%------------------------------------------------------------------------------ % File : SPASS---3.9 % Problem : SWC211+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp % Command : run_spass %d %s % Computer : n021.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 22:02:31 EDT 2022 % Result : Theorem 1.51s 1.76s % Output : Refutation 1.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWC211+1 : TPTP v8.1.0. Released v2.4.0. % 0.03/0.13 % Command : run_spass %d %s % 0.12/0.34 % Computer : n021.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 01:10:40 EDT 2022 % 0.12/0.34 % CPUTime : % 1.51/1.76 % 1.51/1.76 SPASS V 3.9 % 1.51/1.76 SPASS beiseite: Proof found. % 1.51/1.76 % SZS status Theorem % 1.51/1.76 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p % 1.51/1.76 SPASS derived 3406 clauses, backtracked 1021 clauses, performed 32 splits and kept 2500 clauses. % 1.51/1.76 SPASS allocated 102181 KBytes. % 1.51/1.76 SPASS spent 0:00:01.32 on the problem. % 1.51/1.76 0:00:00.04 for the input. % 1.51/1.76 0:00:00.06 for the FLOTTER CNF translation. % 1.51/1.76 0:00:00.03 for inferences. % 1.51/1.76 0:00:00.02 for the backtracking. % 1.51/1.76 0:00:01.00 for the reduction. % 1.51/1.76 % 1.51/1.76 % 1.51/1.76 Here is a proof with depth 6, length 96 : % 1.51/1.76 % SZS output start Refutation % 1.51/1.76 1[0:Inp] || -> ssList(skc5)*. % 1.51/1.76 2[0:Inp] || -> ssList(skc4)*. % 1.51/1.76 3[0:Inp] || -> ssItem(skc7)*. % 1.51/1.76 4[0:Inp] || -> ssItem(skc6)*. % 1.51/1.76 5[0:Inp] || -> ssList(nil)*. % 1.51/1.76 6[0:Inp] || -> cyclefreeP(nil)*. % 1.51/1.76 7[0:Inp] || -> totalorderP(nil)*. % 1.51/1.76 8[0:Inp] || -> strictorderP(nil)*. % 1.51/1.76 9[0:Inp] || -> totalorderedP(nil)*. % 1.51/1.76 10[0:Inp] || -> strictorderedP(nil)*. % 1.51/1.76 11[0:Inp] || -> duplicatefreeP(nil)*. % 1.51/1.76 12[0:Inp] || -> equalelemsP(nil)*. % 1.51/1.76 13[0:Inp] || -> neq(skc5,nil)*. % 1.51/1.76 52[0:Inp] || neq(skc4,nil)* -> . % 1.51/1.76 53[0:Inp] || equal(skc7,skc6)** -> . % 1.51/1.76 68[0:Inp] || equal(skc5,nil)** -> equal(skc4,nil). % 1.51/1.76 70[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*. % 1.51/1.76 71[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*. % 1.51/1.76 72[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*. % 1.51/1.76 73[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*. % 1.51/1.76 74[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*. % 1.51/1.76 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*. % 1.51/1.76 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*. % 1.51/1.76 78[0:Inp] ssList(u) || -> equal(app(nil,u),u)**. % 1.51/1.76 82[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u). % 1.51/1.76 83[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u). % 1.51/1.76 87[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*. % 1.51/1.76 104[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u). % 1.51/1.76 106[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> . % 1.51/1.76 107[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**. % 1.51/1.76 114[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**. % 1.51/1.76 117[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*. % 1.51/1.76 124[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**. % 1.51/1.76 125[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u). % 1.51/1.76 129[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**. % 1.51/1.76 149[0:Inp] ssList(u) ssItem(v) || strictorderedP(cons(v,u))* -> lt(v,hd(u)) equal(nil,u). % 1.51/1.76 150[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(app(tl(v),u),tl(app(v,u)))**. % 1.51/1.76 176[0:Inp] ssItem(u) ssList(v) || equal(app(cons(u,nil),v),skc5)** -> equal(app(v,cons(u,nil)),skc4)**. % 1.51/1.76 196[0:Rew:124.2,176.2] ssList(u) ssItem(v) || equal(cons(v,u),skc5) -> equal(app(u,cons(v,nil)),skc4)**. % 1.51/1.76 241[0:Res:2.0,129.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**. % 1.51/1.76 249[0:Res:2.0,104.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u). % 1.51/1.76 251[0:Res:2.0,106.0] ssItem(u) || equal(cons(u,skc4),nil)** -> . % 1.51/1.76 264[0:Res:2.0,87.0] ssItem(u) || -> ssList(cons(u,skc4))*. % 1.51/1.76 306[0:Res:2.0,149.1] ssItem(u) || strictorderedP(cons(u,skc4))* -> lt(u,hd(skc4)) equal(skc4,nil). % 1.51/1.76 407[0:Res:1.0,150.0] ssList(u) || -> equal(skc5,nil) equal(app(tl(skc5),u),tl(app(skc5,u)))**. % 1.51/1.76 419[0:Res:1.0,114.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**. % 1.51/1.76 424[0:Res:1.0,107.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**. % 1.51/1.76 436[0:Res:1.0,87.0] ssItem(u) || -> ssList(cons(u,skc5))*. % 1.51/1.76 444[0:Res:1.0,82.0] || -> ssItem(hd(skc5))* equal(skc5,nil). % 1.51/1.76 445[0:Res:1.0,83.0] || -> ssList(tl(skc5))* equal(skc5,nil). % 1.51/1.76 478[0:Res:1.0,149.1] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)) equal(skc5,nil). % 1.51/1.76 545[1:Spt:241.0,241.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**. % 1.51/1.76 551[2:Spt:478.3] || -> equal(skc5,nil)**. % 1.51/1.76 558[2:Rew:551.0,68.0] || equal(nil,nil) -> equal(skc4,nil)**. % 1.51/1.76 662[2:Rew:551.0,13.0] || -> neq(nil,nil)*. % 1.51/1.76 706[2:Obv:558.0] || -> equal(skc4,nil)**. % 1.51/1.76 816[2:Rew:706.0,52.0] || neq(nil,nil)* -> . % 1.51/1.76 858[2:MRR:816.0,662.0] || -> . % 1.51/1.76 1054[2:Spt:858.0,478.3,551.0] || equal(skc5,nil)** -> . % 1.51/1.76 1055[2:Spt:858.0,478.0,478.1,478.2] ssItem(u) || strictorderedP(cons(u,skc5))* -> lt(u,hd(skc5)). % 1.51/1.76 1069[3:Spt:306.3] || -> equal(skc4,nil)**. % 1.51/1.76 1099[3:Rew:1069.0,545.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**. % 1.51/1.76 1240[3:Rew:78.1,1099.1] ssList(u) || -> equal(hd(u),hd(nil))*. % 1.51/1.76 1381[3:SpR:424.1,1240.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*. % 1.51/1.76 1384[3:SSi:1381.1,436.1] ssItem(u) || -> equal(u,hd(nil))*. % 1.51/1.76 1470[3:SpR:1384.1,1384.1] ssItem(u) ssItem(v) || -> equal(v,u)*. % 1.51/1.76 1564[3:EmS:1470.0,3.0] ssItem(u) || -> equal(u,skc7)*. % 1.51/1.76 1586[3:EmS:1564.0,4.0] || -> equal(skc7,skc6)**. % 1.51/1.76 1587[3:MRR:1586.0,53.0] || -> . % 1.51/1.76 1769[3:Spt:1587.0,306.3,1069.0] || equal(skc4,nil)** -> . % 1.51/1.76 1770[3:Spt:1587.0,306.0,306.1,306.2] ssItem(u) || strictorderedP(cons(u,skc4))* -> lt(u,hd(skc4)). % 1.51/1.76 1840[0:Res:249.1,52.0] ssList(nil) || -> equal(skc4,nil)**. % 1.51/1.76 1841[0:SSi:1840.0,12.0,11.0,8.0,7.0,6.0,10.0,9.0,5.0] || -> equal(skc4,nil)**. % 1.51/1.76 1842[3:MRR:1841.0,1769.0] || -> . % 1.51/1.76 1843[1:Spt:1842.0,241.1] || -> equal(skc4,nil)**. % 1.51/1.76 1844[0:Rew:1841.0,264.1] ssItem(u) || -> ssList(cons(u,nil))*. % 1.51/1.76 1845[0:Rew:1841.0,251.1] ssItem(u) || equal(cons(u,nil),nil)** -> . % 1.51/1.76 1853[0:Rew:1841.0,52.0] || neq(nil,nil)* -> . % 1.51/1.76 1934[0:Rew:1841.0,196.3] ssList(u) ssItem(v) || equal(cons(v,u),skc5) -> equal(app(u,cons(v,nil)),nil)**. % 1.51/1.76 2089[2:Spt:407.1] || -> equal(skc5,nil)**. % 1.51/1.76 2094[2:Rew:2089.0,13.0] || -> neq(nil,nil)*. % 1.51/1.76 2242[2:MRR:2094.0,1853.0] || -> . % 1.51/1.76 2330[2:Spt:2242.0,407.1,2089.0] || equal(skc5,nil)** -> . % 1.51/1.76 2331[2:Spt:2242.0,407.0,407.2] ssList(u) || -> equal(app(tl(skc5),u),tl(app(skc5,u)))**. % 1.51/1.76 2332[2:MRR:445.1,2330.0] || -> ssList(tl(skc5))*. % 1.51/1.76 2333[2:MRR:444.1,2330.0] || -> ssItem(hd(skc5))*. % 1.51/1.76 2337[2:MRR:419.0,2330.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**. % 1.51/1.76 2899[0:EqR:117.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*. % 1.51/1.76 2902[0:SSi:2899.0,76.1,75.1,72.1,71.1,70.1,74.1,73.1,1844.1] ssItem(u) || -> singletonP(cons(u,nil))*. % 1.51/1.76 4510[0:SpL:1934.3,125.2] ssList(u) ssItem(v) ssList(cons(v,nil)) ssList(u) || equal(cons(v,u),skc5)** equal(nil,nil) -> equal(cons(v,nil),nil)**. % 1.51/1.76 4528[0:Obv:4510.5] ssItem(u) ssList(cons(u,nil)) ssList(v) || equal(cons(u,v),skc5)** -> equal(cons(u,nil),nil)**. % 1.51/1.76 4529[0:SSi:4528.1,76.1,75.1,72.1,71.1,70.1,74.1,73.1,1844.1,2902.1] ssItem(u) ssList(v) || equal(cons(u,v),skc5)** -> equal(cons(u,nil),nil)**. % 1.51/1.76 4530[0:MRR:4529.3,1845.1] ssItem(u) ssList(v) || equal(cons(u,v),skc5)** -> . % 1.51/1.76 5238[2:SpL:2337.0,4530.2] ssItem(hd(skc5)) ssList(tl(skc5)) || equal(skc5,skc5)* -> . % 1.51/1.76 5249[2:Obv:5238.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> . % 1.51/1.76 5250[2:SSi:5249.1,5249.0,2332.0,2333.0] || -> . % 1.51/1.76 % SZS output end Refutation % 1.51/1.76 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax15 ax21 ax23 ax78 ax4 ax81 ax83 ax85 ax70 ax86 % 1.51/1.76 %------------------------------------------------------------------------------