TSTP Solution File: SWC381+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC381+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 22:03:42 EDT 2022
% Result : Theorem 5.46s 5.64s
% Output : Refutation 5.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC381+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n008.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 22:52:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 5.46/5.64
% 5.46/5.64 SPASS V 3.9
% 5.46/5.64 SPASS beiseite: Proof found.
% 5.46/5.64 % SZS status Theorem
% 5.46/5.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/5.64 SPASS derived 5511 clauses, backtracked 1477 clauses, performed 30 splits and kept 3698 clauses.
% 5.46/5.64 SPASS allocated 106540 KBytes.
% 5.46/5.64 SPASS spent 0:00:05.28 on the problem.
% 5.46/5.64 0:00:00.04 for the input.
% 5.46/5.64 0:00:00.06 for the FLOTTER CNF translation.
% 5.46/5.64 0:00:00.06 for inferences.
% 5.46/5.64 0:00:00.10 for the backtracking.
% 5.46/5.64 0:00:04.84 for the reduction.
% 5.46/5.64
% 5.46/5.64
% 5.46/5.64 Here is a proof with depth 6, length 155 :
% 5.46/5.64 % SZS output start Refutation
% 5.46/5.64 1[0:Inp] || -> ssList(skc5)*.
% 5.46/5.64 2[0:Inp] || -> ssList(skc4)*.
% 5.46/5.64 5[0:Inp] || -> ssList(nil)*.
% 5.46/5.64 6[0:Inp] || -> cyclefreeP(nil)*.
% 5.46/5.64 7[0:Inp] || -> totalorderP(nil)*.
% 5.46/5.64 8[0:Inp] || -> strictorderP(nil)*.
% 5.46/5.64 9[0:Inp] || -> totalorderedP(nil)*.
% 5.46/5.64 10[0:Inp] || -> strictorderedP(nil)*.
% 5.46/5.64 11[0:Inp] || -> duplicatefreeP(nil)*.
% 5.46/5.64 12[0:Inp] || -> equalelemsP(nil)*.
% 5.46/5.64 13[0:Inp] || -> ssItem(skf47(u))*.
% 5.46/5.64 51[0:Inp] || -> ssItem(skf44(u,v))*.
% 5.46/5.64 55[0:Inp] || -> ssList(skf48(u,v))*.
% 5.46/5.64 59[0:Inp] || -> SkP0(u,v)* neq(v,nil)*.
% 5.46/5.64 68[0:Inp] || SkP0(skc4,skc5) -> neq(skc5,nil)*.
% 5.46/5.64 69[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 5.46/5.64 70[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 5.46/5.64 71[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 5.46/5.64 72[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 5.46/5.64 73[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 5.46/5.64 74[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 5.46/5.64 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 5.46/5.64 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 5.46/5.64 78[0:Inp] || neq(skc5,nil)* SkP0(skc4,skc5) -> .
% 5.46/5.64 79[0:Inp] || -> SkP0(u,v) memberP(v,skf44(v,u))*.
% 5.46/5.64 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 5.46/5.64 81[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 5.46/5.64 84[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 5.46/5.64 86[0:Inp] || -> SkP0(u,v) equal(cons(skf44(v,u),nil),u)**.
% 5.46/5.64 87[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skf53(u),skf52(u))*.
% 5.46/5.64 90[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 5.46/5.64 106[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 5.46/5.64 108[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 5.46/5.64 109[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 5.46/5.64 110[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 5.46/5.64 111[0:Inp] ssItem(u) ssList(v) || -> equal(tl(cons(u,v)),v)**.
% 5.46/5.64 117[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 5.46/5.64 120[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 5.46/5.64 127[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 5.46/5.64 130[0:Inp] ssItem(u) || memberP(v,u)* equal(cons(u,nil),w)*+ -> SkP0(w,v)*.
% 5.46/5.64 133[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 5.46/5.64 136[0:Inp] ssList(u) ssList(v) || frontsegP(v,u) -> equal(app(u,skf48(v,u)),v)**.
% 5.46/5.64 143[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 5.46/5.64 152[0:Inp] ssList(u) ssItem(v) || totalorderedP(cons(v,u))* -> leq(v,hd(u)) equal(nil,u).
% 5.46/5.64 153[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u).
% 5.46/5.64 173[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skf74(u),cons(skf72(u),skf75(u))),cons(skf73(u),skf76(u))),u)**.
% 5.46/5.64 174[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skf69(u),cons(skf67(u),skf70(u))),cons(skf68(u),skf71(u))),u)**.
% 5.46/5.64 196[0:MRR:68.0,59.1] || -> neq(skc5,nil)*.
% 5.46/5.64 197[0:MRR:78.0,196.0] || SkP0(skc4,skc5)* -> .
% 5.46/5.64 221[0:Res:2.0,174.0] || -> totalorderedP(skc4) equal(app(app(skf69(skc4),cons(skf67(skc4),skf70(skc4))),cons(skf68(skc4),skf71(skc4))),skc4)**.
% 5.46/5.64 222[0:Res:2.0,173.0] || -> strictorderedP(skc4) equal(app(app(skf74(skc4),cons(skf72(skc4),skf75(skc4))),cons(skf73(skc4),skf76(skc4))),skc4)**.
% 5.46/5.64 245[0:Res:2.0,133.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 5.46/5.64 251[0:Res:2.0,117.0] || -> equal(skc4,nil) equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 5.46/5.64 252[0:Res:2.0,106.1] singletonP(skc4) || -> equal(cons(skf47(skc4),nil),skc4)**.
% 5.46/5.64 255[0:Res:2.0,109.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 5.46/5.64 265[0:Res:2.0,87.0] || -> cyclefreeP(skc4) leq(skf53(skc4),skf52(skc4))*.
% 5.46/5.64 276[0:Res:2.0,84.0] || -> ssItem(hd(skc4))* equal(skc4,nil).
% 5.46/5.64 279[0:Res:2.0,81.0] || -> equal(app(skc4,nil),skc4)**.
% 5.46/5.64 308[0:Res:2.0,152.1] ssItem(u) || totalorderedP(cons(u,skc4))* -> leq(u,hd(skc4)) equal(skc4,nil).
% 5.46/5.64 321[0:Res:2.0,120.1] ssItem(u) || equal(cons(u,nil),skc4)** -> singletonP(skc4).
% 5.46/5.64 417[0:Res:1.0,127.0] ssItem(u) || -> equal(app(cons(u,nil),skc5),cons(u,skc5))**.
% 5.46/5.64 425[0:Res:1.0,108.0] ssItem(u) || equal(cons(u,skc5),skc5)** -> .
% 5.46/5.64 449[0:Res:1.0,80.0] || -> equal(app(nil,skc5),skc5)**.
% 5.46/5.64 480[0:Res:1.0,153.1] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)) equal(skc5,nil).
% 5.46/5.64 549[1:Spt:245.0,245.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 5.46/5.64 553[2:Spt:480.3] || -> equal(skc5,nil)**.
% 5.46/5.64 664[2:Rew:553.0,197.0] || SkP0(skc4,nil)* -> .
% 5.46/5.64 1064[0:Res:79.1,69.1] ssItem(skf44(nil,u)) || -> SkP0(u,nil)*.
% 5.46/5.64 1065[0:SSi:1064.0,51.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0] || -> SkP0(u,nil)*.
% 5.46/5.64 1069[2:MRR:664.0,1065.0] || -> .
% 5.46/5.64 1083[2:Spt:1069.0,480.3,553.0] || equal(skc5,nil)** -> .
% 5.46/5.64 1084[2:Spt:1069.0,480.0,480.1,480.2] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)).
% 5.46/5.64 1098[3:Spt:308.3] || -> equal(skc4,nil)**.
% 5.46/5.64 1132[3:Rew:1098.0,255.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 5.46/5.64 1246[3:Rew:1098.0,197.0] || SkP0(nil,skc5)* -> .
% 5.46/5.64 1558[0:SpR:86.1,76.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* equalelemsP(v).
% 5.46/5.64 1559[0:SpR:86.1,75.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* duplicatefreeP(v).
% 5.46/5.64 1560[0:SpR:86.1,72.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* strictorderP(v).
% 5.46/5.64 1561[0:SpR:86.1,71.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* totalorderP(v).
% 5.46/5.64 1562[0:SpR:86.1,70.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* cyclefreeP(v).
% 5.46/5.64 1563[0:SpR:86.1,74.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* strictorderedP(v).
% 5.46/5.64 1564[0:SpR:86.1,73.1] ssItem(skf44(u,v)) || -> SkP0(v,u)* totalorderedP(v).
% 5.46/5.64 1567[0:SpR:86.1,90.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(v,u)* ssList(v).
% 5.46/5.64 1570[3:SpL:86.1,1132.1] ssItem(skf44(u,v)) || equal(v,nil) -> SkP0(v,u)*.
% 5.46/5.64 1571[0:SSi:1558.0,51.0] || -> SkP0(u,v)* equalelemsP(u).
% 5.46/5.64 1572[0:SSi:1559.0,51.0] || -> SkP0(u,v)* duplicatefreeP(u).
% 5.46/5.64 1573[0:SSi:1560.0,51.0] || -> SkP0(u,v)* strictorderP(u).
% 5.46/5.64 1574[0:SSi:1561.0,51.0] || -> SkP0(u,v)* totalorderP(u).
% 5.46/5.64 1575[0:SSi:1562.0,51.0] || -> SkP0(u,v)* cyclefreeP(u).
% 5.46/5.64 1576[0:SSi:1563.0,51.0] || -> SkP0(u,v)* strictorderedP(u).
% 5.46/5.64 1577[0:SSi:1564.0,51.0] || -> SkP0(u,v)* totalorderedP(u).
% 5.46/5.64 1580[3:SSi:1570.0,51.0] || equal(u,nil) -> SkP0(u,v)*.
% 5.46/5.64 1614[3:Res:1580.1,1246.0] || equal(nil,nil)* -> .
% 5.46/5.64 1615[3:Obv:1614.0] || -> .
% 5.46/5.64 1616[3:Spt:1615.0,308.3,1098.0] || equal(skc4,nil)** -> .
% 5.46/5.64 1617[3:Spt:1615.0,308.0,308.1,308.2] ssItem(u) || totalorderedP(cons(u,skc4))* -> leq(u,hd(skc4)).
% 5.46/5.64 1619[3:MRR:276.1,1616.0] || -> ssItem(hd(skc4))*.
% 5.46/5.64 1623[3:MRR:251.0,1616.0] || -> equal(cons(hd(skc4),tl(skc4)),skc4)**.
% 5.46/5.64 1629[0:SSi:1567.1,1567.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,51.0] || -> SkP0(u,v)* ssList(u).
% 5.46/5.64 1639[4:Spt:221.0] || -> totalorderedP(skc4)*.
% 5.46/5.64 1643[5:Spt:222.0] || -> strictorderedP(skc4)*.
% 5.46/5.64 1648[6:Spt:265.0] || -> cyclefreeP(skc4)*.
% 5.46/5.64 1650[0:Res:1577.0,197.0] || -> totalorderedP(skc4)*.
% 5.46/5.64 1651[0:Res:1576.0,197.0] || -> strictorderedP(skc4)*.
% 5.46/5.64 1652[0:Res:1575.0,197.0] || -> cyclefreeP(skc4)*.
% 5.46/5.64 1653[0:Res:1574.0,197.0] || -> totalorderP(skc4)*.
% 5.46/5.64 1654[0:Res:1573.0,197.0] || -> strictorderP(skc4)*.
% 5.46/5.64 1655[0:Res:1572.0,197.0] || -> duplicatefreeP(skc4)*.
% 5.46/5.64 1656[0:Res:1571.0,197.0] || -> equalelemsP(skc4)*.
% 5.46/5.64 1705[0:SpL:86.1,321.1] ssItem(skf44(u,v)) || equal(v,skc4) -> SkP0(v,u)* singletonP(skc4).
% 5.46/5.64 1706[0:SSi:1705.0,51.0] || equal(u,skc4) -> SkP0(u,v)* singletonP(skc4).
% 5.46/5.64 1707[7:Spt:1706.0,1706.1] || equal(u,skc4) -> SkP0(u,v)*.
% 5.46/5.64 1708[7:Res:1707.1,197.0] || equal(skc4,skc4)* -> .
% 5.46/5.64 1709[7:Obv:1708.0] || -> .
% 5.46/5.64 1710[7:Spt:1709.0,1706.2] || -> singletonP(skc4)*.
% 5.46/5.64 1711[7:MRR:252.0,1710.0] || -> equal(cons(skf47(skc4),nil),skc4)**.
% 5.46/5.64 1775[7:SpR:1711.0,111.2] ssItem(skf47(skc4)) ssList(nil) || -> equal(tl(skc4),nil)**.
% 5.46/5.64 1778[7:SSi:1775.1,1775.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,13.0,2.0,1639.0,1643.0,1648.0,1653.0,1654.0,1655.0,1656.0,1710.0] || -> equal(tl(skc4),nil)**.
% 5.46/5.64 1780[7:Rew:1778.0,1623.0] || -> equal(cons(hd(skc4),nil),skc4)**.
% 5.46/5.64 1816[0:SpR:86.1,110.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(v,u) equal(skf44(u,v),hd(v))**.
% 5.74/5.92 1820[0:SSi:1816.1,1816.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,51.0] || -> SkP0(u,v) equal(skf44(v,u),hd(u))**.
% 5.74/5.92 1821[0:Rew:1820.1,79.1] || -> SkP0(u,v) memberP(v,hd(u))*.
% 5.74/5.92 1822[0:Rew:1820.1,86.1] || -> SkP0(u,v)* equal(cons(hd(u),nil),u)**.
% 5.74/5.92 1910[0:SpR:1820.1,51.0] || -> SkP0(u,v)* ssItem(hd(u)).
% 5.74/5.92 2150[0:SpR:1822.1,417.1] ssItem(hd(u)) || -> SkP0(u,v)* equal(cons(hd(u),skc5),app(u,skc5))**.
% 5.74/5.92 2153[0:MRR:2150.0,1910.1] || -> SkP0(u,v)* equal(cons(hd(u),skc5),app(u,skc5))**.
% 5.74/5.92 2263[0:SpL:2153.1,425.1] ssItem(hd(u)) || equal(app(u,skc5),skc5)** -> SkP0(u,v)*.
% 5.74/5.92 2269[0:MRR:2263.0,1910.1] || equal(app(u,skc5),skc5)**+ -> SkP0(u,v)*.
% 5.74/5.92 2336[0:SpL:449.0,2269.0] || equal(skc5,skc5) -> SkP0(nil,u)*.
% 5.74/5.92 2339[0:Obv:2336.0] || -> SkP0(nil,u)*.
% 5.74/5.92 2868[7:SpL:1780.0,130.2] ssItem(hd(skc4)) || memberP(u,hd(skc4))* equal(skc4,v) -> SkP0(v,u)*.
% 5.74/5.92 2872[7:SSi:2868.0,1619.0] || memberP(u,hd(skc4))* equal(skc4,v) -> SkP0(v,u)*.
% 5.74/5.92 3186[1:SpR:136.3,549.1] ssList(skc4) ssList(u) ssList(skf48(u,skc4)) || frontsegP(u,skc4)* -> equal(hd(u),hd(skc4)).
% 5.74/5.92 3201[7:SSi:3186.2,3186.0,55.0,2.0,1639.0,1643.0,1648.0,1653.0,1654.0,1655.0,1656.0,1710.0,2.0,1639.0,1643.0,1648.0,1653.0,1654.0,1655.0,1656.0,1710.0] ssList(u) || frontsegP(u,skc4)* -> equal(hd(u),hd(skc4)).
% 5.74/5.92 4045[0:SpL:279.0,143.3] ssList(skc4) ssList(u) ssList(nil) || equal(skc4,u) -> frontsegP(u,skc4)*.
% 5.74/5.92 4055[7:SSi:4045.2,4045.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0,2.0,1639.0,1643.0,1648.0,1653.0,1654.0,1655.0,1656.0,1710.0] ssList(u) || equal(skc4,u) -> frontsegP(u,skc4)*.
% 5.74/5.92 7473[7:Res:4055.2,3201.1] ssList(u) ssList(u) || equal(skc4,u) -> equal(hd(u),hd(skc4))*.
% 5.74/5.92 7475[7:Obv:7473.0] ssList(u) || equal(skc4,u) -> equal(hd(u),hd(skc4))*.
% 5.74/5.92 8292[7:SpR:7475.2,1821.1] ssList(u) || equal(skc4,u) -> SkP0(u,v)* memberP(v,hd(skc4))*.
% 5.74/5.92 8366[7:MRR:8292.0,1629.1] || equal(skc4,u) -> SkP0(u,v)* memberP(v,hd(skc4))*.
% 5.74/5.92 8367[7:MRR:8366.2,2872.0] || equal(skc4,u) -> SkP0(u,v)*.
% 5.74/5.92 8421[7:Res:8367.1,197.0] || equal(skc4,skc4)* -> .
% 5.74/5.92 8422[7:Obv:8421.0] || -> .
% 5.74/5.92 8423[6:Spt:8422.0,265.0,1648.0] || cyclefreeP(skc4)* -> .
% 5.74/5.92 8424[6:Spt:8422.0,265.1] || -> leq(skf53(skc4),skf52(skc4))*.
% 5.74/5.92 8425[6:MRR:8423.0,1652.0] || -> .
% 5.74/5.92 8722[5:Spt:8425.0,222.0,1643.0] || strictorderedP(skc4)* -> .
% 5.74/5.92 8723[5:Spt:8425.0,222.1] || -> equal(app(app(skf74(skc4),cons(skf72(skc4),skf75(skc4))),cons(skf73(skc4),skf76(skc4))),skc4)**.
% 5.74/5.92 8724[5:MRR:8722.0,1651.0] || -> .
% 5.74/5.92 8901[4:Spt:8724.0,221.0,1639.0] || totalorderedP(skc4)* -> .
% 5.74/5.92 8902[4:Spt:8724.0,221.1] || -> equal(app(app(skf69(skc4),cons(skf67(skc4),skf70(skc4))),cons(skf68(skc4),skf71(skc4))),skc4)**.
% 5.74/5.92 8903[4:MRR:8901.0,1650.0] || -> .
% 5.74/5.92 9006[1:Spt:8903.0,245.1] || -> equal(skc4,nil)**.
% 5.74/5.92 9016[1:Rew:9006.0,197.0] || SkP0(nil,skc5)* -> .
% 5.74/5.92 9199[1:MRR:9016.0,2339.0] || -> .
% 5.74/5.92 % SZS output end Refutation
% 5.74/5.92 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax5 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax75 ax8 ax16 ax18 ax21 ax23 ax25 ax78 ax81 ax85 ax67 ax70 ax12 ax11
% 5.74/5.92
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