TSTP Solution File: SWC100-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC100-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 22:01:43 EDT 2022
% Result : Unsatisfiable 9.08s 9.29s
% Output : Refutation 10.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC100-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n016.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 13:42:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.08/9.29
% 9.08/9.29 SPASS V 3.9
% 9.08/9.29 SPASS beiseite: Proof found.
% 9.08/9.29 % SZS status Theorem
% 9.08/9.29 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.08/9.29 SPASS derived 11758 clauses, backtracked 6472 clauses, performed 89 splits and kept 11843 clauses.
% 9.08/9.29 SPASS allocated 88667 KBytes.
% 9.08/9.29 SPASS spent 0:00:08.93 on the problem.
% 9.08/9.29 0:00:00.04 for the input.
% 9.08/9.29 0:00:00.00 for the FLOTTER CNF translation.
% 9.08/9.29 0:00:00.09 for inferences.
% 9.08/9.29 0:00:00.25 for the backtracking.
% 9.08/9.29 0:00:08.32 for the reduction.
% 9.08/9.29
% 9.08/9.29
% 9.08/9.29 Here is a proof with depth 4, length 164 :
% 9.08/9.29 % SZS output start Refutation
% 9.08/9.29 1[0:Inp] || -> ssList(sk1)*.
% 9.08/9.29 2[0:Inp] || -> ssList(sk2)*.
% 9.08/9.29 5[0:Inp] || -> equal(sk4,sk2)**.
% 9.08/9.29 6[0:Inp] || -> equal(sk3,sk1)**.
% 9.08/9.29 7[0:Inp] || -> ssList(sk5)*.
% 9.08/9.29 8[0:Inp] || -> equal(app(sk3,sk5),sk4)**.
% 9.08/9.29 9[0:Inp] || -> strictorderedP(sk3)*.
% 9.08/9.29 11[0:Inp] || equal(nil,sk3)** -> equal(nil,sk4).
% 9.08/9.29 12[0:Inp] || -> neq(sk2,nil)* equal(nil,sk2).
% 9.08/9.29 13[0:Inp] || frontsegP(sk2,sk1)* neq(sk1,nil) -> equal(nil,sk2).
% 9.08/9.29 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 9.08/9.29 15[0:Inp] || equal(nil,sk1) neq(sk1,nil) frontsegP(sk2,sk1)* -> .
% 9.08/9.29 16[0:Inp] || -> equalelemsP(nil)*.
% 9.08/9.29 17[0:Inp] || -> duplicatefreeP(nil)*.
% 9.08/9.29 18[0:Inp] || -> strictorderedP(nil)*.
% 9.08/9.29 19[0:Inp] || -> totalorderedP(nil)*.
% 9.08/9.29 20[0:Inp] || -> strictorderP(nil)*.
% 9.08/9.29 21[0:Inp] || -> totalorderP(nil)*.
% 9.08/9.29 22[0:Inp] || -> cyclefreeP(nil)*.
% 9.08/9.29 23[0:Inp] || -> ssList(nil)*.
% 9.08/9.29 28[0:Inp] || -> ssList(skaf82(u))*.
% 9.08/9.29 69[0:Inp] || equal(skac2,skac3)** -> .
% 9.08/9.29 74[0:Inp] ssList(u) || -> rearsegP(u,u)*.
% 9.08/9.29 76[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 9.08/9.29 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 9.08/9.29 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 9.08/9.29 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 9.08/9.29 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 9.08/9.29 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 9.08/9.29 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 9.08/9.29 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 9.08/9.29 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 9.08/9.29 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 9.08/9.29 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 9.08/9.29 97[0:Inp] ssList(u) || rearsegP(nil,u)* -> equal(nil,u).
% 9.08/9.29 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 9.08/9.29 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 9.08/9.29 115[0:Inp] ssList(u) ssList(v) || -> equal(u,v) neq(u,v)*.
% 9.08/9.29 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 9.08/9.29 132[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 9.08/9.29 133[0:Inp] ssList(u) ssList(v) || equal(app(u,v),nil)** -> equal(nil,u).
% 9.08/9.29 134[0:Inp] ssList(u) ssList(v) || equal(app(u,v),nil)** -> equal(nil,v).
% 9.08/9.29 135[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 9.08/9.29 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 9.08/9.29 151[0:Inp] ssList(u) ssList(v) ssList(w) || rearsegP(u,v) -> rearsegP(app(w,u),v)*.
% 9.08/9.29 152[0:Inp] ssList(u) ssList(v) ssList(w) || frontsegP(u,v) -> frontsegP(app(u,w),v)*.
% 9.08/9.29 164[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 9.08/9.29 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 9.08/9.29 192[0:Inp] ssList(u) ssList(v) || equal(hd(v),hd(u))* equal(tl(v),tl(u)) -> equal(v,u) equal(nil,v) equal(nil,u).
% 9.08/9.29 201[0:Rew:6.0,9.0] || -> strictorderedP(sk1)*.
% 9.08/9.29 204[0:Rew:6.0,8.0,5.0,8.0] || -> equal(app(sk1,sk5),sk2)**.
% 9.08/9.29 205[0:Rew:12.0,14.0] || equal(sk2,sk1) -> neq(sk2,nil)*.
% 9.08/9.29 206[0:Rew:5.0,11.1,6.0,11.0] || equal(nil,sk1)** -> equal(nil,sk2).
% 9.08/9.29 207[0:Rew:13.2,15.0] || frontsegP(sk2,sk1)* neq(sk1,nil) equal(sk2,sk1) -> .
% 9.08/9.29 284[0:Res:7.0,97.0] || rearsegP(nil,sk5)* -> equal(nil,sk5).
% 9.08/9.29 298[0:Res:7.0,74.0] || -> rearsegP(sk5,sk5)*.
% 9.08/9.29 416[0:Res:2.0,164.0] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,app(v,sk2)))**.
% 9.08/9.29 473[0:Res:2.0,76.0] || -> frontsegP(sk2,sk2)*.
% 9.08/9.29 483[0:Res:2.0,192.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 9.08/9.29 512[0:Res:2.0,138.1] ssList(u) || -> equal(nil,sk2) equal(hd(app(sk2,u)),hd(sk2))**.
% 9.08/9.29 519[0:Res:2.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk2)),u)**.
% 9.08/9.29 524[0:Res:2.0,101.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 9.08/9.29 563[1:Spt:87.1] || -> ssItem(u)*.
% 9.08/9.29 566[1:MRR:524.0,563.0] || -> ssList(cons(u,sk2))*.
% 9.08/9.29 569[1:MRR:85.0,563.0] || -> cyclefreeP(cons(u,nil))*.
% 9.08/9.29 570[1:MRR:84.0,563.0] || -> totalorderP(cons(u,nil))*.
% 9.08/9.29 571[1:MRR:83.0,563.0] || -> strictorderP(cons(u,nil))*.
% 9.08/9.29 572[1:MRR:82.0,563.0] || -> totalorderedP(cons(u,nil))*.
% 9.08/9.29 573[1:MRR:81.0,563.0] || -> strictorderedP(cons(u,nil))*.
% 9.08/9.29 574[1:MRR:80.0,563.0] || -> duplicatefreeP(cons(u,nil))*.
% 9.08/9.29 575[1:MRR:79.0,563.0] || -> equalelemsP(cons(u,nil))*.
% 9.08/9.29 579[1:MRR:519.0,563.0] || -> equal(hd(cons(u,sk2)),u)**.
% 9.08/9.29 593[1:MRR:117.1,117.0,563.0] || -> equal(u,v) neq(u,v)*.
% 9.08/9.29 603[1:MRR:132.1,132.0,563.0] || neq(u,v)* equal(u,v) -> .
% 9.08/9.29 696[1:MRR:135.1,563.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 9.08/9.29 762[1:MRR:185.3,185.2,563.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 9.08/9.29 763[2:Spt:512.0,512.2] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 9.08/9.29 771[3:Spt:483.5] || -> equal(nil,sk2)**.
% 9.08/9.29 852[3:Rew:771.0,89.1] ssList(u) || -> equal(app(sk2,u),u)**.
% 9.08/9.29 853[3:Rew:771.0,88.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 9.08/9.29 858[3:Rew:771.0,569.0] || -> cyclefreeP(cons(u,sk2))*.
% 9.08/9.29 859[3:Rew:771.0,570.0] || -> totalorderP(cons(u,sk2))*.
% 9.08/9.29 860[3:Rew:771.0,571.0] || -> strictorderP(cons(u,sk2))*.
% 9.08/9.29 861[3:Rew:771.0,572.0] || -> totalorderedP(cons(u,sk2))*.
% 9.08/9.29 862[3:Rew:771.0,573.0] || -> strictorderedP(cons(u,sk2))*.
% 9.08/9.29 863[3:Rew:771.0,574.0] || -> duplicatefreeP(cons(u,sk2))*.
% 9.08/9.29 864[3:Rew:771.0,575.0] || -> equalelemsP(cons(u,sk2))*.
% 9.08/9.29 873[3:Rew:771.0,696.1] ssList(u) || -> equal(app(cons(v,sk2),u),cons(v,u))**.
% 9.08/9.29 918[3:Rew:852.1,763.1] ssList(u) || -> equal(hd(u),hd(sk2))*.
% 9.08/9.29 931[3:Rew:853.1,416.2] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,v))**.
% 9.08/9.29 1219[3:SpR:918.1,579.0] ssList(cons(u,sk2)) || -> equal(hd(sk2),u)*.
% 9.08/9.29 1224[3:SSi:1219.0,566.0,858.0,859.0,860.0,861.0,862.0,863.0,864.0] || -> equal(hd(sk2),u)*.
% 9.08/9.29 1287[3:Rew:1224.0,762.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk2))** -> equal(w,x)*.
% 9.08/9.29 1307[3:Rew:1224.0,873.1] ssList(u) || -> equal(app(hd(sk2),u),cons(v,u))*.
% 9.08/9.29 1332[3:Rew:1224.0,931.2] ssList(u) ssList(v) || -> equal(app(u,v),hd(sk2))**.
% 9.08/9.29 1337[3:Rew:1224.0,164.3] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),hd(sk2))**.
% 9.08/9.29 1415[3:Con:1287.1] ssList(u) || equal(cons(v,u),hd(sk2))** -> equal(v,w)*.
% 9.08/9.29 1416[3:AED:69.0,1415.2] ssList(u) || equal(cons(v,u),hd(sk2))** -> .
% 9.08/9.29 1421[3:Rew:1332.2,1337.3] ssList(u) ssList(v) ssList(w) || -> equal(app(hd(sk2),w),hd(sk2))**.
% 9.08/9.29 1422[3:Con:1421.0] ssList(u) || -> equal(app(hd(sk2),u),hd(sk2))**.
% 9.08/9.29 1423[3:Rew:1422.1,1307.1] ssList(u) || -> equal(cons(v,u),hd(sk2))**.
% 9.08/9.29 1424[3:MRR:1423.1,1416.1] ssList(u) || -> .
% 9.08/9.29 1425[3:UnC:1424.0,28.0] || -> .
% 9.08/9.29 1471[3:Spt:1425.0,483.5,771.0] || equal(nil,sk2)** -> .
% 9.08/9.29 1472[3:Spt:1425.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 9.08/9.29 1477[3:MRR:206.1,1471.0] || equal(nil,sk1)** -> .
% 9.08/9.29 1482[3:MRR:13.2,1471.0] || frontsegP(sk2,sk1)* neq(sk1,nil) -> .
% 9.08/9.29 2295[1:Res:205.1,603.0] || equal(sk2,sk1) equal(nil,sk2)** -> .
% 9.08/9.29 2766[0:SpL:204.0,134.2] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk5).
% 9.08/9.29 2780[0:SpL:204.0,133.2] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk1).
% 9.08/9.29 3709[0:SpR:204.0,151.4] ssList(sk5) ssList(u) ssList(sk1) || rearsegP(sk5,u)* -> rearsegP(sk2,u).
% 9.08/9.29 4950[0:SSi:3709.2,201.0,1.0] ssList(sk5) ssList(u) || rearsegP(sk5,u)* -> rearsegP(sk2,u).
% 9.08/9.29 4951[0:MRR:4950.0,7.0] ssList(u) || rearsegP(sk5,u)* -> rearsegP(sk2,u).
% 9.08/9.29 4981[0:SpR:204.0,152.4] ssList(sk1) ssList(u) ssList(sk5) || frontsegP(sk1,u) -> frontsegP(sk2,u)*.
% 9.08/9.29 6627[0:Res:298.0,4951.1] ssList(sk5) || -> rearsegP(sk2,sk5)*.
% 9.08/9.29 9414[0:SSi:6627.0,7.0] || -> rearsegP(sk2,sk5)*.
% 9.08/9.29 9455[0:SSi:4981.2,4981.0,7.0,201.0,1.0] ssList(u) || frontsegP(sk1,u) -> frontsegP(sk2,u)*.
% 9.08/9.29 10104[3:Res:9455.2,1482.0] ssList(sk1) || frontsegP(sk1,sk1)* neq(sk1,nil) -> .
% 9.08/9.29 10107[3:SSi:10104.0,201.0,1.0] || frontsegP(sk1,sk1)* neq(sk1,nil) -> .
% 9.08/9.29 10112[3:Res:76.1,10107.0] ssList(sk1) || neq(sk1,nil)* -> .
% 9.08/9.29 10113[3:SSi:10112.0,201.0,1.0] || neq(sk1,nil)* -> .
% 9.08/9.29 10114[3:Res:593.1,10113.0] || -> equal(nil,sk1)**.
% 9.08/9.29 10115[3:MRR:10114.0,1477.0] || -> .
% 10.42/10.64 10116[2:Spt:10115.0,512.1] || -> equal(nil,sk2)**.
% 10.42/10.64 10167[2:Rew:10116.0,88.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 10.42/10.64 10417[2:Rew:10116.0,284.1,10116.0,284.0] || rearsegP(sk2,sk5)* -> equal(sk5,sk2).
% 10.42/10.64 10418[2:MRR:10417.0,9414.0] || -> equal(sk5,sk2)**.
% 10.42/10.64 10422[2:Rew:10418.0,204.0] || -> equal(app(sk1,sk2),sk2)**.
% 10.42/10.64 10562[2:Rew:10116.0,2295.1] || equal(sk2,sk1) equal(sk2,sk2)* -> .
% 10.42/10.64 10563[2:Obv:10562.1] || equal(sk2,sk1)** -> .
% 10.42/10.64 10964[2:SpR:10167.1,10422.0] ssList(sk1) || -> equal(sk2,sk1)**.
% 10.42/10.64 10975[2:SSi:10964.0,201.0,1.0] || -> equal(sk2,sk1)**.
% 10.42/10.64 10976[2:MRR:10975.0,10563.0] || -> .
% 10.42/10.64 10993[1:Spt:10976.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 10.42/10.64 10996[0:SSi:2766.0,201.0,1.0] ssList(sk5) || equal(nil,sk2)** -> equal(nil,sk5).
% 10.42/10.64 10997[0:MRR:10996.0,7.0] || equal(nil,sk2)** -> equal(nil,sk5).
% 10.42/10.64 11001[0:Rew:10997.1,2780.3] ssList(sk1) ssList(sk5) || equal(nil,sk2)** -> equal(sk5,sk1).
% 10.42/10.64 11002[0:SSi:11001.0,201.0,1.0] ssList(sk5) || equal(nil,sk2)** -> equal(sk5,sk1).
% 10.42/10.64 11003[0:MRR:11002.0,7.0] || equal(nil,sk2)** -> equal(sk5,sk1).
% 10.42/10.64 11004[0:Rew:11003.1,10997.1] || equal(nil,sk2)** -> equal(nil,sk1).
% 10.42/10.64 16098[2:Spt:483.5] || -> equal(nil,sk2)**.
% 10.42/10.64 16121[2:Rew:16098.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 10.42/10.64 16234[2:Rew:16098.0,11004.0] || equal(sk2,sk2) -> equal(nil,sk1)**.
% 10.42/10.64 16252[2:Rew:16098.0,207.1] || frontsegP(sk2,sk1)* neq(sk1,sk2) equal(sk2,sk1) -> .
% 10.42/10.64 16439[2:Obv:16234.0] || -> equal(nil,sk1)**.
% 10.42/10.64 16440[2:Rew:16098.0,16439.0] || -> equal(sk2,sk1)**.
% 10.42/10.64 16446[2:Rew:16440.0,473.0] || -> frontsegP(sk1,sk1)*.
% 10.42/10.64 16561[2:Rew:16440.0,16121.0] || equal(sk1,sk1) -> neq(sk2,sk2)*.
% 10.42/10.64 16579[2:Obv:16561.0] || -> neq(sk2,sk2)*.
% 10.42/10.64 16580[2:Rew:16440.0,16579.0] || -> neq(sk1,sk1)*.
% 10.42/10.64 16649[2:Rew:16440.0,16252.2,16440.0,16252.1,16440.0,16252.0] || frontsegP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 10.42/10.64 16650[2:Obv:16649.2] || frontsegP(sk1,sk1)* neq(sk1,sk1) -> .
% 10.42/10.64 16651[2:MRR:16650.0,16650.1,16446.0,16580.0] || -> .
% 10.42/10.64 16925[2:Spt:16651.0,483.5,16098.0] || equal(nil,sk2)** -> .
% 10.42/10.64 16926[2:Spt:16651.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 10.42/10.64 16933[2:MRR:206.1,16925.0] || equal(nil,sk1)** -> .
% 10.42/10.64 16936[2:MRR:13.2,16925.0] || frontsegP(sk2,sk1)* neq(sk1,nil) -> .
% 10.42/10.64 17736[2:Res:9455.2,16936.0] ssList(sk1) || frontsegP(sk1,sk1)* neq(sk1,nil) -> .
% 10.42/10.64 17737[2:SSi:17736.0,201.0,1.0] || frontsegP(sk1,sk1)* neq(sk1,nil) -> .
% 10.42/10.64 17744[2:Res:76.1,17737.0] ssList(sk1) || neq(sk1,nil)* -> .
% 10.42/10.64 17745[2:SSi:17744.0,201.0,1.0] || neq(sk1,nil)* -> .
% 10.42/10.64 17913[2:Res:115.3,17745.0] ssList(sk1) ssList(nil) || -> equal(nil,sk1)**.
% 10.42/10.64 17914[2:SSi:17913.1,17913.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,201.0,1.0] || -> equal(nil,sk1)**.
% 10.42/10.64 17915[2:MRR:17914.0,16933.0] || -> .
% 10.42/10.64 % SZS output end Refutation
% 10.42/10.64 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_11 co1_12 co1_13 co1_14 co1_15 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause54 clause59 clause61 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause82 clause86 clause97 clause100 clause102 clause117 clause118 clause119 clause120 clause123 clause136 clause137 clause149 clause170 clause177
% 10.42/10.64
%------------------------------------------------------------------------------