TSTP Solution File: SWC182-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC182-1 : 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 22:02:18 EDT 2022
% Result : Unsatisfiable 5.13s 5.32s
% Output : Refutation 6.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC182-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % 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 05:30:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.13/5.32
% 5.13/5.32 SPASS V 3.9
% 5.13/5.32 SPASS beiseite: Proof found.
% 5.13/5.32 % SZS status Theorem
% 5.13/5.32 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.13/5.32 SPASS derived 10405 clauses, backtracked 7537 clauses, performed 134 splits and kept 11935 clauses.
% 5.13/5.32 SPASS allocated 86621 KBytes.
% 5.13/5.32 SPASS spent 0:00:04.97 on the problem.
% 5.13/5.32 0:00:00.04 for the input.
% 5.13/5.32 0:00:00.00 for the FLOTTER CNF translation.
% 5.13/5.32 0:00:00.06 for inferences.
% 5.13/5.32 0:00:00.12 for the backtracking.
% 5.13/5.32 0:00:04.52 for the reduction.
% 5.13/5.32
% 5.13/5.32
% 5.13/5.32 Here is a proof with depth 6, length 273 :
% 5.13/5.32 % SZS output start Refutation
% 5.13/5.32 1[0:Inp] || -> ssList(sk1)*.
% 5.13/5.32 5[0:Inp] || -> equal(nil,sk3)**.
% 5.13/5.32 7[0:Inp] || -> equal(sk3,sk1)**.
% 5.13/5.32 8[0:Inp] || -> ssItem(sk5)*.
% 5.13/5.32 9[0:Inp] || -> ssList(sk6)*.
% 5.13/5.32 10[0:Inp] || -> ssList(sk7)*.
% 5.13/5.32 11[0:Inp] || -> equal(app(app(sk6,cons(sk5,nil)),sk7),sk1)**.
% 5.13/5.32 12[0:Inp] || -> memberP(sk7,sk5)* memberP(sk6,sk5).
% 5.13/5.32 13[0:Inp] || -> equalelemsP(nil)*.
% 5.13/5.32 14[0:Inp] || -> duplicatefreeP(nil)*.
% 5.13/5.32 15[0:Inp] || -> strictorderedP(nil)*.
% 5.13/5.32 16[0:Inp] || -> totalorderedP(nil)*.
% 5.13/5.32 17[0:Inp] || -> strictorderP(nil)*.
% 5.13/5.32 18[0:Inp] || -> totalorderP(nil)*.
% 5.13/5.32 19[0:Inp] || -> cyclefreeP(nil)*.
% 5.13/5.32 21[0:Inp] || -> ssItem(skac3)*.
% 5.13/5.32 22[0:Inp] || -> ssItem(skac2)*.
% 5.13/5.32 25[0:Inp] || -> ssList(skaf82(u))*.
% 5.13/5.32 66[0:Inp] || equal(skac2,skac3)** -> .
% 5.13/5.32 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 5.13/5.32 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 5.13/5.32 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 5.13/5.32 79[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 5.13/5.32 80[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 5.13/5.32 81[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 5.13/5.32 82[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 5.13/5.32 83[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 5.13/5.32 84[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 5.13/5.32 85[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 5.13/5.32 86[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 5.13/5.32 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 5.13/5.32 97[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 5.13/5.32 98[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 5.13/5.32 109[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 5.13/5.32 110[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 5.13/5.32 128[0:Inp] ssItem(u) ssList(v) || equal(cons(u,nil),v)* -> singletonP(v)*.
% 5.13/5.32 130[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 5.13/5.32 131[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 5.13/5.32 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 5.13/5.32 146[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u)) -> lt(v,hd(u))* equal(nil,u).
% 5.13/5.32 150[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 5.13/5.32 169[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 5.13/5.32 173[0:Inp] ssItem(u) ssItem(v) ssList(w) || memberP(cons(v,w),u)* -> equal(u,v) memberP(w,u).
% 5.13/5.32 182[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 5.13/5.32 189[0:Inp] ssList(u) ssList(v) || equal(tl(u),tl(v)) equal(hd(u),hd(v))* -> equal(nil,v) equal(u,v) equal(nil,u).
% 5.13/5.32 200[0:Rew:7.0,5.0] || -> equal(nil,sk1)**.
% 5.13/5.32 202[0:Rew:200.0,19.0] || -> cyclefreeP(sk1)*.
% 5.13/5.32 203[0:Rew:200.0,18.0] || -> totalorderP(sk1)*.
% 5.13/5.32 204[0:Rew:200.0,17.0] || -> strictorderP(sk1)*.
% 5.13/5.32 205[0:Rew:200.0,16.0] || -> totalorderedP(sk1)*.
% 5.13/5.32 206[0:Rew:200.0,15.0] || -> strictorderedP(sk1)*.
% 5.13/5.32 207[0:Rew:200.0,14.0] || -> duplicatefreeP(sk1)*.
% 5.13/5.32 208[0:Rew:200.0,13.0] || -> equalelemsP(sk1)*.
% 5.13/5.32 213[0:Rew:200.0,83.1] ssItem(u) || memberP(sk1,u)* -> .
% 5.13/5.32 214[0:Rew:200.0,82.1] ssItem(u) || -> cyclefreeP(cons(u,sk1))*.
% 5.13/5.32 215[0:Rew:200.0,81.1] ssItem(u) || -> totalorderP(cons(u,sk1))*.
% 5.13/5.32 216[0:Rew:200.0,80.1] ssItem(u) || -> strictorderP(cons(u,sk1))*.
% 5.13/5.32 217[0:Rew:200.0,79.1] ssItem(u) || -> totalorderedP(cons(u,sk1))*.
% 5.13/5.32 218[0:Rew:200.0,78.1] ssItem(u) || -> strictorderedP(cons(u,sk1))*.
% 5.13/5.32 219[0:Rew:200.0,77.1] ssItem(u) || -> duplicatefreeP(cons(u,sk1))*.
% 5.13/5.32 220[0:Rew:200.0,76.1] ssItem(u) || -> equalelemsP(cons(u,sk1))*.
% 5.13/5.32 221[0:Rew:200.0,86.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 5.13/5.32 222[0:Rew:200.0,85.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 5.13/5.32 224[0:Rew:200.0,89.2] ssList(u) || -> ssList(tl(u))* equal(sk1,u).
% 5.13/5.32 227[0:Rew:200.0,11.0] || -> equal(app(app(sk6,cons(sk5,sk1)),sk7),sk1)**.
% 5.13/5.32 235[0:Rew:200.0,110.2] ssList(u) ssItem(v) || equal(cons(v,u),sk1)** -> .
% 5.13/5.32 238[0:Rew:200.0,128.2] ssList(u) ssItem(v) || equal(cons(v,sk1),u)*+ -> singletonP(u)*.
% 5.13/5.32 242[0:Rew:200.0,131.3,200.0,131.2] ssList(u) ssList(v) || equal(app(u,v),sk1)** -> equal(sk1,v).
% 5.13/5.32 243[0:Rew:200.0,130.3,200.0,130.2] ssList(u) ssList(v) || equal(app(u,v),sk1)** -> equal(sk1,u).
% 5.13/5.32 246[0:Rew:200.0,135.2] ssList(u) ssList(v) || -> equal(sk1,u) equal(hd(app(u,v)),hd(u))**.
% 5.13/5.32 248[0:Rew:200.0,146.4] ssItem(u) ssList(v) || strictorderedP(cons(u,v)) -> lt(u,hd(v))* equal(sk1,v).
% 5.13/5.32 257[0:Rew:200.0,189.6,200.0,189.4] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(sk1,v) equal(sk1,u).
% 5.13/5.32 279[0:Res:10.0,173.0] ssItem(u) ssItem(v) || memberP(cons(v,sk7),u)* -> equal(u,v) memberP(sk7,u).
% 5.13/5.32 311[0:Res:10.0,242.0] ssList(u) || equal(app(u,sk7),sk1)** -> equal(sk7,sk1).
% 5.13/5.32 339[0:Res:10.0,84.0] || -> ssItem(u)* duplicatefreeP(sk7)*.
% 5.13/5.32 354[0:Res:10.0,257.1] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(sk1,u) equal(sk7,sk1).
% 5.13/5.32 383[0:Res:10.0,246.1] ssList(u) || -> equal(sk7,sk1) equal(hd(app(sk7,u)),hd(sk7))**.
% 5.13/5.32 390[0:Res:10.0,109.1] ssItem(u) || -> equal(hd(cons(u,sk7)),u)**.
% 5.13/5.32 391[0:Res:10.0,235.1] ssItem(u) || equal(cons(u,sk7),sk1)** -> .
% 5.13/5.32 395[0:Res:10.0,98.1] ssItem(u) || -> ssList(cons(u,sk7))*.
% 5.13/5.32 406[0:Res:10.0,169.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk7),cons(v,app(u,sk7)))**.
% 5.13/5.32 462[0:Res:9.0,248.0] ssItem(u) || strictorderedP(cons(u,sk6)) -> lt(u,hd(sk6))* equal(sk6,sk1).
% 5.13/5.32 466[0:Res:9.0,150.0] ssItem(u) ssItem(v) || equal(u,v) -> memberP(cons(v,sk6),u)*.
% 5.13/5.32 506[0:Res:9.0,224.0] || -> ssList(tl(sk6))* equal(sk6,sk1).
% 5.13/5.32 510[0:Res:9.0,84.0] || -> ssItem(u)* duplicatefreeP(sk6)*.
% 5.13/5.32 555[0:Res:9.0,243.1] ssList(u) || equal(app(sk6,u),sk1)** -> equal(sk6,sk1).
% 5.13/5.32 565[0:Res:9.0,97.1] ssList(u) || -> ssList(app(sk6,u))*.
% 5.13/5.32 600[1:Spt:84.1] || -> ssItem(u)*.
% 5.13/5.32 604[1:MRR:395.0,600.0] || -> ssList(cons(u,sk7))*.
% 5.13/5.32 606[1:MRR:214.0,600.0] || -> cyclefreeP(cons(u,sk1))*.
% 5.13/5.32 607[1:MRR:215.0,600.0] || -> totalorderP(cons(u,sk1))*.
% 5.13/5.32 608[1:MRR:216.0,600.0] || -> strictorderP(cons(u,sk1))*.
% 5.13/5.32 609[1:MRR:217.0,600.0] || -> totalorderedP(cons(u,sk1))*.
% 5.13/5.32 610[1:MRR:218.0,600.0] || -> strictorderedP(cons(u,sk1))*.
% 5.13/5.32 611[1:MRR:219.0,600.0] || -> duplicatefreeP(cons(u,sk1))*.
% 5.13/5.32 612[1:MRR:220.0,600.0] || -> equalelemsP(cons(u,sk1))*.
% 5.13/5.32 619[1:MRR:391.0,600.0] || equal(cons(u,sk7),sk1)** -> .
% 5.13/5.32 620[1:MRR:390.0,600.0] || -> equal(hd(cons(u,sk7)),u)**.
% 5.13/5.32 725[1:MRR:98.1,600.0] ssList(u) || -> ssList(cons(v,u))*.
% 5.13/5.32 730[1:MRR:238.1,600.0] ssList(u) || equal(cons(v,sk1),u)*+ -> singletonP(u)*.
% 5.13/5.32 734[1:MRR:406.1,600.0] ssList(u) || -> equal(app(cons(v,u),sk7),cons(v,app(u,sk7)))**.
% 5.13/5.32 795[1:MRR:182.3,182.2,600.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 5.13/5.32 798[2:Spt:383.0,383.2] ssList(u) || -> equal(hd(app(sk7,u)),hd(sk7))**.
% 5.13/5.32 804[3:Spt:354.5] || -> equal(sk7,sk1)**.
% 5.13/5.32 805[3:Rew:804.0,798.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 5.13/5.32 907[3:Rew:804.0,604.0] || -> ssList(cons(u,sk1))*.
% 5.13/5.32 909[3:Rew:804.0,620.0] || -> equal(hd(cons(u,sk1)),u)**.
% 5.13/5.32 922[3:Rew:804.0,734.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 5.13/5.32 974[3:Rew:221.1,805.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 5.13/5.32 999[3:Rew:222.1,922.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 5.13/5.32 1342[3:SpR:974.1,909.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 5.13/5.32 1349[3:SSi:1342.0,606.0,607.0,608.0,609.0,610.0,611.0,612.0,907.0] || -> equal(hd(sk1),u)*.
% 5.13/5.32 1424[3:Rew:1349.0,999.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 5.13/5.32 1569[3:Rew:1349.0,795.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 5.13/5.32 1685[3:Con:1569.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 5.13/5.32 1686[3:AED:66.0,1685.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 5.13/5.32 1687[3:Rew:1424.1,1686.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 5.13/5.32 1688[3:Obv:1687.1] ssList(u) || -> .
% 5.13/5.32 1689[3:UnC:1688.0,25.0] || -> .
% 5.13/5.32 1796[3:Spt:1689.0,354.5,804.0] || equal(sk7,sk1)** -> .
% 5.13/5.32 1797[3:Spt:1689.0,354.0,354.1,354.2,354.3,354.4] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(sk1,u).
% 5.13/5.32 1807[3:MRR:311.2,1796.0] ssList(u) || equal(app(u,sk7),sk1)** -> .
% 5.13/5.32 2721[3:SpL:227.0,1807.1] ssList(app(sk6,cons(sk5,sk1))) || equal(sk1,sk1)* -> .
% 5.13/5.32 2722[3:Obv:2721.1] ssList(app(sk6,cons(sk5,sk1))) || -> .
% 5.13/5.32 2723[3:SSi:2722.0,565.0,725.0,208.0,207.0,202.0,203.0,204.0,205.0,206.0,1.0,606.0,607.0,608.0,609.0,610.0,611.1,612.1] || -> .
% 5.13/5.32 2724[2:Spt:2723.0,383.1] || -> equal(sk7,sk1)**.
% 5.13/5.32 2733[2:Rew:2724.0,604.0] || -> ssList(cons(u,sk1))*.
% 5.13/5.32 2734[2:Rew:2724.0,619.0] || equal(cons(u,sk1),sk1)** -> .
% 5.13/5.32 2744[2:Rew:2724.0,227.0] || -> equal(app(app(sk6,cons(sk5,sk1)),sk1),sk1)**.
% 5.13/5.32 3220[2:SpR:2744.0,222.1] ssList(app(sk6,cons(sk5,sk1))) || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 5.13/5.32 3391[1:EqR:730.1] ssList(cons(u,sk1)) || -> singletonP(cons(u,sk1))*.
% 5.13/5.32 3393[2:SSi:3391.0,606.0,607.0,608.0,609.0,610.0,611.0,612.0,2733.0] || -> singletonP(cons(u,sk1))*.
% 5.13/5.32 4704[2:SSi:3220.0,97.0,9.0,606.0,607.0,608.0,609.0,610.0,611.0,612.0,2733.0,3393.2] || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 5.13/5.32 4863[2:SpL:4704.0,242.2] ssList(sk6) ssList(cons(sk5,sk1)) || equal(sk1,sk1) -> equal(cons(sk5,sk1),sk1)**.
% 5.13/5.32 4995[2:Obv:4863.2] ssList(sk6) ssList(cons(sk5,sk1)) || -> equal(cons(sk5,sk1),sk1)**.
% 5.13/5.32 4996[2:SSi:4995.1,4995.0,606.0,607.0,608.0,609.0,610.0,611.0,612.0,2733.0,3393.0,9.0] || -> equal(cons(sk5,sk1),sk1)**.
% 5.13/5.32 4997[2:MRR:4996.0,2734.0] || -> .
% 5.13/5.32 5001[1:Spt:4997.0,84.0,84.2] ssList(u) || -> duplicatefreeP(u)*.
% 5.13/5.32 5014[2:Spt:383.0,383.2] ssList(u) || -> equal(hd(app(sk7,u)),hd(sk7))**.
% 5.13/5.32 5054[3:Spt:510.0] || -> ssItem(u)*.
% 5.13/5.32 5058[3:MRR:220.0,5054.0] || -> equalelemsP(cons(u,sk1))*.
% 5.13/5.32 5059[3:MRR:219.0,5054.0] || -> duplicatefreeP(cons(u,sk1))*.
% 5.13/5.32 5060[3:MRR:218.0,5054.0] || -> strictorderedP(cons(u,sk1))*.
% 5.13/5.32 5061[3:MRR:217.0,5054.0] || -> totalorderedP(cons(u,sk1))*.
% 5.13/5.32 5062[3:MRR:216.0,5054.0] || -> strictorderP(cons(u,sk1))*.
% 5.13/5.32 5063[3:MRR:215.0,5054.0] || -> totalorderP(cons(u,sk1))*.
% 5.13/5.32 5064[3:MRR:214.0,5054.0] || -> cyclefreeP(cons(u,sk1))*.
% 5.13/5.32 5065[3:MRR:213.0,5054.0] || memberP(sk1,u)* -> .
% 5.13/5.32 5066[3:MRR:395.0,5054.0] || -> ssList(cons(u,sk7))*.
% 5.13/5.32 5069[3:MRR:390.0,5054.0] || -> equal(hd(cons(u,sk7)),u)**.
% 5.13/5.32 5114[3:MRR:466.1,466.0,5054.0] || equal(u,v) -> memberP(cons(v,sk6),u)*.
% 5.13/5.32 5133[3:MRR:279.1,279.0,5054.0] || memberP(cons(u,sk7),v)* -> equal(v,u) memberP(sk7,v).
% 5.13/5.32 5179[3:MRR:98.1,5054.0] ssList(u) || -> ssList(cons(v,u))*.
% 5.13/5.32 5251[4:Spt:354.5] || -> equal(sk7,sk1)**.
% 5.13/5.32 5252[4:Rew:5251.0,5014.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 5.13/5.32 5360[4:Rew:5251.0,5066.0] || -> ssList(cons(u,sk1))*.
% 5.13/5.32 5361[4:Rew:5251.0,5069.0] || -> equal(hd(cons(u,sk1)),u)**.
% 5.13/5.32 5363[4:Rew:5251.0,5133.0] || memberP(cons(u,sk1),v)* -> equal(v,u) memberP(sk7,v).
% 5.13/5.32 5429[4:Rew:221.1,5252.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 5.13/5.32 5442[4:Rew:5251.0,5363.2] || memberP(cons(u,sk1),v)* -> equal(v,u) memberP(sk1,v).
% 5.13/5.32 5443[4:MRR:5442.2,5065.0] || memberP(cons(u,sk1),v)* -> equal(v,u).
% 5.13/5.32 5854[4:SpR:5429.1,5361.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 5.13/5.32 5861[4:SSi:5854.0,5058.0,5059.0,5060.0,5061.0,5062.0,5063.0,5064.0,5360.0] || -> equal(hd(sk1),u)*.
% 5.13/5.32 6111[4:Rew:5861.0,5114.1] || equal(u,v)* -> memberP(hd(sk1),u)*.
% 5.13/5.32 6126[4:Rew:5861.0,5443.0] || memberP(hd(sk1),u)* -> equal(u,v)*.
% 5.13/5.32 6139[4:AED:66.0,6111.0] || -> memberP(hd(sk1),u)*.
% 5.13/5.32 6141[4:AED:66.0,6126.1] || memberP(hd(sk1),u)* -> .
% 5.13/5.32 6142[4:MRR:6141.0,6139.0] || -> .
% 5.13/5.32 6332[4:Spt:6142.0,354.5,5251.0] || equal(sk7,sk1)** -> .
% 5.13/5.32 6333[4:Spt:6142.0,354.0,354.1,354.2,354.3,354.4] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(sk1,u).
% 5.13/5.32 6344[4:MRR:311.2,6332.0] ssList(u) || equal(app(u,sk7),sk1)** -> .
% 5.13/5.32 6823[4:SpL:227.0,6344.1] ssList(app(sk6,cons(sk5,sk1))) || equal(sk1,sk1)* -> .
% 5.13/5.32 6825[4:Obv:6823.1] ssList(app(sk6,cons(sk5,sk1))) || -> .
% 5.13/5.32 6826[4:SSi:6825.0,565.0,5179.0,208.0,207.0,202.0,203.0,204.0,205.0,206.0,1.0,5064.0,5063.0,5062.0,5061.0,5060.0,5059.1,5058.1] || -> .
% 5.13/5.32 6827[3:Spt:6826.0,510.1] || -> duplicatefreeP(sk6)*.
% 5.13/5.32 6830[4:Spt:339.0] || -> ssItem(u)*.
% 5.13/5.32 6834[4:MRR:395.0,6830.0] || -> ssList(cons(u,sk7))*.
% 5.13/5.32 6836[4:MRR:214.0,6830.0] || -> cyclefreeP(cons(u,sk1))*.
% 5.13/5.32 6837[4:MRR:215.0,6830.0] || -> totalorderP(cons(u,sk1))*.
% 5.13/5.32 6838[4:MRR:216.0,6830.0] || -> strictorderP(cons(u,sk1))*.
% 5.13/5.32 6839[4:MRR:217.0,6830.0] || -> totalorderedP(cons(u,sk1))*.
% 5.13/5.32 6840[4:MRR:218.0,6830.0] || -> strictorderedP(cons(u,sk1))*.
% 5.13/5.32 6841[4:MRR:219.0,6830.0] || -> duplicatefreeP(cons(u,sk1))*.
% 5.13/5.32 6842[4:MRR:220.0,6830.0] || -> equalelemsP(cons(u,sk1))*.
% 5.13/5.32 6850[4:MRR:390.0,6830.0] || -> equal(hd(cons(u,sk7)),u)**.
% 5.13/5.32 6955[4:MRR:98.1,6830.0] ssList(u) || -> ssList(cons(v,u))*.
% 5.13/5.32 6964[4:MRR:406.1,6830.0] ssList(u) || -> equal(app(cons(v,u),sk7),cons(v,app(u,sk7)))**.
% 5.13/5.32 7025[4:MRR:182.3,182.2,6830.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 5.13/5.32 7026[5:Spt:354.5] || -> equal(sk7,sk1)**.
% 5.13/5.32 7127[5:Rew:7026.0,5014.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 5.13/5.32 7134[5:Rew:7026.0,6834.0] || -> ssList(cons(u,sk1))*.
% 5.13/5.32 7136[5:Rew:7026.0,6850.0] || -> equal(hd(cons(u,sk1)),u)**.
% 5.13/5.32 7150[5:Rew:7026.0,6964.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 5.13/5.32 7200[5:Rew:221.1,7127.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 5.13/5.32 7229[5:Rew:222.1,7150.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 5.13/5.32 7615[5:SpR:7200.1,7136.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 5.13/5.32 7622[5:SSi:7615.0,6836.0,6837.0,6838.0,6839.0,6840.0,6841.0,6842.0,7134.0] || -> equal(hd(sk1),u)*.
% 5.13/5.32 7687[5:Rew:7622.0,7229.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 5.13/5.32 7848[5:Rew:7622.0,7025.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 5.13/5.32 7970[5:Con:7848.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 5.13/5.32 7971[5:AED:66.0,7970.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 5.13/5.32 7972[5:Rew:7687.1,7971.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 5.13/5.32 7973[5:Obv:7972.1] ssList(u) || -> .
% 5.13/5.32 7974[5:UnC:7973.0,9.0] || -> .
% 5.13/5.32 8158[5:Spt:7974.0,354.5,7026.0] || equal(sk7,sk1)** -> .
% 5.13/5.32 8159[5:Spt:7974.0,354.0,354.1,354.2,354.3,354.4] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(sk1,u).
% 5.13/5.32 8170[5:MRR:311.2,8158.0] ssList(u) || equal(app(u,sk7),sk1)** -> .
% 5.13/5.32 8632[5:SpL:227.0,8170.1] ssList(app(sk6,cons(sk5,sk1))) || equal(sk1,sk1)* -> .
% 5.13/5.32 8634[5:Obv:8632.1] ssList(app(sk6,cons(sk5,sk1))) || -> .
% 5.13/5.32 8635[5:SSi:8634.0,565.0,6955.0,208.0,207.0,202.0,203.0,204.0,205.0,206.0,1.0,6842.0,6841.0,6840.0,6839.0,6838.0,6837.1,6836.1] || -> .
% 5.13/5.32 8636[4:Spt:8635.0,339.1] || -> duplicatefreeP(sk7)*.
% 5.13/5.32 8637[5:Spt:354.5] || -> equal(sk7,sk1)**.
% 5.13/5.32 8738[5:Rew:8637.0,5014.1] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 5.13/5.32 8744[5:Rew:8637.0,395.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 5.13/5.32 8745[5:Rew:8637.0,390.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 5.13/5.32 8811[5:Rew:221.1,8738.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 5.13/5.32 9268[5:SpR:8745.1,8811.1] ssItem(u) ssList(cons(u,sk1)) || -> equal(u,hd(sk1))*.
% 5.13/5.32 9272[5:SSi:9268.1,220.1,219.1,218.1,217.1,216.1,215.1,214.1,8744.1] ssItem(u) || -> equal(u,hd(sk1))*.
% 5.13/5.32 9372[5:SpR:9272.1,9272.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 5.13/5.32 9813[0:EqR:238.2] ssList(cons(u,sk1)) ssItem(u) || -> singletonP(cons(u,sk1))*.
% 5.13/5.32 9875[5:EmS:9372.0,8.0] ssItem(u) || -> equal(u,sk5)*.
% 5.13/5.32 9894[5:EmS:9875.0,21.0] || -> equal(skac3,sk5)**.
% 5.13/5.32 9895[5:EmS:9875.0,22.0] || -> equal(skac2,sk5)**.
% 5.13/5.32 9896[5:Rew:9894.0,66.0] || equal(skac2,sk5)** -> .
% 5.13/5.32 10081[5:Rew:9895.0,9896.0] || equal(sk5,sk5)* -> .
% 5.13/5.32 10082[5:Obv:10081.0] || -> .
% 5.13/5.32 10120[5:Spt:10082.0,354.5,8637.0] || equal(sk7,sk1)** -> .
% 5.13/5.32 10121[5:Spt:10082.0,354.0,354.1,354.2,354.3,354.4] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(sk1,u).
% 5.13/5.32 10131[5:MRR:311.2,10120.0] ssList(u) || equal(app(u,sk7),sk1)** -> .
% 5.13/5.32 10133[0:SSi:9813.0,98.1,208.1,207.1,202.1,203.1,204.1,205.1,206.0,1.0,220.0,219.0,218.0,217.0,216.0,215.0,214.2] ssItem(u) || -> singletonP(cons(u,sk1))*.
% 5.13/5.32 10615[5:SpL:227.0,10131.1] ssList(app(sk6,cons(sk5,sk1))) || equal(sk1,sk1)* -> .
% 5.13/5.32 10662[5:Obv:10615.1] ssList(app(sk6,cons(sk5,sk1))) || -> .
% 5.13/5.32 10663[5:SSi:10662.0,97.0,6827.1,9.0,98.1,8.0,208.1,207.0,202.1,203.0,204.1,205.0,206.1,1.0,220.1,8.0,219.1,8.0,218.0,8.0,217.0,8.0,216.0,8.0,215.0,8.0,214.2,8.0,10133.0,8.2] || -> .
% 5.13/5.32 10665[2:Spt:10663.0,383.1] || -> equal(sk7,sk1)**.
% 6.03/6.24 10679[2:Rew:10665.0,395.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 6.03/6.24 10689[2:Rew:10665.0,12.0] || -> memberP(sk1,sk5) memberP(sk6,sk5)*.
% 6.03/6.24 10690[2:Rew:10665.0,227.0] || -> equal(app(app(sk6,cons(sk5,sk1)),sk1),sk1)**.
% 6.03/6.24 10927[3:Spt:510.0] || -> ssItem(u)*.
% 6.03/6.24 10930[3:MRR:220.0,10927.0] || -> equalelemsP(cons(u,sk1))*.
% 6.03/6.24 10931[3:MRR:219.0,10927.0] || -> duplicatefreeP(cons(u,sk1))*.
% 6.03/6.24 10932[3:MRR:218.0,10927.0] || -> strictorderedP(cons(u,sk1))*.
% 6.03/6.24 10933[3:MRR:217.0,10927.0] || -> totalorderedP(cons(u,sk1))*.
% 6.03/6.24 10934[3:MRR:216.0,10927.0] || -> strictorderP(cons(u,sk1))*.
% 6.03/6.24 10935[3:MRR:215.0,10927.0] || -> totalorderP(cons(u,sk1))*.
% 6.03/6.24 10936[3:MRR:214.0,10927.0] || -> cyclefreeP(cons(u,sk1))*.
% 6.03/6.24 10937[3:MRR:213.0,10927.0] || memberP(sk1,u)* -> .
% 6.03/6.24 10946[3:MRR:10133.0,10927.0] || -> singletonP(cons(u,sk1))*.
% 6.03/6.24 11013[3:MRR:10679.0,10927.0] || -> ssList(cons(u,sk1))*.
% 6.03/6.24 11105[3:MRR:10689.0,10937.0] || -> memberP(sk6,sk5)*.
% 6.03/6.24 11107[4:Spt:506.1] || -> equal(sk6,sk1)**.
% 6.03/6.24 11211[4:Rew:11107.0,11105.0] || -> memberP(sk1,sk5)*.
% 6.03/6.24 11257[4:MRR:11211.0,10937.0] || -> .
% 6.03/6.24 11351[4:Spt:11257.0,506.1,11107.0] || equal(sk6,sk1)** -> .
% 6.03/6.24 11352[4:Spt:11257.0,506.0] || -> ssList(tl(sk6))*.
% 6.03/6.24 11360[4:MRR:555.2,11351.0] ssList(u) || equal(app(sk6,u),sk1)** -> .
% 6.03/6.24 11418[2:SpR:10690.0,222.1] ssList(app(sk6,cons(sk5,sk1))) || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 6.03/6.24 11637[3:SSi:11418.0,97.0,9.0,10930.0,10931.0,10932.0,10933.0,10934.0,10935.0,10936.0,10946.0,11013.2] || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 6.03/6.24 11671[4:SpL:11637.0,11360.1] ssList(cons(sk5,sk1)) || equal(sk1,sk1)* -> .
% 6.03/6.24 11673[4:Obv:11671.1] ssList(cons(sk5,sk1)) || -> .
% 6.03/6.24 11674[4:SSi:11673.0,10930.0,10931.0,10932.0,10933.0,10934.0,10935.0,10936.0,10946.0,11013.0] || -> .
% 6.03/6.24 11675[3:Spt:11674.0,510.1] || -> duplicatefreeP(sk6)*.
% 6.03/6.24 11676[4:Spt:462.3] || -> equal(sk6,sk1)**.
% 6.03/6.24 11763[4:Rew:11676.0,10689.1] || -> memberP(sk1,sk5)* memberP(sk1,sk5)*.
% 6.03/6.24 11831[4:Obv:11763.0] || -> memberP(sk1,sk5)*.
% 6.03/6.24 11932[4:Res:11831.0,213.1] ssItem(sk5) || -> .
% 6.03/6.24 11933[4:SSi:11932.0,8.0] || -> .
% 6.03/6.24 11934[4:Spt:11933.0,462.3,11676.0] || equal(sk6,sk1)** -> .
% 6.03/6.24 11935[4:Spt:11933.0,462.0,462.1,462.2] ssItem(u) || strictorderedP(cons(u,sk6)) -> lt(u,hd(sk6))*.
% 6.03/6.24 16198[3:SSi:11418.0,97.0,11675.1,9.0,214.1,8.0,215.1,8.0,10133.1,8.0,216.1,8.0,217.1,8.0,218.1,8.0,219.1,8.0,220.1,8.0,10679.0,8.2] || -> equal(app(sk6,cons(sk5,sk1)),sk1)**.
% 6.03/6.24 16325[3:SpL:16198.0,243.2] ssList(sk6) ssList(cons(sk5,sk1)) || equal(sk1,sk1) -> equal(sk6,sk1)**.
% 6.03/6.24 16673[3:Obv:16325.2] ssList(sk6) ssList(cons(sk5,sk1)) || -> equal(sk6,sk1)**.
% 6.03/6.24 16674[3:SSi:16673.1,16673.0,214.0,8.0,215.0,8.1,10133.0,8.1,216.0,8.1,217.0,8.1,218.0,8.1,219.0,8.1,220.0,8.1,10679.0,8.1,11675.0,9.1] || -> equal(sk6,sk1)**.
% 6.03/6.24 16675[4:MRR:16674.0,11934.0] || -> .
% 6.03/6.24 % SZS output end Refutation
% 6.03/6.24 Formulae used in the proof : co1_1 co1_5 co1_7 co1_8 co1_9 co1_10 co1_11 co1_12 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause9 clause10 clause13 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause74 clause77 clause85 clause86 clause97 clause98 clause116 clause118 clause119 clause123 clause134 clause138 clause157 clause161 clause170 clause177
% 6.03/6.24
%------------------------------------------------------------------------------