TSTP Solution File: SWC380-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC380-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 22:03:42 EDT 2022
% Result : Unsatisfiable 3.82s 3.99s
% Output : Refutation 4.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC380-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 11 22:28:38 EDT 2022
% 0.19/0.34 % CPUTime :
% 3.82/3.99
% 3.82/3.99 SPASS V 3.9
% 3.82/3.99 SPASS beiseite: Proof found.
% 3.82/3.99 % SZS status Theorem
% 3.82/3.99 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.82/3.99 SPASS derived 8186 clauses, backtracked 4889 clauses, performed 69 splits and kept 7790 clauses.
% 3.82/3.99 SPASS allocated 84562 KBytes.
% 3.82/3.99 SPASS spent 0:00:03.64 on the problem.
% 3.82/3.99 0:00:00.04 for the input.
% 3.82/3.99 0:00:00.00 for the FLOTTER CNF translation.
% 3.82/3.99 0:00:00.06 for inferences.
% 3.82/3.99 0:00:00.09 for the backtracking.
% 3.82/3.99 0:00:03.23 for the reduction.
% 3.82/3.99
% 3.82/3.99
% 3.82/3.99 Here is a proof with depth 3, length 265 :
% 3.82/3.99 % SZS output start Refutation
% 3.82/3.99 1[0:Inp] || -> ssList(sk1)*.
% 3.82/3.99 2[0:Inp] || -> ssList(sk2)*.
% 3.82/3.99 5[0:Inp] || -> equal(sk4,sk2)**.
% 3.82/3.99 6[0:Inp] || -> equal(sk3,sk1)**.
% 3.82/3.99 7[0:Inp] || -> neq(sk2,nil)* neq(sk2,nil)*.
% 3.82/3.99 10[0:Inp] || -> ssItem(sk5) neq(sk2,nil)*.
% 3.82/3.99 11[0:Inp] || -> ssList(sk6) neq(sk2,nil)*.
% 3.82/3.99 14[0:Inp] ssItem(u) || equal(cons(u,nil),sk1)** memberP(sk2,u) neq(sk4,nil) -> .
% 3.82/3.99 15[0:Inp] || neq(sk4,nil)* -> ssItem(sk5).
% 3.82/3.99 16[0:Inp] || neq(sk4,nil)* -> ssList(sk6).
% 3.82/3.99 17[0:Inp] || neq(sk4,nil) -> equal(cons(sk5,nil),sk3)**.
% 3.82/3.99 18[0:Inp] || neq(sk4,nil) -> equal(app(cons(sk5,nil),sk6),sk4)**.
% 3.82/3.99 19[0:Inp] || -> equalelemsP(nil)*.
% 3.82/3.99 20[0:Inp] || -> duplicatefreeP(nil)*.
% 3.82/3.99 21[0:Inp] || -> strictorderedP(nil)*.
% 3.82/3.99 22[0:Inp] || -> totalorderedP(nil)*.
% 3.82/3.99 23[0:Inp] || -> strictorderP(nil)*.
% 3.82/3.99 24[0:Inp] || -> totalorderP(nil)*.
% 3.82/3.99 25[0:Inp] || -> cyclefreeP(nil)*.
% 3.82/3.99 26[0:Inp] || -> ssList(nil)*.
% 3.82/3.99 30[0:Inp] || -> ssItem(skaf83(u))*.
% 3.82/3.99 31[0:Inp] || -> ssList(skaf82(u))*.
% 3.82/3.99 65[0:Inp] || -> ssItem(skaf44(u))*.
% 3.82/3.99 72[0:Inp] || equal(skac2,skac3)** -> .
% 3.82/3.99 82[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.82/3.99 86[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.82/3.99 87[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.82/3.99 88[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.82/3.99 90[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 3.82/3.99 91[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 3.82/3.99 92[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.82/3.99 95[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 3.82/3.99 104[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 3.82/3.99 106[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 3.82/3.99 114[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 3.82/3.99 115[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 3.82/3.99 116[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 3.82/3.99 117[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 3.82/3.99 119[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 3.82/3.99 122[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 3.82/3.99 127[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 3.82/3.99 130[0:Inp] ssItem(u) ssList(v) || equal(nil,v) -> strictorderedP(cons(u,v))*.
% 3.82/3.99 131[0:Inp] ssItem(u) ssList(v) || equal(nil,v) -> totalorderedP(cons(u,v))*.
% 3.82/3.99 134[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 3.82/3.99 135[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 3.82/3.99 138[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.82/3.99 141[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 3.82/3.99 151[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(app(tl(u),v),tl(app(u,v)))**.
% 3.82/3.99 152[0:Inp] ssItem(u) ssList(v) || strictorderedP(cons(u,v)) -> lt(u,hd(v))* equal(nil,v).
% 3.82/3.99 156[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 3.82/3.99 158[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 3.82/3.99 175[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 3.82/3.99 181[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 3.82/3.99 182[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 3.82/3.99 188[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.82/3.99 195[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).
% 3.82/3.99 206[0:Rew:5.0,16.0] || neq(sk2,nil)* -> ssList(sk6).
% 3.82/3.99 207[0:MRR:206.0,11.1] || -> ssList(sk6)*.
% 3.82/3.99 208[0:Rew:5.0,15.0] || neq(sk2,nil)* -> ssItem(sk5).
% 3.82/3.99 209[0:MRR:208.0,10.1] || -> ssItem(sk5)*.
% 3.82/3.99 210[0:Obv:7.0] || -> neq(sk2,nil)*.
% 3.82/3.99 211[0:Rew:6.0,17.1,5.0,17.0] || neq(sk2,nil) -> equal(cons(sk5,nil),sk1)**.
% 3.82/3.99 212[0:MRR:211.0,210.0] || -> equal(cons(sk5,nil),sk1)**.
% 3.82/3.99 213[0:Rew:212.0,18.1,5.0,18.1,5.0,18.0] || neq(sk2,nil) -> equal(app(sk1,sk6),sk2)**.
% 3.82/3.99 214[0:MRR:213.0,210.0] || -> equal(app(sk1,sk6),sk2)**.
% 3.82/3.99 215[0:Rew:5.0,14.3] ssItem(u) || equal(cons(u,nil),sk1)** memberP(sk2,u) neq(sk2,nil) -> .
% 3.82/3.99 216[0:MRR:215.3,210.0] ssItem(u) || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 3.82/3.99 278[0:Res:2.0,122.0] || -> equal(nil,sk2) equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 3.82/3.99 298[0:Res:2.0,95.0] || -> ssList(tl(sk2))* equal(nil,sk2).
% 3.82/3.99 302[0:Res:2.0,90.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 3.82/3.99 317[0:Res:2.0,195.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 3.82/3.99 346[0:Res:2.0,141.1] ssList(u) || -> equal(nil,sk2) equal(hd(app(sk2,u)),hd(sk2))**.
% 3.82/3.99 369[0:Res:2.0,175.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk2),cons(v,app(u,sk2)))**.
% 3.82/3.99 410[0:Res:1.0,182.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 3.82/3.99 411[0:Res:1.0,181.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 3.82/3.99 425[0:Res:1.0,152.0] ssItem(u) || strictorderedP(cons(u,sk1)) -> lt(u,hd(sk1))* equal(nil,sk1).
% 3.82/3.99 452[0:Res:1.0,119.1] singletonP(sk1) || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 3.82/3.99 468[0:Res:1.0,106.0] || -> cyclefreeP(sk1) leq(skaf49(sk1),skaf50(sk1))*.
% 3.82/3.99 473[0:Res:1.0,90.0] || -> ssItem(u)* duplicatefreeP(sk1)*.
% 3.82/3.99 488[0:Res:1.0,195.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 3.82/3.99 505[0:Res:1.0,151.1] ssList(u) || -> equal(nil,sk1) equal(app(tl(sk1),u),tl(app(sk1,u)))**.
% 3.82/3.99 517[0:Res:1.0,141.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 3.82/3.99 522[0:Res:1.0,134.1] ssItem(u) || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 3.82/3.99 523[0:Res:1.0,114.1] ssItem(u) || -> equal(tl(cons(u,sk1)),sk1)**.
% 3.82/3.99 524[0:Res:1.0,115.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 3.82/3.99 525[0:Res:1.0,116.1] ssItem(u) || equal(cons(u,sk1),nil)** -> .
% 3.82/3.99 526[0:Res:1.0,117.1] ssItem(u) || equal(cons(u,sk1),sk1)** -> .
% 3.82/3.99 529[0:Res:1.0,104.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 3.82/3.99 567[1:Spt:90.1] || -> ssItem(u)*.
% 3.82/3.99 570[1:MRR:529.0,567.0] || -> ssList(cons(u,sk1))*.
% 3.82/3.99 581[1:MRR:526.0,567.0] || equal(cons(u,sk1),sk1)** -> .
% 3.82/3.99 583[1:MRR:524.0,567.0] || -> equal(hd(cons(u,sk1)),u)**.
% 3.82/3.99 607[1:MRR:216.0,567.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 3.82/3.99 608[1:MRR:135.1,135.0,567.0] || neq(u,v)* equal(u,v) -> .
% 3.82/3.99 650[1:MRR:156.1,156.0,567.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 3.82/3.99 694[1:MRR:117.1,567.0] ssList(u) || equal(cons(v,u),u)** -> .
% 3.82/3.99 696[1:MRR:115.1,567.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 3.82/3.99 697[1:MRR:114.1,567.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 3.82/3.99 699[1:MRR:138.1,567.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.82/3.99 702[1:MRR:369.1,567.0] ssList(u) || -> equal(app(cons(v,u),sk2),cons(v,app(u,sk2)))**.
% 3.82/3.99 763[1:MRR:188.3,188.2,567.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.82/3.99 764[2:Spt:517.0,517.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 3.82/3.99 766[3:Spt:346.0,346.2] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 3.82/3.99 768[4:Spt:505.0,505.2] ssList(u) || -> equal(app(tl(sk1),u),tl(app(sk1,u)))**.
% 3.82/3.99 772[5:Spt:488.5] || -> equal(nil,sk1)**.
% 3.82/3.99 849[5:Rew:772.0,212.0] || -> equal(cons(sk5,sk1),sk1)**.
% 3.82/3.99 889[5:MRR:849.0,581.0] || -> .
% 3.82/3.99 975[5:Spt:889.0,488.5,772.0] || equal(nil,sk1)** -> .
% 3.82/3.99 976[5:Spt:889.0,488.0,488.1,488.2,488.3,488.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 3.82/3.99 992[6:Spt:317.5] || -> equal(nil,sk2)**.
% 3.82/3.99 1044[6:Rew:992.0,91.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 3.82/3.99 1045[6:Rew:992.0,92.1] ssList(u) || -> equal(app(sk2,u),u)**.
% 3.82/3.99 1127[6:Rew:1044.1,702.1] ssList(u) || -> equal(app(cons(v,u),sk2),cons(v,u))**.
% 3.82/3.99 1128[6:Rew:1045.1,766.1] ssList(u) || -> equal(hd(u),hd(sk2))*.
% 3.82/3.99 1264[6:SpR:1128.1,583.0] ssList(cons(u,sk1)) || -> equal(hd(sk2),u)*.
% 3.82/3.99 1270[6:SSi:1264.0,570.0] || -> equal(hd(sk2),u)*.
% 3.82/3.99 1357[6:Rew:1270.0,1127.1] ssList(u) || -> equal(cons(v,u),hd(sk2))**.
% 3.82/3.99 1481[6:Rew:1270.0,763.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk2))** -> equal(w,x)*.
% 3.82/3.99 1600[6:Con:1481.1] ssList(u) || equal(cons(v,u),hd(sk2))** -> equal(v,w)*.
% 3.82/3.99 1601[6:AED:72.0,1600.2] ssList(u) || equal(cons(v,u),hd(sk2))** -> .
% 3.82/3.99 1602[6:Rew:1357.1,1601.1] ssList(u) || equal(hd(sk2),hd(sk2))* -> .
% 3.82/3.99 1603[6:Obv:1602.1] ssList(u) || -> .
% 3.82/3.99 1604[6:UnC:1603.0,31.0] || -> .
% 3.82/3.99 1771[6:Spt:1604.0,317.5,992.0] || equal(nil,sk2)** -> .
% 3.82/3.99 1772[6:Spt:1604.0,317.0,317.1,317.2,317.3,317.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 3.82/3.99 1778[6:MRR:278.0,1771.0] || -> equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 3.82/3.99 1865[1:Res:210.0,608.0] || equal(nil,sk2)** -> .
% 3.82/3.99 1937[1:SpR:212.0,696.1] ssList(nil) || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 1943[1:SSi:1937.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0] || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 1950[2:Rew:1943.0,764.1] ssList(u) || -> equal(hd(app(sk1,u)),sk5)**.
% 3.82/3.99 1979[1:SpR:212.0,697.1] ssList(nil) || -> equal(tl(sk1),nil)**.
% 3.82/3.99 1981[1:SSi:1979.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0] || -> equal(tl(sk1),nil)**.
% 3.82/3.99 1984[4:Rew:1981.0,768.1] ssList(u) || -> equal(tl(app(sk1,u)),app(nil,u))**.
% 3.82/3.99 1996[4:Rew:92.1,1984.1] ssList(u) || -> equal(tl(app(sk1,u)),u)**.
% 3.82/3.99 2014[1:SpL:212.0,607.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 3.82/3.99 2015[1:Obv:2014.1] || memberP(sk2,sk5)* -> .
% 3.82/3.99 2034[2:SpR:214.0,1950.1] ssList(sk6) || -> equal(hd(sk2),sk5)**.
% 3.82/3.99 2077[4:SpR:214.0,1996.1] ssList(sk6) || -> equal(tl(sk2),sk6)**.
% 3.82/3.99 2287[1:SpR:212.0,699.1] ssList(u) || -> equal(app(sk1,u),cons(sk5,u))**.
% 3.82/3.99 2360[2:SSi:2034.0,207.0] || -> equal(hd(sk2),sk5)**.
% 3.82/3.99 2361[6:Rew:2360.0,1778.0] || -> equal(cons(sk5,tl(sk2)),sk2)**.
% 3.82/3.99 2362[4:SSi:2077.0,207.0] || -> equal(tl(sk2),sk6)**.
% 3.82/3.99 2365[6:Rew:2362.0,2361.0] || -> equal(cons(sk5,sk6),sk2)**.
% 3.82/3.99 2464[6:SpR:2365.0,650.2] ssList(sk6) || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 2469[6:SSi:2464.0,207.0] || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 2528[6:Res:2469.1,2015.0] || equal(sk5,sk5)* -> .
% 3.82/3.99 2529[6:Obv:2528.0] || -> .
% 3.82/3.99 2530[4:Spt:2529.0,505.1] || -> equal(nil,sk1)**.
% 3.82/3.99 2580[4:Rew:2530.0,92.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 3.82/3.99 2663[4:Rew:2287.1,2580.1] ssList(u) || -> equal(cons(sk5,u),u)**.
% 3.82/3.99 2664[4:MRR:2663.1,694.1] ssList(u) || -> .
% 3.82/3.99 2665[4:UnC:2664.0,207.0] || -> .
% 3.82/3.99 2744[3:Spt:2665.0,346.1] || -> equal(nil,sk2)**.
% 3.82/3.99 2785[3:Rew:2744.0,1865.0] || equal(sk2,sk2)* -> .
% 3.82/3.99 2786[3:Obv:2785.0] || -> .
% 3.82/3.99 2944[2:Spt:2786.0,517.1] || -> equal(nil,sk1)**.
% 3.82/3.99 3042[2:Rew:2287.1,92.1,2944.0,92.1] ssList(u) || -> equal(cons(sk5,u),u)**.
% 3.82/3.99 3043[2:MRR:3042.1,694.1] ssList(u) || -> .
% 3.82/3.99 3044[2:UnC:3043.0,207.0] || -> .
% 3.82/3.99 3132[1:Spt:3044.0,90.0,90.2] ssList(u) || -> duplicatefreeP(u)*.
% 3.82/3.99 3140[2:Spt:517.0,517.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 3.82/3.99 3142[2:SpR:214.0,3140.1] ssList(sk6) || -> equal(hd(sk2),hd(sk1))**.
% 3.82/3.99 3143[2:SSi:3142.0,207.0] || -> equal(hd(sk2),hd(sk1))**.
% 3.82/3.99 3145[2:Rew:3143.0,278.1] || -> equal(nil,sk2) equal(cons(hd(sk1),tl(sk2)),sk2)**.
% 3.82/3.99 3153[3:Spt:473.0] || -> ssItem(u)*.
% 3.82/3.99 3184[3:MRR:216.0,3153.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 3.82/3.99 3199[3:MRR:135.1,135.0,3153.0] || neq(u,v)* equal(u,v) -> .
% 3.82/3.99 3225[3:MRR:156.1,156.0,3153.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 3.82/3.99 3281[3:MRR:115.1,3153.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 3.82/3.99 3963[3:Res:210.0,3199.0] || equal(nil,sk2)** -> .
% 3.82/3.99 4276[3:SpR:212.0,3281.1] ssList(nil) || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 4280[3:SSi:4276.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0] || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 4334[3:SpL:212.0,3184.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 3.82/3.99 4335[3:Obv:4334.1] || memberP(sk2,sk5)* -> .
% 3.82/3.99 4644[3:MRR:298.1,3963.0] || -> ssList(tl(sk2))*.
% 3.82/3.99 4658[3:Rew:4280.0,3145.1] || -> equal(nil,sk2) equal(cons(sk5,tl(sk2)),sk2)**.
% 3.82/3.99 4659[3:MRR:4658.0,3963.0] || -> equal(cons(sk5,tl(sk2)),sk2)**.
% 3.82/3.99 4747[3:SpR:4659.0,3225.2] ssList(tl(sk2)) || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 4752[3:SSi:4747.0,4644.0] || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 4901[3:Res:4752.1,4335.0] || equal(sk5,sk5)* -> .
% 3.82/3.99 4902[3:Obv:4901.0] || -> .
% 3.82/3.99 4903[3:Spt:4902.0,473.1] || -> duplicatefreeP(sk1)*.
% 3.82/3.99 4915[4:Spt:302.0] || -> ssItem(u)*.
% 3.82/3.99 4955[4:MRR:216.0,4915.0] || memberP(sk2,u) equal(cons(u,nil),sk1)** -> .
% 3.82/3.99 4956[4:MRR:135.1,135.0,4915.0] || neq(u,v)* equal(u,v) -> .
% 3.82/3.99 4998[4:MRR:156.1,156.0,4915.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 3.82/3.99 5044[4:MRR:115.1,4915.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 3.82/3.99 5433[4:Res:210.0,4956.0] || equal(nil,sk2)** -> .
% 3.82/3.99 5481[4:SpR:212.0,5044.1] ssList(nil) || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 5486[4:SSi:5481.0,26.0,25.0,24.0,23.0,22.0,21.0,20.0,19.0] || -> equal(hd(sk1),sk5)**.
% 3.82/3.99 5535[4:SpL:212.0,4955.1] || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 3.82/3.99 5536[4:Obv:5535.1] || memberP(sk2,sk5)* -> .
% 3.82/3.99 6109[4:MRR:298.1,5433.0] || -> ssList(tl(sk2))*.
% 3.82/3.99 6125[4:Rew:5486.0,3145.1] || -> equal(nil,sk2) equal(cons(sk5,tl(sk2)),sk2)**.
% 3.82/3.99 6126[4:MRR:6125.0,5433.0] || -> equal(cons(sk5,tl(sk2)),sk2)**.
% 3.82/3.99 6259[4:SpR:6126.0,4998.2] ssList(tl(sk2)) || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 6267[4:SSi:6259.0,6109.0] || equal(u,sk5) -> memberP(sk2,u)*.
% 3.82/3.99 6415[4:Res:6267.1,5536.0] || equal(sk5,sk5)* -> .
% 3.82/3.99 6416[4:Obv:6415.0] || -> .
% 3.82/3.99 6417[4:Spt:6416.0,302.1] || -> duplicatefreeP(sk2)*.
% 3.82/3.99 6419[5:Spt:425.3] || -> equal(nil,sk1)**.
% 3.82/3.99 6436[5:Rew:6419.0,212.0] || -> equal(cons(sk5,sk1),sk1)**.
% 3.82/3.99 6891[5:SpL:6436.0,526.1] ssItem(sk5) || equal(sk1,sk1)* -> .
% 3.82/3.99 6892[5:Obv:6891.1] ssItem(sk5) || -> .
% 3.82/3.99 6893[5:SSi:6892.0,209.0] || -> .
% 3.82/3.99 6894[5:Spt:6893.0,425.3,6419.0] || equal(nil,sk1)** -> .
% 3.82/3.99 6895[5:Spt:6893.0,425.0,425.1,425.2] ssItem(u) || strictorderedP(cons(u,sk1)) -> lt(u,hd(sk1))*.
% 3.82/3.99 6936[6:Spt:410.0] || -> totalorderedP(sk1)*.
% 3.82/3.99 6940[7:Spt:411.0] || -> strictorderedP(sk1)*.
% 3.82/3.99 6945[8:Spt:468.0] || -> cyclefreeP(sk1)*.
% 3.82/3.99 6971[0:SpR:212.0,87.1] ssItem(sk5) || -> totalorderP(sk1)*.
% 3.82/3.99 6972[0:SpR:212.0,86.1] ssItem(sk5) || -> strictorderP(sk1)*.
% 3.82/3.99 6976[0:SpR:212.0,82.1] ssItem(sk5) || -> equalelemsP(sk1)*.
% 3.82/3.99 6977[0:SSi:6976.0,209.0] || -> equalelemsP(sk1)*.
% 3.82/3.99 7083[0:SpL:212.0,522.1] ssItem(sk5) || equal(sk1,sk1) -> singletonP(sk1)*.
% 3.82/3.99 7084[0:Obv:7083.1] ssItem(sk5) || -> singletonP(sk1)*.
% 3.82/3.99 7085[0:SSi:7084.0,209.0] || -> singletonP(sk1)*.
% 3.82/4.00 7086[0:MRR:452.0,7085.0] || -> equal(cons(skaf44(sk1),nil),sk1)**.
% 3.82/4.00 7104[0:SpR:7086.0,88.1] ssItem(skaf44(sk1)) || -> cyclefreeP(sk1)*.
% 3.82/4.00 7113[0:SpL:119.2,116.2] ssList(u) singletonP(u) ssList(nil) ssItem(skaf44(u)) || equal(u,nil)* -> .
% 3.82/4.00 7119[0:SSi:7113.3,7113.2,65.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0] ssList(u) singletonP(u) || equal(u,nil)* -> .
% 3.82/4.00 7262[0:SpL:212.0,216.2] ssItem(sk5) || memberP(sk2,sk5)* equal(sk1,sk1) -> .
% 3.82/4.00 7264[0:Obv:7262.2] ssItem(sk5) || memberP(sk2,sk5)* -> .
% 3.82/4.00 7265[0:SSi:7264.0,209.0] || memberP(sk2,sk5)* -> .
% 3.82/4.00 7291[0:SpR:127.2,114.2] ssList(u) ssList(skaf82(u)) ssItem(skaf83(u)) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 3.82/4.00 7304[0:SSi:7291.2,7291.1,30.0,31.0] ssList(u) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 3.82/4.00 7466[0:SpL:212.0,134.2] ssList(u) ssItem(sk5) || equal(sk1,u) -> singletonP(u)*.
% 3.82/4.00 7469[0:SSi:7466.1,209.0] ssList(u) || equal(sk1,u) -> singletonP(u)*.
% 3.82/4.00 7537[0:EmS:7119.0,7119.1,31.0,7469.2] ssList(skaf82(u)) || equal(skaf82(u),nil)** equal(skaf82(u),sk1) -> .
% 3.82/4.00 7572[0:SSi:7537.0,31.0] || equal(skaf82(u),nil)** equal(skaf82(u),sk1) -> .
% 3.82/4.00 7601[0:SpR:212.0,130.3] ssItem(sk5) ssList(nil) || equal(nil,nil) -> strictorderedP(sk1)*.
% 3.82/4.00 7608[0:Obv:7601.2] ssItem(sk5) ssList(nil) || -> strictorderedP(sk1)*.
% 3.82/4.00 7621[0:SpR:212.0,131.3] ssItem(sk5) ssList(nil) || equal(nil,nil) -> totalorderedP(sk1)*.
% 3.82/4.00 7627[0:Obv:7621.2] ssItem(sk5) ssList(nil) || -> totalorderedP(sk1)*.
% 3.82/4.00 7687[0:SpR:7304.2,523.1] ssList(cons(u,sk1)) ssItem(u) || -> equal(cons(u,sk1),nil) equal(skaf82(cons(u,sk1)),sk1)**.
% 3.82/4.00 7697[0:SSi:7687.0,529.1] ssItem(u) || -> equal(cons(u,sk1),nil) equal(skaf82(cons(u,sk1)),sk1)**.
% 3.82/4.00 7698[0:MRR:7697.1,525.1] ssItem(u) || -> equal(skaf82(cons(u,sk1)),sk1)**.
% 3.82/4.00 9256[0:SpR:212.0,156.4] ssItem(u) ssItem(sk5) ssList(nil) || equal(u,sk5) -> memberP(sk1,u)*.
% 3.82/4.00 9260[0:SSi:9256.2,9256.1,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0,209.0] ssItem(u) || equal(u,sk5) -> memberP(sk1,u)*.
% 3.82/4.00 9572[0:SpR:214.0,158.4] ssItem(u) ssList(sk1) ssList(sk6) || memberP(sk1,u) -> memberP(sk2,u)*.
% 3.82/4.00 10483[0:SSi:6972.0,209.0] || -> strictorderP(sk1)*.
% 4.17/4.39 10484[0:SSi:6971.0,209.0] || -> totalorderP(sk1)*.
% 4.17/4.39 10539[8:SSi:9572.2,9572.1,207.0,1.0,4903.0,6936.0,6940.0,6945.0,6977.0,7085.0] ssItem(u) || memberP(sk1,u) -> memberP(sk2,u)*.
% 4.17/4.39 11639[8:Res:10539.2,7265.0] ssItem(sk5) || memberP(sk1,sk5)* -> .
% 4.17/4.39 11640[8:SSi:11639.0,209.0] || memberP(sk1,sk5)* -> .
% 4.17/4.39 11641[8:Res:9260.2,11640.0] ssItem(sk5) || equal(sk5,sk5)* -> .
% 4.17/4.39 11642[8:Obv:11641.1] ssItem(sk5) || -> .
% 4.17/4.39 11643[8:SSi:11642.0,209.0] || -> .
% 4.17/4.39 11644[8:Spt:11643.0,468.0,6945.0] || cyclefreeP(sk1)* -> .
% 4.17/4.39 11645[8:Spt:11643.0,468.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 4.17/4.39 11648[7:SSi:7104.0,65.0,1.0,4903.0,6936.0,6940.0,6977.0,7085.0,10483.0,10484.0] || -> cyclefreeP(sk1)*.
% 4.17/4.39 11649[8:MRR:11648.0,11644.0] || -> .
% 4.17/4.39 11799[7:Spt:11649.0,411.0,6940.0] || strictorderedP(sk1)* -> .
% 4.17/4.39 11800[7:Spt:11649.0,411.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 4.17/4.39 11807[0:SSi:7608.1,7608.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0,209.0] || -> strictorderedP(sk1)*.
% 4.17/4.39 11808[7:MRR:11807.0,11799.0] || -> .
% 4.17/4.39 11926[6:Spt:11808.0,410.0,6936.0] || totalorderedP(sk1)* -> .
% 4.17/4.39 11927[6:Spt:11808.0,410.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 4.17/4.39 11934[0:SSi:7627.1,7627.0,19.0,20.0,21.0,22.0,23.0,24.0,25.0,26.0,209.0] || -> totalorderedP(sk1)*.
% 4.17/4.39 11935[6:MRR:11934.0,11926.0] || -> .
% 4.17/4.39 12023[2:Spt:11935.0,517.1] || -> equal(nil,sk1)**.
% 4.17/4.39 12090[2:Rew:12023.0,7572.0] || equal(skaf82(u),sk1)** equal(skaf82(u),sk1)** -> .
% 4.17/4.39 12387[2:Obv:12090.0] || equal(skaf82(u),sk1)** -> .
% 4.17/4.39 12388[2:MRR:7698.1,12387.0] ssItem(u) || -> .
% 4.17/4.39 12389[2:UnC:12388.0,30.0] || -> .
% 4.17/4.39 % SZS output end Refutation
% 4.17/4.39 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_10 co1_11 co1_14 co1_15 co1_16 co1_17 co1_18 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause12 clause13 clause47 clause54 clause64 clause68 clause69 clause70 clause72 clause73 clause74 clause77 clause86 clause88 clause96 clause97 clause98 clause99 clause101 clause104 clause109 clause112 clause113 clause116 clause117 clause120 clause123 clause133 clause134 clause138 clause140 clause157 clause163 clause164 clause170 clause177
% 4.17/4.39
%------------------------------------------------------------------------------