TSTP Solution File: SWC407+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC407+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 22:03:53 EDT 2022
% Result : Theorem 2.39s 2.55s
% Output : Refutation 2.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC407+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n022.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sun Jun 12 01:35:33 EDT 2022
% 0.06/0.25 % CPUTime :
% 2.39/2.55
% 2.39/2.55 SPASS V 3.9
% 2.39/2.55 SPASS beiseite: Proof found.
% 2.39/2.55 % SZS status Theorem
% 2.39/2.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.39/2.55 SPASS derived 4331 clauses, backtracked 1329 clauses, performed 37 splits and kept 3224 clauses.
% 2.39/2.55 SPASS allocated 103843 KBytes.
% 2.39/2.55 SPASS spent 0:00:02.29 on the problem.
% 2.39/2.55 0:00:00.02 for the input.
% 2.39/2.55 0:00:00.03 for the FLOTTER CNF translation.
% 2.39/2.55 0:00:00.04 for inferences.
% 2.39/2.55 0:00:00.05 for the backtracking.
% 2.39/2.55 0:00:01.98 for the reduction.
% 2.39/2.55
% 2.39/2.55
% 2.39/2.55 Here is a proof with depth 5, length 148 :
% 2.39/2.55 % SZS output start Refutation
% 2.39/2.55 1[0:Inp] || -> ssItem(skc7)*.
% 2.39/2.55 2[0:Inp] || -> ssList(skc6)*.
% 2.39/2.55 3[0:Inp] || -> ssList(skc5)*.
% 2.39/2.55 6[0:Inp] || -> ssList(nil)*.
% 2.39/2.55 7[0:Inp] || -> cyclefreeP(nil)*.
% 2.39/2.55 8[0:Inp] || -> totalorderP(nil)*.
% 2.39/2.55 9[0:Inp] || -> strictorderP(nil)*.
% 2.39/2.55 10[0:Inp] || -> totalorderedP(nil)*.
% 2.39/2.55 11[0:Inp] || -> strictorderedP(nil)*.
% 2.39/2.55 12[0:Inp] || -> duplicatefreeP(nil)*.
% 2.39/2.55 13[0:Inp] || -> equalelemsP(nil)*.
% 2.39/2.55 14[0:Inp] || -> memberP(skc5,skc7)*.
% 2.39/2.55 15[0:Inp] || -> ssItem(skf47(u))*.
% 2.39/2.55 53[0:Inp] || -> ssItem(skf44(u,v))*.
% 2.39/2.55 54[0:Inp] || memberP(skc6,skc7)* -> .
% 2.39/2.55 70[0:Inp] || SkP0(skc6,skc5)* -> equal(nil,skc6).
% 2.39/2.55 71[0:Inp] || SkP0(skc6,skc5)* -> equal(nil,skc5).
% 2.39/2.55 72[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 2.39/2.55 73[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.39/2.55 74[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.39/2.55 75[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.39/2.55 76[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.39/2.55 77[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.39/2.55 78[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.39/2.55 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.39/2.55 81[0:Inp] || -> SkP0(u,v) memberP(u,skf44(u,v))*.
% 2.39/2.55 86[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 2.39/2.55 88[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 2.39/2.55 89[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf53(u),skf52(u))*.
% 2.39/2.55 91[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(skf78(u),skf77(u))**.
% 2.39/2.55 108[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 2.39/2.55 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 2.39/2.55 113[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 2.39/2.55 119[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 2.39/2.55 122[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 2.39/2.55 171[0:Inp] ssList(u) ssItem(v) ssItem(w) || memberP(cons(v,u),w)* -> memberP(u,w) equal(w,v).
% 2.39/2.55 174[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf74(u),cons(skf72(u),skf75(u))),cons(skf73(u),skf76(u))),u)**.
% 2.39/2.55 175[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf69(u),cons(skf67(u),skf70(u))),cons(skf68(u),skf71(u))),u)**.
% 2.39/2.55 176[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skf64(u),cons(skf62(u),skf65(u))),cons(skf63(u),skf66(u))),u)**.
% 2.39/2.55 177[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skf59(u),cons(skf57(u),skf60(u))),cons(skf58(u),skf61(u))),u)**.
% 2.39/2.55 188[0:Inp] ssList(u) ssList(v) || equal(tl(u),tl(v))* equal(hd(u),hd(v)) -> equal(u,v) equal(nil,v) equal(nil,u).
% 2.39/2.55 197[0:Rew:71.1,70.1] || SkP0(skc6,skc5)* -> equal(skc6,skc5).
% 2.39/2.55 219[0:Res:3.0,177.0] || -> totalorderP(skc5) equal(app(app(skf59(skc5),cons(skf57(skc5),skf60(skc5))),cons(skf58(skc5),skf61(skc5))),skc5)**.
% 2.39/2.55 220[0:Res:3.0,176.0] || -> strictorderP(skc5) equal(app(app(skf64(skc5),cons(skf62(skc5),skf65(skc5))),cons(skf63(skc5),skf66(skc5))),skc5)**.
% 2.39/2.55 221[0:Res:3.0,175.0] || -> totalorderedP(skc5) equal(app(app(skf69(skc5),cons(skf67(skc5),skf70(skc5))),cons(skf68(skc5),skf71(skc5))),skc5)**.
% 2.39/2.55 222[0:Res:3.0,174.0] || -> strictorderedP(skc5) equal(app(app(skf74(skc5),cons(skf72(skc5),skf75(skc5))),cons(skf73(skc5),skf76(skc5))),skc5)**.
% 2.39/2.55 251[0:Res:3.0,119.0] || -> equal(nil,skc5) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.39/2.55 252[0:Res:3.0,108.1] singletonP(skc5) || -> equal(cons(skf47(skc5),nil),skc5)**.
% 2.39/2.55 265[0:Res:3.0,89.0] || -> cyclefreeP(skc5) leq(skf53(skc5),skf52(skc5))*.
% 2.39/2.55 267[0:Res:3.0,91.0] || -> duplicatefreeP(skc5) equal(skf78(skc5),skf77(skc5))**.
% 2.39/2.55 276[0:Res:3.0,86.0] || -> ssItem(hd(skc5))* equal(nil,skc5).
% 2.39/2.55 286[0:Res:3.0,188.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 2.39/2.55 321[0:Res:3.0,122.1] ssItem(u) || equal(cons(u,nil),skc5)** -> singletonP(skc5).
% 2.39/2.55 457[0:Res:2.0,188.1] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u) equal(nil,skc6).
% 2.39/2.55 557[1:Spt:457.5] || -> equal(nil,skc6)**.
% 2.39/2.55 630[1:Rew:557.0,13.0] || -> equalelemsP(skc6)*.
% 2.39/2.55 631[1:Rew:557.0,12.0] || -> duplicatefreeP(skc6)*.
% 2.39/2.55 632[1:Rew:557.0,11.0] || -> strictorderedP(skc6)*.
% 2.39/2.55 633[1:Rew:557.0,10.0] || -> totalorderedP(skc6)*.
% 2.39/2.55 634[1:Rew:557.0,9.0] || -> strictorderP(skc6)*.
% 2.39/2.55 635[1:Rew:557.0,8.0] || -> totalorderP(skc6)*.
% 2.39/2.55 636[1:Rew:557.0,7.0] || -> cyclefreeP(skc6)*.
% 2.39/2.55 652[1:Rew:557.0,72.1] ssItem(u) || memberP(skc6,u)* -> .
% 2.39/2.55 758[2:Spt:197.1] || -> equal(skc6,skc5)**.
% 2.39/2.55 832[2:Rew:758.0,54.0] || memberP(skc5,skc7)* -> .
% 2.39/2.55 918[2:MRR:832.0,14.0] || -> .
% 2.39/2.55 1011[2:Spt:918.0,197.1,758.0] || equal(skc6,skc5)** -> .
% 2.39/2.55 1012[2:Spt:918.0,197.0] || SkP0(skc6,skc5)* -> .
% 2.39/2.55 1061[1:Res:81.1,652.1] ssItem(skf44(skc6,u)) || -> SkP0(skc6,u)*.
% 2.39/2.55 1062[1:SSi:1061.0,53.0,636.0,635.0,634.0,633.0,632.0,631.0,630.0,2.0] || -> SkP0(skc6,u)*.
% 2.39/2.55 1063[2:UnC:1062.0,1012.0] || -> .
% 2.39/2.55 1064[1:Spt:1063.0,457.5,557.0] || equal(nil,skc6)** -> .
% 2.39/2.55 1065[1:Spt:1063.0,457.0,457.1,457.2,457.3,457.4] ssList(u) || equal(tl(skc6),tl(u))* equal(hd(skc6),hd(u)) -> equal(nil,u) equal(skc6,u).
% 2.39/2.55 1080[2:Spt:286.5] || -> equal(nil,skc5)**.
% 2.39/2.55 1115[2:Rew:1080.0,72.1] ssItem(u) || memberP(skc5,u)* -> .
% 2.39/2.55 1271[2:Res:14.0,1115.1] ssItem(skc7) || -> .
% 2.39/2.55 1273[2:SSi:1271.0,1.0] || -> .
% 2.39/2.55 1275[2:Spt:1273.0,286.5,1080.0] || equal(nil,skc5)** -> .
% 2.39/2.55 1276[2:Spt:1273.0,286.0,286.1,286.2,286.3,286.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 2.39/2.55 1278[2:MRR:276.1,1275.0] || -> ssItem(hd(skc5))*.
% 2.39/2.55 1282[2:MRR:71.1,1275.0] || SkP0(skc6,skc5)* -> .
% 2.39/2.55 1283[2:MRR:251.0,1275.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.39/2.55 1299[3:Spt:221.0] || -> totalorderedP(skc5)*.
% 2.39/2.55 1303[4:Spt:222.0] || -> strictorderedP(skc5)*.
% 2.39/2.55 1308[5:Spt:265.0] || -> cyclefreeP(skc5)*.
% 2.39/2.55 1312[6:Spt:219.0] || -> totalorderP(skc5)*.
% 2.39/2.55 1313[7:Spt:220.0] || -> strictorderP(skc5)*.
% 2.39/2.55 1321[8:Spt:267.0] || -> duplicatefreeP(skc5)*.
% 2.39/2.55 1401[0:SpR:88.1,79.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 2.39/2.55 1402[0:SpR:88.1,78.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* duplicatefreeP(v).
% 2.39/2.55 1403[0:SpR:88.1,77.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderedP(v).
% 2.39/2.55 1404[0:SpR:88.1,76.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderedP(v).
% 2.39/2.55 1405[0:SpR:88.1,75.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* strictorderP(v).
% 2.39/2.55 1406[0:SpR:88.1,74.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* totalorderP(v).
% 2.39/2.55 1407[0:SpR:88.1,73.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* cyclefreeP(v).
% 2.39/2.55 1410[0:SSi:1401.0,53.0] || -> SkP0(u,v)* equalelemsP(v).
% 2.39/2.55 1411[0:SSi:1402.0,53.0] || -> SkP0(u,v)* duplicatefreeP(v).
% 2.39/2.55 1412[0:SSi:1403.0,53.0] || -> SkP0(u,v)* strictorderedP(v).
% 2.39/2.55 1413[0:SSi:1404.0,53.0] || -> SkP0(u,v)* totalorderedP(v).
% 2.39/2.55 1414[0:SSi:1405.0,53.0] || -> SkP0(u,v)* strictorderP(v).
% 2.39/2.55 1415[0:SSi:1406.0,53.0] || -> SkP0(u,v)* totalorderP(v).
% 2.39/2.55 1416[0:SSi:1407.0,53.0] || -> SkP0(u,v)* cyclefreeP(v).
% 2.39/2.55 1418[2:Res:1410.0,1282.0] || -> equalelemsP(skc5)*.
% 2.39/2.55 1420[2:Res:1411.0,1282.0] || -> duplicatefreeP(skc5)*.
% 2.39/2.55 1421[2:Res:1412.0,1282.0] || -> strictorderedP(skc5)*.
% 2.39/2.55 1422[2:Res:1413.0,1282.0] || -> totalorderedP(skc5)*.
% 2.39/2.55 1423[2:Res:1414.0,1282.0] || -> strictorderP(skc5)*.
% 2.39/2.55 1424[2:Res:1415.0,1282.0] || -> totalorderP(skc5)*.
% 2.39/2.55 1425[2:Res:1416.0,1282.0] || -> cyclefreeP(skc5)*.
% 2.39/2.55 1431[0:SpL:88.1,321.1] ssItem(skf44(u,v)) || equal(v,skc5) -> SkP0(u,v)* singletonP(skc5).
% 2.39/2.55 1432[0:SSi:1431.0,53.0] || equal(u,skc5) -> SkP0(v,u)* singletonP(skc5).
% 2.39/2.55 1433[9:Spt:1432.0,1432.1] || equal(u,skc5) -> SkP0(v,u)*.
% 2.39/2.55 1434[9:Res:1433.1,1282.0] || equal(skc5,skc5)* -> .
% 2.39/2.55 1435[9:Obv:1434.0] || -> .
% 2.39/2.55 1436[9:Spt:1435.0,1432.2] || -> singletonP(skc5)*.
% 2.39/2.55 1437[9:MRR:252.0,1436.0] || -> equal(cons(skf47(skc5),nil),skc5)**.
% 2.39/2.55 1515[9:SpR:1437.0,113.2] ssItem(skf47(skc5)) ssList(nil) || -> equal(tl(skc5),nil)**.
% 2.39/2.55 1519[9:SSi:1515.1,1515.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,15.0,3.0,1299.0,1303.0,1308.0,1312.0,1313.0,1321.0,1418.0,1436.0] || -> equal(tl(skc5),nil)**.
% 2.44/2.65 1522[9:Rew:1519.0,1283.0] || -> equal(cons(hd(skc5),nil),skc5)**.
% 2.44/2.65 1562[0:SpR:88.1,112.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 2.44/2.65 1566[0:SSi:1562.1,1562.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,53.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 2.44/2.65 1567[0:Rew:1566.1,81.1] || -> SkP0(u,v) memberP(u,hd(v))*.
% 2.44/2.65 5787[9:SpL:1522.0,171.3] ssList(nil) ssItem(hd(skc5)) ssItem(u) || memberP(skc5,u) -> memberP(nil,u)* equal(u,hd(skc5)).
% 2.44/2.65 5793[9:SSi:5787.1,5787.0,1278.0,13.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0] ssItem(u) || memberP(skc5,u) -> memberP(nil,u)* equal(u,hd(skc5)).
% 2.44/2.65 5794[9:MRR:5793.2,72.1] ssItem(u) || memberP(skc5,u)* -> equal(u,hd(skc5)).
% 2.44/2.65 5813[9:Res:14.0,5794.1] ssItem(skc7) || -> equal(hd(skc5),skc7)**.
% 2.44/2.65 5816[9:SSi:5813.0,1.0] || -> equal(hd(skc5),skc7)**.
% 2.44/2.65 5982[9:SpR:5816.0,1567.1] || -> SkP0(u,skc5) memberP(u,skc7)*.
% 2.44/2.65 6477[9:Res:5982.1,54.0] || -> SkP0(skc6,skc5)*.
% 2.44/2.65 6482[9:MRR:6477.0,1282.0] || -> .
% 2.44/2.65 6485[8:Spt:6482.0,267.0,1321.0] || duplicatefreeP(skc5)* -> .
% 2.44/2.65 6486[8:Spt:6482.0,267.1] || -> equal(skf78(skc5),skf77(skc5))**.
% 2.44/2.65 6487[8:MRR:6485.0,1420.0] || -> .
% 2.44/2.65 6583[7:Spt:6487.0,220.0,1313.0] || strictorderP(skc5)* -> .
% 2.44/2.65 6584[7:Spt:6487.0,220.1] || -> equal(app(app(skf64(skc5),cons(skf62(skc5),skf65(skc5))),cons(skf63(skc5),skf66(skc5))),skc5)**.
% 2.44/2.65 6585[7:MRR:6583.0,1423.0] || -> .
% 2.44/2.65 6706[6:Spt:6585.0,219.0,1312.0] || totalorderP(skc5)* -> .
% 2.44/2.65 6707[6:Spt:6585.0,219.1] || -> equal(app(app(skf59(skc5),cons(skf57(skc5),skf60(skc5))),cons(skf58(skc5),skf61(skc5))),skc5)**.
% 2.44/2.65 6708[6:MRR:6706.0,1424.0] || -> .
% 2.44/2.65 6759[5:Spt:6708.0,265.0,1308.0] || cyclefreeP(skc5)* -> .
% 2.44/2.65 6760[5:Spt:6708.0,265.1] || -> leq(skf53(skc5),skf52(skc5))*.
% 2.44/2.65 6761[5:MRR:6759.0,1425.0] || -> .
% 2.44/2.65 6859[4:Spt:6761.0,222.0,1303.0] || strictorderedP(skc5)* -> .
% 2.44/2.65 6860[4:Spt:6761.0,222.1] || -> equal(app(app(skf74(skc5),cons(skf72(skc5),skf75(skc5))),cons(skf73(skc5),skf76(skc5))),skc5)**.
% 2.44/2.65 6861[4:MRR:6859.0,1421.0] || -> .
% 2.44/2.65 6961[3:Spt:6861.0,221.0,1299.0] || totalorderedP(skc5)* -> .
% 2.44/2.65 6962[3:Spt:6861.0,221.1] || -> equal(app(app(skf69(skc5),cons(skf67(skc5),skf70(skc5))),cons(skf68(skc5),skf71(skc5))),skc5)**.
% 2.44/2.65 6963[3:MRR:6961.0,1422.0] || -> .
% 2.44/2.65 % SZS output end Refutation
% 2.44/2.65 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax75 ax8 ax13 ax23 ax25 ax78 ax37 ax12 ax11 ax10 ax9 ax77
% 2.44/2.65
%------------------------------------------------------------------------------