TSTP Solution File: SWC218+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC218+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 22:02:33 EDT 2022
% Result : Theorem 1.28s 1.46s
% Output : Refutation 1.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC218+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 20:06:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.28/1.46
% 1.28/1.46 SPASS V 3.9
% 1.28/1.46 SPASS beiseite: Proof found.
% 1.28/1.46 % SZS status Theorem
% 1.28/1.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.28/1.46 SPASS derived 2211 clauses, backtracked 1057 clauses, performed 21 splits and kept 2207 clauses.
% 1.28/1.46 SPASS allocated 100509 KBytes.
% 1.28/1.46 SPASS spent 0:00:01.08 on the problem.
% 1.28/1.46 0:00:00.04 for the input.
% 1.28/1.46 0:00:00.07 for the FLOTTER CNF translation.
% 1.28/1.46 0:00:00.01 for inferences.
% 1.28/1.46 0:00:00.01 for the backtracking.
% 1.28/1.46 0:00:00.73 for the reduction.
% 1.28/1.46
% 1.28/1.46
% 1.28/1.46 Here is a proof with depth 6, length 101 :
% 1.28/1.46 % SZS output start Refutation
% 1.28/1.46 1[0:Inp] || -> ssItem(skc11)*.
% 1.28/1.46 2[0:Inp] || -> ssList(skc10)*.
% 1.28/1.46 3[0:Inp] || -> ssList(skc9)*.
% 1.28/1.46 4[0:Inp] || -> ssList(skc8)*.
% 1.28/1.46 5[0:Inp] || -> ssList(skc7)*.
% 1.28/1.46 6[0:Inp] || -> ssItem(skc13)*.
% 1.28/1.46 7[0:Inp] || -> ssItem(skc12)*.
% 1.28/1.46 8[0:Inp] || -> ssList(nil)*.
% 1.28/1.46 9[0:Inp] || -> cyclefreeP(nil)*.
% 1.28/1.46 10[0:Inp] || -> totalorderP(nil)*.
% 1.28/1.46 11[0:Inp] || -> strictorderP(nil)*.
% 1.28/1.46 12[0:Inp] || -> totalorderedP(nil)*.
% 1.28/1.46 13[0:Inp] || -> strictorderedP(nil)*.
% 1.28/1.46 14[0:Inp] || -> duplicatefreeP(nil)*.
% 1.28/1.46 15[0:Inp] || -> equalelemsP(nil)*.
% 1.28/1.46 54[0:Inp] || neq(skc7,nil)* -> .
% 1.28/1.46 55[0:Inp] || equal(skc13,skc12)** -> .
% 1.28/1.46 62[0:Inp] || -> equal(app(skc9,skc10),skc8)**.
% 1.28/1.46 72[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 1.28/1.46 73[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 1.28/1.46 74[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 1.28/1.46 75[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 1.28/1.46 76[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 1.28/1.46 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 1.28/1.46 78[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 1.28/1.46 80[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 1.28/1.46 81[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 1.28/1.46 82[0:Inp] || -> equal(app(app(skc9,cons(skc11,nil)),skc10),skc7)**.
% 1.28/1.46 90[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 1.28/1.46 91[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 1.28/1.46 107[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 1.28/1.46 108[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),v)** -> .
% 1.28/1.46 110[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 1.28/1.46 120[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 1.28/1.46 128[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,u).
% 1.28/1.46 129[0:Inp] ssList(u) ssList(v) || equal(app(v,u),nil)** -> equal(nil,v).
% 1.28/1.46 132[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 1.28/1.46 186[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).
% 1.28/1.46 242[0:Res:5.0,132.0] ssList(u) || -> equal(skc7,nil) equal(hd(app(skc7,u)),hd(skc7))**.
% 1.28/1.46 250[0:Res:5.0,107.0] ssList(u) || -> neq(skc7,u)* equal(skc7,u).
% 1.28/1.46 253[0:Res:5.0,110.0] ssItem(u) || -> equal(hd(cons(u,skc7)),u)**.
% 1.28/1.46 265[0:Res:5.0,90.0] ssItem(u) || -> ssList(cons(u,skc7))*.
% 1.28/1.46 283[0:Res:5.0,186.1] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u) equal(skc7,nil).
% 1.28/1.46 413[0:Res:4.0,132.0] ssList(u) || -> equal(skc8,nil) equal(hd(app(skc8,u)),hd(skc8))**.
% 1.28/1.46 542[1:Spt:242.0,242.2] ssList(u) || -> equal(hd(app(skc7,u)),hd(skc7))**.
% 1.28/1.46 550[2:Spt:283.5] || -> equal(skc7,nil)**.
% 1.28/1.46 551[2:Rew:550.0,542.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 1.28/1.46 567[2:Rew:550.0,265.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 1.28/1.46 568[2:Rew:550.0,253.1] ssItem(u) || -> equal(hd(cons(u,nil)),u)**.
% 1.28/1.46 722[2:Rew:80.1,551.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 1.28/1.46 1180[2:SpR:568.1,722.1] ssItem(u) ssList(cons(u,nil)) || -> equal(u,hd(nil))*.
% 1.28/1.46 1183[2:SSi:1180.1,78.1,77.1,74.1,73.1,72.1,76.1,75.1,567.1] ssItem(u) || -> equal(u,hd(nil))*.
% 1.28/1.46 1254[2:SpR:1183.1,1183.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 1.28/1.46 1296[2:EmS:1254.0,1.0] ssItem(u) || -> equal(u,skc11)*.
% 1.28/1.46 1318[2:EmS:1296.0,6.0] || -> equal(skc13,skc11)**.
% 1.28/1.46 1319[2:EmS:1296.0,7.0] || -> equal(skc12,skc11)**.
% 1.28/1.46 1321[2:Rew:1318.0,55.0] || equal(skc12,skc11)** -> .
% 1.28/1.46 1430[2:Rew:1319.0,1321.0] || equal(skc11,skc11)* -> .
% 1.28/1.46 1431[2:Obv:1430.0] || -> .
% 1.28/1.46 1462[2:Spt:1431.0,283.5,550.0] || equal(skc7,nil)** -> .
% 1.28/1.46 1463[2:Spt:1431.0,283.0,283.1,283.2,283.3,283.4] ssList(u) || equal(tl(skc7),tl(u))* equal(hd(skc7),hd(u)) -> equal(nil,u) equal(skc7,u).
% 1.28/1.46 1821[0:Res:250.1,54.0] ssList(nil) || -> equal(skc7,nil)**.
% 1.28/1.46 1822[0:SSi:1821.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0] || -> equal(skc7,nil)**.
% 1.28/1.46 1823[2:MRR:1822.0,1462.0] || -> .
% 1.28/1.46 1824[1:Spt:1823.0,242.1] || -> equal(skc7,nil)**.
% 1.28/1.46 1836[0:Rew:1822.0,82.0] || -> equal(app(app(skc9,cons(skc11,nil)),skc10),nil)**.
% 1.28/1.46 1839[0:Rew:1822.0,265.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 1.28/1.46 2068[2:Spt:413.1] || -> equal(skc8,nil)**.
% 1.28/1.46 2078[2:Rew:2068.0,62.0] || -> equal(app(skc9,skc10),nil)**.
% 1.28/1.46 2647[0:EqR:120.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.28/1.46 2649[0:SSi:2647.0,78.1,77.1,74.1,73.1,72.1,76.1,75.1,1839.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 1.28/1.46 2864[2:SpL:2078.0,128.2] ssList(skc10) ssList(skc9) || equal(nil,nil) -> equal(skc10,nil)**.
% 1.28/1.46 2869[2:Obv:2864.2] ssList(skc10) ssList(skc9) || -> equal(skc10,nil)**.
% 1.28/1.46 2870[2:SSi:2869.1,2869.0,3.0,2.0] || -> equal(skc10,nil)**.
% 1.28/1.46 2872[2:Rew:2870.0,2078.0] || -> equal(app(skc9,nil),nil)**.
% 1.28/1.46 2873[2:Rew:2870.0,1836.0] || -> equal(app(app(skc9,cons(skc11,nil)),nil),nil)**.
% 1.28/1.46 2983[2:SpR:2872.0,81.1] ssList(skc9) || -> equal(skc9,nil)**.
% 1.28/1.46 2989[2:SSi:2983.0,3.0] || -> equal(skc9,nil)**.
% 1.28/1.46 3024[2:Rew:2989.0,2873.0] || -> equal(app(app(nil,cons(skc11,nil)),nil),nil)**.
% 1.28/1.46 3095[2:SpR:80.1,3024.0] ssList(cons(skc11,nil)) || -> equal(app(cons(skc11,nil),nil),nil)**.
% 1.28/1.46 3097[2:Rew:81.1,3095.1] ssList(cons(skc11,nil)) || -> equal(cons(skc11,nil),nil)**.
% 1.28/1.46 3098[2:SSi:3097.0,78.0,1.1,77.0,1.1,74.0,1.1,73.0,1.1,72.0,1.1,76.0,1.1,75.0,1.1,1839.0,1.1,2649.0,1.1] || -> equal(cons(skc11,nil),nil)**.
% 1.28/1.46 3141[2:SpL:3098.0,108.2] ssItem(skc11) ssList(nil) || equal(nil,nil)* -> .
% 1.28/1.46 3150[2:Obv:3141.2] ssItem(skc11) ssList(nil) || -> .
% 1.28/1.46 3151[2:SSi:3150.1,3150.0,15.0,14.0,11.0,10.0,9.0,13.0,12.0,8.0,1.0] || -> .
% 1.28/1.46 3162[2:Spt:3151.0,413.1,2068.0] || equal(skc8,nil)** -> .
% 1.28/1.46 3163[2:Spt:3151.0,413.0,413.2] ssList(u) || -> equal(hd(app(skc8,u)),hd(skc8))**.
% 1.28/1.46 3210[0:SpL:1836.0,129.2] ssList(skc10) ssList(app(skc9,cons(skc11,nil))) || equal(nil,nil) -> equal(app(skc9,cons(skc11,nil)),nil)**.
% 1.28/1.46 3213[0:Obv:3210.2] ssList(skc10) ssList(app(skc9,cons(skc11,nil))) || -> equal(app(skc9,cons(skc11,nil)),nil)**.
% 1.28/1.46 3214[0:SSi:3213.1,3213.0,91.0,3.0,78.1,1.0,77.1,1.0,74.1,1.0,73.1,1.0,72.1,1.0,76.1,1.0,75.1,1.0,1839.1,1.0,2649.1,1.0,2.2] || -> equal(app(skc9,cons(skc11,nil)),nil)**.
% 1.28/1.46 3215[0:Rew:3214.0,1836.0] || -> equal(app(nil,skc10),nil)**.
% 1.28/1.46 3225[0:SpR:3215.0,80.1] ssList(skc10) || -> equal(skc10,nil)**.
% 1.28/1.46 3232[0:SSi:3225.0,2.0] || -> equal(skc10,nil)**.
% 1.28/1.46 3234[0:Rew:3232.0,62.0] || -> equal(app(skc9,nil),skc8)**.
% 1.28/1.46 3346[0:SpR:3234.0,81.1] ssList(skc9) || -> equal(skc9,skc8)**.
% 1.28/1.46 3353[0:SSi:3346.0,3.0] || -> equal(skc9,skc8)**.
% 1.28/1.46 3356[0:Rew:3353.0,3214.0] || -> equal(app(skc8,cons(skc11,nil)),nil)**.
% 1.28/1.46 3436[0:SpL:3356.0,129.2] ssList(cons(skc11,nil)) ssList(skc8) || equal(nil,nil) -> equal(skc8,nil)**.
% 1.28/1.46 3604[0:Obv:3436.2] ssList(cons(skc11,nil)) ssList(skc8) || -> equal(skc8,nil)**.
% 1.28/1.46 3605[0:SSi:3604.1,3604.0,4.0,78.1,1.0,77.1,1.0,74.1,1.0,73.1,1.0,72.1,1.0,76.1,1.0,75.1,1.0,1839.1,1.0,2649.1,1.0] || -> equal(skc8,nil)**.
% 1.28/1.46 3606[2:MRR:3605.0,3162.0] || -> .
% 1.28/1.46 % SZS output end Refutation
% 1.28/1.46 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax84 ax16 ax26 ax15 ax18 ax23 ax4 ax83 ax85 ax77
% 1.28/1.46
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