TSTP Solution File: SWC099-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC099-1 : 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 22:01:42 EDT 2022
% Result : Unsatisfiable 11.04s 11.22s
% Output : Refutation 13.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC099-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 09:10:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.04/11.22
% 11.04/11.22 SPASS V 3.9
% 11.04/11.22 SPASS beiseite: Proof found.
% 11.04/11.22 % SZS status Theorem
% 11.04/11.22 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.04/11.22 SPASS derived 18236 clauses, backtracked 9763 clauses, performed 219 splits and kept 17308 clauses.
% 11.04/11.22 SPASS allocated 94871 KBytes.
% 11.04/11.22 SPASS spent 0:0:10.86 on the problem.
% 11.04/11.22 0:00:00.04 for the input.
% 11.04/11.22 0:00:00.00 for the FLOTTER CNF translation.
% 11.04/11.22 0:00:00.16 for inferences.
% 11.04/11.22 0:00:00.38 for the backtracking.
% 11.04/11.22 0:0:10.02 for the reduction.
% 11.04/11.22
% 11.04/11.22
% 11.04/11.22 Here is a proof with depth 5, length 156 :
% 11.04/11.22 % SZS output start Refutation
% 11.04/11.22 1[0:Inp] || -> ssList(sk1)*.
% 11.04/11.22 4[0:Inp] || -> ssList(sk4)*.
% 11.04/11.22 5[0:Inp] || -> equal(sk2,sk4)**.
% 11.04/11.22 6[0:Inp] || -> equal(sk3,sk1)**.
% 11.04/11.22 7[0:Inp] || -> frontsegP(sk4,sk3)*.
% 11.04/11.22 8[0:Inp] || -> equalelemsP(sk3)*.
% 11.04/11.22 9[0:Inp] ssList(u) equalelemsP(u) || frontsegP(sk4,u)* segmentP(u,sk3) neq(sk3,u) -> .
% 11.04/11.22 11[0:Inp] || neq(sk1,nil) frontsegP(sk2,sk1)* -> equal(nil,sk2).
% 11.04/11.22 12[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 11.04/11.22 25[0:Inp] || -> ssItem(skaf83(u))*.
% 11.04/11.22 26[0:Inp] || -> ssList(skaf82(u))*.
% 11.04/11.22 67[0:Inp] || equal(skac2,skac3)** -> .
% 11.04/11.22 69[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 11.04/11.22 70[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 11.04/11.22 77[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 11.04/11.22 78[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 11.04/11.22 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 11.04/11.22 80[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 11.04/11.22 81[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 11.04/11.22 82[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 11.04/11.22 83[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 11.04/11.22 85[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 11.04/11.22 86[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 11.04/11.22 87[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 11.04/11.22 97[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 11.04/11.22 98[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 11.04/11.22 99[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 11.04/11.22 110[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 11.04/11.22 112[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 11.04/11.22 115[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 11.04/11.22 122[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 11.04/11.22 129[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 11.04/11.22 130[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 11.04/11.22 133[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 11.04/11.22 136[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 11.04/11.22 157[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,w),u)*+ -> frontsegP(u,v)*.
% 11.04/11.22 170[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 11.04/11.22 183[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 11.04/11.22 190[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).
% 11.04/11.22 192[0:Inp] ssList(u) duplicatefreeP(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 11.04/11.22 199[0:Rew:6.0,8.0] || -> equalelemsP(sk1)*.
% 11.04/11.22 201[0:Rew:6.0,7.0] || -> frontsegP(sk4,sk1)*.
% 11.04/11.22 204[0:Rew:5.0,12.1] || equal(nil,sk1) -> neq(sk4,nil)*.
% 11.04/11.22 205[0:Rew:5.0,11.2,5.0,11.1] || neq(sk1,nil) frontsegP(sk4,sk1)* -> equal(nil,sk4).
% 11.04/11.22 206[0:MRR:205.1,201.0] || neq(sk1,nil)* -> equal(nil,sk4).
% 11.04/11.22 209[0:Rew:6.0,9.4,6.0,9.3] equalelemsP(u) ssList(u) || segmentP(u,sk1) neq(sk1,u) frontsegP(sk4,u)* -> .
% 11.04/11.22 273[0:Res:4.0,122.0] || -> equal(nil,sk4) equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 11.04/11.22 311[0:Res:4.0,190.1] ssList(u) || equal(hd(u),hd(sk4))* equal(tl(u),tl(sk4)) -> equal(u,sk4) equal(nil,u) equal(nil,sk4).
% 11.04/11.22 352[0:Res:4.0,99.1] ssItem(u) || -> ssList(cons(u,sk4))*.
% 11.04/11.22 418[0:Res:1.0,209.0] equalelemsP(sk1) || frontsegP(sk4,sk1)* segmentP(sk1,sk1) neq(sk1,sk1) -> .
% 11.04/11.22 460[0:Res:1.0,97.0] || frontsegP(nil,sk1)* -> equal(nil,sk1).
% 11.04/11.22 470[0:Res:1.0,70.0] || -> segmentP(sk1,sk1)*.
% 11.04/11.22 483[0:Res:1.0,190.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 11.04/11.22 512[0:Res:1.0,136.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 11.04/11.22 519[0:Res:1.0,110.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 11.04/11.22 521[0:Res:1.0,112.1] ssItem(u) || equal(cons(u,sk1),sk1)** -> .
% 11.04/11.22 524[0:Res:1.0,99.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 11.04/11.22 535[0:Res:1.0,170.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 11.04/11.22 563[0:MRR:418.0,418.1,418.2,199.0,201.0,470.0] || neq(sk1,sk1)* -> .
% 11.04/11.22 565[1:Spt:85.1] || -> ssItem(u)*.
% 11.04/11.22 568[1:MRR:524.0,565.0] || -> ssList(cons(u,sk1))*.
% 11.04/11.22 571[1:MRR:83.0,565.0] || -> cyclefreeP(cons(u,nil))*.
% 11.04/11.22 572[1:MRR:82.0,565.0] || -> totalorderP(cons(u,nil))*.
% 11.04/11.22 573[1:MRR:81.0,565.0] || -> strictorderP(cons(u,nil))*.
% 11.04/11.22 574[1:MRR:80.0,565.0] || -> totalorderedP(cons(u,nil))*.
% 11.04/11.22 575[1:MRR:79.0,565.0] || -> strictorderedP(cons(u,nil))*.
% 11.04/11.22 576[1:MRR:78.0,565.0] || -> duplicatefreeP(cons(u,nil))*.
% 11.04/11.22 577[1:MRR:77.0,565.0] || -> equalelemsP(cons(u,nil))*.
% 11.04/11.22 579[1:MRR:521.0,565.0] || equal(cons(u,sk1),sk1)** -> .
% 11.04/11.22 581[1:MRR:519.0,565.0] || -> equal(hd(cons(u,sk1)),u)**.
% 11.04/11.22 595[1:MRR:115.1,115.0,565.0] || -> equal(u,v) neq(u,v)*.
% 11.04/11.22 605[1:MRR:130.1,130.0,565.0] || neq(u,v)* equal(u,v) -> .
% 11.04/11.22 695[1:MRR:129.1,565.0] ssList(u) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 11.04/11.22 696[1:MRR:133.1,565.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 11.04/11.22 697[1:MRR:535.1,565.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 11.04/11.22 760[1:MRR:183.3,183.2,565.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 11.04/11.22 761[2:Spt:512.0,512.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 11.04/11.22 769[3:Spt:311.5] || -> equal(nil,sk4)**.
% 11.04/11.22 777[3:Rew:769.0,204.1] || equal(nil,sk1) -> neq(sk4,sk4)*.
% 11.04/11.22 796[3:Rew:769.0,460.1] || frontsegP(nil,sk1)* -> equal(sk4,sk1).
% 11.04/11.22 905[3:Rew:769.0,777.0] || equal(sk4,sk1) -> neq(sk4,sk4)*.
% 11.04/11.22 911[3:Rew:769.0,796.0] || frontsegP(sk4,sk1)* -> equal(sk4,sk1).
% 11.04/11.22 912[3:MRR:911.0,201.0] || -> equal(sk4,sk1)**.
% 11.04/11.22 1013[3:Rew:912.0,905.0] || equal(sk1,sk1) -> neq(sk4,sk4)*.
% 11.04/11.22 1047[3:Obv:1013.0] || -> neq(sk4,sk4)*.
% 11.04/11.22 1048[3:Rew:912.0,1047.0] || -> neq(sk1,sk1)*.
% 11.04/11.22 1049[3:MRR:1048.0,563.0] || -> .
% 11.04/11.22 1201[3:Spt:1049.0,311.5,769.0] || equal(nil,sk4)** -> .
% 11.04/11.22 1202[3:Spt:1049.0,311.0,311.1,311.2,311.3,311.4] ssList(u) || equal(hd(u),hd(sk4))* equal(tl(u),tl(sk4)) -> equal(u,sk4) equal(nil,u).
% 11.04/11.22 1207[3:MRR:206.1,1201.0] || neq(sk1,nil)* -> .
% 11.04/11.22 1217[4:Spt:483.5] || -> equal(nil,sk1)**.
% 11.04/11.22 1234[4:Rew:1217.0,577.0] || -> equalelemsP(cons(u,sk1))*.
% 11.04/11.22 1235[4:Rew:1217.0,576.0] || -> duplicatefreeP(cons(u,sk1))*.
% 11.04/11.22 1236[4:Rew:1217.0,575.0] || -> strictorderedP(cons(u,sk1))*.
% 11.04/11.22 1237[4:Rew:1217.0,574.0] || -> totalorderedP(cons(u,sk1))*.
% 11.04/11.22 1238[4:Rew:1217.0,573.0] || -> strictorderP(cons(u,sk1))*.
% 11.04/11.22 1239[4:Rew:1217.0,572.0] || -> totalorderP(cons(u,sk1))*.
% 11.04/11.22 1240[4:Rew:1217.0,571.0] || -> cyclefreeP(cons(u,sk1))*.
% 11.04/11.22 1268[4:Rew:1217.0,86.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 11.04/11.22 1269[4:Rew:1217.0,87.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 11.04/11.22 1350[4:Rew:1268.1,697.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 11.04/11.22 1360[4:Rew:1269.1,761.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 11.04/11.22 1435[4:SpR:1360.1,581.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 11.04/11.22 1442[4:SSi:1435.0,1234.0,568.0,1235.0,1236.0,1237.0,1238.0,1239.0,1240.0] || -> equal(hd(sk1),u)*.
% 11.04/11.22 1492[4:Rew:1442.0,1350.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 11.04/11.22 1661[4:Rew:1442.0,760.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 11.04/11.22 1775[4:Con:1661.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 11.04/11.22 1776[4:AED:67.0,1775.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 11.04/11.22 1777[4:Rew:1492.1,1776.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 11.04/11.22 1778[4:Obv:1777.1] ssList(u) || -> .
% 11.04/11.22 1779[4:UnC:1778.0,26.0] || -> .
% 11.04/11.22 1950[4:Spt:1779.0,483.5,1217.0] || equal(nil,sk1)** -> .
% 11.04/11.22 1951[4:Spt:1779.0,483.0,483.1,483.2,483.3,483.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 11.04/11.22 1990[3:Res:595.1,1207.0] || -> equal(nil,sk1)**.
% 11.04/11.22 1991[4:MRR:1990.0,1950.0] || -> .
% 11.04/11.22 1992[2:Spt:1991.0,512.1] || -> equal(nil,sk1)**.
% 11.04/11.22 2009[2:Rew:1992.0,571.0] || -> cyclefreeP(cons(u,sk1))*.
% 11.04/11.22 2010[2:Rew:1992.0,572.0] || -> totalorderP(cons(u,sk1))*.
% 11.04/11.22 2011[2:Rew:1992.0,573.0] || -> strictorderP(cons(u,sk1))*.
% 11.04/11.22 2012[2:Rew:1992.0,574.0] || -> totalorderedP(cons(u,sk1))*.
% 11.04/11.22 2013[2:Rew:1992.0,575.0] || -> strictorderedP(cons(u,sk1))*.
% 13.81/13.99 2014[2:Rew:1992.0,576.0] || -> duplicatefreeP(cons(u,sk1))*.
% 13.81/13.99 2015[2:Rew:1992.0,577.0] || -> equalelemsP(cons(u,sk1))*.
% 13.81/13.99 2026[2:Rew:1992.0,69.1] ssList(u) || -> segmentP(u,sk1)*.
% 13.81/13.99 2058[2:Rew:1992.0,695.1] ssList(u) || equal(cons(v,sk1),u)*+ -> singletonP(u)*.
% 13.81/13.99 2059[2:Rew:1992.0,696.1] ssList(u) || -> equal(app(cons(v,sk1),u),cons(v,u))**.
% 13.81/13.99 2080[2:MRR:209.2,2026.1] equalelemsP(u) ssList(u) || neq(sk1,u) frontsegP(sk4,u)* -> .
% 13.81/13.99 2088[2:Rew:1992.0,204.1,1992.0,204.0] || equal(sk1,sk1) -> neq(sk4,sk1)*.
% 13.81/13.99 2089[2:Obv:2088.0] || -> neq(sk4,sk1)*.
% 13.81/13.99 2123[2:Rew:1992.0,273.0] || -> equal(sk4,sk1) equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 13.81/13.99 2644[2:Res:2089.0,605.0] || equal(sk4,sk1)** -> .
% 13.81/13.99 2826[2:EqR:2058.1] ssList(cons(u,sk1)) || -> singletonP(cons(u,sk1))*.
% 13.81/13.99 2827[2:SSi:2826.0,568.0,2009.0,2010.0,2011.0,2012.0,2013.0,2014.0,2015.0] || -> singletonP(cons(u,sk1))*.
% 13.81/13.99 4727[0:EqR:157.3] ssList(app(u,v)) ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 13.81/13.99 4742[0:SSi:4727.0,98.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 13.81/13.99 5092[2:SpR:2059.1,4742.2] ssList(u) ssList(cons(v,sk1)) ssList(u) || -> frontsegP(cons(v,u),cons(v,sk1))*.
% 13.81/13.99 5109[2:Obv:5092.0] ssList(cons(u,sk1)) ssList(v) || -> frontsegP(cons(u,v),cons(u,sk1))*.
% 13.81/13.99 5110[2:SSi:5109.0,568.0,2009.0,2010.0,2011.0,2012.0,2013.0,2014.0,2015.0,2827.0] ssList(u) || -> frontsegP(cons(v,u),cons(v,sk1))*.
% 13.81/13.99 5278[2:MRR:2123.0,2644.0] || -> equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 13.81/13.99 5646[2:SpR:5278.0,5110.1] ssList(skaf82(sk4)) || -> frontsegP(sk4,cons(skaf83(sk4),sk1))*.
% 13.81/13.99 7409[2:SSi:5646.0,26.0,4.0] || -> frontsegP(sk4,cons(skaf83(sk4),sk1))*.
% 13.81/13.99 7650[2:Res:7409.0,2080.3] equalelemsP(cons(skaf83(sk4),sk1)) ssList(cons(skaf83(sk4),sk1)) || neq(sk1,cons(skaf83(sk4),sk1))* -> .
% 13.81/13.99 7651[2:SSi:7650.1,7650.0,568.0,2009.0,2010.0,2011.0,2012.0,2013.0,2014.0,2015.0,2827.0,568.0,2009.0,2010.0,2011.0,2012.0,2013.0,2014.0,2015.0,2827.0] || neq(sk1,cons(skaf83(sk4),sk1))* -> .
% 13.81/13.99 7661[2:Res:595.1,7651.0] || -> equal(cons(skaf83(sk4),sk1),sk1)**.
% 13.81/13.99 7662[2:MRR:7661.0,579.0] || -> .
% 13.81/13.99 7663[1:Spt:7662.0,85.0,85.2] ssList(u) || -> duplicatefreeP(u)*.
% 13.81/13.99 7677[1:MRR:192.1,7663.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 13.81/13.99 19123[0:SpR:170.3,98.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 13.81/13.99 19152[0:Obv:19123.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 13.81/13.99 19153[0:SSi:19152.2,99.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 13.81/13.99 27743[1:EqR:7677.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 13.81/13.99 27771[1:SSi:27743.0,98.2,98.2,99.2,99.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 13.81/13.99 27772[1:MRR:19153.3,27771.1] ssList(u) ssItem(v) ssList(w) || -> .
% 13.81/13.99 27775[1:Con:27772.2] ssList(u) ssItem(v) || -> .
% 13.81/13.99 27777[1:MRR:352.1,27775.0] ssItem(u) || -> .
% 13.81/13.99 27779[1:UnC:27777.0,25.0] || -> .
% 13.81/13.99 % SZS output end Refutation
% 13.81/13.99 Formulae used in the proof : co1_1 co1_4 co1_5 co1_6 co1_7 co1_8 co1_9 co1_11 co1_12 clause12 clause13 clause54 clause56 clause57 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause84 clause85 clause86 clause97 clause99 clause102 clause109 clause116 clause117 clause120 clause123 clause144 clause157 clause170 clause177 clause179
% 13.81/13.99
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