%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SWC027+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n005.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 22:01:12 EDT 2022 % Result : Theorem 1.02s 1.28s % Output : Refutation 1.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC027+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.13 % Command : run_spass %d %s % 0.13/0.34 % Computer : n005.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 : Sun Jun 12 15:42:09 EDT 2022 % 0.13/0.34 % CPUTime : % 1.02/1.28 % 1.02/1.28 SPASS V 3.9 % 1.02/1.28 SPASS beiseite: Proof found. % 1.02/1.28 % SZS status Theorem % 1.02/1.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.02/1.28 SPASS derived 1620 clauses, backtracked 969 clauses, performed 36 splits and kept 2044 clauses. % 1.02/1.28 SPASS allocated 99475 KBytes. % 1.02/1.28 SPASS spent 0:00:00.92 on the problem. % 1.02/1.28 0:00:00.04 for the input. % 1.02/1.28 0:00:00.07 for the FLOTTER CNF translation. % 1.02/1.28 0:00:00.01 for inferences. % 1.02/1.28 0:00:00.01 for the backtracking. % 1.02/1.28 0:00:00.57 for the reduction. % 1.02/1.28 % 1.02/1.28 % 1.02/1.28 Here is a proof with depth 5, length 107 : % 1.02/1.28 % SZS output start Refutation % 1.02/1.28 1[0:Inp] || -> ssList(skc5)*. % 1.02/1.28 2[0:Inp] || -> ssList(skc4)*. % 1.02/1.28 4[0:Inp] || -> ssItem(skc6)*. % 1.02/1.28 6[0:Inp] || -> cyclefreeP(nil)*. % 1.02/1.28 7[0:Inp] || -> totalorderP(nil)*. % 1.02/1.28 8[0:Inp] || -> strictorderP(nil)*. % 1.02/1.28 9[0:Inp] || -> totalorderedP(nil)*. % 1.02/1.28 10[0:Inp] || -> strictorderedP(nil)*. % 1.02/1.28 11[0:Inp] || -> duplicatefreeP(nil)*. % 1.02/1.28 12[0:Inp] || -> equalelemsP(nil)*. % 1.02/1.28 51[0:Inp] || -> ssItem(skf44(u,v))*. % 1.02/1.28 59[0:Inp] || -> SkP1(u,v)* equal(nil,v). % 1.02/1.28 68[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc5). % 1.02/1.28 69[0:Inp] || SkP0(skc5,skc4)* -> equal(nil,skc4). % 1.02/1.28 70[0:Inp] || equal(nil,u) -> SkP1(u,v)*. % 1.02/1.28 71[0:Inp] ssItem(u) || memberP(nil,u)* -> . % 1.02/1.28 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*. % 1.02/1.28 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*. % 1.02/1.28 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*. % 1.02/1.28 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*. % 1.02/1.28 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*. % 1.02/1.28 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*. % 1.02/1.28 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*. % 1.02/1.28 80[0:Inp] || SkP1(skc5,skc4)* SkP1(skc4,skc5) -> . % 1.02/1.28 81[0:Inp] || -> SkP0(u,v) memberP(u,skf44(u,v))*. % 1.02/1.28 82[0:Inp] ssList(u) || -> equal(app(nil,u),u)**. % 1.02/1.28 88[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**. % 1.02/1.28 92[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*. % 1.02/1.28 110[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> . % 1.02/1.28 112[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**. % 1.02/1.28 134[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**. % 1.02/1.28 189[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). % 1.02/1.28 198[0:Rew:69.1,68.1] || SkP0(skc5,skc4)* -> equal(skc5,skc4). % 1.02/1.28 246[0:Res:2.0,134.0] ssList(u) || -> equal(nil,skc4) equal(hd(app(skc4,u)),hd(skc4))**. % 1.02/1.28 255[0:Res:2.0,110.0] ssItem(u) || equal(cons(u,skc4),skc4)** -> . % 1.02/1.28 257[0:Res:2.0,112.0] ssItem(u) || -> equal(hd(cons(u,skc4)),u)**. % 1.02/1.28 269[0:Res:2.0,92.0] ssItem(u) || -> ssList(cons(u,skc4))*. % 1.02/1.28 287[0:Res:2.0,189.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(nil,skc4). % 1.02/1.28 458[0:Res:1.0,189.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(nil,skc5). % 1.02/1.28 552[1:Spt:246.0,246.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**. % 1.02/1.28 558[2:Spt:458.5] || -> equal(nil,skc5)**. % 1.02/1.28 587[2:Rew:558.0,70.0] || equal(skc5,u) -> SkP1(u,v)*. % 1.02/1.28 633[2:Rew:558.0,12.0] || -> equalelemsP(skc5)*. % 1.02/1.28 634[2:Rew:558.0,11.0] || -> duplicatefreeP(skc5)*. % 1.02/1.28 635[2:Rew:558.0,10.0] || -> strictorderedP(skc5)*. % 1.02/1.28 636[2:Rew:558.0,9.0] || -> totalorderedP(skc5)*. % 1.02/1.28 637[2:Rew:558.0,8.0] || -> strictorderP(skc5)*. % 1.02/1.28 638[2:Rew:558.0,7.0] || -> totalorderP(skc5)*. % 1.02/1.28 639[2:Rew:558.0,6.0] || -> cyclefreeP(skc5)*. % 1.02/1.28 655[2:Rew:558.0,71.1] ssItem(u) || memberP(skc5,u)* -> . % 1.02/1.28 761[3:Spt:198.1] || -> equal(skc5,skc4)**. % 1.02/1.28 805[3:Rew:761.0,587.0] || equal(skc4,u) -> SkP1(u,v)*. % 1.02/1.28 841[3:Rew:761.0,80.0] || SkP1(skc4,skc4) SkP1(skc4,skc5)* -> . % 1.02/1.28 946[3:Rew:761.0,841.1] || SkP1(skc4,skc4)* SkP1(skc4,skc4)* -> . % 1.02/1.28 947[3:Obv:946.0] || SkP1(skc4,skc4)* -> . % 1.02/1.28 1021[3:Res:805.1,947.0] || equal(skc4,skc4)* -> . % 1.02/1.28 1022[3:Obv:1021.0] || -> . % 1.02/1.28 1023[3:Spt:1022.0,198.1,761.0] || equal(skc5,skc4)** -> . % 1.02/1.28 1024[3:Spt:1022.0,198.0] || SkP0(skc5,skc4)* -> . % 1.02/1.28 1079[2:Res:81.1,655.1] ssItem(skf44(skc5,u)) || -> SkP0(skc5,u)*. % 1.02/1.28 1080[2:SSi:1079.0,51.0,639.0,638.0,637.0,636.0,635.0,634.0,633.0,1.0] || -> SkP0(skc5,u)*. % 1.02/1.28 1081[3:UnC:1080.0,1024.0] || -> . % 1.02/1.28 1082[2:Spt:1081.0,458.5,558.0] || equal(nil,skc5)** -> . % 1.02/1.28 1083[2:Spt:1081.0,458.0,458.1,458.2,458.3,458.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u). % 1.02/1.28 1098[3:Spt:287.5] || -> equal(nil,skc4)**. % 1.02/1.28 1115[3:Rew:1098.0,1082.0] || equal(skc5,skc4)** -> . % 1.02/1.28 1140[3:Rew:1098.0,72.1] ssItem(u) || -> cyclefreeP(cons(u,skc4))*. % 1.02/1.28 1141[3:Rew:1098.0,73.1] ssItem(u) || -> totalorderP(cons(u,skc4))*. % 1.02/1.28 1142[3:Rew:1098.0,74.1] ssItem(u) || -> strictorderP(cons(u,skc4))*. % 1.02/1.28 1143[3:Rew:1098.0,75.1] ssItem(u) || -> totalorderedP(cons(u,skc4))*. % 1.02/1.28 1144[3:Rew:1098.0,76.1] ssItem(u) || -> strictorderedP(cons(u,skc4))*. % 1.02/1.28 1145[3:Rew:1098.0,77.1] ssItem(u) || -> duplicatefreeP(cons(u,skc4))*. % 1.02/1.28 1146[3:Rew:1098.0,78.1] ssItem(u) || -> equalelemsP(cons(u,skc4))*. % 1.02/1.28 1174[3:Rew:1098.0,82.1] ssList(u) || -> equal(app(skc4,u),u)**. % 1.02/1.28 1180[3:Rew:1098.0,88.1] || -> SkP0(u,v) equal(cons(skf44(u,v),skc4),v)**. % 1.02/1.28 1197[3:MRR:198.1,1115.0] || SkP0(skc5,skc4)* -> . % 1.02/1.28 1227[3:Rew:1174.1,552.1] ssList(u) || -> equal(hd(u),hd(skc4))*. % 1.02/1.28 1334[3:SpR:257.1,1227.1] ssItem(u) ssList(cons(u,skc4)) || -> equal(u,hd(skc4))*. % 1.02/1.28 1337[3:SSi:1334.1,269.1,1140.1,1141.1,1142.1,1143.1,1144.1,1145.1,1146.1] ssItem(u) || -> equal(u,hd(skc4))*. % 1.02/1.28 1506[3:SpR:1180.1,257.1] ssItem(skf44(u,v)) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**. % 1.02/1.28 1521[3:SSi:1506.0,51.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**. % 1.02/1.28 1523[3:Rew:1521.1,1180.1] || -> SkP0(u,v)* equal(cons(hd(v),skc4),v)**. % 1.02/1.28 1554[3:SpR:1337.1,1523.1] ssItem(u) || -> SkP0(v,skc4)* equal(cons(u,skc4),skc4)**. % 1.02/1.28 1559[3:MRR:1554.2,255.1] ssItem(u) || -> SkP0(v,skc4)*. % 1.02/1.28 1581[3:EmS:1559.0,4.0] || -> SkP0(u,skc4)*. % 1.02/1.28 1602[3:UnC:1581.0,1197.0] || -> . % 1.02/1.28 1603[3:Spt:1602.0,287.5,1098.0] || equal(nil,skc4)** -> . % 1.02/1.28 1604[3:Spt:1602.0,287.0,287.1,287.2,287.3,287.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u). % 1.02/1.28 1661[0:Res:59.0,80.0] || SkP1(skc4,skc5)* -> equal(nil,skc4). % 1.02/1.28 1662[3:MRR:1661.1,1603.0] || SkP1(skc4,skc5)* -> . % 1.02/1.28 1663[3:Res:59.0,1662.0] || -> equal(nil,skc5)**. % 1.02/1.28 1664[3:MRR:1663.0,1082.0] || -> . % 1.02/1.28 1665[1:Spt:1664.0,246.1] || -> equal(nil,skc4)**. % 1.02/1.28 1715[1:Rew:1665.0,70.0] || equal(skc4,u) -> SkP1(u,v)*. % 1.02/1.28 1735[1:Rew:1665.0,88.1] || -> SkP0(u,v) equal(cons(skf44(u,v),skc4),v)**. % 1.02/1.28 1839[2:Spt:198.1] || -> equal(skc5,skc4)**. % 1.02/1.28 1985[2:Rew:1839.0,80.0] || SkP1(skc4,skc4) SkP1(skc4,skc5)* -> . % 1.02/1.28 2005[2:Rew:1839.0,1985.1] || SkP1(skc4,skc4)* SkP1(skc4,skc4)* -> . % 1.02/1.28 2006[2:Obv:2005.0] || SkP1(skc4,skc4)* -> . % 1.02/1.28 2078[2:Res:1715.1,2006.0] || equal(skc4,skc4)* -> . % 1.02/1.28 2079[2:Obv:2078.0] || -> . % 1.02/1.28 2080[2:Spt:2079.0,198.1,1839.0] || equal(skc5,skc4)** -> . % 1.02/1.28 2081[2:Spt:2079.0,198.0] || SkP0(skc5,skc4)* -> . % 1.02/1.28 2190[1:SpL:1735.1,255.1] ssItem(skf44(u,v)) || equal(v,skc4) -> SkP0(u,v)*. % 1.02/1.28 2200[1:SSi:2190.0,51.0] || equal(u,skc4) -> SkP0(v,u)*. % 1.02/1.28 2237[2:Res:2200.1,2081.0] || equal(skc4,skc4)* -> . % 1.02/1.28 2238[2:Obv:2237.0] || -> . % 1.02/1.28 % SZS output end Refutation % 1.02/1.28 Formulae used in the proof : co1 ax2 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax38 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax16 ax18 ax23 ax85 ax77 % 1.02/1.28 %------------------------------------------------------------------------------