TSTP Solution File: SWC169+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC169+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 22:02:12 EDT 2022
% Result : Theorem 13.25s 13.51s
% Output : Refutation 13.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC169+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n026.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 18:23:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 13.25/13.51
% 13.25/13.51 SPASS V 3.9
% 13.25/13.51 SPASS beiseite: Proof found.
% 13.25/13.51 % SZS status Theorem
% 13.25/13.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.25/13.51 SPASS derived 10094 clauses, backtracked 4339 clauses, performed 42 splits and kept 7780 clauses.
% 13.25/13.51 SPASS allocated 113004 KBytes.
% 13.25/13.51 SPASS spent 0:0:12.23 on the problem.
% 13.25/13.51 0:00:00.04 for the input.
% 13.25/13.51 0:00:00.06 for the FLOTTER CNF translation.
% 13.25/13.51 0:00:00.11 for inferences.
% 13.25/13.51 0:00:00.42 for the backtracking.
% 13.25/13.51 0:0:11.34 for the reduction.
% 13.25/13.51
% 13.25/13.51
% 13.25/13.51 Here is a proof with depth 6, length 97 :
% 13.25/13.51 % SZS output start Refutation
% 13.25/13.51 1[0:Inp] || -> ssList(skc13)*.
% 13.25/13.51 2[0:Inp] || -> ssList(skc12)*.
% 13.25/13.51 3[0:Inp] || -> ssItem(skc11)*.
% 13.25/13.51 4[0:Inp] || -> ssItem(skc10)*.
% 13.25/13.51 6[0:Inp] || -> ssList(skc8)*.
% 13.25/13.51 7[0:Inp] || -> ssItem(skc15)*.
% 13.25/13.51 8[0:Inp] || -> ssItem(skc14)*.
% 13.25/13.51 9[0:Inp] || -> ssList(nil)*.
% 13.25/13.51 10[0:Inp] || -> cyclefreeP(nil)*.
% 13.25/13.51 11[0:Inp] || -> totalorderP(nil)*.
% 13.25/13.51 12[0:Inp] || -> strictorderP(nil)*.
% 13.25/13.51 13[0:Inp] || -> totalorderedP(nil)*.
% 13.25/13.51 14[0:Inp] || -> strictorderedP(nil)*.
% 13.25/13.51 15[0:Inp] || -> duplicatefreeP(nil)*.
% 13.25/13.51 16[0:Inp] || -> equalelemsP(nil)*.
% 13.25/13.51 17[0:Inp] || -> ssItem(skf47(u))*.
% 13.25/13.51 55[0:Inp] || -> ssItem(skf44(u,v))*.
% 13.25/13.51 56[0:Inp] || neq(skc10,skc11)* -> .
% 13.25/13.51 57[0:Inp] || equal(skc15,skc14)** -> .
% 13.25/13.51 73[0:Inp] || SkP0(skc9,skc8)* -> equal(nil,skc8).
% 13.25/13.51 75[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 13.25/13.51 76[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 13.25/13.51 77[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 13.25/13.51 78[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 13.25/13.51 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 13.25/13.51 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 13.25/13.51 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 13.25/13.51 84[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 13.25/13.51 90[0:Inp] || -> SkP0(u,v) equal(cons(skf44(u,v),nil),v)**.
% 13.25/13.51 94[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 13.25/13.51 95[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 13.25/13.51 109[0:Inp] ssItem(u) ssItem(v) || -> neq(v,u)* equal(v,u).
% 13.25/13.51 110[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skf47(u),nil),u)**.
% 13.25/13.51 114[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 13.25/13.51 116[0:Inp] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc11,nil)),skc13),skc8)**.
% 13.25/13.51 125[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 13.25/13.51 132[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 13.25/13.51 137[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 13.25/13.51 163[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 13.25/13.51 191[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).
% 13.25/13.51 196[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)* -> .
% 13.25/13.51 248[0:Res:6.0,137.0] ssList(u) || -> equal(nil,skc8) equal(hd(app(skc8,u)),hd(skc8))**.
% 13.25/13.51 259[0:Res:6.0,114.0] ssItem(u) || -> equal(hd(cons(u,skc8)),u)**.
% 13.25/13.51 271[0:Res:6.0,94.0] ssItem(u) || -> ssList(cons(u,skc8))*.
% 13.25/13.51 289[0:Res:6.0,191.1] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u) equal(nil,skc8).
% 13.25/13.51 554[1:Spt:248.0,248.2] ssList(u) || -> equal(hd(app(skc8,u)),hd(skc8))**.
% 13.25/13.51 1622[2:Spt:289.5] || -> equal(nil,skc8)**.
% 13.25/13.51 1658[2:Rew:1622.0,75.1] ssItem(u) || -> cyclefreeP(cons(u,skc8))*.
% 13.25/13.51 1659[2:Rew:1622.0,76.1] ssItem(u) || -> totalorderP(cons(u,skc8))*.
% 13.25/13.51 1660[2:Rew:1622.0,77.1] ssItem(u) || -> strictorderP(cons(u,skc8))*.
% 13.25/13.51 1661[2:Rew:1622.0,78.1] ssItem(u) || -> totalorderedP(cons(u,skc8))*.
% 13.25/13.51 1662[2:Rew:1622.0,79.1] ssItem(u) || -> strictorderedP(cons(u,skc8))*.
% 13.25/13.51 1663[2:Rew:1622.0,80.1] ssItem(u) || -> duplicatefreeP(cons(u,skc8))*.
% 13.25/13.51 1664[2:Rew:1622.0,81.1] ssItem(u) || -> equalelemsP(cons(u,skc8))*.
% 13.25/13.51 1670[2:Rew:1622.0,84.1] ssList(u) || -> equal(app(skc8,u),u)**.
% 13.25/13.51 1750[2:Rew:1670.1,554.1] ssList(u) || -> equal(hd(u),hd(skc8))*.
% 13.25/13.51 1823[2:SpR:1750.1,259.1] ssList(cons(u,skc8)) ssItem(u) || -> equal(hd(skc8),u)*.
% 13.25/13.51 1832[2:SSi:1823.0,271.1,1658.1,1659.1,1660.1,1661.1,1662.1,1663.1,1664.1] ssItem(u) || -> equal(hd(skc8),u)*.
% 13.25/13.51 1850[2:SpR:1832.1,1832.1] ssItem(u) ssItem(v) || -> equal(u,v)*.
% 13.25/13.51 2038[2:EmS:1850.0,8.0] ssItem(u) || -> equal(skc14,u)*.
% 13.25/13.51 2063[2:EmS:2038.0,7.0] || -> equal(skc15,skc14)**.
% 13.25/13.51 2066[2:MRR:2063.0,57.0] || -> .
% 13.25/13.51 2282[2:Spt:2066.0,289.5,1622.0] || equal(nil,skc8)** -> .
% 13.25/13.51 2283[2:Spt:2066.0,289.0,289.1,289.2,289.3,289.4] ssList(u) || equal(tl(skc8),tl(u))* equal(hd(skc8),hd(u)) -> equal(nil,u) equal(skc8,u).
% 13.25/13.51 2289[2:MRR:73.1,2282.0] || SkP0(skc9,skc8)* -> .
% 13.25/13.51 2407[0:SpR:90.1,81.1] ssItem(skf44(u,v)) || -> SkP0(u,v)* equalelemsP(v).
% 13.25/13.51 2415[0:SSi:2407.0,55.0] || -> SkP0(u,v)* equalelemsP(v).
% 13.25/13.51 2423[2:Res:2415.0,2289.0] || -> equalelemsP(skc8)*.
% 13.25/13.51 2489[0:SpR:110.2,80.1] ssList(u) singletonP(u) ssItem(skf47(u)) || -> duplicatefreeP(u)*.
% 13.25/13.51 2500[0:SSi:2489.2,17.0] ssList(u) singletonP(u) || -> duplicatefreeP(u)*.
% 13.25/13.51 2565[0:SpR:90.1,114.2] ssItem(skf44(u,v)) ssList(nil) || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 13.25/13.51 2569[0:SSi:2565.1,2565.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,55.0] || -> SkP0(u,v) equal(skf44(u,v),hd(v))**.
% 13.25/13.51 2571[0:Rew:2569.1,90.1] || -> SkP0(u,v)* equal(cons(hd(v),nil),v)**.
% 13.25/13.51 2633[0:SpR:2569.1,55.0] || -> SkP0(u,v)* ssItem(hd(v))*.
% 13.25/13.51 2718[0:Res:109.2,56.0] ssItem(skc11) ssItem(skc10) || -> equal(skc11,skc10)**.
% 13.25/13.51 2719[0:SSi:2718.1,2718.0,4.0,3.0] || -> equal(skc11,skc10)**.
% 13.25/13.51 2722[0:Rew:2719.0,116.0] || -> equal(app(app(app(skc12,cons(skc10,nil)),cons(skc10,nil)),skc13),skc8)**.
% 13.25/13.51 3146[0:EqR:125.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 13.25/13.51 3151[0:SSi:3146.0,81.0,80.0,79.0,78.0,77.0,76.0,75.0,94.0,16.2,15.1,14.1,13.1,12.1,11.1,10.1,9.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 13.25/13.51 3202[0:SpR:2571.1,3151.1] ssItem(hd(u)) || -> SkP0(v,u)* singletonP(u).
% 13.25/13.51 3204[0:MRR:3202.0,2633.1] || -> SkP0(u,v)* singletonP(v).
% 13.25/13.51 3207[2:Res:3204.0,2289.0] || -> singletonP(skc8)*.
% 13.25/13.51 5182[0:SpR:163.3,2722.0] 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)**.
% 13.25/13.51 5239[0:SSi:5182.2,5182.1,5182.0,95.0,2.0,81.0,4.0,80.0,4.0,79.0,4.0,78.0,4.0,77.2,4.0,76.1,4.0,75.1,4.0,3151.1,4.0,94.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,81.0,4.0,80.0,4.0,79.0,4.0,78.0,4.0,77.2,4.0,76.1,4.0,75.1,4.0,3151.1,4.0,94.1,4.0,16.1,15.0,14.1,13.0,12.1,11.0,10.1,9.0,1.2] || -> equal(app(app(skc12,cons(skc10,nil)),app(cons(skc10,nil),skc13)),skc8)**.
% 13.25/13.51 10531[0:SpR:132.2,5239.0] ssItem(skc10) ssList(skc13) || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 13.25/13.51 10545[0:SSi:10531.1,10531.0,1.0,4.0] || -> equal(app(app(skc12,cons(skc10,nil)),cons(skc10,skc13)),skc8)**.
% 13.25/13.51 13905[0:SpL:10545.0,196.8] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) ssItem(skc10) duplicatefreeP(u) || equal(skc10,skc10)* equal(skc8,u)* -> .
% 13.25/13.51 13923[0:Obv:13905.7] ssList(u) ssList(skc13) ssList(nil) ssList(skc12) ssItem(skc10) duplicatefreeP(u) || equal(skc8,u)* -> .
% 13.25/13.51 13924[0:SSi:13923.4,13923.3,13923.2,13923.1,4.0,2.0,16.0,15.0,14.0,13.0,12.0,11.0,10.0,9.0,1.0] ssList(u) duplicatefreeP(u) || equal(skc8,u)* -> .
% 13.25/13.51 13987[0:EmS:13924.0,13924.1,6.0,2500.2] singletonP(skc8) ssList(skc8) || equal(skc8,skc8)* -> .
% 13.25/13.51 13991[0:EmS:13924.0,13924.1,9.0,15.0] || equal(nil,skc8)** -> .
% 13.25/13.51 15545[0:Obv:13987.2] singletonP(skc8) ssList(skc8) || -> .
% 13.25/13.51 15546[2:SSi:15545.1,6.0,2423.0] singletonP(skc8) || -> .
% 13.25/13.51 15547[2:MRR:15546.0,3207.0] || -> .
% 13.25/13.51 15724[1:Spt:15547.0,248.1] || -> equal(nil,skc8)**.
% 13.25/13.51 16177[1:Rew:15724.0,13991.0] || equal(skc8,skc8)* -> .
% 13.25/13.51 16178[1:Obv:16177.0] || -> .
% 13.25/13.51 % SZS output end Refutation
% 13.25/13.51 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
% 13.25/13.51
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