TSTP Solution File: SWC172+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC172+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 22:02:14 EDT 2022
% Result : Theorem 13.47s 13.64s
% Output : Refutation 13.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC172+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 12:18:50 EDT 2022
% 0.18/0.33 % CPUTime :
% 13.47/13.64
% 13.47/13.64 SPASS V 3.9
% 13.47/13.64 SPASS beiseite: Proof found.
% 13.47/13.64 % SZS status Theorem
% 13.47/13.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.47/13.64 SPASS derived 10103 clauses, backtracked 4340 clauses, performed 42 splits and kept 7788 clauses.
% 13.47/13.64 SPASS allocated 113063 KBytes.
% 13.47/13.64 SPASS spent 0:0:12.36 on the problem.
% 13.47/13.64 0:00:00.04 for the input.
% 13.47/13.64 0:00:00.06 for the FLOTTER CNF translation.
% 13.47/13.64 0:00:00.11 for inferences.
% 13.47/13.64 0:00:00.42 for the backtracking.
% 13.47/13.64 0:0:11.51 for the reduction.
% 13.47/13.64
% 13.47/13.64
% 13.47/13.64 Here is a proof with depth 6, length 97 :
% 13.47/13.64 % SZS output start Refutation
% 13.47/13.64 1[0:Inp] || -> ssList(skc13)*.
% 13.47/13.64 2[0:Inp] || -> ssList(skc12)*.
% 13.47/13.64 3[0:Inp] || -> ssItem(skc11)*.
% 13.47/13.64 4[0:Inp] || -> ssItem(skc10)*.
% 13.47/13.64 6[0:Inp] || -> ssList(skc8)*.
% 13.47/13.64 7[0:Inp] || -> ssItem(skc15)*.
% 13.47/13.64 8[0:Inp] || -> ssItem(skc14)*.
% 13.47/13.64 9[0:Inp] || -> ssList(nil)*.
% 13.47/13.64 10[0:Inp] || -> cyclefreeP(nil)*.
% 13.47/13.64 11[0:Inp] || -> totalorderP(nil)*.
% 13.47/13.64 12[0:Inp] || -> strictorderP(nil)*.
% 13.47/13.64 13[0:Inp] || -> totalorderedP(nil)*.
% 13.47/13.64 14[0:Inp] || -> strictorderedP(nil)*.
% 13.47/13.64 15[0:Inp] || -> duplicatefreeP(nil)*.
% 13.47/13.64 16[0:Inp] || -> equalelemsP(nil)*.
% 13.47/13.64 17[0:Inp] || -> ssItem(skf47(u))*.
% 13.47/13.64 55[0:Inp] || -> ssItem(skf44(u,v))*.
% 13.47/13.64 56[0:Inp] || neq(skc10,skc11)* -> .
% 13.47/13.64 57[0:Inp] || equal(skc15,skc14)** -> .
% 13.47/13.64 73[0:Inp] || SkP0(skc9,skc8)* -> equal(nil,skc8).
% 13.47/13.64 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 13.47/13.64 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 13.47/13.64 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 13.47/13.64 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 13.47/13.64 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 13.47/13.64 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 13.47/13.64 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 13.47/13.64 84[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 13.47/13.64 90[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 13.47/13.64 94[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 13.47/13.64 95[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 13.47/13.64 109[0:Inp] ssItem(u) ssItem(v) || -> neq(v,u)* equal(v,u).
% 13.47/13.64 110[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 13.47/13.64 114[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 13.47/13.64 116[0:Inp] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8)**.
% 13.47/13.64 125[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 13.47/13.64 132[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 13.47/13.64 137[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 13.47/13.64 163[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 13.47/13.64 192[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).
% 13.47/13.64 197[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) ssItem(y) ssItem(z) duplicatefreeP(u) || equal(z,y) equal(app(app(x,cons(z,w)),cons(y,v)),u)* -> .
% 13.47/13.64 249[0:Res:6.0,137.0] ssList(u) || -> equal(nil,skc8) equal(hd(app(skc8,u)),hd(skc8))**.
% 13.47/13.64 260[0:Res:6.0,114.0] ssItem(u) || -> equal(hd(cons(u,skc8)),u)**.
% 13.47/13.64 272[0:Res:6.0,94.0] ssItem(u) || -> ssList(cons(u,skc8))*.
% 13.47/13.64 290[0:Res:6.0,192.1] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u) equal(nil,skc8).
% 13.47/13.64 555[1:Spt:249.0,249.2] ssList(u) || -> equal(hd(app(skc8,u)),hd(skc8))**.
% 13.47/13.64 1624[2:Spt:290.5] || -> equal(nil,skc8)**.
% 13.47/13.64 1660[2:Rew:1624.0,75.1] ssItem(u) || -> cyclefreeP(cons(u,skc8))*.
% 13.47/13.64 1661[2:Rew:1624.0,76.1] ssItem(u) || -> totalorderP(cons(u,skc8))*.
% 13.47/13.64 1662[2:Rew:1624.0,77.1] ssItem(u) || -> strictorderP(cons(u,skc8))*.
% 13.47/13.64 1663[2:Rew:1624.0,78.1] ssItem(u) || -> totalorderedP(cons(u,skc8))*.
% 13.47/13.64 1664[2:Rew:1624.0,79.1] ssItem(u) || -> strictorderedP(cons(u,skc8))*.
% 13.47/13.64 1665[2:Rew:1624.0,80.1] ssItem(u) || -> duplicatefreeP(cons(u,skc8))*.
% 13.47/13.64 1666[2:Rew:1624.0,81.1] ssItem(u) || -> equalelemsP(cons(u,skc8))*.
% 13.47/13.64 1672[2:Rew:1624.0,84.1] ssList(u) || -> equal(app(skc8,u),u)**.
% 13.47/13.64 1752[2:Rew:1672.1,555.1] ssList(u) || -> equal(hd(u),hd(skc8))*.
% 13.47/13.64 1825[2:SpR:1752.1,260.1] ssList(cons(u,skc8)) ssItem(u) || -> equal(hd(skc8),u)*.
% 13.47/13.64 1834[2:SSi:1825.0,272.1,1660.1,1661.1,1662.1,1663.1,1664.1,1665.1,1666.1] ssItem(u) || -> equal(hd(skc8),u)*.
% 13.47/13.64 1852[2:SpR:1834.1,1834.1] ssItem(u) ssItem(v) || -> equal(u,v)*.
% 13.47/13.64 2041[2:EmS:1852.0,8.0] ssItem(u) || -> equal(skc14,u)*.
% 13.47/13.64 2066[2:EmS:2041.0,7.0] || -> equal(skc15,skc14)**.
% 13.47/13.64 2069[2:MRR:2066.0,57.0] || -> .
% 13.47/13.64 2285[2:Spt:2069.0,290.5,1624.0] || equal(nil,skc8)** -> .
% 13.47/13.64 2286[2:Spt:2069.0,290.0,290.1,290.2,290.3,290.4] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u).
% 13.47/13.64 2292[2:MRR:73.1,2285.0] || SkP0(skc9,skc8)* -> .
% 13.47/13.64 2410[0:SpR:90.1,81.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 13.47/13.64 2418[0:SSi:2410.0,55.0] || -> SkP0(u,v)* equalelemsP(v).
% 13.47/13.64 2426[2:Res:2418.0,2292.0] || -> equalelemsP(skc8)*.
% 13.47/13.64 2492[0:SpR:110.2,80.1] ssList(u) singletonP(u) ssItem(skf47(u)) || -> duplicatefreeP(u)*.
% 13.47/13.64 2503[0:SSi:2492.2,17.0] ssList(u) singletonP(u) || -> duplicatefreeP(u)*.
% 13.47/13.64 2568[0:SpR:90.1,114.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 13.47/13.64 2572[0:SSi:2568.1,2568.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,55.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 13.47/13.64 2574[0:Rew:2572.1,90.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 13.47/13.64 2638[0:SpR:2572.1,55.0] || -> SkP0(u,v)* ssItem(hd(v)).
% 13.47/13.64 2719[0:Res:109.2,56.0] ssItem(skc11) ssItem(skc10) || -> equal(skc11,skc10)**.
% 13.47/13.64 2720[0:SSi:2719.1,2719.0,4.0,3.0] || -> equal(skc11,skc10)**.
% 13.47/13.64 2723[0:Rew:2720.0,116.0] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc10,nil)),skc13),skc8)**.
% 13.47/13.64 3144[0:EqR:125.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 13.47/13.64 3149[0:SSi:3144.0,81.0,80.0,79.0,78.0,77.0,76.0,75.0,94.0,16.2,15.1,14.1,13.1,12.1,11.1,10.1,9.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 13.47/13.64 3200[0:SpR:2574.1,3149.1] ssItem(hd(u)) || -> SkP0(v,u)* singletonP(u).
% 13.47/13.64 3202[0:MRR:3200.0,2638.1] || -> SkP0(u,v)* singletonP(v).
% 13.47/13.64 3205[2:Res:3202.0,2292.0] || -> singletonP(skc8)*.
% 13.47/13.64 5191[0:SpR:163.3,2723.0] ssList(skc13) ssList(cons(skc10,nil)) ssList(app(skc12,cons(skc10,nil))) || -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8)**.
% 13.47/13.64 5248[0:SSi:5191.2,5191.1,5191.0,95.0,2.0,81.0,4.0,80.0,4.0,79.0,4.0,78.0,4.0,77.2,4.0,76.1,4.0,75.1,4.0,3149.1,4.0,94.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,81.0,4.0,80.0,4.0,79.0,4.0,78.0,4.0,77.2,4.0,76.1,4.0,75.1,4.0,3149.1,4.0,94.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,1.2] || -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8)**.
% 13.47/13.64 10560[0:SpR:132.2,5248.0] ssItem(skc10) ssList(skc13) || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 13.47/13.64 10574[0:SSi:10560.1,10560.0,1.0,4.0] || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 13.47/13.64 13934[0:SpL:10574.0,197.8] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) ssItem(skc10) duplicatefreeP(u) || equal(skc10,skc10)* equal(skc8,u)* -> .
% 13.47/13.64 13952[0:Obv:13934.7] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) duplicatefreeP(u) || equal(skc8,u)* -> .
% 13.47/13.64 13953[0:SSi:13952.4,13952.3,13952.2,13952.1,4.0,2.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,1.0] ssList(u) duplicatefreeP(u) || equal(skc8,u)* -> .
% 13.47/13.64 14016[0:EmS:13953.0,13953.1,6.0,2503.2] singletonP(skc8) ssList(skc8) || equal(skc8,skc8)* -> .
% 13.47/13.64 14020[0:EmS:13953.0,13953.1,9.0,15.0] || equal(nil,skc8)** -> .
% 13.47/13.64 15574[0:Obv:14016.2] singletonP(skc8) ssList(skc8) || -> .
% 13.47/13.64 15575[2:SSi:15574.1,6.0,2426.0] singletonP(skc8) || -> .
% 13.47/13.64 15576[2:MRR:15575.0,3205.0] || -> .
% 13.47/13.64 15753[1:Spt:15576.0,249.1] || -> equal(nil,skc8)**.
% 13.47/13.64 16209[1:Rew:15753.0,14020.0] || equal(skc8,skc8)* -> .
% 13.47/13.64 16210[1:Obv:16209.0] || -> .
% 13.47/13.64 % SZS output end Refutation
% 13.47/13.64 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax4 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax16 ax26 ax1 ax23 ax81 ax85 ax82 ax77 ax13
% 13.47/13.64
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