TSTP Solution File: SWC297-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC297-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 22:03:08 EDT 2022
% Result : Unsatisfiable 132.99s 133.22s
% Output : Refutation 176.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC297-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n012.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 11:25:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 132.99/133.22
% 132.99/133.22 SPASS V 3.9
% 132.99/133.22 SPASS beiseite: Proof found.
% 132.99/133.22 % SZS status Theorem
% 132.99/133.22 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 132.99/133.22 SPASS derived 58371 clauses, backtracked 35252 clauses, performed 177 splits and kept 55913 clauses.
% 132.99/133.22 SPASS allocated 143091 KBytes.
% 132.99/133.22 SPASS spent 0:2:12.75 on the problem.
% 132.99/133.22 0:00:00.04 for the input.
% 132.99/133.22 0:00:00.00 for the FLOTTER CNF translation.
% 132.99/133.22 0:00:00.69 for inferences.
% 132.99/133.22 0:00:06.88 for the backtracking.
% 132.99/133.22 0:02:04.47 for the reduction.
% 132.99/133.22
% 132.99/133.22
% 132.99/133.22 Here is a proof with depth 5, length 279 :
% 132.99/133.22 % SZS output start Refutation
% 132.99/133.22 1[0:Inp] || -> ssList(sk1)*.
% 132.99/133.22 2[0:Inp] || -> ssList(sk2)*.
% 132.99/133.22 5[0:Inp] || -> equal(sk4,sk2)**.
% 132.99/133.22 6[0:Inp] || -> equal(sk3,sk1)**.
% 132.99/133.22 8[0:Inp] || -> ssList(sk6)*.
% 132.99/133.22 9[0:Inp] || -> ssList(sk7)*.
% 132.99/133.22 10[0:Inp] || -> equal(app(app(sk6,cons(sk5,nil)),sk7),sk1)**.
% 132.99/133.22 12[0:Inp] || -> memberP(sk7,sk8)* memberP(sk6,sk8).
% 132.99/133.22 16[0:Inp] || equal(nil,sk4) -> equal(sk3,nil)**.
% 132.99/133.22 18[0:Inp] || neq(sk4,nil) -> equal(cons(sk9,nil),sk3)**.
% 132.99/133.22 20[0:Inp] || -> equalelemsP(nil)*.
% 132.99/133.22 21[0:Inp] || -> duplicatefreeP(nil)*.
% 132.99/133.22 22[0:Inp] || -> strictorderedP(nil)*.
% 132.99/133.22 23[0:Inp] || -> totalorderedP(nil)*.
% 132.99/133.22 24[0:Inp] || -> strictorderP(nil)*.
% 132.99/133.22 25[0:Inp] || -> totalorderP(nil)*.
% 132.99/133.22 26[0:Inp] || -> cyclefreeP(nil)*.
% 132.99/133.22 27[0:Inp] || -> ssList(nil)*.
% 132.99/133.22 31[0:Inp] || -> ssItem(skaf83(u))*.
% 132.99/133.22 32[0:Inp] || -> ssList(skaf82(u))*.
% 132.99/133.22 73[0:Inp] || equal(skac2,skac3)** -> .
% 132.99/133.22 83[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 132.99/133.22 84[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 132.99/133.22 85[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 132.99/133.22 86[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 132.99/133.22 87[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 132.99/133.22 88[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 132.99/133.22 89[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 132.99/133.22 90[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 132.99/133.22 91[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 132.99/133.22 93[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 132.99/133.22 104[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 132.99/133.22 105[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 132.99/133.22 115[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 132.99/133.22 116[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 132.99/133.22 117[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 132.99/133.22 118[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 132.99/133.22 120[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 132.99/133.22 121[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 132.99/133.22 128[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 132.99/133.22 135[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 132.99/133.22 138[0:Inp] ssList(u) ssList(v) || equal(app(u,v),nil)** -> equal(nil,v).
% 132.99/133.22 139[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 132.99/133.22 142[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 132.99/133.22 152[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(app(tl(u),v),tl(app(u,v)))**.
% 132.99/133.22 157[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 132.99/133.22 159[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 132.99/133.22 160[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(w,u) -> memberP(app(v,w),u)*.
% 132.99/133.22 164[0:Inp] ssList(u) ssList(v) || equal(nil,v) equal(nil,u) -> equal(app(u,v),nil)**.
% 132.99/133.22 168[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 132.99/133.22 176[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 132.99/133.22 180[0:Inp] ssItem(u) ssItem(v) ssList(w) || memberP(cons(v,w),u)* -> equal(u,v) memberP(w,u).
% 132.99/133.22 189[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 132.99/133.22 194[0:Inp] ssList(u) ssItem(v) ssList(w) ssList(x) || equal(app(w,cons(v,x)),u)*+ -> memberP(u,v)*.
% 132.99/133.22 196[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).
% 132.99/133.22 198[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)* -> .
% 132.99/133.22 209[0:Rew:6.0,16.1,5.0,16.0] || equal(nil,sk2)** -> equal(nil,sk1).
% 132.99/133.22 210[0:Rew:6.0,18.1,5.0,18.0] || neq(sk2,nil) -> equal(cons(sk9,nil),sk1)**.
% 132.99/133.22 370[0:Res:9.0,138.0] ssList(u) || equal(app(u,sk7),nil)** -> equal(nil,sk7).
% 132.99/133.22 413[0:Res:9.0,196.1] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(nil,u) equal(nil,sk7).
% 132.99/133.22 442[0:Res:9.0,142.1] ssList(u) || -> equal(nil,sk7) equal(hd(app(sk7,u)),hd(sk7))**.
% 132.99/133.22 445[0:Res:9.0,139.1] ssItem(u) || -> equal(app(cons(u,nil),sk7),cons(u,sk7))**.
% 132.99/133.22 448[0:Res:9.0,115.1] ssItem(u) || -> equal(tl(cons(u,sk7)),sk7)**.
% 132.99/133.22 449[0:Res:9.0,116.1] ssItem(u) || -> equal(hd(cons(u,sk7)),u)**.
% 132.99/133.22 450[0:Res:9.0,117.1] ssItem(u) || equal(cons(u,sk7),nil)** -> .
% 132.99/133.22 451[0:Res:9.0,118.1] ssItem(u) || equal(cons(u,sk7),sk7)** -> .
% 132.99/133.22 454[0:Res:9.0,105.1] ssItem(u) || -> ssList(cons(u,sk7))*.
% 132.99/133.22 490[1:Spt:91.1] || -> ssItem(u)*.
% 132.99/133.22 493[1:MRR:454.0,490.0] || -> ssList(cons(u,sk7))*.
% 132.99/133.22 494[1:MRR:90.0,490.0] || memberP(nil,u)* -> .
% 132.99/133.22 495[1:MRR:89.0,490.0] || -> cyclefreeP(cons(u,nil))*.
% 132.99/133.22 496[1:MRR:88.0,490.0] || -> totalorderP(cons(u,nil))*.
% 132.99/133.22 497[1:MRR:87.0,490.0] || -> strictorderP(cons(u,nil))*.
% 132.99/133.22 498[1:MRR:86.0,490.0] || -> totalorderedP(cons(u,nil))*.
% 132.99/133.22 499[1:MRR:85.0,490.0] || -> strictorderedP(cons(u,nil))*.
% 132.99/133.22 500[1:MRR:84.0,490.0] || -> duplicatefreeP(cons(u,nil))*.
% 132.99/133.22 501[1:MRR:83.0,490.0] || -> equalelemsP(cons(u,nil))*.
% 132.99/133.22 503[1:MRR:451.0,490.0] || equal(cons(u,sk7),sk7)** -> .
% 132.99/133.22 504[1:MRR:450.0,490.0] || equal(cons(u,sk7),nil)** -> .
% 132.99/133.22 505[1:MRR:449.0,490.0] || -> equal(hd(cons(u,sk7)),u)**.
% 132.99/133.22 506[1:MRR:448.0,490.0] || -> equal(tl(cons(u,sk7)),sk7)**.
% 132.99/133.22 528[1:MRR:445.0,490.0] || -> equal(app(cons(u,nil),sk7),cons(u,sk7))**.
% 132.99/133.22 529[1:MRR:121.1,121.0,490.0] || -> equal(u,v) neq(u,v)*.
% 132.99/133.22 587[1:MRR:160.0,490.0] ssList(u) ssList(v) || memberP(v,w) -> memberP(app(u,v),w)*.
% 132.99/133.22 588[1:MRR:159.0,490.0] ssList(u) ssList(v) || memberP(u,w) -> memberP(app(u,v),w)*.
% 132.99/133.22 590[1:MRR:157.1,157.0,490.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 132.99/133.22 609[1:MRR:180.1,180.0,490.0] ssList(u) || memberP(cons(v,u),w)* -> equal(w,v) memberP(u,w).
% 132.99/133.22 625[1:MRR:105.1,490.0] ssList(u) || -> ssList(cons(v,u))*.
% 132.99/133.22 627[1:MRR:117.1,490.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 132.99/133.22 628[1:MRR:116.1,490.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 132.99/133.22 629[1:MRR:115.1,490.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 132.99/133.22 630[1:MRR:135.1,490.0] ssList(u) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 132.99/133.22 631[1:MRR:139.1,490.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 132.99/133.22 639[1:MRR:194.1,490.0] ssList(u) ssList(v) ssList(w) || equal(app(v,cons(x,w)),u)*+ -> memberP(u,x)*.
% 132.99/133.22 683[1:MRR:189.3,189.2,490.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 132.99/133.22 684[2:Spt:442.0,442.2] ssList(u) || -> equal(hd(app(sk7,u)),hd(sk7))**.
% 132.99/133.22 688[3:Spt:413.5] || -> equal(nil,sk7)**.
% 132.99/133.22 741[3:Rew:688.0,93.1] ssList(u) || -> equal(app(sk7,u),u)**.
% 132.99/133.22 747[3:Rew:688.0,495.0] || -> cyclefreeP(cons(u,sk7))*.
% 132.99/133.22 748[3:Rew:688.0,496.0] || -> totalorderP(cons(u,sk7))*.
% 132.99/133.22 749[3:Rew:688.0,497.0] || -> strictorderP(cons(u,sk7))*.
% 132.99/133.22 750[3:Rew:688.0,498.0] || -> totalorderedP(cons(u,sk7))*.
% 132.99/133.22 751[3:Rew:688.0,499.0] || -> strictorderedP(cons(u,sk7))*.
% 132.99/133.22 752[3:Rew:688.0,500.0] || -> duplicatefreeP(cons(u,sk7))*.
% 132.99/133.22 753[3:Rew:688.0,501.0] || -> equalelemsP(cons(u,sk7))*.
% 132.99/133.22 759[3:Rew:688.0,631.1] ssList(u) || -> equal(app(cons(v,sk7),u),cons(v,u))**.
% 132.99/133.22 797[3:Rew:741.1,684.1] ssList(u) || -> equal(hd(u),hd(sk7))*.
% 132.99/133.22 1335[3:SpR:797.1,505.0] ssList(cons(u,sk7)) || -> equal(hd(sk7),u)*.
% 132.99/133.22 1340[3:SSi:1335.0,753.0,752.0,751.0,750.0,749.0,748.0,747.0,493.0] || -> equal(hd(sk7),u)*.
% 132.99/133.22 1446[3:Rew:1340.0,759.1] ssList(u) || -> equal(cons(v,u),hd(sk7))**.
% 132.99/133.22 1457[3:Rew:1340.0,683.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk7))** -> equal(w,x)*.
% 132.99/133.22 1530[3:Con:1457.1] ssList(u) || equal(cons(v,u),hd(sk7))** -> equal(v,w)*.
% 132.99/133.22 1531[3:AED:73.0,1530.2] ssList(u) || equal(cons(v,u),hd(sk7))** -> .
% 132.99/133.22 1532[3:Rew:1446.1,1531.1] ssList(u) || equal(hd(sk7),hd(sk7))* -> .
% 132.99/133.22 1533[3:Obv:1532.1] ssList(u) || -> .
% 132.99/133.22 1534[3:UnC:1533.0,2.0] || -> .
% 132.99/133.22 1620[3:Spt:1534.0,413.5,688.0] || equal(nil,sk7)** -> .
% 132.99/133.22 1621[3:Spt:1534.0,413.0,413.1,413.2,413.3,413.4] ssList(u) || equal(hd(u),hd(sk7))* equal(tl(u),tl(sk7)) -> equal(u,sk7) equal(nil,u).
% 132.99/133.22 1631[3:MRR:370.2,1620.0] ssList(u) || equal(app(u,sk7),nil)** -> .
% 132.99/133.22 1635[4:Spt:209.1] || -> equal(nil,sk1)**.
% 132.99/133.22 1637[4:Rew:1635.0,20.0] || -> equalelemsP(sk1)*.
% 132.99/133.22 1638[4:Rew:1635.0,21.0] || -> duplicatefreeP(sk1)*.
% 132.99/133.22 1639[4:Rew:1635.0,22.0] || -> strictorderedP(sk1)*.
% 132.99/133.22 1640[4:Rew:1635.0,23.0] || -> totalorderedP(sk1)*.
% 132.99/133.22 1641[4:Rew:1635.0,24.0] || -> strictorderP(sk1)*.
% 132.99/133.22 1642[4:Rew:1635.0,25.0] || -> totalorderP(sk1)*.
% 132.99/133.22 1643[4:Rew:1635.0,26.0] || -> cyclefreeP(sk1)*.
% 132.99/133.22 1649[4:Rew:1635.0,501.0] || -> equalelemsP(cons(u,sk1))*.
% 132.99/133.22 1650[4:Rew:1635.0,500.0] || -> duplicatefreeP(cons(u,sk1))*.
% 132.99/133.22 1651[4:Rew:1635.0,499.0] || -> strictorderedP(cons(u,sk1))*.
% 132.99/133.22 1652[4:Rew:1635.0,498.0] || -> totalorderedP(cons(u,sk1))*.
% 132.99/133.22 1653[4:Rew:1635.0,497.0] || -> strictorderP(cons(u,sk1))*.
% 132.99/133.22 1654[4:Rew:1635.0,496.0] || -> totalorderP(cons(u,sk1))*.
% 132.99/133.22 1655[4:Rew:1635.0,495.0] || -> cyclefreeP(cons(u,sk1))*.
% 132.99/133.22 1674[4:Rew:1635.0,10.0] || -> equal(app(app(sk6,cons(sk5,sk1)),sk7),sk1)**.
% 132.99/133.22 1701[4:Rew:1635.0,1631.1] ssList(u) || equal(app(u,sk7),sk1)** -> .
% 132.99/133.22 1783[4:SpL:1674.0,1701.1] ssList(app(sk6,cons(sk5,sk1))) || equal(sk1,sk1)* -> .
% 132.99/133.22 1786[4:Obv:1783.1] ssList(app(sk6,cons(sk5,sk1))) || -> .
% 132.99/133.22 1852[4:SoR:1786.0,104.2] ssList(cons(sk5,sk1)) ssList(sk6) || -> .
% 132.99/133.22 1859[4:SSi:1852.1,1852.0,8.0,625.0,1.0,1637.0,1638.0,1639.0,1640.0,1641.0,1642.0,1643.0,1649.0,1650.0,1651.0,1652.0,1653.0,1654.1,1655.0] || -> .
% 132.99/133.22 1860[4:Spt:1859.0,209.1,1635.0] || equal(nil,sk1)** -> .
% 132.99/133.22 1861[4:Spt:1859.0,209.0] || equal(nil,sk2)** -> .
% 132.99/133.22 1910[1:SpR:210.1,495.0] || neq(sk2,nil)* -> cyclefreeP(sk1).
% 132.99/133.22 1911[1:SpR:210.1,496.0] || neq(sk2,nil)* -> totalorderP(sk1).
% 132.99/133.22 1912[1:SpR:210.1,497.0] || neq(sk2,nil)* -> strictorderP(sk1).
% 132.99/133.22 1913[1:SpR:210.1,498.0] || neq(sk2,nil)* -> totalorderedP(sk1).
% 132.99/133.22 1914[1:SpR:210.1,499.0] || neq(sk2,nil)* -> strictorderedP(sk1).
% 132.99/133.22 1915[1:SpR:210.1,500.0] || neq(sk2,nil)* -> duplicatefreeP(sk1).
% 132.99/133.22 1916[1:SpR:210.1,501.0] || neq(sk2,nil)* -> equalelemsP(sk1).
% 132.99/133.22 1918[1:SpR:210.1,629.1] ssList(nil) || neq(sk2,nil)* -> equal(tl(sk1),nil).
% 132.99/133.22 1919[1:SpR:210.1,628.1] ssList(nil) || neq(sk2,nil)* -> equal(hd(sk1),sk9).
% 132.99/133.22 1923[1:SSi:1918.0,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] || neq(sk2,nil)* -> equal(tl(sk1),nil).
% 132.99/133.22 1924[1:SSi:1919.0,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] || neq(sk2,nil)* -> equal(hd(sk1),sk9).
% 132.99/133.22 1925[1:Res:529.1,1910.0] || -> equal(nil,sk2) cyclefreeP(sk1)*.
% 132.99/133.22 1926[4:MRR:1925.0,1861.0] || -> cyclefreeP(sk1)*.
% 132.99/133.22 1927[1:Res:529.1,1911.0] || -> equal(nil,sk2) totalorderP(sk1)*.
% 132.99/133.22 1928[4:MRR:1927.0,1861.0] || -> totalorderP(sk1)*.
% 132.99/133.22 1932[1:Res:529.1,1912.0] || -> equal(nil,sk2) strictorderP(sk1)*.
% 132.99/133.22 1933[4:MRR:1932.0,1861.0] || -> strictorderP(sk1)*.
% 132.99/133.22 1934[1:Res:529.1,1913.0] || -> equal(nil,sk2) totalorderedP(sk1)*.
% 132.99/133.22 1935[4:MRR:1934.0,1861.0] || -> totalorderedP(sk1)*.
% 132.99/133.22 1938[1:Res:529.1,1914.0] || -> equal(nil,sk2) strictorderedP(sk1)*.
% 132.99/133.22 1939[4:MRR:1938.0,1861.0] || -> strictorderedP(sk1)*.
% 132.99/133.22 1940[1:Res:529.1,1915.0] || -> equal(nil,sk2) duplicatefreeP(sk1)*.
% 132.99/133.22 1941[4:MRR:1940.0,1861.0] || -> duplicatefreeP(sk1)*.
% 132.99/133.22 1944[1:Res:529.1,1916.0] || -> equal(nil,sk2) equalelemsP(sk1)*.
% 132.99/133.22 1945[4:MRR:1944.0,1861.0] || -> equalelemsP(sk1)*.
% 132.99/133.22 1946[1:Res:529.1,1923.0] || -> equal(nil,sk2) equal(tl(sk1),nil)**.
% 132.99/133.22 1947[4:MRR:1946.0,1861.0] || -> equal(tl(sk1),nil)**.
% 132.99/133.22 1952[1:Res:529.1,1924.0] || -> equal(nil,sk2) equal(hd(sk1),sk9)**.
% 132.99/133.22 1953[4:MRR:1952.0,1861.0] || -> equal(hd(sk1),sk9)**.
% 132.99/133.22 2054[1:EqR:630.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 132.99/133.22 2057[1:SSi:2054.0,625.0,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,495.0,496.0,497.0,498.0,499.0,500.0,501.1] || -> singletonP(cons(u,nil))*.
% 132.99/133.22 2059[1:SpR:210.1,2057.0] || neq(sk2,nil)* -> singletonP(sk1).
% 132.99/133.22 2061[1:Res:529.1,2059.0] || -> equal(nil,sk2) singletonP(sk1)*.
% 132.99/133.22 2062[4:MRR:2061.0,1861.0] || -> singletonP(sk1)*.
% 132.99/133.22 2130[1:SpR:120.2,629.1] ssList(u) singletonP(u) ssList(nil) || -> equal(tl(u),nil)**.
% 132.99/133.22 2140[1:SSi:2130.2,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] ssList(u) singletonP(u) || -> equal(tl(u),nil)**.
% 132.99/133.22 2169[1:SpR:2140.2,506.0] ssList(cons(u,sk7)) singletonP(cons(u,sk7)) || -> equal(nil,sk7)**.
% 132.99/133.22 2176[1:SSi:2169.0,493.0] singletonP(cons(u,sk7)) || -> equal(nil,sk7)**.
% 132.99/133.22 2177[3:MRR:2176.1,1620.0] singletonP(cons(u,sk7)) || -> .
% 132.99/133.22 2180[3:SoR:2177.0,630.2] ssList(cons(u,sk7)) || equal(cons(v,nil),cons(u,sk7))* -> .
% 132.99/133.22 2181[3:SSi:2180.0,493.0] || equal(cons(u,nil),cons(v,sk7))* -> .
% 132.99/133.22 2202[1:SpR:128.2,629.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 132.99/133.22 2203[1:SpR:128.2,628.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 132.99/133.22 2212[1:SSi:2202.1,32.0] ssList(u) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 132.99/133.22 2217[1:Rew:2212.2,152.3] ssList(u) ssList(v) || -> equal(nil,u) equal(app(skaf82(u),v),tl(app(u,v)))**.
% 132.99/133.22 2219[1:SSi:2203.1,32.0] ssList(u) || -> equal(nil,u) equal(hd(u),skaf83(u))**.
% 132.99/133.22 2645[1:SpR:10.0,588.3] ssList(app(sk6,cons(sk5,nil))) ssList(sk7) || memberP(app(sk6,cons(sk5,nil)),u)* -> memberP(sk1,u).
% 132.99/133.22 2658[1:SpL:120.2,609.1] ssList(u) singletonP(u) ssList(nil) || memberP(u,v)* -> equal(v,skaf44(u)) memberP(nil,v)*.
% 132.99/133.22 2672[1:SSi:2658.2,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] ssList(u) singletonP(u) || memberP(u,v)* -> equal(v,skaf44(u)) memberP(nil,v)*.
% 132.99/133.22 2673[1:MRR:2672.4,494.0] ssList(u) singletonP(u) || memberP(u,v)* -> equal(v,skaf44(u)).
% 132.99/133.22 3482[1:SpL:2217.3,138.2] ssList(u) ssList(v) ssList(skaf82(u)) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 132.99/133.22 3491[1:Obv:3482.1] ssList(u) ssList(skaf82(u)) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 132.99/133.22 3492[1:SSi:3491.1,32.0] ssList(u) ssList(v) || equal(tl(app(u,v)),nil)** -> equal(nil,u) equal(nil,v).
% 132.99/133.22 3746[1:SpR:164.4,587.3] ssList(u) ssList(v) ssList(u) ssList(v) || equal(nil,v) equal(nil,u)* memberP(v,w)* -> memberP(nil,w)*.
% 132.99/133.22 3784[1:Obv:3746.1] ssList(u) ssList(v) || equal(nil,v) equal(nil,u)* memberP(v,w)* -> memberP(nil,w)*.
% 132.99/133.22 3785[1:Con:3784.0] ssList(u) || equal(nil,u) memberP(u,v)* -> memberP(nil,v)*.
% 132.99/133.22 3786[1:MRR:3785.3,494.0] ssList(u) || equal(nil,u) memberP(u,v)* -> .
% 132.99/133.22 4436[0:SpR:93.1,168.3] ssList(u) ssList(nil) ssList(u) ssList(v) || -> equal(app(nil,app(u,v)),app(u,v))**.
% 132.99/133.22 4467[0:Obv:4436.0] ssList(nil) ssList(u) ssList(v) || -> equal(app(nil,app(u,v)),app(u,v))**.
% 132.99/133.22 4468[0:SSi:4467.0,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] ssList(u) ssList(v) || -> equal(app(nil,app(u,v)),app(u,v))**.
% 132.99/133.22 6470[1:EqR:639.3] ssList(app(u,cons(v,w))) ssList(u) ssList(w) || -> memberP(app(u,cons(v,w)),v)*.
% 132.99/133.22 6494[1:SSi:6470.0,104.1,625.2] ssList(u) ssList(v) || -> memberP(app(u,cons(w,v)),w)*.
% 132.99/133.22 8537[4:SpR:2212.2,1947.0] ssList(sk1) || -> equal(nil,sk1) equal(skaf82(sk1),nil)**.
% 132.99/133.22 8570[1:SpR:2219.2,628.1] ssList(cons(u,v)) ssList(v) || -> equal(cons(u,v),nil) equal(skaf83(cons(u,v)),u)**.
% 132.99/133.22 8586[1:SSi:8570.0,625.1] ssList(u) || -> equal(cons(v,u),nil) equal(skaf83(cons(v,u)),v)**.
% 132.99/133.22 8587[1:MRR:8586.1,627.1] ssList(u) || -> equal(skaf83(cons(v,u)),v)**.
% 132.99/133.22 8795[4:SSi:8537.0,1.0,1926.0,1928.0,1933.0,1935.0,1939.0,1941.0,1945.0,2062.0] || -> equal(nil,sk1) equal(skaf82(sk1),nil)**.
% 132.99/133.22 8796[4:MRR:8795.0,1860.0] || -> equal(skaf82(sk1),nil)**.
% 132.99/133.22 8807[1:SSi:2645.0,104.0,8.0,2057.0,501.0,500.0,499.0,498.0,497.0,496.1,495.0,625.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0,27.2] ssList(sk7) || memberP(app(sk6,cons(sk5,nil)),u)* -> memberP(sk1,u).
% 132.99/133.22 8808[1:MRR:8807.0,9.0] || memberP(app(sk6,cons(sk5,nil)),u)* -> memberP(sk1,u).
% 132.99/133.22 8836[4:SpR:1953.0,2219.2] ssList(sk1) || -> equal(nil,sk1) equal(skaf83(sk1),sk9)**.
% 132.99/133.22 8841[4:SSi:8836.0,1.0,1926.0,1928.0,1933.0,1935.0,1939.0,1941.0,1945.0,2062.0] || -> equal(nil,sk1) equal(skaf83(sk1),sk9)**.
% 132.99/133.22 8842[4:MRR:8841.0,1860.0] || -> equal(skaf83(sk1),sk9)**.
% 132.99/133.22 8844[4:SpR:8796.0,128.2] ssList(sk1) || -> equal(nil,sk1) equal(cons(skaf83(sk1),nil),sk1)**.
% 132.99/133.22 8850[4:Rew:8842.0,8844.2] ssList(sk1) || -> equal(nil,sk1) equal(cons(sk9,nil),sk1)**.
% 132.99/133.22 8851[4:SSi:8850.0,1.0,1926.0,1928.0,1933.0,1935.0,1939.0,1941.0,1945.0,2062.0] || -> equal(nil,sk1) equal(cons(sk9,nil),sk1)**.
% 132.99/133.22 8852[4:MRR:8851.0,1860.0] || -> equal(cons(sk9,nil),sk1)**.
% 132.99/133.22 8889[0:SpR:10.0,168.3] ssList(sk6) ssList(cons(sk5,nil)) ssList(sk7) || -> equal(app(sk6,app(cons(sk5,nil),sk7)),sk1)**.
% 132.99/133.22 8905[1:Rew:631.1,8889.3] ssList(sk6) ssList(cons(sk5,nil)) ssList(sk7) || -> equal(app(sk6,cons(sk5,sk7)),sk1)**.
% 132.99/133.22 10574[1:Res:587.3,8808.0] ssList(sk6) ssList(cons(sk5,nil)) || memberP(cons(sk5,nil),u)* -> memberP(sk1,u).
% 176.03/176.28 10575[1:SSi:10574.1,10574.0,2057.0,501.0,500.0,499.0,498.0,497.0,496.0,495.0,625.0,20.1,21.0,22.0,23.0,24.0,25.0,26.0,27.0,8.0] || memberP(cons(sk5,nil),u)* -> memberP(sk1,u).
% 176.03/176.28 11374[4:SpR:8852.0,528.0] || -> equal(app(sk1,sk7),cons(sk9,sk7))**.
% 176.03/176.28 11390[4:SpL:8852.0,2181.0] || equal(cons(u,sk7),sk1)** -> .
% 176.03/176.28 19123[1:Res:590.2,10575.0] ssList(nil) || equal(u,sk5) -> memberP(sk1,u)*.
% 176.03/176.28 19939[1:SpR:120.2,8587.1] ssList(u) singletonP(u) ssList(nil) || -> equal(skaf44(u),skaf83(u))**.
% 176.03/176.28 19942[1:SSi:19939.2,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] ssList(u) singletonP(u) || -> equal(skaf44(u),skaf83(u))**.
% 176.03/176.28 19946[1:Rew:19942.2,2673.3] ssList(u) singletonP(u) || memberP(u,v)* -> equal(v,skaf83(u)).
% 176.03/176.28 25031[1:SSi:19123.0,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0] || equal(u,sk5) -> memberP(sk1,u)*.
% 176.03/176.28 29716[1:Res:25031.1,3786.2] ssList(sk1) || equal(u,sk5)* equal(nil,sk1)** -> .
% 176.03/176.28 29745[1:AED:73.0,29716.1] ssList(sk1) || equal(nil,sk1)** -> .
% 176.03/176.28 37372[1:SSi:8905.2,8905.1,8905.0,9.0,495.0,496.0,497.0,498.0,499.0,500.0,2057.0,501.0,625.1,27.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,8.0] || -> equal(app(sk6,cons(sk5,sk7)),sk1)**.
% 176.03/176.28 38525[1:SpR:37372.0,6494.2] ssList(sk6) ssList(sk7) || -> memberP(sk1,sk5)*.
% 176.03/176.28 47437[1:SpR:37372.0,4468.2] ssList(sk6) ssList(cons(sk5,sk7)) || -> equal(app(nil,sk1),sk1)**.
% 176.03/176.28 55249[1:SpL:37372.0,3492.2] ssList(sk6) ssList(cons(sk5,sk7)) || equal(tl(sk1),nil) -> equal(nil,sk6) equal(cons(sk5,sk7),nil)**.
% 176.03/176.28 55292[4:Rew:1947.0,55249.2] ssList(sk6) ssList(cons(sk5,sk7)) || equal(nil,nil) -> equal(nil,sk6) equal(cons(sk5,sk7),nil)**.
% 176.03/176.28 55293[4:Obv:55292.2] ssList(sk6) ssList(cons(sk5,sk7)) || -> equal(nil,sk6) equal(cons(sk5,sk7),nil)**.
% 176.03/176.28 69941[1:SSi:38525.1,38525.0,9.0,8.0] || -> memberP(sk1,sk5)*.
% 176.03/176.28 69958[1:SSi:47437.1,47437.0,625.0,9.0,8.1] || -> equal(app(nil,sk1),sk1)**.
% 176.03/176.28 69981[4:SSi:55293.1,55293.0,625.0,9.0,8.1] || -> equal(nil,sk6) equal(cons(sk5,sk7),nil)**.
% 176.03/176.28 69982[4:MRR:69981.1,504.0] || -> equal(nil,sk6)**.
% 176.03/176.28 70023[4:Rew:69982.0,8852.0] || -> equal(cons(sk9,sk6),sk1)**.
% 176.03/176.28 70038[4:Rew:69982.0,10.0] || -> equal(app(app(sk6,cons(sk5,sk6)),sk7),sk1)**.
% 176.03/176.28 70266[4:Rew:69982.0,69958.0] || -> equal(app(sk6,sk1),sk1)**.
% 176.03/176.28 71701[1:Res:69941.0,19946.2] ssList(sk1) singletonP(sk1) || -> equal(skaf83(sk1),sk5)**.
% 176.03/176.28 71703[4:Rew:8842.0,71701.2] ssList(sk1) singletonP(sk1) || -> equal(sk9,sk5)**.
% 176.03/176.28 71704[4:SSi:71703.1,71703.0,1.0,1926.0,1928.0,1933.0,1935.0,1939.0,1941.0,1945.0,2062.0,1.0,1926.0,1928.0,1933.0,1935.0,1939.0,1941.0,1945.0,2062.0] || -> equal(sk9,sk5)**.
% 176.03/176.28 71716[4:Rew:71704.0,11374.0] || -> equal(app(sk1,sk7),cons(sk5,sk7))**.
% 176.03/176.28 71773[4:Rew:71704.0,70023.0] || -> equal(cons(sk5,sk6),sk1)**.
% 176.03/176.28 71818[4:Rew:71773.0,70038.0] || -> equal(app(app(sk6,sk1),sk7),sk1)**.
% 176.03/176.28 71831[4:Rew:71716.0,71818.0,70266.0,71818.0] || -> equal(cons(sk5,sk7),sk1)**.
% 176.03/176.28 71832[4:MRR:71831.0,11390.0] || -> .
% 176.03/176.28 71863[2:Spt:71832.0,442.1] || -> equal(nil,sk7)**.
% 176.03/176.28 71880[2:Rew:71863.0,494.0] || memberP(sk7,u)* -> .
% 176.03/176.28 72091[2:MRR:12.0,71880.0] || -> memberP(sk6,sk8)*.
% 176.03/176.28 72093[2:Rew:71863.0,1946.1,71863.0,1946.0] || -> equal(sk7,sk2) equal(tl(sk1),sk7)**.
% 176.03/176.28 72095[2:Rew:71863.0,29745.1] ssList(sk1) || equal(sk7,sk1)** -> .
% 176.03/176.28 72096[2:SSi:72095.0,1.0] || equal(sk7,sk1)** -> .
% 176.03/176.28 72101[2:Rew:71863.0,209.1,71863.0,209.0] || equal(sk7,sk2)** -> equal(sk7,sk1).
% 176.03/176.28 72102[2:MRR:72101.1,72096.0] || equal(sk7,sk2)** -> .
% 176.03/176.28 72111[2:MRR:72093.0,72102.0] || -> equal(tl(sk1),sk7)**.
% 176.03/176.28 73273[2:Rew:71863.0,55249.4,71863.0,55249.3,72111.0,55249.2,71863.0,55249.2] ssList(sk6) ssList(cons(sk5,sk7)) || equal(sk7,sk7) -> equal(sk7,sk6) equal(cons(sk5,sk7),sk7)**.
% 176.03/176.28 73274[2:Obv:73273.2] ssList(sk6) ssList(cons(sk5,sk7)) || -> equal(sk7,sk6) equal(cons(sk5,sk7),sk7)**.
% 176.03/176.28 73275[2:SSi:73274.1,73274.0,625.0,9.0,8.1] || -> equal(sk7,sk6) equal(cons(sk5,sk7),sk7)**.
% 176.03/176.28 73276[2:MRR:73275.1,503.0] || -> equal(sk7,sk6)**.
% 176.03/176.28 73772[2:Rew:73276.0,71880.0] || memberP(sk6,u)* -> .
% 176.03/176.28 73914[2:UnC:73772.0,72091.0] || -> .
% 176.03/176.28 75031[1:Spt:73914.0,91.0,91.2] ssList(u) || -> duplicatefreeP(u)*.
% 176.03/176.28 75146[1:MRR:198.1,75031.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 176.03/176.28 93159[0:SpR:176.3,104.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 176.03/176.28 93200[0:Obv:93159.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 176.03/176.28 93201[0:SSi:93200.2,105.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 176.03/176.28 95365[1:EqR:75146.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 176.03/176.28 95390[1:SSi:95365.0,104.2,104.2,105.2,105.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 176.03/176.28 95391[1:MRR:93201.3,95390.1] ssList(u) ssItem(v) ssList(w) || -> .
% 176.03/176.28 95394[1:Con:95391.2] ssList(u) ssItem(v) || -> .
% 176.03/176.28 95895[1:MRR:454.1,95394.0] ssItem(u) || -> .
% 176.03/176.28 95896[1:UnC:95895.0,31.0] || -> .
% 176.03/176.28 % SZS output end Refutation
% 176.03/176.28 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_8 co1_9 co1_10 co1_12 co1_16 co1_18 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause74 clause85 clause86 clause96 clause97 clause98 clause99 clause101 clause102 clause109 clause116 clause119 clause120 clause123 clause133 clause138 clause140 clause141 clause145 clause149 clause157 clause161 clause170 clause175 clause177 clause179
% 176.03/176.28
%------------------------------------------------------------------------------