TSTP Solution File: SWC207+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC207+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 22:02:29 EDT 2022
% Result : Theorem 1.05s 1.29s
% Output : Refutation 1.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC207+1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 11 22:55:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.05/1.29
% 1.05/1.29 SPASS V 3.9
% 1.05/1.29 SPASS beiseite: Proof found.
% 1.05/1.29 % SZS status Theorem
% 1.05/1.29 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.05/1.29 SPASS derived 1639 clauses, backtracked 973 clauses, performed 38 splits and kept 2043 clauses.
% 1.05/1.29 SPASS allocated 99436 KBytes.
% 1.05/1.29 SPASS spent 0:00:00.93 on the problem.
% 1.05/1.29 0:00:00.04 for the input.
% 1.05/1.29 0:00:00.07 for the FLOTTER CNF translation.
% 1.05/1.29 0:00:00.01 for inferences.
% 1.05/1.29 0:00:00.01 for the backtracking.
% 1.05/1.29 0:00:00.57 for the reduction.
% 1.05/1.29
% 1.05/1.29
% 1.05/1.29 Here is a proof with depth 5, length 104 :
% 1.05/1.29 % SZS output start Refutation
% 1.05/1.29 1[0:Inp] || -> ssList(skc5)*.
% 1.05/1.29 2[0:Inp] || -> ssList(skc4)*.
% 1.05/1.29 4[0:Inp] || -> ssItem(skc6)*.
% 1.05/1.29 5[0:Inp] || -> ssList(nil)*.
% 1.05/1.29 6[0:Inp] || -> cyclefreeP(nil)*.
% 1.05/1.29 7[0:Inp] || -> totalorderP(nil)*.
% 1.05/1.29 8[0:Inp] || -> strictorderP(nil)*.
% 1.05/1.29 9[0:Inp] || -> totalorderedP(nil)*.
% 1.05/1.29 10[0:Inp] || -> strictorderedP(nil)*.
% 1.05/1.29 11[0:Inp] || -> duplicatefreeP(nil)*.
% 1.05/1.29 12[0:Inp] || -> equalelemsP(nil)*.
% 1.05/1.29 13[0:Inp] || -> neq(skc5,nil)*.
% 1.05/1.29 52[0:Inp] || -> ssItem(skf44(u,v))*.
% 1.05/1.29 53[0:Inp] || neq(skc4,nil)* -> .
% 1.05/1.29 69[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc5).
% 1.05/1.29 70[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc4).
% 1.05/1.29 71[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 1.05/1.29 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 1.05/1.29 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 1.05/1.29 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 1.05/1.29 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 1.05/1.29 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 1.05/1.29 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 1.05/1.29 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 1.05/1.29 80[0:Inp] || -> SkP0(u,v) memberP(u,skf44(u,v))*.
% 1.05/1.29 81[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 1.05/1.29 87[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 1.05/1.29 91[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 1.05/1.29 108[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 1.05/1.29 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 1.05/1.29 111[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 1.05/1.29 133[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 1.05/1.29 188[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).
% 1.05/1.29 197[0:Rew:70.1,69.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4).
% 1.05/1.29 245[0:Res:2.0,133.0] ssList(u) || -> equal(nil,skc4) equal(hd(app(skc4,u)),hd(skc4))**.
% 1.05/1.29 253[0:Res:2.0,108.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 1.05/1.29 254[0:Res:2.0,109.0] ssItem(u) || equal(cons(u,skc4),skc4)** -> .
% 1.05/1.29 256[0:Res:2.0,111.0] ssItem(u) || -> equal(hd(cons(u,skc4)),u)**.
% 1.05/1.29 268[0:Res:2.0,91.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 1.05/1.29 286[0:Res:2.0,188.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(nil,skc4).
% 1.05/1.29 457[0:Res:1.0,188.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5).
% 1.05/1.29 551[1:Spt:245.0,245.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 1.05/1.29 557[2:Spt:457.5] || -> equal(nil,skc5)**.
% 1.05/1.29 630[2:Rew:557.0,12.0] || -> equalelemsP(skc5)*.
% 1.05/1.29 631[2:Rew:557.0,11.0] || -> duplicatefreeP(skc5)*.
% 1.05/1.29 632[2:Rew:557.0,10.0] || -> strictorderedP(skc5)*.
% 1.05/1.29 633[2:Rew:557.0,9.0] || -> totalorderedP(skc5)*.
% 1.05/1.29 634[2:Rew:557.0,8.0] || -> strictorderP(skc5)*.
% 1.05/1.29 635[2:Rew:557.0,7.0] || -> totalorderP(skc5)*.
% 1.05/1.29 636[2:Rew:557.0,6.0] || -> cyclefreeP(skc5)*.
% 1.05/1.29 645[2:Rew:557.0,13.0] || -> neq(skc5,skc5)*.
% 1.05/1.29 646[2:Rew:557.0,53.0] || neq(skc4,skc5)* -> .
% 1.05/1.29 654[2:Rew:557.0,71.1] ssItem(u) || memberP(skc5,u)* -> .
% 1.05/1.29 760[3:Spt:197.1] || -> equal(skc5,skc4)**.
% 1.05/1.29 872[3:Rew:760.0,645.0] || -> neq(skc4,skc4)*.
% 1.05/1.29 873[3:Rew:760.0,646.0] || neq(skc4,skc4)* -> .
% 1.05/1.29 921[3:MRR:873.0,872.0] || -> .
% 1.05/1.29 1014[3:Spt:921.0,197.1,760.0] || equal(skc5,skc4)** -> .
% 1.05/1.29 1015[3:Spt:921.0,197.0] || SkP0(skc5,skc4)* -> .
% 1.05/1.29 1064[2:Res:80.1,654.1] ssItem(skf44(skc5,u)) || -> SkP0(skc5,u)*.
% 1.05/1.29 1065[2:SSi:1064.0,52.0,636.0,635.0,634.0,633.0,632.0,631.0,630.0,1.0] || -> SkP0(skc5,u)*.
% 1.05/1.29 1066[3:UnC:1065.0,1015.0] || -> .
% 1.05/1.29 1067[2:Spt:1066.0,457.5,557.0] || equal(nil,skc5)** -> .
% 1.05/1.29 1068[2:Spt:1066.0,457.0,457.1,457.2,457.3,457.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 1.05/1.29 1083[3:Spt:286.5] || -> equal(nil,skc4)**.
% 1.05/1.29 1102[3:Rew:1083.0,1067.0] || equal(skc5,skc4)** -> .
% 1.05/1.29 1121[3:Rew:1083.0,72.1] ssItem(u) || -> cyclefreeP(cons(u,skc4))*.
% 1.05/1.29 1122[3:Rew:1083.0,73.1] ssItem(u) || -> totalorderP(cons(u,skc4))*.
% 1.05/1.29 1123[3:Rew:1083.0,74.1] ssItem(u) || -> strictorderP(cons(u,skc4))*.
% 1.05/1.29 1124[3:Rew:1083.0,75.1] ssItem(u) || -> totalorderedP(cons(u,skc4))*.
% 1.05/1.29 1125[3:Rew:1083.0,76.1] ssItem(u) || -> strictorderedP(cons(u,skc4))*.
% 1.05/1.29 1126[3:Rew:1083.0,77.1] ssItem(u) || -> duplicatefreeP(cons(u,skc4))*.
% 1.05/1.29 1127[3:Rew:1083.0,78.1] ssItem(u) || -> equalelemsP(cons(u,skc4))*.
% 1.05/1.29 1133[3:Rew:1083.0,81.1] ssList(u) || -> equal(app(skc4,u),u)**.
% 1.05/1.29 1162[3:Rew:1083.0,87.1] || -> SkP0(u,v) equal(cons(skf44(u,v),skc4),v)**.
% 1.05/1.29 1182[3:MRR:197.1,1102.0] || SkP0(skc5,skc4)* -> .
% 1.05/1.29 1212[3:Rew:1133.1,551.1] ssList(u) || -> equal(hd(u),hd(skc4))*.
% 1.05/1.29 1319[3:SpR:256.1,1212.1] ssItem(u) ssList(cons(u,skc4)) || -> equal(u,hd(skc4))*.
% 1.05/1.29 1322[3:SSi:1319.1,268.1,1121.1,1122.1,1123.1,1124.1,1125.1,1126.1,1127.1] ssItem(u) || -> equal(u,hd(skc4))*.
% 1.05/1.29 1489[3:SpR:1162.1,256.1] ssItem(skf44(u,v)) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 1.05/1.29 1504[3:SSi:1489.0,52.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 1.05/1.29 1506[3:Rew:1504.1,1162.1] || -> SkP0(u,v)* equal(cons(hd(v),skc4),v)**.
% 1.05/1.29 1537[3:SpR:1322.1,1506.1] ssItem(u) || -> SkP0(v,skc4)* equal(cons(u,skc4),skc4)**.
% 1.05/1.29 1542[3:MRR:1537.2,254.1] ssItem(u) || -> SkP0(v,skc4)*.
% 1.05/1.29 1564[3:EmS:1542.0,4.0] || -> SkP0(u,skc4)*.
% 1.05/1.29 1585[3:UnC:1564.0,1182.0] || -> .
% 1.05/1.29 1586[3:Spt:1585.0,286.5,1083.0] || equal(nil,skc4)** -> .
% 1.05/1.29 1587[3:Spt:1585.0,286.0,286.1,286.2,286.3,286.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 1.05/1.29 1680[0:Res:253.1,53.0] ssList(nil) || -> equal(nil,skc4)**.
% 1.05/1.29 1681[0:SSi:1680.0,12.0,11.0,10.0,9.0,8.0,7.0,6.0,5.0] || -> equal(nil,skc4)**.
% 1.05/1.29 1682[3:MRR:1681.0,1586.0] || -> .
% 1.05/1.29 1683[1:Spt:1682.0,245.1] || -> equal(nil,skc4)**.
% 1.05/1.29 1699[0:Rew:1681.0,13.0] || -> neq(skc5,skc4)*.
% 1.05/1.29 1702[0:Rew:1681.0,53.0] || neq(skc4,skc4)* -> .
% 1.05/1.29 1751[0:Rew:1681.0,87.1] || -> SkP0(u,v) equal(cons(skf44(u,v),skc4),v)**.
% 1.05/1.29 1857[2:Spt:197.1] || -> equal(skc5,skc4)**.
% 1.05/1.29 1977[2:Rew:1857.0,1699.0] || -> neq(skc4,skc4)*.
% 1.05/1.29 2008[2:MRR:1977.0,1702.0] || -> .
% 1.05/1.29 2091[2:Spt:2008.0,197.1,1857.0] || equal(skc5,skc4)** -> .
% 1.05/1.29 2092[2:Spt:2008.0,197.0] || SkP0(skc5,skc4)* -> .
% 1.05/1.29 2203[0:SpL:1751.1,254.1] ssItem(skf44(u,v)) || equal(v,skc4) -> SkP0(u,v)*.
% 1.05/1.29 2213[0:SSi:2203.0,52.0] || equal(u,skc4) -> SkP0(v,u)*.
% 1.05/1.29 2250[2:Res:2213.1,2092.0] || equal(skc4,skc4)* -> .
% 1.05/1.29 2251[2:Obv:2250.0] || -> .
% 1.05/1.29 % SZS output end Refutation
% 1.05/1.29 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax16 ax15 ax18 ax23 ax85 ax77
% 1.05/1.29
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