TSTP Solution File: SWC214+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC214+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 22:02:32 EDT 2022
% Result : Theorem 2.87s 3.06s
% Output : Refutation 2.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC214+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.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 16:02:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.87/3.06
% 2.87/3.06 SPASS V 3.9
% 2.87/3.06 SPASS beiseite: Proof found.
% 2.87/3.06 % SZS status Theorem
% 2.87/3.06 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.87/3.06 SPASS derived 4859 clauses, backtracked 1210 clauses, performed 43 splits and kept 3428 clauses.
% 2.87/3.06 SPASS allocated 105067 KBytes.
% 2.87/3.06 SPASS spent 0:00:02.52 on the problem.
% 2.87/3.06 0:00:00.04 for the input.
% 2.87/3.06 0:00:00.06 for the FLOTTER CNF translation.
% 2.87/3.06 0:00:00.05 for inferences.
% 2.87/3.06 0:00:00.05 for the backtracking.
% 2.87/3.06 0:00:02.14 for the reduction.
% 2.87/3.06
% 2.87/3.06
% 2.87/3.06 Here is a proof with depth 6, length 109 :
% 2.87/3.06 % SZS output start Refutation
% 2.87/3.06 1[0:Inp] || -> ssList(skc5)*.
% 2.87/3.06 2[0:Inp] || -> ssList(skc4)*.
% 2.87/3.06 4[0:Inp] || -> ssItem(skc7)*.
% 2.87/3.06 5[0:Inp] || -> ssItem(skc6)*.
% 2.87/3.06 6[0:Inp] || -> ssList(nil)*.
% 2.87/3.06 7[0:Inp] || -> cyclefreeP(nil)*.
% 2.87/3.06 8[0:Inp] || -> totalorderP(nil)*.
% 2.87/3.06 9[0:Inp] || -> strictorderP(nil)*.
% 2.87/3.06 10[0:Inp] || -> totalorderedP(nil)*.
% 2.87/3.06 11[0:Inp] || -> strictorderedP(nil)*.
% 2.87/3.06 12[0:Inp] || -> duplicatefreeP(nil)*.
% 2.87/3.06 13[0:Inp] || -> equalelemsP(nil)*.
% 2.87/3.06 14[0:Inp] || -> neq(skc5,nil)*.
% 2.87/3.06 15[0:Inp] || -> frontsegP(skc5,skc4)*.
% 2.87/3.06 54[0:Inp] || neq(skc4,nil)* -> .
% 2.87/3.06 55[0:Inp] || equal(skc7,skc6)** -> .
% 2.87/3.06 68[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 2.87/3.06 71[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 2.87/3.06 72[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 2.87/3.06 73[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 2.87/3.06 74[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 2.87/3.06 75[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 2.87/3.06 76[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 2.87/3.06 77[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 2.87/3.06 79[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 2.87/3.06 83[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 2.87/3.06 84[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 2.87/3.06 88[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 2.87/3.06 89[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 2.87/3.06 90[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 2.87/3.06 105[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 2.87/3.06 107[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 2.87/3.06 108[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 2.87/3.06 115[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 2.87/3.06 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 2.87/3.06 125[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 2.87/3.06 130[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 2.87/3.06 140[0:Inp] strictorderedP(u) ssList(u) || segmentP(u,skc4) neq(skc4,u) frontsegP(skc5,u)* -> .
% 2.87/3.06 141[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 2.87/3.06 185[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).
% 2.87/3.06 245[0:Res:2.0,130.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 2.87/3.06 253[0:Res:2.0,105.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 2.87/3.06 255[0:Res:2.0,107.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 2.87/3.06 268[0:Res:2.0,88.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 2.87/3.06 270[0:Res:2.0,90.0] || frontsegP(nil,skc4)* -> equal(skc4,nil).
% 2.87/3.06 286[0:Res:2.0,185.1] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u) equal(skc4,nil).
% 2.87/3.06 423[0:Res:1.0,115.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.87/3.06 428[0:Res:1.0,108.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 2.87/3.06 440[0:Res:1.0,88.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 2.87/3.06 448[0:Res:1.0,83.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 2.87/3.06 449[0:Res:1.0,84.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 2.87/3.06 458[0:Res:1.0,185.1] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u) equal(skc5,nil).
% 2.87/3.06 554[1:Spt:245.0,245.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 2.87/3.06 558[2:Spt:458.5] || -> equal(skc5,nil)**.
% 2.87/3.06 669[2:Rew:558.0,15.0] || -> frontsegP(nil,skc4)*.
% 2.87/3.06 670[2:Rew:558.0,14.0] || -> neq(nil,nil)*.
% 2.87/3.06 713[2:MRR:270.0,669.0] || -> equal(skc4,nil)**.
% 2.87/3.06 822[2:Rew:713.0,54.0] || neq(nil,nil)* -> .
% 2.87/3.06 865[2:MRR:822.0,670.0] || -> .
% 2.87/3.06 1060[2:Spt:865.0,458.5,558.0] || equal(skc5,nil)** -> .
% 2.87/3.06 1061[2:Spt:865.0,458.0,458.1,458.2,458.3,458.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 2.87/3.06 1076[3:Spt:286.5] || -> equal(skc4,nil)**.
% 2.87/3.06 1109[3:Rew:1076.0,554.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 2.87/3.06 1246[3:Rew:79.1,1109.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 2.87/3.06 1438[3:SpR:428.1,1246.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 2.87/3.06 1441[3:SSi:1438.1,440.1] ssItem(u) || -> equal(u,hd(nil))*.
% 2.87/3.06 1538[3:SpR:1441.1,1441.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 2.87/3.06 1767[3:EmS:1538.0,4.0] ssItem(u) || -> equal(u,skc7)*.
% 2.87/3.06 1793[3:EmS:1767.0,5.0] || -> equal(skc7,skc6)**.
% 2.87/3.06 1794[3:MRR:1793.0,55.0] || -> .
% 2.87/3.06 2048[3:Spt:1794.0,286.5,1076.0] || equal(skc4,nil)** -> .
% 2.87/3.06 2049[3:Spt:1794.0,286.0,286.1,286.2,286.3,286.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 2.87/3.06 2127[0:Res:253.1,54.0] ssList(nil) || -> equal(skc4,nil)**.
% 2.87/3.06 2129[0:SSi:2127.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc4,nil)**.
% 2.87/3.06 2130[3:MRR:2129.0,2048.0] || -> .
% 2.87/3.06 2131[1:Spt:2130.0,245.1] || -> equal(skc4,nil)**.
% 2.87/3.06 2132[0:Rew:2129.0,253.2] ssList(u) || -> neq(skc4,u)* equal(nil,u).
% 2.87/3.06 2142[0:Rew:2129.0,54.0] || neq(nil,nil)* -> .
% 2.87/3.06 2146[0:Rew:2129.0,268.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 2.87/3.06 2147[0:Rew:2129.0,255.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 2.87/3.06 2179[0:Rew:2129.0,140.3] strictorderedP(u) ssList(u) || segmentP(u,skc4) neq(nil,u) frontsegP(skc5,u)* -> .
% 2.87/3.06 2275[0:Rew:2129.0,2132.1] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 2.87/3.06 2357[0:Rew:2129.0,2179.2] strictorderedP(u) ssList(u) || segmentP(u,nil) neq(nil,u) frontsegP(skc5,u)* -> .
% 2.87/3.06 2358[0:MRR:2357.2,68.1] strictorderedP(u) ssList(u) || neq(nil,u) frontsegP(skc5,u)* -> .
% 2.87/3.06 2382[2:Spt:458.5] || -> equal(skc5,nil)**.
% 2.87/3.06 2385[2:Rew:2382.0,14.0] || -> neq(nil,nil)*.
% 2.87/3.06 2536[2:MRR:2385.0,2142.0] || -> .
% 2.87/3.06 2625[2:Spt:2536.0,458.5,2382.0] || equal(skc5,nil)** -> .
% 2.87/3.06 2626[2:Spt:2536.0,458.0,458.1,458.2,458.3,458.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 2.87/3.06 2627[2:MRR:449.1,2625.0] || -> ssList(tl(skc5))*.
% 2.87/3.06 2628[2:MRR:448.1,2625.0] || -> ssItem(hd(skc5))*.
% 2.87/3.06 2632[2:MRR:423.0,2625.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 2.87/3.06 3221[0:EqR:118.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 2.87/3.06 3223[0:SSi:3221.0,77.1,76.1,73.1,72.1,71.1,75.1,74.1,2146.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 2.87/3.06 4837[0:EqR:141.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 2.87/3.06 4856[0:SSi:4837.1,89.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 2.87/3.06 5526[0:SpR:125.2,4856.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 2.87/3.06 5545[0:Obv:5526.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 2.87/3.06 5546[0:SSi:5545.1,77.1,76.1,73.1,72.1,71.1,75.1,74.1,2146.1,3223.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 2.87/3.06 7197[2:SpR:2632.0,5546.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 2.87/3.06 7425[2:SSi:7197.1,2627.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 2.87/3.06 7426[2:MRR:7425.0,2628.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 2.87/3.06 7683[2:Res:7426.0,2358.3] strictorderedP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 2.87/3.06 7685[2:SSi:7683.1,7683.0,77.0,2628.1,76.0,2628.1,73.0,2628.1,72.0,2628.1,71.0,2628.1,75.0,2628.1,74.0,2628.1,2146.0,2628.1,3223.0,2628.1,77.0,2628.1,76.0,2628.1,73.0,2628.1,72.0,2628.1,71.0,2628.1,75.0,2628.1,74.0,2628.1,2146.0,2628.1,3223.0,2628.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 2.87/3.06 7742[2:Res:2275.1,7685.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 2.87/3.06 7745[2:SSi:7742.0,77.0,2628.1,76.0,2628.1,73.0,2628.1,72.0,2628.1,71.0,2628.1,75.0,2628.1,74.0,2628.1,2146.0,2628.1,3223.0,2628.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 2.87/3.06 7803[2:SpL:7745.0,2147.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 2.87/3.06 7826[2:Obv:7803.1] ssItem(hd(skc5)) || -> .
% 2.87/3.06 7827[2:SSi:7826.0,2628.0] || -> .
% 2.87/3.06 % SZS output end Refutation
% 2.87/3.06 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax46 ax15 ax21 ax23 ax78 ax4 ax81 ax85 ax5 ax77
% 2.87/3.06
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