TSTP Solution File: SWC386-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC386-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:03:44 EDT 2022
% Result : Unsatisfiable 2.54s 2.73s
% Output : Refutation 2.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC386-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 11:55:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.54/2.73
% 2.54/2.73 SPASS V 3.9
% 2.54/2.73 SPASS beiseite: Proof found.
% 2.54/2.73 % SZS status Theorem
% 2.54/2.73 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.54/2.73 SPASS derived 5317 clauses, backtracked 4283 clauses, performed 83 splits and kept 7361 clauses.
% 2.54/2.73 SPASS allocated 80149 KBytes.
% 2.54/2.73 SPASS spent 0:00:02.37 on the problem.
% 2.54/2.73 0:00:00.04 for the input.
% 2.54/2.73 0:00:00.00 for the FLOTTER CNF translation.
% 2.54/2.73 0:00:00.02 for inferences.
% 2.54/2.73 0:00:00.04 for the backtracking.
% 2.54/2.73 0:00:02.04 for the reduction.
% 2.54/2.73
% 2.54/2.73
% 2.54/2.73 Here is a proof with depth 6, length 257 :
% 2.54/2.73 % SZS output start Refutation
% 2.54/2.73 1[0:Inp] || -> ssList(sk1)*.
% 2.54/2.73 2[0:Inp] || -> ssList(sk2)*.
% 2.54/2.73 5[0:Inp] || -> equal(sk4,sk2)**.
% 2.54/2.73 6[0:Inp] || -> equal(sk3,sk1)**.
% 2.54/2.73 7[0:Inp] || -> ssItem(sk5)* equal(nil,sk4).
% 2.54/2.73 8[0:Inp] || -> ssItem(sk5)* equal(nil,sk3).
% 2.54/2.73 9[0:Inp] || -> equal(cons(sk5,nil),sk3)** equal(nil,sk4).
% 2.54/2.73 10[0:Inp] || -> memberP(sk4,sk5)* equal(nil,sk4).
% 2.54/2.73 11[0:Inp] || -> equal(cons(sk5,nil),sk3)** equal(nil,sk3).
% 2.54/2.73 12[0:Inp] || -> memberP(sk4,sk5)* equal(nil,sk3).
% 2.54/2.73 13[0:Inp] || -> neq(sk2,nil)* equal(nil,sk2).
% 2.54/2.73 14[0:Inp] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1)** -> equal(nil,sk2).
% 2.54/2.73 15[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 2.54/2.73 17[0:Inp] || -> equalelemsP(nil)*.
% 2.54/2.73 19[0:Inp] || -> strictorderedP(nil)*.
% 2.54/2.73 20[0:Inp] || -> totalorderedP(nil)*.
% 2.54/2.73 21[0:Inp] || -> strictorderP(nil)*.
% 2.54/2.73 22[0:Inp] || -> totalorderP(nil)*.
% 2.54/2.73 23[0:Inp] || -> cyclefreeP(nil)*.
% 2.54/2.73 25[0:Inp] || -> ssItem(skac3)*.
% 2.54/2.73 26[0:Inp] || -> ssItem(skac2)*.
% 2.54/2.73 29[0:Inp] || -> ssList(skaf82(u))*.
% 2.54/2.73 70[0:Inp] || equal(skac2,skac3)** -> .
% 2.54/2.73 80[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.54/2.73 81[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.54/2.73 82[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.54/2.73 83[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.54/2.73 84[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.54/2.73 85[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.54/2.73 86[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.54/2.73 87[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.54/2.73 88[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 2.54/2.73 89[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 2.54/2.73 90[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 2.54/2.73 102[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 2.54/2.73 113[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 2.54/2.73 115[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 2.54/2.73 131[0:Inp] ssList(u) ssList(v) || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 133[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 139[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 2.54/2.73 173[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 2.54/2.73 186[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 2.54/2.73 193[0:Inp] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(nil,v) equal(nil,u).
% 2.54/2.73 204[0:Rew:6.0,8.1] || -> ssItem(sk5)* equal(nil,sk1).
% 2.54/2.73 205[0:Rew:204.1,7.1,5.0,7.1] || -> ssItem(sk5)* equal(sk2,sk1).
% 2.54/2.73 206[0:Rew:6.0,12.1,5.0,12.0] || -> equal(nil,sk1) memberP(sk2,sk5)*.
% 2.54/2.73 207[0:Rew:206.1,10.1,5.0,10.1,5.0,10.0] || -> equal(sk2,sk1) memberP(sk2,sk5)*.
% 2.54/2.73 208[0:Rew:13.0,15.0] || equal(sk2,sk1) -> neq(sk2,nil)*.
% 2.54/2.73 209[0:Rew:6.0,11.1,6.0,11.0] || -> equal(nil,sk1) equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 210[0:Rew:209.1,9.1,5.0,9.1,6.0,9.0] || -> equal(sk2,sk1) equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 297[0:Res:2.0,88.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 2.54/2.73 312[0:Res:2.0,193.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 2.54/2.73 341[0:Res:2.0,139.1] ssList(u) || -> equal(nil,sk2) equal(hd(app(sk2,u)),hd(sk2))**.
% 2.54/2.73 443[0:Res:1.0,131.0] ssList(u) || neq(u,sk1)* equal(u,sk1) -> .
% 2.54/2.73 468[0:Res:1.0,88.0] || -> ssItem(u)* duplicatefreeP(sk1)*.
% 2.54/2.73 483[0:Res:1.0,193.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 2.54/2.73 512[0:Res:1.0,139.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 2.54/2.73 519[0:Res:1.0,113.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 2.54/2.73 521[0:Res:1.0,115.1] ssItem(u) || equal(cons(u,sk1),sk1)** -> .
% 2.54/2.73 524[0:Res:1.0,102.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 2.54/2.73 535[0:Res:1.0,173.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 2.54/2.73 562[1:Spt:88.1] || -> ssItem(u)*.
% 2.54/2.73 567[1:MRR:87.0,562.0] || memberP(nil,u)* -> .
% 2.54/2.73 576[1:MRR:521.0,562.0] || equal(cons(u,sk1),sk1)** -> .
% 2.54/2.73 602[1:MRR:133.1,133.0,562.0] || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 631[1:MRR:14.0,562.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> equal(nil,sk2).
% 2.54/2.73 768[2:Spt:483.5] || -> equal(nil,sk1)**.
% 2.54/2.73 797[2:Rew:768.0,208.1] || equal(sk2,sk1) -> neq(sk2,sk1)*.
% 2.54/2.73 798[2:Rew:768.0,210.1] || -> equal(sk2,sk1) equal(cons(sk5,sk1),sk1)**.
% 2.54/2.73 911[2:MRR:797.1,602.0] || equal(sk2,sk1)** -> .
% 2.54/2.73 919[2:MRR:798.0,798.1,911.0,576.0] || -> .
% 2.54/2.73 984[2:Spt:919.0,483.5,768.0] || equal(nil,sk1)** -> .
% 2.54/2.73 985[2:Spt:919.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.54/2.73 987[2:MRR:206.0,984.0] || -> memberP(sk2,sk5)*.
% 2.54/2.73 991[2:MRR:209.0,984.0] || -> equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 1003[3:Spt:312.5] || -> equal(nil,sk2)**.
% 2.54/2.73 1032[3:Rew:1003.0,567.0] || memberP(sk2,u)* -> .
% 2.54/2.73 1102[3:UnC:1032.0,987.0] || -> .
% 2.54/2.73 1178[3:Spt:1102.0,312.5,1003.0] || equal(nil,sk2)** -> .
% 2.54/2.73 1179[3:Spt:1102.0,312.0,312.1,312.2,312.3,312.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.54/2.73 1192[3:MRR:631.2,1178.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 2.54/2.73 1408[3:SpL:991.0,1192.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 2.54/2.73 1409[3:Obv:1408.1] || memberP(sk2,sk5)* -> .
% 2.54/2.73 1410[3:MRR:1409.0,987.0] || -> .
% 2.54/2.73 1411[1:Spt:1410.0,88.0,88.2] ssList(u) || -> duplicatefreeP(u)*.
% 2.54/2.73 1419[2:Spt:341.0,341.2] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 2.54/2.73 1423[3:Spt:512.0,512.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 2.54/2.73 1443[4:Spt:468.0] || -> ssItem(u)*.
% 2.54/2.73 1454[4:MRR:87.0,1443.0] || memberP(nil,u)* -> .
% 2.54/2.73 1464[4:MRR:521.0,1443.0] || equal(cons(u,sk1),sk1)** -> .
% 2.54/2.73 1488[4:MRR:133.1,133.0,1443.0] || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 1509[4:MRR:14.0,1443.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> equal(nil,sk2).
% 2.54/2.73 1643[5:Spt:483.5] || -> equal(nil,sk1)**.
% 2.54/2.73 1723[5:Rew:1643.0,208.1] || equal(sk2,sk1) -> neq(sk2,sk1)*.
% 2.54/2.73 1724[5:Rew:1643.0,210.1] || -> equal(sk2,sk1) equal(cons(sk5,sk1),sk1)**.
% 2.54/2.73 1788[5:MRR:1723.1,1488.0] || equal(sk2,sk1)** -> .
% 2.54/2.73 1821[5:MRR:1724.0,1724.1,1788.0,1464.0] || -> .
% 2.54/2.73 1864[5:Spt:1821.0,483.5,1643.0] || equal(nil,sk1)** -> .
% 2.54/2.73 1865[5:Spt:1821.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.54/2.73 1867[5:MRR:206.0,1864.0] || -> memberP(sk2,sk5)*.
% 2.54/2.73 1871[5:MRR:209.0,1864.0] || -> equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 1885[6:Spt:312.5] || -> equal(nil,sk2)**.
% 2.54/2.73 1902[6:Rew:1885.0,1454.0] || memberP(sk2,u)* -> .
% 2.54/2.73 1983[6:UnC:1902.0,1867.0] || -> .
% 2.54/2.73 2062[6:Spt:1983.0,312.5,1885.0] || equal(nil,sk2)** -> .
% 2.54/2.73 2063[6:Spt:1983.0,312.0,312.1,312.2,312.3,312.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.54/2.73 2078[6:MRR:1509.2,2062.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 2.54/2.73 2300[6:SpL:1871.0,2078.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 2.54/2.73 2301[6:Obv:2300.1] || memberP(sk2,sk5)* -> .
% 2.54/2.73 2302[6:MRR:2301.0,1867.0] || -> .
% 2.54/2.73 2303[4:Spt:2302.0,468.1] || -> duplicatefreeP(sk1)*.
% 2.54/2.73 2306[5:Spt:297.0] || -> ssItem(u)*.
% 2.54/2.73 2311[5:MRR:87.0,2306.0] || memberP(nil,u)* -> .
% 2.54/2.73 2320[5:MRR:521.0,2306.0] || equal(cons(u,sk1),sk1)** -> .
% 2.54/2.73 2346[5:MRR:133.1,133.0,2306.0] || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 2375[5:MRR:14.0,2306.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> equal(nil,sk2).
% 2.54/2.73 2504[6:Spt:483.5] || -> equal(nil,sk1)**.
% 2.54/2.73 2584[6:Rew:2504.0,208.1] || equal(sk2,sk1) -> neq(sk2,sk1)*.
% 2.54/2.73 2585[6:Rew:2504.0,210.1] || -> equal(sk2,sk1) equal(cons(sk5,sk1),sk1)**.
% 2.54/2.73 2649[6:MRR:2584.1,2346.0] || equal(sk2,sk1)** -> .
% 2.54/2.73 2682[6:MRR:2585.0,2585.1,2649.0,2320.0] || -> .
% 2.54/2.73 2725[6:Spt:2682.0,483.5,2504.0] || equal(nil,sk1)** -> .
% 2.54/2.73 2726[6:Spt:2682.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.54/2.73 2728[6:MRR:206.0,2725.0] || -> memberP(sk2,sk5)*.
% 2.54/2.73 2732[6:MRR:209.0,2725.0] || -> equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 2744[7:Spt:312.5] || -> equal(nil,sk2)**.
% 2.54/2.73 2773[7:Rew:2744.0,2311.0] || memberP(sk2,u)* -> .
% 2.54/2.73 2841[7:UnC:2773.0,2728.0] || -> .
% 2.54/2.73 2919[7:Spt:2841.0,312.5,2744.0] || equal(nil,sk2)** -> .
% 2.54/2.73 2920[7:Spt:2841.0,312.0,312.1,312.2,312.3,312.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.54/2.73 2935[7:MRR:2375.2,2919.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 2.54/2.73 3158[7:SpL:2732.0,2935.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 2.54/2.73 3159[7:Obv:3158.1] || memberP(sk2,sk5)* -> .
% 2.54/2.73 3160[7:MRR:3159.0,2728.0] || -> .
% 2.54/2.73 3161[5:Spt:3160.0,297.1] || -> duplicatefreeP(sk2)*.
% 2.54/2.73 3162[6:Spt:483.5] || -> equal(nil,sk1)**.
% 2.54/2.73 3186[6:Rew:3162.0,90.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 2.54/2.73 3246[6:Rew:3162.0,80.1] ssItem(u) || -> equalelemsP(cons(u,sk1))*.
% 2.54/2.73 3247[6:Rew:3162.0,81.1] ssItem(u) || -> duplicatefreeP(cons(u,sk1))*.
% 2.54/2.73 3248[6:Rew:3162.0,82.1] ssItem(u) || -> strictorderedP(cons(u,sk1))*.
% 2.54/2.73 3249[6:Rew:3162.0,83.1] ssItem(u) || -> totalorderedP(cons(u,sk1))*.
% 2.54/2.73 3250[6:Rew:3162.0,84.1] ssItem(u) || -> strictorderP(cons(u,sk1))*.
% 2.54/2.73 3251[6:Rew:3162.0,85.1] ssItem(u) || -> totalorderP(cons(u,sk1))*.
% 2.54/2.73 3252[6:Rew:3162.0,86.1] ssItem(u) || -> cyclefreeP(cons(u,sk1))*.
% 2.54/2.73 3323[6:Rew:3186.1,1423.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 2.54/2.73 3630[6:SpR:519.1,3323.1] ssItem(u) ssList(cons(u,sk1)) || -> equal(u,hd(sk1))*.
% 2.54/2.73 3632[6:SSi:3630.1,524.1,3246.1,3247.1,3248.1,3249.1,3250.1,3251.1,3252.1] ssItem(u) || -> equal(u,hd(sk1))*.
% 2.54/2.73 3695[6:SpR:3632.1,3632.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 2.54/2.73 3746[6:EmS:3695.0,25.0] ssItem(u) || -> equal(u,skac3)*.
% 2.54/2.73 3770[6:EmS:3746.0,26.0] || -> equal(skac2,skac3)**.
% 2.54/2.73 3771[6:MRR:3770.0,70.0] || -> .
% 2.54/2.73 3904[6:Spt:3771.0,483.5,3162.0] || equal(nil,sk1)** -> .
% 2.54/2.73 3905[6:Spt:3771.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 2.54/2.73 3906[6:MRR:204.1,3904.0] || -> ssItem(sk5)*.
% 2.54/2.73 3908[6:MRR:206.0,3904.0] || -> memberP(sk2,sk5)*.
% 2.54/2.73 3913[6:MRR:209.0,3904.0] || -> equal(cons(sk5,nil),sk1)**.
% 2.54/2.73 3930[7:Spt:312.5] || -> equal(nil,sk2)**.
% 2.54/2.73 3966[7:Rew:3930.0,87.1] ssItem(u) || memberP(sk2,u)* -> .
% 2.54/2.73 4127[7:Res:3908.0,3966.1] ssItem(sk5) || -> .
% 2.54/2.73 4128[7:SSi:4127.0,3906.0] || -> .
% 2.54/2.73 4129[7:Spt:4128.0,312.5,3930.0] || equal(nil,sk2)** -> .
% 2.54/2.73 4130[7:Spt:4128.0,312.0,312.1,312.2,312.3,312.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 2.54/2.73 4147[7:MRR:14.3,4129.0] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 2.54/2.73 4550[7:SpL:3913.0,4147.2] ssItem(sk5) || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 2.54/2.73 4553[7:Obv:4550.2] ssItem(sk5) || memberP(sk2,sk5)* -> .
% 2.54/2.73 4554[7:SSi:4553.0,3906.0] || memberP(sk2,sk5)* -> .
% 2.54/2.73 4555[7:MRR:4554.0,3908.0] || -> .
% 2.54/2.73 4559[3:Spt:4555.0,512.1] || -> equal(nil,sk1)**.
% 2.54/2.73 4590[3:Rew:4559.0,80.1] ssItem(u) || -> equalelemsP(cons(u,sk1))*.
% 2.54/2.73 4591[3:Rew:4559.0,81.1] ssItem(u) || -> duplicatefreeP(cons(u,sk1))*.
% 2.54/2.73 4592[3:Rew:4559.0,82.1] ssItem(u) || -> strictorderedP(cons(u,sk1))*.
% 2.54/2.73 4593[3:Rew:4559.0,83.1] ssItem(u) || -> totalorderedP(cons(u,sk1))*.
% 2.54/2.73 4594[3:Rew:4559.0,84.1] ssItem(u) || -> strictorderP(cons(u,sk1))*.
% 2.54/2.73 4595[3:Rew:4559.0,85.1] ssItem(u) || -> totalorderP(cons(u,sk1))*.
% 2.54/2.73 4596[3:Rew:4559.0,86.1] ssItem(u) || -> cyclefreeP(cons(u,sk1))*.
% 2.54/2.73 4599[3:Rew:4559.0,90.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 2.54/2.73 4600[3:Rew:4559.0,89.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 2.54/2.73 4664[3:Rew:4559.0,210.1] || -> equal(sk2,sk1) equal(cons(sk5,sk1),sk1)**.
% 2.54/2.73 4685[3:Rew:4600.1,535.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 2.54/2.73 4741[4:Spt:297.0] || -> ssItem(u)*.
% 2.54/2.73 4744[4:MRR:524.0,4741.0] || -> ssList(cons(u,sk1))*.
% 2.54/2.73 4747[4:MRR:521.0,4741.0] || equal(cons(u,sk1),sk1)** -> .
% 2.54/2.73 4748[4:MRR:519.0,4741.0] || -> equal(hd(cons(u,sk1)),u)**.
% 2.54/2.73 4811[4:MRR:4590.0,4741.0] || -> equalelemsP(cons(u,sk1))*.
% 2.54/2.73 4812[4:MRR:4591.0,4741.0] || -> duplicatefreeP(cons(u,sk1))*.
% 2.54/2.73 4813[4:MRR:4592.0,4741.0] || -> strictorderedP(cons(u,sk1))*.
% 2.54/2.73 4814[4:MRR:4593.0,4741.0] || -> totalorderedP(cons(u,sk1))*.
% 2.54/2.73 4815[4:MRR:4594.0,4741.0] || -> strictorderP(cons(u,sk1))*.
% 2.54/2.73 4816[4:MRR:4595.0,4741.0] || -> totalorderP(cons(u,sk1))*.
% 2.54/2.73 4817[4:MRR:4596.0,4741.0] || -> cyclefreeP(cons(u,sk1))*.
% 2.54/2.73 4913[4:MRR:4685.1,4741.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 2.54/2.73 4916[4:MRR:186.3,186.2,4741.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 2.54/2.73 4917[4:MRR:4664.1,4747.0] || -> equal(sk2,sk1)**.
% 2.54/2.73 4993[4:Rew:4917.0,1419.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 2.54/2.73 5042[4:Rew:4599.1,4993.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 2.54/2.73 5156[4:SpR:5042.1,4748.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 2.54/2.73 5161[4:SSi:5156.0,4744.0,4811.0,4812.0,4813.0,4814.0,4815.0,4816.0,4817.0] || -> equal(hd(sk1),u)*.
% 2.54/2.73 5188[4:Rew:5161.0,4913.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 2.54/2.73 5278[4:Rew:5161.0,4916.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 2.54/2.73 5352[4:Con:5278.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 2.54/2.73 5353[4:AED:70.0,5352.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 2.54/2.73 5354[4:Rew:5188.1,5353.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 2.54/2.73 5355[4:Obv:5354.1] ssList(u) || -> .
% 2.54/2.73 5356[4:UnC:5355.0,29.0] || -> .
% 2.54/2.73 5427[4:Spt:5356.0,297.1] || -> duplicatefreeP(sk2)*.
% 2.54/2.73 5430[5:Spt:205.1] || -> equal(sk2,sk1)**.
% 2.54/2.73 5459[5:Rew:5430.0,1419.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 2.54/2.73 5600[5:Rew:4599.1,5459.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 2.54/2.73 5785[5:SpR:519.1,5600.1] ssItem(u) ssList(cons(u,sk1)) || -> equal(u,hd(sk1))*.
% 2.54/2.73 5788[5:SSi:5785.1,524.1,4596.1,4595.1,4594.1,4593.1,4592.1,4591.1,4590.1] ssItem(u) || -> equal(u,hd(sk1))*.
% 2.54/2.73 5857[5:SpR:5788.1,5788.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 2.54/2.73 5923[5:EmS:5857.0,25.0] ssItem(u) || -> equal(u,skac3)*.
% 2.54/2.73 5943[5:EmS:5923.0,26.0] || -> equal(skac2,skac3)**.
% 2.54/2.73 5944[5:MRR:5943.0,70.0] || -> .
% 2.54/2.73 6103[5:Spt:5944.0,205.1,5430.0] || equal(sk2,sk1)** -> .
% 2.54/2.73 6104[5:Spt:5944.0,205.0] || -> ssItem(sk5)*.
% 2.54/2.73 6111[5:MRR:4664.0,6103.0] || -> equal(cons(sk5,sk1),sk1)**.
% 2.54/2.73 6149[5:SpL:6111.0,521.1] ssItem(sk5) || equal(sk1,sk1)* -> .
% 2.54/2.73 6152[5:Obv:6149.1] ssItem(sk5) || -> .
% 2.54/2.73 6153[5:SSi:6152.0,6104.0] || -> .
% 2.54/2.73 6154[2:Spt:6153.0,341.1] || -> equal(nil,sk2)**.
% 2.54/2.73 6155[2:Rew:6154.0,17.0] || -> equalelemsP(sk2)*.
% 2.54/2.73 6157[2:Rew:6154.0,19.0] || -> strictorderedP(sk2)*.
% 2.54/2.73 6158[2:Rew:6154.0,20.0] || -> totalorderedP(sk2)*.
% 2.54/2.73 6159[2:Rew:6154.0,21.0] || -> strictorderP(sk2)*.
% 2.54/2.73 6160[2:Rew:6154.0,22.0] || -> totalorderP(sk2)*.
% 2.54/2.73 6161[2:Rew:6154.0,23.0] || -> cyclefreeP(sk2)*.
% 2.54/2.73 6196[2:Rew:6154.0,87.1] ssItem(u) || memberP(sk2,u)* -> .
% 2.54/2.73 6208[2:Rew:6154.0,208.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 2.54/2.73 6324[3:Spt:468.0] || -> ssItem(u)*.
% 2.54/2.73 6338[3:MRR:133.1,133.0,6324.0] || neq(u,v)* equal(u,v) -> .
% 2.54/2.73 6378[3:MRR:6196.0,6324.0] || memberP(sk2,u)* -> .
% 2.54/2.73 6500[3:MRR:207.1,6378.0] || -> equal(sk2,sk1)**.
% 2.54/2.73 6562[3:Rew:6500.0,6208.0] || equal(sk1,sk1) -> neq(sk2,sk2)*.
% 2.54/2.73 6616[3:Obv:6562.0] || -> neq(sk2,sk2)*.
% 2.54/2.73 6617[3:Rew:6500.0,6616.0] || -> neq(sk1,sk1)*.
% 2.54/2.73 6747[3:Res:6617.0,6338.0] || equal(sk1,sk1)* -> .
% 2.54/2.73 6749[3:Obv:6747.0] || -> .
% 2.54/2.73 6750[3:Spt:6749.0,468.1] || -> duplicatefreeP(sk1)*.
% 2.54/2.73 6751[4:Spt:205.1] || -> equal(sk2,sk1)**.
% 2.54/2.73 6753[4:Rew:6751.0,6161.0] || -> cyclefreeP(sk1)*.
% 2.54/2.73 6754[4:Rew:6751.0,6160.0] || -> totalorderP(sk1)*.
% 2.54/2.73 6755[4:Rew:6751.0,6159.0] || -> strictorderP(sk1)*.
% 2.54/2.73 6756[4:Rew:6751.0,6158.0] || -> totalorderedP(sk1)*.
% 2.54/2.73 6757[4:Rew:6751.0,6157.0] || -> strictorderedP(sk1)*.
% 2.54/2.73 6759[4:Rew:6751.0,6155.0] || -> equalelemsP(sk1)*.
% 2.54/2.73 6776[4:Rew:6751.0,6208.0] || equal(sk1,sk1) -> neq(sk2,sk2)*.
% 2.54/2.73 6930[4:Obv:6776.0] || -> neq(sk2,sk2)*.
% 2.54/2.73 6931[4:Rew:6751.0,6930.0] || -> neq(sk1,sk1)*.
% 2.54/2.73 7079[4:Res:6931.0,443.1] ssList(sk1) || equal(sk1,sk1)* -> .
% 2.54/2.73 7082[4:Obv:7079.1] ssList(sk1) || -> .
% 2.54/2.73 7083[4:SSi:7082.0,1.0,6750.0,6753.0,6754.0,6755.0,6756.0,6757.0,6759.0] || -> .
% 2.54/2.73 7084[4:Spt:7083.0,205.1,6751.0] || equal(sk2,sk1)** -> .
% 2.54/2.73 7085[4:Spt:7083.0,205.0] || -> ssItem(sk5)*.
% 2.54/2.73 7087[4:MRR:207.0,7084.0] || -> memberP(sk2,sk5)*.
% 2.54/2.73 7130[4:Res:7087.0,6196.1] ssItem(sk5) || -> .
% 2.54/2.73 7131[4:SSi:7130.0,7085.0] || -> .
% 2.54/2.73 % SZS output end Refutation
% 2.54/2.73 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_11 co1_12 co1_13 co1_14 co1_15 clause1 clause3 clause4 clause5 clause6 clause7 clause9 clause10 clause13 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause74 clause86 clause97 clause99 clause115 clause117 clause123 clause157 clause170 clause177
% 2.65/2.83
%------------------------------------------------------------------------------