TSTP Solution File: SWC219-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC219-1 : 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 22:02:34 EDT 2022
% Result : Unsatisfiable 6.33s 6.54s
% Output : Refutation 7.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC219-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 18:39:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 6.33/6.54
% 6.33/6.54 SPASS V 3.9
% 6.33/6.54 SPASS beiseite: Proof found.
% 6.33/6.54 % SZS status Theorem
% 6.33/6.54 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/6.54 SPASS derived 11777 clauses, backtracked 2716 clauses, performed 60 splits and kept 7557 clauses.
% 6.33/6.54 SPASS allocated 88883 KBytes.
% 6.33/6.54 SPASS spent 0:00:06.17 on the problem.
% 6.33/6.54 0:00:00.04 for the input.
% 6.33/6.54 0:00:00.00 for the FLOTTER CNF translation.
% 6.33/6.54 0:00:00.12 for inferences.
% 6.33/6.54 0:00:00.17 for the backtracking.
% 6.33/6.54 0:00:05.60 for the reduction.
% 6.33/6.54
% 6.33/6.54
% 6.33/6.54 Here is a proof with depth 5, length 162 :
% 6.33/6.54 % SZS output start Refutation
% 6.33/6.54 1[0:Inp] || -> ssList(sk1)*.
% 6.33/6.54 2[0:Inp] || -> ssList(sk2)*.
% 6.33/6.54 5[0:Inp] || -> equal(sk4,sk2)**.
% 6.33/6.54 6[0:Inp] || -> equal(sk3,sk1)**.
% 6.33/6.54 7[0:Inp] || equal(nil,sk1)** -> .
% 6.33/6.54 9[0:Inp] ssList(u) ssList(v) ssItem(w) || equal(app(app(v,cons(w,nil)),u),sk1)**+ -> memberP(v,sk5(u,v,w))*.
% 6.33/6.54 18[0:Inp] || -> equal(cons(sk6,nil),sk3)** equal(nil,sk3).
% 6.33/6.54 19[0:Inp] || -> memberP(sk4,sk6)* equal(nil,sk3).
% 6.33/6.54 21[0:Inp] || -> equalelemsP(nil)*.
% 6.33/6.54 22[0:Inp] || -> duplicatefreeP(nil)*.
% 6.33/6.54 23[0:Inp] || -> strictorderedP(nil)*.
% 6.33/6.54 24[0:Inp] || -> totalorderedP(nil)*.
% 6.33/6.54 25[0:Inp] || -> strictorderP(nil)*.
% 6.33/6.54 26[0:Inp] || -> totalorderP(nil)*.
% 6.33/6.54 27[0:Inp] || -> cyclefreeP(nil)*.
% 6.33/6.54 28[0:Inp] || -> ssList(nil)*.
% 6.33/6.54 32[0:Inp] || -> ssItem(skaf83(u))*.
% 6.33/6.54 33[0:Inp] || -> ssList(skaf82(u))*.
% 6.33/6.54 84[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 6.33/6.54 85[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 6.33/6.54 86[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 6.33/6.54 87[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 6.33/6.54 88[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 6.33/6.54 89[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 6.33/6.54 90[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 6.33/6.54 91[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 6.33/6.54 92[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 6.33/6.54 94[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 6.33/6.54 105[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 6.33/6.54 106[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 6.33/6.54 108[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 6.33/6.54 116[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 6.33/6.54 117[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 6.33/6.54 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 6.33/6.54 121[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 6.33/6.54 129[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 6.33/6.54 136[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.33/6.54 140[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 6.33/6.54 143[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 6.33/6.54 177[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.33/6.54 183[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 6.33/6.54 184[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 6.33/6.54 185[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 6.33/6.54 186[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 6.33/6.54 197[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).
% 6.33/6.54 199[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)* -> .
% 6.33/6.54 210[0:Rew:6.0,19.1,5.0,19.0] || -> memberP(sk2,sk6)* equal(nil,sk1).
% 6.33/6.54 211[0:MRR:210.1,7.0] || -> memberP(sk2,sk6)*.
% 6.33/6.54 213[0:Rew:6.0,18.1,6.0,18.0] || -> equal(cons(sk6,nil),sk1)** equal(nil,sk1).
% 6.33/6.54 214[0:MRR:213.1,7.0] || -> equal(cons(sk6,nil),sk1)**.
% 6.33/6.54 319[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).
% 6.33/6.54 420[0:Res:1.0,186.0] || -> totalorderP(sk1) equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 6.33/6.54 421[0:Res:1.0,185.0] || -> strictorderP(sk1) equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 6.33/6.54 422[0:Res:1.0,184.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 6.33/6.54 423[0:Res:1.0,183.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 6.33/6.54 480[0:Res:1.0,108.0] || -> cyclefreeP(sk1) leq(skaf49(sk1),skaf50(sk1))*.
% 6.33/6.54 537[0:Res:1.0,140.1] ssItem(u) || -> equal(app(cons(u,nil),sk1),cons(u,sk1))**.
% 6.33/6.54 539[0:Res:1.0,136.1] ssItem(u) || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 6.33/6.54 546[0:Res:1.0,106.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 6.33/6.54 603[1:Spt:92.1] || -> ssItem(u)*.
% 6.33/6.54 608[1:MRR:91.0,603.0] || memberP(nil,u)* -> .
% 6.33/6.54 609[1:MRR:90.0,603.0] || -> cyclefreeP(cons(u,nil))*.
% 6.33/6.54 610[1:MRR:89.0,603.0] || -> totalorderP(cons(u,nil))*.
% 6.33/6.54 611[1:MRR:88.0,603.0] || -> strictorderP(cons(u,nil))*.
% 6.33/6.54 612[1:MRR:87.0,603.0] || -> totalorderedP(cons(u,nil))*.
% 6.33/6.54 613[1:MRR:86.0,603.0] || -> strictorderedP(cons(u,nil))*.
% 6.33/6.54 614[1:MRR:85.0,603.0] || -> duplicatefreeP(cons(u,nil))*.
% 6.33/6.54 615[1:MRR:84.0,603.0] || -> equalelemsP(cons(u,nil))*.
% 6.33/6.54 627[1:MRR:539.0,603.0] || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 6.33/6.54 633[1:MRR:537.0,603.0] || -> equal(app(cons(u,nil),sk1),cons(u,sk1))**.
% 6.33/6.54 727[1:MRR:106.1,603.0] ssList(u) || -> ssList(cons(v,u))*.
% 6.33/6.54 729[1:MRR:118.1,603.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 6.33/6.54 730[1:MRR:117.1,603.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 6.33/6.54 731[1:MRR:116.1,603.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 6.33/6.54 732[1:MRR:136.1,603.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 6.33/6.54 811[1:MRR:177.2,603.0] ssList(u) ssList(v) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 6.33/6.54 816[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))*.
% 6.33/6.54 822[2:Spt:319.5] || -> equal(nil,sk2)**.
% 6.33/6.54 892[2:Rew:822.0,608.0] || memberP(sk2,u)* -> .
% 6.33/6.54 938[2:UnC:892.0,211.0] || -> .
% 6.33/6.54 1013[2:Spt:938.0,319.5,822.0] || equal(nil,sk2)** -> .
% 6.33/6.54 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).
% 6.33/6.54 1028[3:Spt:423.0] || -> strictorderedP(sk1)*.
% 6.33/6.54 1031[4:Spt:422.0] || -> totalorderedP(sk1)*.
% 6.33/6.54 1042[5:Spt:480.0] || -> cyclefreeP(sk1)*.
% 6.33/6.54 1046[6:Spt:421.0] || -> strictorderP(sk1)*.
% 6.33/6.54 1047[7:Spt:420.0] || -> totalorderP(sk1)*.
% 6.33/6.54 1052[1:SpR:214.0,615.0] || -> equalelemsP(sk1)*.
% 6.33/6.54 1053[1:SpR:214.0,614.0] || -> duplicatefreeP(sk1)*.
% 6.33/6.54 1054[1:SpR:214.0,613.0] || -> strictorderedP(sk1)*.
% 6.33/6.54 1055[1:SpR:214.0,612.0] || -> totalorderedP(sk1)*.
% 6.33/6.54 1056[1:SpR:214.0,611.0] || -> strictorderP(sk1)*.
% 6.33/6.54 1057[1:SpR:214.0,610.0] || -> totalorderP(sk1)*.
% 6.33/6.54 1058[1:SpR:214.0,609.0] || -> cyclefreeP(sk1)*.
% 6.33/6.54 1100[1:SpL:214.0,627.0] || equal(sk1,sk1) -> singletonP(sk1)*.
% 6.33/6.54 1101[1:Obv:1100.0] || -> singletonP(sk1)*.
% 6.33/6.54 1373[1:EqR:732.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 6.33/6.54 1376[1:SSi:1373.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.1] || -> singletonP(cons(u,nil))*.
% 6.33/6.54 1447[1:SpL:121.2,729.1] ssList(u) singletonP(u) ssList(nil) || equal(u,nil)* -> .
% 6.33/6.54 1451[1:SSi:1447.2,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0] ssList(u) singletonP(u) || equal(u,nil)* -> .
% 6.33/6.54 1538[1:SpR:129.2,730.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 6.33/6.54 1539[1:SpR:129.2,731.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 6.33/6.54 1554[1:SSi:1538.1,33.0] ssList(u) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 6.33/6.54 1561[1:Rew:1554.2,143.3] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),skaf83(u))**.
% 6.33/6.54 1564[1:SSi:1539.1,33.0] ssList(u) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 6.33/6.54 2326[1:SpR:633.0,1561.3] ssList(cons(u,nil)) ssList(sk1) || -> equal(cons(u,nil),nil) equal(hd(cons(u,sk1)),skaf83(cons(u,nil)))**.
% 6.33/6.54 2332[1:Rew:730.1,2326.3] ssList(cons(u,nil)) ssList(sk1) || -> equal(cons(u,nil),nil) equal(skaf83(cons(u,nil)),u)**.
% 6.33/6.54 2333[7:SSi:2332.1,2332.0,1028.0,1.0,1031.0,1042.0,1046.0,1047.0,1052.0,1053.0,1101.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.1,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1376.0] || -> equal(cons(u,nil),nil) equal(skaf83(cons(u,nil)),u)**.
% 6.33/6.54 2392[1:EmS:1451.0,1451.1,33.0,732.2] ssList(skaf82(u)) || equal(skaf82(u),nil) equal(cons(v,nil),skaf82(u))* -> .
% 7.56/7.73 2473[1:SSi:2392.0,33.0] || equal(skaf82(u),nil) equal(cons(v,nil),skaf82(u))* -> .
% 7.56/7.73 2642[7:SpR:2333.1,129.2] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.56/7.73 2646[7:SpR:121.2,2333.1] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),nil)** equal(skaf44(u),skaf83(u)).
% 7.56/7.73 2647[7:Rew:121.2,2646.2] ssList(u) singletonP(u) || -> equal(u,nil) equal(skaf44(u),skaf83(u))**.
% 7.56/7.73 2648[7:MRR:2647.2,1451.2] ssList(u) singletonP(u) || -> equal(skaf44(u),skaf83(u))**.
% 7.56/7.73 2649[7:Rew:2648.2,121.2] ssList(u) singletonP(u) || -> equal(cons(skaf83(u),nil),u)**.
% 7.56/7.73 2659[7:Obv:2642.1] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.56/7.73 2660[7:SSi:2659.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1376.1] || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.56/7.73 2884[1:SpR:1564.2,731.1] ssList(cons(u,v)) ssList(v) || -> equal(cons(u,v),nil) equal(skaf82(cons(u,v)),v)**.
% 7.56/7.73 2889[1:SSi:2884.0,727.1] ssList(u) || -> equal(cons(v,u),nil) equal(skaf82(cons(v,u)),u)**.
% 7.56/7.73 2890[1:MRR:2889.1,729.1] ssList(u) || -> equal(skaf82(cons(v,u)),u)**.
% 7.56/7.73 2898[7:SpR:2649.2,2890.1] ssList(u) singletonP(u) ssList(nil) || -> equal(skaf82(u),nil)**.
% 7.56/7.73 2900[7:SSi:2898.2,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0] ssList(u) singletonP(u) || -> equal(skaf82(u),nil)**.
% 7.56/7.73 3171[7:SpL:2900.2,2473.1] ssList(u) singletonP(u) || equal(skaf82(u),nil)** equal(cons(v,nil),nil)** -> .
% 7.56/7.73 3176[7:Rew:2900.2,3171.2] ssList(u) singletonP(u) || equal(nil,nil) equal(cons(v,nil),nil)** -> .
% 7.56/7.73 3177[7:Obv:3176.2] ssList(u) singletonP(u) || equal(cons(v,nil),nil)** -> .
% 7.56/7.73 4089[7:EmS:3177.0,3177.1,1.0,1101.0] || equal(cons(u,nil),nil)** -> .
% 7.56/7.73 4092[7:MRR:2660.0,4089.0] || -> equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 7.56/7.73 4105[7:SpR:4092.0,727.1] ssList(skaf82(cons(u,nil))) || -> ssList(cons(u,nil))*.
% 7.56/7.73 4140[7:SSi:4105.0,33.0,727.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.1,1376.0] || -> ssList(cons(u,nil))*.
% 7.56/7.73 4739[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))*.
% 7.56/7.73 4758[1:Rew:94.1,4739.3,811.2,4739.3] ssList(cons(u,nil)) ssList(v) ssList(nil) || equal(cons(u,v),sk1) -> memberP(nil,sk5(v,nil,u))*.
% 7.56/7.73 4759[7:SSi:4758.2,4758.0,21.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1376.0,4140.0] ssList(u) || equal(cons(v,u),sk1) -> memberP(nil,sk5(u,nil,v))*.
% 7.56/7.73 4760[7:MRR:4759.2,608.0] ssList(u) || equal(cons(v,u),sk1)** -> .
% 7.56/7.73 4781[7:SpL:4092.0,4760.1] ssList(skaf82(cons(u,nil))) || equal(cons(u,nil),sk1)** -> .
% 7.56/7.73 4787[7:SSi:4781.0,33.0,615.0,614.0,613.0,612.0,611.0,610.0,609.0,1376.0,4140.0] || equal(cons(u,nil),sk1)** -> .
% 7.56/7.73 4788[7:UnC:4787.0,214.0] || -> .
% 7.56/7.73 4791[7:Spt:4788.0,420.0,1047.0] || totalorderP(sk1)* -> .
% 7.56/7.73 4792[7:Spt:4788.0,420.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 7.56/7.73 4793[7:MRR:4791.0,1057.0] || -> .
% 7.56/7.73 4887[6:Spt:4793.0,421.0,1046.0] || strictorderP(sk1)* -> .
% 7.56/7.73 4888[6:Spt:4793.0,421.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 7.56/7.73 4889[6:MRR:4887.0,1056.0] || -> .
% 7.56/7.73 4901[5:Spt:4889.0,480.0,1042.0] || cyclefreeP(sk1)* -> .
% 7.56/7.73 4902[5:Spt:4889.0,480.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 7.56/7.73 4903[5:MRR:4901.0,1058.0] || -> .
% 7.56/7.73 4915[4:Spt:4903.0,422.0,1031.0] || totalorderedP(sk1)* -> .
% 7.56/7.73 4916[4:Spt:4903.0,422.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 7.56/7.73 4917[4:MRR:4915.0,1055.0] || -> .
% 7.56/7.73 4937[3:Spt:4917.0,423.0,1028.0] || strictorderedP(sk1)* -> .
% 7.56/7.73 4938[3:Spt:4917.0,423.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 7.56/7.73 4939[3:MRR:4937.0,1054.0] || -> .
% 7.56/7.73 4958[1:Spt:4939.0,92.0,92.2] ssList(u) || -> duplicatefreeP(u)*.
% 7.56/7.73 4975[1:MRR:199.1,4958.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 7.56/7.73 15679[0:SpR:177.3,105.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 7.56/7.73 15721[0:Obv:15679.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 7.56/7.73 15722[0:SSi:15721.2,106.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 7.56/7.73 17685[1:EqR:4975.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 7.56/7.73 17712[1:SSi:17685.0,105.2,105.2,106.2,106.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 7.56/7.73 17714[1:MRR:15722.3,17712.1] ssList(u) ssItem(v) ssList(w) || -> .
% 7.56/7.73 17720[1:Con:17714.2] ssList(u) ssItem(v) || -> .
% 7.56/7.73 17721[1:MRR:546.1,17720.0] ssItem(u) || -> .
% 7.56/7.73 17725[1:UnC:17721.0,32.0] || -> .
% 7.56/7.73 % SZS output end Refutation
% 7.56/7.73 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
% 7.56/7.73
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