**.
% 3.45/3.62 4667[4:SSi:4666.1,4666.0,3.0,98.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2629.2,4.2,2.0] || -> equal(skc13,nil) equal(hd(skc13),skc11)**.
% 3.45/3.62 4669[0:SSi:4658.2,4658.0,98.0,97.0,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.1,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2629.0,4.0,2.2,3.2] ssList(u) || equal(skc9,u) -> frontsegP(u,skc13)*.
% 3.45/3.62 4670[0:SSi:4652.2,4652.0,3.0,98.0,97.1,4.0,17.1,16.0,13.1,12.0,11.1,15.0,14.1,10.0,81.1,4.0,80.1,4.0,77.1,4.0,76.0,4.0,75.0,4.0,79.0,4.0,78.0,4.0,2629.2,4.2,2.0] ssList(u) || frontsegP(skc13,u)* -> frontsegP(skc9,u).
% 3.45/3.62 4822[12:Spt:4667.0] || -> equal(skc13,nil)**.
% 3.45/3.62 4825[12:Rew:4822.0,1921.0] || -> memberP(nil,skc15)*.
% 3.45/3.62 4866[12:Res:4825.0,74.1] ssItem(skc15) || -> .
% 3.45/3.62 4867[12:SSi:4866.0,1.0] || -> .
% 3.45/3.62 4868[12:Spt:4867.0,4667.0,4822.0] || equal(skc13,nil)** -> .
% 3.45/3.62 4869[12:Spt:4867.0,4667.1] || -> equal(hd(skc13),skc11)**.
% 3.45/3.62 4873[12:SpR:4869.0,124.2] ssList(skc13) || -> equal(skc13,nil) equal(cons(skc11,tl(skc13)),skc13)**.
% 3.45/3.62 4877[12:MRR:4873.0,4873.1,3.0,4868.0] || -> equal(cons(skc11,tl(skc13)),skc13)**.
% 3.45/3.62 5187[0:Res:64.1,4670.1] ssList(skc13) ssList(skc13) || -> frontsegP(skc9,skc13)*.
% 3.45/3.62 5190[0:Obv:5187.0] ssList(skc13) || -> frontsegP(skc9,skc13)*.
% 3.45/3.62 5191[0:SSi:5190.0,3.0] || -> frontsegP(skc9,skc13)*.
% 3.45/3.62 5193[0:Res:5191.0,145.2] ssList(skc9) ssList(skc13) || frontsegP(skc13,skc9)* -> equal(skc13,skc9).
% 3.45/3.62 5194[10:SSi:5193.1,5193.0,3.0,7.0,1905.0,1909.0,1914.0,1918.0,1919.0,1949.0,1953.0,2009.0] || frontsegP(skc13,skc9)* -> equal(skc13,skc9).
% 3.45/3.62 5233[0:Res:4669.2,99.1] ssList(nil) ssList(skc13) || equal(skc9,nil) -> equal(skc13,nil)**.
% 3.45/3.62 5294[10:SpR:2282.1,4051.2] ssList(u) ssList(skc9) ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.45/3.62 5317[10:Obv:5294.0] ssList(skc9) ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.45/3.62 5318[10:SSi:5317.0,7.0,1905.0,1909.0,1914.0,1918.0,1919.0,1949.0,1953.0,2009.0] ssList(u) || -> frontsegP(cons(skc11,u),skc9)*.
% 3.45/3.62 5388[12:SpR:4877.0,5318.1] ssList(tl(skc13)) || -> frontsegP(skc13,skc9)*.
% 3.45/3.62 5392[12:SoR:5388.0,93.1] ssList(skc13) || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.45/3.62 5393[12:SSi:5392.0,3.0] || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.45/3.62 5394[12:MRR:5393.1,4868.0] || -> frontsegP(skc13,skc9)*.
% 3.45/3.62 5395[12:MRR:5194.0,5394.0] || -> equal(skc13,skc9)**.
% 3.45/3.62 5406[12:Rew:5395.0,4664.0] || -> equal(app(skc9,cons(skc12,skc14)),skc9)**.
% 3.45/3.62 5513[12:SpR:5406.0,2282.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.45/3.62 5525[12:SSi:5513.0,97.0,4.0,2.2] || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.45/3.62 5577[12:SpR:5525.0,2286.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),tl(skc9))**.
% 3.45/3.62 5598[12:Rew:2090.0,5577.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),nil)**.
% 3.45/3.62 5599[12:SSi:5598.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),nil)**.
% 3.68/3.85 5632[12:SpL:5599.0,116.2] ssItem(skc12) ssList(skc14) || equal(nil,nil)* -> .
% 3.68/3.85 5640[12:Obv:5632.2] ssItem(skc12) ssList(skc14) || -> .
% 3.68/3.85 5641[12:SSi:5640.1,5640.0,2.0,4.0] || -> .
% 3.68/3.85 5661[11:Spt:5641.0,83.0,1920.0] || -> SkP0(skc12,skc15,skc13)*.
% 3.68/3.85 5662[11:Spt:5641.0,83.1] || -> memberP(skc14,skc15)*.
% 3.68/3.85 5850[12:Spt:4667.0] || -> equal(skc13,nil)**.
% 3.68/3.85 5857[12:Rew:5850.0,4664.0] || -> equal(app(nil,cons(skc12,skc14)),skc9)**.
% 3.68/3.85 6284[12:SpR:5857.0,85.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),skc9)**.
% 3.68/3.85 6305[12:SSi:6284.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),skc9)**.
% 3.68/3.85 6332[12:SpR:6305.0,118.2] ssItem(skc12) ssList(skc14) || -> equal(tl(skc9),skc14)**.
% 3.68/3.85 6348[12:Rew:2090.0,6332.2] ssItem(skc12) ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 6349[12:SSi:6348.1,6348.0,2.0,4.0] || -> equal(skc14,nil)**.
% 3.68/3.85 6355[12:Rew:6349.0,5662.0] || -> memberP(nil,skc15)*.
% 3.68/3.85 6467[12:Res:6355.0,74.1] ssItem(skc15) || -> .
% 3.68/3.85 6468[12:SSi:6467.0,1.0] || -> .
% 3.68/3.85 6469[12:Spt:6468.0,4667.0,5850.0] || equal(skc13,nil)** -> .
% 3.68/3.85 6470[12:Spt:6468.0,4667.1] || -> equal(hd(skc13),skc11)**.
% 3.68/3.85 6476[12:SpR:6470.0,124.2] ssList(skc13) || -> equal(skc13,nil) equal(cons(skc11,tl(skc13)),skc13)**.
% 3.68/3.85 6480[12:MRR:6476.0,6476.1,3.0,6469.0] || -> equal(cons(skc11,tl(skc13)),skc13)**.
% 3.68/3.85 6581[12:SpR:6480.0,5318.1] ssList(tl(skc13)) || -> frontsegP(skc13,skc9)*.
% 3.68/3.85 7061[12:SoR:6581.0,93.1] ssList(skc13) || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.68/3.85 7062[12:SSi:7061.0,3.0] || -> frontsegP(skc13,skc9)* equal(skc13,nil).
% 3.68/3.85 7063[12:MRR:7062.1,6469.0] || -> frontsegP(skc13,skc9)*.
% 3.68/3.85 7064[12:MRR:5194.0,7063.0] || -> equal(skc13,skc9)**.
% 3.68/3.85 7073[12:Rew:7064.0,4664.0] || -> equal(app(skc9,cons(skc12,skc14)),skc9)**.
% 3.68/3.85 7186[12:SpR:7073.0,2282.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.68/3.85 7202[12:SSi:7186.0,97.0,4.0,2.2] || -> equal(cons(skc11,cons(skc12,skc14)),skc9)**.
% 3.68/3.85 7216[12:SpR:7202.0,2286.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),tl(skc9))**.
% 3.68/3.85 7238[12:Rew:2090.0,7216.1] ssList(cons(skc12,skc14)) || -> equal(cons(skc12,skc14),nil)**.
% 3.68/3.85 7239[12:SSi:7238.0,97.0,4.0,2.2] || -> equal(cons(skc12,skc14),nil)**.
% 3.68/3.85 7287[12:SpL:7239.0,116.2] ssItem(skc12) ssList(skc14) || equal(nil,nil)* -> .
% 3.68/3.85 7299[12:Obv:7287.2] ssItem(skc12) ssList(skc14) || -> .
% 3.68/3.85 7300[12:SSi:7299.1,7299.0,2.0,4.0] || -> .
% 3.68/3.85 7325[10:Spt:7300.0,224.0,1919.0] || strictorderP(skc9)* -> .
% 3.68/3.85 7326[10:Spt:7300.0,224.1] || -> equal(app(app(skf62(skc9),cons(skf60(skc9),skf63(skc9))),cons(skf61(skc9),skf64(skc9))),skc9)**.
% 3.68/3.85 7327[9:SSi:2013.0,18.0,7.0,1905.0,1909.0,1914.0,1918.0,1949.0,1953.0,2009.0] || -> strictorderP(skc9)*.
% 3.68/3.85 7328[10:MRR:7327.0,7325.0] || -> .
% 3.68/3.85 7411[9:Spt:7328.0,223.0,1918.0] || totalorderP(skc9)* -> .
% 3.68/3.85 7412[9:Spt:7328.0,223.1] || -> equal(app(app(skf57(skc9),cons(skf55(skc9),skf58(skc9))),cons(skf56(skc9),skf59(skc9))),skc9)**.
% 3.68/3.85 7414[8:SSi:2014.0,18.0,7.0,1905.0,1909.0,1914.0,1949.0,1953.0,2009.0] || -> totalorderP(skc9)*.
% 3.68/3.85 7415[9:MRR:7414.0,7411.0] || -> .
% 3.68/3.85 7491[8:Spt:7415.0,269.0,1914.0] || cyclefreeP(skc9)* -> .
% 3.68/3.85 7492[8:Spt:7415.0,269.1] || -> leq(skf51(skc9),skf50(skc9))*.
% 3.68/3.85 7494[7:SSi:2015.0,18.0,7.0,1905.0,1909.0,1949.0,1953.0,2009.0] || -> cyclefreeP(skc9)*.
% 3.68/3.85 7495[8:MRR:7494.0,7491.0] || -> .
% 3.68/3.85 7594[7:Spt:7495.0,226.0,1909.0] || strictorderedP(skc9)* -> .
% 3.68/3.85 7595[7:Spt:7495.0,226.1] || -> equal(app(app(skf72(skc9),cons(skf70(skc9),skf73(skc9))),cons(skf71(skc9),skf74(skc9))),skc9)**.
% 3.68/3.85 7597[6:SSi:2016.0,18.0,7.0,1905.0,1949.0,1953.0,2009.0] || -> strictorderedP(skc9)*.
% 3.68/3.85 7598[7:MRR:7597.0,7594.0] || -> .
% 3.68/3.85 7705[6:Spt:7598.0,225.0,1905.0] || totalorderedP(skc9)* -> .
% 3.68/3.85 7706[6:Spt:7598.0,225.1] || -> equal(app(app(skf67(skc9),cons(skf65(skc9),skf68(skc9))),cons(skf66(skc9),skf69(skc9))),skc9)**.
% 3.68/3.85 7708[4:SSi:2017.0,18.0,7.0,1949.0,1953.0,2009.0] || -> totalorderedP(skc9)*.
% 3.68/3.85 7709[6:MRR:7708.0,7705.0] || -> .
% 3.68/3.85 7802[3:Spt:7709.0,243.1] || -> equal(skc9,nil)**.
% 3.68/3.85 8170[3:Rew:7802.0,4027.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.68/3.85 8171[3:Obv:8170.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 8172[3:SSi:8171.1,8171.0,2.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] || -> equal(skc14,nil)**.
% 3.68/3.85 8176[3:Rew:8172.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.68/3.85 8192[3:Rew:7802.0,5233.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.68/3.85 8193[3:Obv:8192.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 8194[3:SSi:8193.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 8195[3:MRR:8194.0,3.0] || -> equal(skc13,nil)**.
% 3.68/3.85 8197[3:Rew:8195.0,8176.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.68/3.85 8208[3:Obv:8197.0] || -> memberP(nil,skc15)*.
% 3.68/3.85 8541[3:Res:8208.0,74.1] ssItem(skc15) || -> .
% 3.68/3.85 8542[3:SSi:8541.0,1.0] || -> .
% 3.68/3.85 8543[2:Spt:8542.0,249.1] || -> equal(skc9,nil)**.
% 3.68/3.85 8693[2:Rew:8543.0,4027.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.68/3.85 8694[2:Obv:8693.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 8695[2:SSi:8694.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 8696[2:MRR:8695.0,2.0] || -> equal(skc14,nil)**.
% 3.68/3.85 8706[2:Rew:8696.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.68/3.85 8717[2:Rew:8543.0,5233.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.68/3.85 8718[2:Obv:8717.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 8719[2:SSi:8718.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 8720[2:MRR:8719.0,3.0] || -> equal(skc13,nil)**.
% 3.68/3.85 8723[2:Rew:8720.0,8706.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.68/3.85 8732[2:Obv:8723.0] || -> memberP(nil,skc15)*.
% 3.68/3.85 9150[2:Res:8732.0,74.1] ssItem(skc15) || -> .
% 3.68/3.85 9151[2:SSi:9150.0,1.0] || -> .
% 3.68/3.85 9152[1:Spt:9151.0,420.1] || -> equal(skc10,nil)**.
% 3.68/3.85 9185[1:Rew:9152.0,71.0] || equal(nil,nil) -> equal(skc9,nil)**.
% 3.68/3.85 9186[1:Obv:9185.0] || -> equal(skc9,nil)**.
% 3.68/3.85 9309[1:Rew:9186.0,4027.2] ssList(nil) ssList(skc14) || equal(nil,nil) -> equal(skc14,nil)**.
% 3.68/3.85 9310[1:Obv:9309.2] ssList(nil) ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 9311[1:SSi:9310.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc14) || -> equal(skc14,nil)**.
% 3.68/3.85 9312[1:MRR:9311.0,2.0] || -> equal(skc14,nil)**.
% 3.68/3.85 9316[1:Rew:9312.0,1064.1] || -> memberP(skc13,skc15)* memberP(nil,skc15).
% 3.68/3.85 9333[1:Rew:9186.0,5233.2] ssList(nil) ssList(skc13) || equal(nil,nil) -> equal(skc13,nil)**.
% 3.68/3.85 9334[1:Obv:9333.2] ssList(nil) ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 9335[1:SSi:9334.0,17.0,16.0,13.0,12.0,11.0,15.0,14.0,10.0] ssList(skc13) || -> equal(skc13,nil)**.
% 3.68/3.85 9336[1:MRR:9335.0,3.0] || -> equal(skc13,nil)**.
% 3.68/3.85 9338[1:Rew:9336.0,9316.0] || -> memberP(nil,skc15)* memberP(nil,skc15)*.
% 3.68/3.85 9348[1:Obv:9338.0] || -> memberP(nil,skc15)*.
% 3.68/3.85 9749[1:Res:9348.0,74.1] ssItem(skc15) || -> .
% 3.68/3.85 9750[1:SSi:9749.0,1.0] || -> .
% 3.68/3.85 % SZS output end Refutation
% 3.68/3.85 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
% 3.68/3.85
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