TSTP Solution File: SWC239-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC239-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 22:02:43 EDT 2022
% Result : Unsatisfiable 6.05s 6.25s
% Output : Refutation 7.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWC239-1 : TPTP v8.1.0. Released v2.4.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.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 : Sat Jun 11 21:42:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.05/6.25
% 6.05/6.25 SPASS V 3.9
% 6.05/6.25 SPASS beiseite: Proof found.
% 6.05/6.25 % SZS status Theorem
% 6.05/6.25 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.05/6.25 SPASS derived 11772 clauses, backtracked 2723 clauses, performed 60 splits and kept 7432 clauses.
% 6.05/6.25 SPASS allocated 88873 KBytes.
% 6.05/6.25 SPASS spent 0:00:05.87 on the problem.
% 6.05/6.25 0:00:00.04 for the input.
% 6.05/6.25 0:00:00.00 for the FLOTTER CNF translation.
% 6.05/6.25 0:00:00.12 for inferences.
% 6.05/6.25 0:00:00.16 for the backtracking.
% 6.05/6.25 0:00:05.31 for the reduction.
% 6.05/6.25
% 6.05/6.25
% 6.05/6.25 Here is a proof with depth 5, length 162 :
% 6.05/6.25 % SZS output start Refutation
% 6.05/6.25 1[0:Inp] || -> ssList(sk1)*.
% 6.05/6.25 2[0:Inp] || -> ssList(sk2)*.
% 6.05/6.25 5[0:Inp] || -> equal(sk4,sk2)**.
% 6.05/6.25 6[0:Inp] || -> equal(sk3,sk1)**.
% 6.05/6.25 7[0:Inp] || equal(nil,sk1)** -> .
% 6.05/6.25 9[0:Inp] ssList(u) ssList(v) ssItem(w) || equal(app(app(v,cons(w,nil)),u),sk1)**+ -> memberP(v,sk5(u,v,w))*.
% 6.05/6.25 18[0:Inp] || -> equal(cons(sk6,nil),sk3)** equal(nil,sk3).
% 6.05/6.25 19[0:Inp] || -> memberP(sk4,sk6)* equal(nil,sk3).
% 6.05/6.25 21[0:Inp] || -> equalelemsP(nil)*.
% 6.05/6.25 22[0:Inp] || -> duplicatefreeP(nil)*.
% 6.05/6.25 23[0:Inp] || -> strictorderedP(nil)*.
% 6.05/6.25 24[0:Inp] || -> totalorderedP(nil)*.
% 6.05/6.25 25[0:Inp] || -> strictorderP(nil)*.
% 6.05/6.25 26[0:Inp] || -> totalorderP(nil)*.
% 6.05/6.25 27[0:Inp] || -> cyclefreeP(nil)*.
% 6.05/6.25 28[0:Inp] || -> ssList(nil)*.
% 6.05/6.25 32[0:Inp] || -> ssItem(skaf83(u))*.
% 6.05/6.25 33[0:Inp] || -> ssList(skaf82(u))*.
% 6.05/6.25 84[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 6.05/6.25 85[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 6.05/6.25 86[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 6.05/6.25 87[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 6.05/6.25 88[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 6.05/6.25 89[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 6.05/6.25 90[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 6.05/6.25 91[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 6.05/6.25 92[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 6.05/6.25 94[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 6.05/6.25 105[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 6.05/6.25 106[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 6.05/6.25 108[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 6.05/6.25 116[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 6.05/6.25 117[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 6.05/6.25 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 6.05/6.25 121[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 6.05/6.25 129[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 6.05/6.25 136[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.05/6.25 140[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.05/6.25 143[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 6.05/6.25 177[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.05/6.25 183[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 6.05/6.25 184[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 6.05/6.25 185[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 6.05/6.25 186[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 6.05/6.25 197[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).
% 6.05/6.25 199[0:Inp] ssList(u) duplicatefreeP(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 6.05/6.25 210[0:Rew:6.0,19.1,5.0,19.0] || -> memberP(sk2,sk6)* equal(nil,sk1).
% 6.05/6.25 211[0:MRR:210.1,7.0] || -> memberP(sk2,sk6)*.
% 6.05/6.25 213[0:Rew:6.0,18.1,6.0,18.0] || -> equal(cons(sk6,nil),sk1)** equal(nil,sk1).
% 6.05/6.25 214[0:MRR:213.1,7.0] || -> equal(cons(sk6,nil),sk1)**.
% 6.05/6.25 319[0:Res:2.0,197.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 6.05/6.25 420[0:Res:1.0,186.0] || -> totalorderP(sk1) equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 6.05/6.25 421[0:Res:1.0,185.0] || -> strictorderP(sk1) equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 6.05/6.25 422[0:Res:1.0,184.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 6.05/6.25 423[0:Res:1.0,183.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 6.05/6.25 480[0:Res:1.0,108.0] || -> cyclefreeP(sk1) leq(skaf49(sk1),skaf50(sk1))*.
% 6.05/6.25 537[0:Res:1.0,140.1] ssItem(u) || -> equal(app(cons(u,nil),sk1),cons(u,sk1))**.
% 6.05/6.25 539[0:Res:1.0,136.1] ssItem(u) || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 6.05/6.25 546[0:Res:1.0,106.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 6.05/6.25 603[1:Spt:92.1] || -> ssItem(u)*.
% 6.05/6.25 608[1:MRR:91.0,603.0] || memberP(nil,u)* -> .
% 6.05/6.25 609[1:MRR:90.0,603.0] || -> cyclefreeP(cons(u,nil))*.
% 6.05/6.25 610[1:MRR:89.0,603.0] || -> totalorderP(cons(u,nil))*.
% 6.05/6.25 611[1:MRR:88.0,603.0] || -> strictorderP(cons(u,nil))*.
% 6.05/6.25 612[1:MRR:87.0,603.0] || -> totalorderedP(cons(u,nil))*.
% 6.05/6.25 613[1:MRR:86.0,603.0] || -> strictorderedP(cons(u,nil))*.
% 6.05/6.25 614[1:MRR:85.0,603.0] || -> duplicatefreeP(cons(u,nil))*.
% 6.05/6.25 615[1:MRR:84.0,603.0] || -> equalelemsP(cons(u,nil))*.
% 6.05/6.25 627[1:MRR:539.0,603.0] || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 6.05/6.25 633[1:MRR:537.0,603.0] || -> equal(app(cons(u,nil),sk1),cons(u,sk1))**.
% 6.05/6.25 727[1:MRR:106.1,603.0] ssList(u) || -> ssList(cons(v,u))*.
% 6.05/6.25 729[1:MRR:118.1,603.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 6.05/6.25 730[1:MRR:117.1,603.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 6.05/6.25 731[1:MRR:116.1,603.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 6.05/6.25 732[1:MRR:136.1,603.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.05/6.25 811[1:MRR:177.2,603.0] ssList(u) ssList(v) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.05/6.25 816[1:MRR:9.2,603.0] ssList(u) ssList(v) || equal(app(app(v,cons(w,nil)),u),sk1)**+ -> memberP(v,sk5(u,v,w))*.
% 6.05/6.25 822[2:Spt:319.5] || -> equal(nil,sk2)**.
% 6.05/6.25 892[2:Rew:822.0,608.0] || memberP(sk2,u)* -> .
% 6.05/6.25 938[2:UnC:892.0,211.0] || -> .
% 6.05/6.25 1013[2:Spt:938.0,319.5,822.0] || equal(nil,sk2)** -> .
% 6.05/6.25 1014[2:Spt:938.0,319.0,319.1,319.2,319.3,319.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 6.05/6.25 1028[3:Spt:423.0] || -> strictorderedP(sk1)*.
% 6.05/6.25 1031[4:Spt:422.0] || -> totalorderedP(sk1)*.
% 6.05/6.25 1042[5:Spt:480.0] || -> cyclefreeP(sk1)*.
% 6.05/6.25 1046[6:Spt:421.0] || -> strictorderP(sk1)*.
% 6.05/6.25 1047[7:Spt:420.0] || -> totalorderP(sk1)*.
% 6.05/6.25 1052[1:SpR:214.0,615.0] || -> equalelemsP(sk1)*.
% 6.05/6.25 1053[1:SpR:214.0,614.0] || -> duplicatefreeP(sk1)*.
% 6.05/6.25 1054[1:SpR:214.0,613.0] || -> strictorderedP(sk1)*.
% 6.05/6.25 1055[1:SpR:214.0,612.0] || -> totalorderedP(sk1)*.
% 6.05/6.25 1056[1:SpR:214.0,611.0] || -> strictorderP(sk1)*.
% 6.05/6.25 1057[1:SpR:214.0,610.0] || -> totalorderP(sk1)*.
% 6.05/6.25 1058[1:SpR:214.0,609.0] || -> cyclefreeP(sk1)*.
% 6.05/6.25 1100[1:SpL:214.0,627.0] || equal(sk1,sk1) -> singletonP(sk1)*.
% 6.05/6.25 1101[1:Obv:1100.0] || -> singletonP(sk1)*.
% 6.05/6.25 1361[1:EqR:732.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 6.05/6.25 1364[1:SSi:1361.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.1] || -> singletonP(cons(u,nil))*.
% 6.05/6.25 1427[1:SpL:121.2,729.1] ssList(u) singletonP(u) ssList(nil) || equal(u,nil)* -> .
% 6.05/6.25 1431[1:SSi:1427.2,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0] ssList(u) singletonP(u) || equal(u,nil)* -> .
% 6.05/6.25 1511[1:SpR:129.2,730.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 6.05/6.25 1512[1:SpR:129.2,731.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 6.05/6.25 1527[1:SSi:1511.1,33.0] ssList(u) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 6.05/6.25 1534[1:Rew:1527.2,143.3] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),skaf83(u))**.
% 6.05/6.25 1537[1:SSi:1512.1,33.0] ssList(u) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 6.05/6.25 2252[1:SpR:633.0,1534.3] ssList(cons(u,nil)) ssList(sk1) || -> equal(cons(u,nil),nil) equal(hd(cons(u,sk1)),skaf83(cons(u,nil)))**.
% 6.05/6.25 2257[1:Rew:730.1,2252.3] ssList(cons(u,nil)) ssList(sk1) || -> equal(cons(u,nil),nil) equal(skaf83(cons(u,nil)),u)**.
% 6.05/6.25 2258[7:SSi:2257.1,2257.0,1028.0,1.0,1031.0,1042.0,1046.0,1047.0,1052.0,1053.0,1101.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.1,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1364.0] || -> equal(cons(u,nil),nil) equal(skaf83(cons(u,nil)),u)**.
% 6.05/6.25 2273[1:EmS:1431.0,1431.1,33.0,732.2] ssList(skaf82(u)) || equal(skaf82(u),nil) equal(cons(v,nil),skaf82(u))* -> .
% 7.25/7.43 2354[1:SSi:2273.0,33.0] || equal(skaf82(u),nil) equal(cons(v,nil),skaf82(u))* -> .
% 7.25/7.43 2536[7:SpR:2258.1,129.2] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.25/7.43 2539[7:SpR:121.2,2258.1] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),nil)** equal(skaf44(u),skaf83(u)).
% 7.25/7.43 2540[7:Rew:121.2,2539.2] ssList(u) singletonP(u) || -> equal(u,nil) equal(skaf44(u),skaf83(u))**.
% 7.25/7.43 2541[7:MRR:2540.2,1431.2] ssList(u) singletonP(u) || -> equal(skaf44(u),skaf83(u))**.
% 7.25/7.43 2542[7:Rew:2541.2,121.2] ssList(u) singletonP(u) || -> equal(cons(skaf83(u),nil),u)**.
% 7.25/7.43 2550[7:Obv:2536.1] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.25/7.43 2551[7:SSi:2550.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1364.1] || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.25/7.43 2680[1:SpR:1537.2,731.1] ssList(cons(u,v)) ssList(v) || -> equal(cons(u,v),nil) equal(skaf82(cons(u,v)),v)**.
% 7.25/7.43 2685[1:SSi:2680.0,727.1] ssList(u) || -> equal(cons(v,u),nil) equal(skaf82(cons(v,u)),u)**.
% 7.25/7.43 2686[1:MRR:2685.1,729.1] ssList(u) || -> equal(skaf82(cons(v,u)),u)**.
% 7.25/7.43 2694[7:SpR:2542.2,2686.1] ssList(u) singletonP(u) ssList(nil) || -> equal(skaf82(u),nil)**.
% 7.25/7.43 2696[7:SSi:2694.2,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0] ssList(u) singletonP(u) || -> equal(skaf82(u),nil)**.
% 7.25/7.43 2968[7:SpL:2696.2,2354.1] ssList(u) singletonP(u) || equal(skaf82(u),nil)** equal(cons(v,nil),nil)** -> .
% 7.25/7.43 2973[7:Rew:2696.2,2968.2] ssList(u) singletonP(u) || equal(nil,nil) equal(cons(v,nil),nil)** -> .
% 7.25/7.43 2974[7:Obv:2973.2] ssList(u) singletonP(u) || equal(cons(v,nil),nil)** -> .
% 7.25/7.43 3917[7:EmS:2974.0,2974.1,1.0,1101.0] || equal(cons(u,nil),nil)** -> .
% 7.25/7.43 3919[7:MRR:2551.0,3917.0] || -> equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.25/7.43 3956[7:SpR:3919.0,727.1] ssList(skaf82(cons(u,nil))) || -> ssList(cons(u,nil))*.
% 7.25/7.43 3992[7:SSi:3956.0,33.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.1,1364.0] || -> ssList(cons(u,nil))*.
% 7.25/7.43 4663[1:SpL:94.1,816.2] ssList(cons(u,nil)) ssList(v) ssList(nil) || equal(app(cons(u,nil),v),sk1) -> memberP(nil,sk5(v,nil,u))*.
% 7.25/7.43 4682[1:Rew:94.1,4663.3,811.2,4663.3] ssList(cons(u,nil)) ssList(v) ssList(nil) || equal(cons(u,v),sk1) -> memberP(nil,sk5(v,nil,u))*.
% 7.25/7.43 4683[7:SSi:4682.2,4682.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1364.0,3992.0] ssList(u) || equal(cons(v,u),sk1) -> memberP(nil,sk5(u,nil,v))*.
% 7.25/7.43 4684[7:MRR:4683.2,608.0] ssList(u) || equal(cons(v,u),sk1)** -> .
% 7.25/7.43 4705[7:SpL:3919.0,4684.1] ssList(skaf82(cons(u,nil))) || equal(cons(u,nil),sk1)** -> .
% 7.25/7.43 4711[7:SSi:4705.0,33.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1364.0,3992.0] || equal(cons(u,nil),sk1)** -> .
% 7.25/7.43 4712[7:UnC:4711.0,214.0] || -> .
% 7.25/7.43 4715[7:Spt:4712.0,420.0,1047.0] || totalorderP(sk1)* -> .
% 7.25/7.43 4716[7:Spt:4712.0,420.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 7.25/7.43 4717[7:MRR:4715.0,1057.0] || -> .
% 7.25/7.43 4814[6:Spt:4717.0,421.0,1046.0] || strictorderP(sk1)* -> .
% 7.25/7.43 4815[6:Spt:4717.0,421.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 7.25/7.43 4816[6:MRR:4814.0,1056.0] || -> .
% 7.25/7.43 4828[5:Spt:4816.0,480.0,1042.0] || cyclefreeP(sk1)* -> .
% 7.25/7.43 4829[5:Spt:4816.0,480.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 7.25/7.43 4830[5:MRR:4828.0,1058.0] || -> .
% 7.25/7.43 4842[4:Spt:4830.0,422.0,1031.0] || totalorderedP(sk1)* -> .
% 7.25/7.43 4843[4:Spt:4830.0,422.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 7.25/7.43 4844[4:MRR:4842.0,1055.0] || -> .
% 7.25/7.43 4864[3:Spt:4844.0,423.0,1028.0] || strictorderedP(sk1)* -> .
% 7.25/7.43 4865[3:Spt:4844.0,423.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 7.25/7.43 4866[3:MRR:4864.0,1054.0] || -> .
% 7.25/7.43 4885[1:Spt:4866.0,92.0,92.2] ssList(u) || -> duplicatefreeP(u)*.
% 7.25/7.43 4902[1:MRR:199.1,4885.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 7.25/7.43 15574[0:SpR:177.3,105.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 7.25/7.43 15619[0:Obv:15574.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 7.25/7.43 15620[0:SSi:15619.2,106.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 7.25/7.43 17626[1:EqR:4902.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 7.25/7.43 17653[1:SSi:17626.0,105.2,105.2,106.2,106.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 7.25/7.43 17655[1:MRR:15620.3,17653.1] ssList(u) ssItem(v) ssList(w) || -> .
% 7.25/7.43 17661[1:Con:17655.2] ssList(u) ssItem(v) || -> .
% 7.25/7.43 17662[1:MRR:546.1,17661.0] ssItem(u) || -> .
% 7.25/7.43 17666[1:UnC:17662.0,32.0] || -> .
% 7.25/7.43 % SZS output end Refutation
% 7.25/7.43 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_9 co1_18 co1_19 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause88 clause96 clause97 clause98 clause101 clause109 clause116 clause120 clause123 clause157 clause163 clause164 clause165 clause166 clause177 clause179
% 7.25/7.43
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