TSTP Solution File: SWC125+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC125+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 22:01:53 EDT 2022
% Result : Theorem 44.61s 44.81s
% Output : Refutation 50.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC125+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n028.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 01:57:06 EDT 2022
% 0.14/0.35 % CPUTime :
% 44.61/44.81
% 44.61/44.81 SPASS V 3.9
% 44.61/44.81 SPASS beiseite: Proof found.
% 44.61/44.81 % SZS status Theorem
% 44.61/44.81 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.61/44.81 SPASS derived 20958 clauses, backtracked 8193 clauses, performed 74 splits and kept 12190 clauses.
% 44.61/44.81 SPASS allocated 129645 KBytes.
% 44.61/44.81 SPASS spent 0:0:44.41 on the problem.
% 44.61/44.81 0:00:00.04 for the input.
% 44.61/44.81 0:00:00.07 for the FLOTTER CNF translation.
% 44.61/44.81 0:00:00.35 for inferences.
% 44.61/44.81 0:00:01.55 for the backtracking.
% 44.61/44.81 0:0:41.98 for the reduction.
% 44.61/44.81
% 44.61/44.81
% 44.61/44.81 Here is a proof with depth 7, length 125 :
% 44.61/44.81 % SZS output start Refutation
% 44.61/44.81 1[0:Inp] || -> ssList(skc5)*.
% 44.61/44.81 2[0:Inp] || -> ssList(skc4)*.
% 44.61/44.81 4[0:Inp] || -> ssItem(skc7)*.
% 44.61/44.81 5[0:Inp] || -> ssItem(skc6)*.
% 44.61/44.81 6[0:Inp] || -> ssList(nil)*.
% 44.61/44.81 7[0:Inp] || -> cyclefreeP(nil)*.
% 44.61/44.81 8[0:Inp] || -> totalorderP(nil)*.
% 44.61/44.81 9[0:Inp] || -> strictorderP(nil)*.
% 44.61/44.81 10[0:Inp] || -> totalorderedP(nil)*.
% 44.61/44.81 11[0:Inp] || -> strictorderedP(nil)*.
% 44.61/44.81 12[0:Inp] || -> duplicatefreeP(nil)*.
% 44.61/44.81 13[0:Inp] || -> equalelemsP(nil)*.
% 44.61/44.81 14[0:Inp] || -> neq(skc5,nil)*.
% 44.61/44.81 15[0:Inp] || -> segmentP(skc5,skc4)*.
% 44.61/44.81 54[0:Inp] || equal(skc7,skc6)** -> .
% 44.61/44.81 57[0:Inp] || -> ssList(skf46(u,v))*.
% 44.61/44.81 67[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 44.61/44.81 70[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 44.61/44.81 71[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 44.61/44.81 72[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 44.61/44.81 73[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 44.61/44.81 74[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 44.61/44.81 75[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 44.61/44.81 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 44.61/44.81 78[0:Inp] || neq(skc4,nil) segmentP(skc5,skc4)* -> .
% 44.61/44.81 79[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 44.61/44.81 83[0:Inp] ssList(u) || -> ssItem(hd(u))* equal(nil,u).
% 44.61/44.81 84[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 44.61/44.81 88[0:Inp] ssItem(u) ssList(v) || -> ssList(cons(u,v))*.
% 44.61/44.81 89[0:Inp] ssList(u) ssList(v) || -> ssList(app(v,u))*.
% 44.61/44.81 94[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 44.61/44.81 105[0:Inp] ssList(u) ssList(v) || -> neq(v,u)* equal(v,u).
% 44.61/44.81 107[0:Inp] ssItem(u) ssList(v) || equal(cons(u,v),nil)** -> .
% 44.61/44.81 108[0:Inp] ssItem(u) ssList(v) || -> equal(hd(cons(u,v)),u)**.
% 44.61/44.81 115[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 44.61/44.81 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 44.61/44.81 125[0:Inp] ssItem(u) ssList(v) || -> equal(app(cons(u,nil),v),cons(u,v))**.
% 44.61/44.81 130[0:Inp] ssList(u) ssList(v) || -> equal(nil,v) equal(hd(app(v,u)),hd(v))**.
% 44.61/44.81 133[0:Inp] ssList(u) ssList(v) || frontsegP(v,u) -> equal(app(u,skf46(v,u)),v)**.
% 44.61/44.81 140[0:Inp] strictorderedP(u) ssList(u) || segmentP(u,skc4)* neq(skc4,u) segmentP(skc5,u)* -> .
% 44.61/44.81 141[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(u,w),v)*+ -> frontsegP(v,u)*.
% 44.61/44.81 157[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(w,v),u),app(w,app(v,u)))**.
% 44.61/44.81 183[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(u,x),v),w)* -> segmentP(w,x)*.
% 44.61/44.81 185[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).
% 44.61/44.81 194[0:MRR:78.1,15.0] || neq(skc4,nil)* -> .
% 44.61/44.81 199[0:Rew:157.3,183.4] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(x,app(u,w)),v)*+ -> segmentP(v,u)*.
% 44.61/44.81 246[0:Res:2.0,130.0] ssList(u) || -> equal(skc4,nil) equal(hd(app(skc4,u)),hd(skc4))**.
% 44.61/44.81 254[0:Res:2.0,105.0] ssList(u) || -> neq(skc4,u)* equal(skc4,u).
% 44.61/44.81 256[0:Res:2.0,107.0] ssItem(u) || equal(cons(u,skc4),nil)** -> .
% 44.61/44.81 269[0:Res:2.0,88.0] ssItem(u) || -> ssList(cons(u,skc4))*.
% 44.61/44.81 275[0:Res:2.0,94.0] || segmentP(nil,skc4)* -> equal(skc4,nil).
% 44.61/44.81 287[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).
% 44.61/44.81 413[0:Res:1.0,133.0] ssList(u) || frontsegP(skc5,u) -> equal(app(u,skf46(skc5,u)),skc5)**.
% 44.61/44.81 424[0:Res:1.0,115.0] || -> equal(skc5,nil) equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 44.61/44.81 429[0:Res:1.0,108.0] ssItem(u) || -> equal(hd(cons(u,skc5)),u)**.
% 44.61/44.81 441[0:Res:1.0,88.0] ssItem(u) || -> ssList(cons(u,skc5))*.
% 44.61/44.81 449[0:Res:1.0,83.0] || -> ssItem(hd(skc5))* equal(skc5,nil).
% 44.61/44.81 450[0:Res:1.0,84.0] || -> ssList(tl(skc5))* equal(skc5,nil).
% 44.61/44.81 459[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).
% 44.61/44.81 555[1:Spt:246.0,246.2] ssList(u) || -> equal(hd(app(skc4,u)),hd(skc4))**.
% 44.61/44.81 559[2:Spt:459.5] || -> equal(skc5,nil)**.
% 44.61/44.81 670[2:Rew:559.0,15.0] || -> segmentP(nil,skc4)*.
% 44.61/44.81 671[2:Rew:559.0,14.0] || -> neq(nil,nil)*.
% 44.61/44.81 714[2:MRR:275.0,670.0] || -> equal(skc4,nil)**.
% 44.61/44.81 823[2:Rew:714.0,194.0] || neq(nil,nil)* -> .
% 44.61/44.81 866[2:MRR:823.0,671.0] || -> .
% 44.61/44.81 1061[2:Spt:866.0,459.5,559.0] || equal(skc5,nil)** -> .
% 44.61/44.81 1062[2:Spt:866.0,459.0,459.1,459.2,459.3,459.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 44.61/44.81 1077[3:Spt:287.5] || -> equal(skc4,nil)**.
% 44.61/44.81 1111[3:Rew:1077.0,555.1] ssList(u) || -> equal(hd(app(nil,u)),hd(nil))**.
% 44.61/44.81 1247[3:Rew:79.1,1111.1] ssList(u) || -> equal(hd(u),hd(nil))*.
% 44.61/44.81 1437[3:SpR:429.1,1247.1] ssItem(u) ssList(cons(u,skc5)) || -> equal(u,hd(nil))*.
% 44.61/44.81 1440[3:SSi:1437.1,441.1] ssItem(u) || -> equal(u,hd(nil))*.
% 44.61/44.81 1537[3:SpR:1440.1,1440.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 44.61/44.81 1766[3:EmS:1537.0,4.0] ssItem(u) || -> equal(u,skc7)*.
% 44.61/44.81 1792[3:EmS:1766.0,5.0] || -> equal(skc7,skc6)**.
% 44.61/44.81 1793[3:MRR:1792.0,54.0] || -> .
% 44.61/44.81 2047[3:Spt:1793.0,287.5,1077.0] || equal(skc4,nil)** -> .
% 44.61/44.81 2048[3:Spt:1793.0,287.0,287.1,287.2,287.3,287.4] ssList(u) || equal(tl(skc4),tl(u))* equal(hd(skc4),hd(u)) -> equal(nil,u) equal(skc4,u).
% 44.61/44.81 2864[0:Res:254.1,194.0] ssList(nil) || -> equal(skc4,nil)**.
% 44.61/44.81 2866[0:SSi:2864.0,13.0,12.0,9.0,8.0,7.0,11.0,10.0,6.0] || -> equal(skc4,nil)**.
% 44.61/44.81 2867[3:MRR:2866.0,2047.0] || -> .
% 44.61/44.81 2868[1:Spt:2867.0,246.1] || -> equal(skc4,nil)**.
% 44.61/44.81 2869[0:Rew:2866.0,254.2] ssList(u) || -> neq(skc4,u)* equal(nil,u).
% 44.61/44.81 2878[0:Rew:2866.0,194.0] || neq(nil,nil)* -> .
% 44.61/44.81 2884[0:Rew:2866.0,269.1] ssItem(u) || -> ssList(cons(u,nil))*.
% 44.61/44.81 2885[0:Rew:2866.0,256.1] ssItem(u) || equal(cons(u,nil),nil)** -> .
% 44.61/44.81 2916[0:Rew:2866.0,140.3] strictorderedP(u) ssList(u) || segmentP(u,skc4)* neq(nil,u) segmentP(skc5,u)* -> .
% 44.61/44.81 3013[0:Rew:2866.0,2869.1] ssList(u) || -> neq(nil,u)* equal(nil,u).
% 44.61/44.81 3093[0:Rew:2866.0,2916.2] strictorderedP(u) ssList(u) || segmentP(u,nil)* neq(nil,u) segmentP(skc5,u)* -> .
% 44.61/44.81 3094[0:MRR:3093.2,67.1] strictorderedP(u) ssList(u) || neq(nil,u) segmentP(skc5,u)* -> .
% 44.61/44.81 3118[2:Spt:459.5] || -> equal(skc5,nil)**.
% 44.61/44.81 3120[2:Rew:3118.0,14.0] || -> neq(nil,nil)*.
% 44.61/44.81 3272[2:MRR:3120.0,2878.0] || -> .
% 44.61/44.81 3362[2:Spt:3272.0,459.5,3118.0] || equal(skc5,nil)** -> .
% 44.61/44.81 3363[2:Spt:3272.0,459.0,459.1,459.2,459.3,459.4] ssList(u) || equal(tl(skc5),tl(u))* equal(hd(skc5),hd(u)) -> equal(nil,u) equal(skc5,u).
% 44.61/44.81 3364[2:MRR:450.1,3362.0] || -> ssList(tl(skc5))*.
% 44.61/44.81 3365[2:MRR:449.1,3362.0] || -> ssItem(hd(skc5))*.
% 44.61/44.81 3369[2:MRR:424.0,3362.0] || -> equal(cons(hd(skc5),tl(skc5)),skc5)**.
% 44.61/44.81 3837[0:EqR:118.2] ssList(cons(u,nil)) ssItem(u) || -> singletonP(cons(u,nil))*.
% 44.61/44.81 3839[0:SSi:3837.0,76.1,75.1,72.1,71.1,70.1,74.1,73.1,2884.1] ssItem(u) || -> singletonP(cons(u,nil))*.
% 44.61/44.81 5221[0:EqR:141.3] ssList(u) ssList(app(u,v)) ssList(v) || -> frontsegP(app(u,v),u)*.
% 44.61/44.81 5237[0:SSi:5221.1,89.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 44.61/44.81 5690[0:SpR:125.2,5237.2] ssItem(u) ssList(v) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 44.61/44.81 5705[0:Obv:5690.1] ssItem(u) ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 44.61/44.81 5706[0:SSi:5705.1,76.1,75.1,72.1,71.1,70.1,74.1,73.1,2884.1,3839.1] ssItem(u) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 44.61/44.81 6715[2:SpR:3369.0,5706.2] ssItem(hd(skc5)) ssList(tl(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 44.61/44.81 7496[0:EqR:199.4] ssList(u) ssList(app(v,app(u,w))) ssList(w) ssList(v) || -> segmentP(app(v,app(u,w)),u)*.
% 44.61/44.81 7533[0:SSi:7496.1,89.2,89.2] ssList(u) ssList(v) ssList(w) || -> segmentP(app(w,app(u,v)),u)*.
% 44.61/44.81 16646[0:SpR:79.1,7533.3] ssList(app(u,v)) ssList(u) ssList(v) ssList(nil) || -> segmentP(app(u,v),u)*.
% 44.61/44.81 16664[0:SSi:16646.3,16646.0,13.2,12.0,9.0,8.0,7.0,11.0,10.0,6.0,89.0] ssList(u) ssList(v) || -> segmentP(app(u,v),u)*.
% 44.61/44.81 20225[0:SpR:413.2,16664.2] ssList(u) ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 44.61/44.81 20250[0:Obv:20225.0] ssList(u) ssList(skf46(skc5,u)) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 44.61/44.81 32833[2:SSi:6715.1,3364.0] ssItem(hd(skc5)) || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 50.73/50.90 32834[2:MRR:32833.0,3365.0] || -> frontsegP(skc5,cons(hd(skc5),nil))*.
% 50.73/50.90 32839[0:SSi:20250.1,57.0,1.0] ssList(u) || frontsegP(skc5,u)* -> segmentP(skc5,u).
% 50.73/50.90 35424[2:Res:32834.0,32839.1] ssList(cons(hd(skc5),nil)) || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 50.73/50.90 35430[2:SSi:35424.0,76.0,3365.1,75.0,3365.1,72.0,3365.1,71.0,3365.1,70.0,3365.1,74.0,3365.1,73.0,3365.1,2884.0,3365.1,3839.0,3365.1] || -> segmentP(skc5,cons(hd(skc5),nil))*.
% 50.73/50.90 35443[2:Res:35430.0,3094.3] strictorderedP(cons(hd(skc5),nil)) ssList(cons(hd(skc5),nil)) || neq(nil,cons(hd(skc5),nil))* -> .
% 50.73/50.90 35448[2:SSi:35443.1,35443.0,76.0,3365.1,75.0,3365.1,72.0,3365.1,71.0,3365.1,70.0,3365.1,74.0,3365.1,73.0,3365.1,2884.0,3365.1,3839.0,3365.1,76.0,3365.1,75.0,3365.1,72.0,3365.1,71.0,3365.1,70.0,3365.1,74.0,3365.1,73.0,3365.1,2884.0,3365.1,3839.0,3365.1] || neq(nil,cons(hd(skc5),nil))* -> .
% 50.73/50.90 35455[2:Res:3013.1,35448.0] ssList(cons(hd(skc5),nil)) || -> equal(cons(hd(skc5),nil),nil)**.
% 50.73/50.90 35456[2:SSi:35455.0,76.0,3365.1,75.0,3365.1,72.0,3365.1,71.0,3365.1,70.0,3365.1,74.0,3365.1,73.0,3365.1,2884.0,3365.1,3839.0,3365.1] || -> equal(cons(hd(skc5),nil),nil)**.
% 50.73/50.90 35556[2:SpL:35456.0,2885.1] ssItem(hd(skc5)) || equal(nil,nil)* -> .
% 50.73/50.90 35601[2:Obv:35556.1] ssItem(hd(skc5)) || -> .
% 50.73/50.90 35602[2:SSi:35601.0,3365.0] || -> .
% 50.73/50.90 % SZS output end Refutation
% 50.73/50.90 Formulae used in the proof : co1 ax2 ax17 ax60 ax62 ax64 ax66 ax69 ax72 ax74 ax5 ax57 ax59 ax61 ax63 ax65 ax68 ax71 ax73 ax28 ax75 ax76 ax16 ax26 ax58 ax15 ax21 ax23 ax78 ax4 ax81 ax85 ax82 ax7 ax77
% 50.73/50.90
%------------------------------------------------------------------------------