TSTP Solution File: SWC346-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC346-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.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 22:03:27 EDT 2022
% Result : Unsatisfiable 65.28s 65.45s
% Output : Refutation 105.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC346-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n014.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 03:26:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 65.28/65.45
% 65.28/65.45 SPASS V 3.9
% 65.28/65.45 SPASS beiseite: Proof found.
% 65.28/65.45 % SZS status Theorem
% 65.28/65.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 65.28/65.45 SPASS derived 39318 clauses, backtracked 14268 clauses, performed 138 splits and kept 25758 clauses.
% 65.28/65.45 SPASS allocated 118224 KBytes.
% 65.28/65.45 SPASS spent 0:01:04.98 on the problem.
% 65.28/65.45 0:00:00.05 for the input.
% 65.28/65.45 0:00:00.00 for the FLOTTER CNF translation.
% 65.28/65.45 0:00:00.63 for inferences.
% 65.28/65.45 0:00:02.90 for the backtracking.
% 65.28/65.45 0:01:00.68 for the reduction.
% 65.28/65.45
% 65.28/65.45
% 65.28/65.45 Here is a proof with depth 4, length 337 :
% 65.28/65.45 % SZS output start Refutation
% 65.28/65.45 1[0:Inp] || -> ssList(sk1)*.
% 65.28/65.45 2[0:Inp] || -> ssList(sk2)*.
% 65.28/65.45 5[0:Inp] || -> equal(sk4,sk2)**.
% 65.28/65.45 6[0:Inp] || -> equal(sk3,sk1)**.
% 65.28/65.45 8[0:Inp] || -> ssItem(sk5)* equal(nil,sk3).
% 65.28/65.45 15[0:Inp] || -> ssList(sk6)* equal(nil,sk3).
% 65.28/65.45 16[0:Inp] || -> ssList(sk7)* equal(nil,sk3).
% 65.28/65.45 17[0:Inp] || -> equal(cons(sk5,nil),sk3)** equal(nil,sk3).
% 65.28/65.45 18[0:Inp] || -> equal(app(app(sk6,sk3),sk7),sk4)** equal(nil,sk3).
% 65.28/65.45 21[0:Inp] || strictorderedP(sk1) segmentP(sk2,sk1)* -> .
% 65.28/65.45 22[0:Inp] || -> equalelemsP(nil)*.
% 65.28/65.45 23[0:Inp] || -> duplicatefreeP(nil)*.
% 65.28/65.45 24[0:Inp] || -> strictorderedP(nil)*.
% 65.28/65.45 25[0:Inp] || -> totalorderedP(nil)*.
% 65.28/65.45 26[0:Inp] || -> strictorderP(nil)*.
% 65.28/65.45 27[0:Inp] || -> totalorderP(nil)*.
% 65.28/65.45 28[0:Inp] || -> cyclefreeP(nil)*.
% 65.28/65.45 29[0:Inp] || -> ssList(nil)*.
% 65.28/65.45 77[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 65.28/65.45 85[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 65.28/65.45 86[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 65.28/65.45 87[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 65.28/65.45 88[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 65.28/65.45 89[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 65.28/65.45 90[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 65.28/65.45 91[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 65.28/65.45 93[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 65.28/65.45 94[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 65.28/65.45 95[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 65.28/65.45 98[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 65.28/65.45 101[0:Inp] ssList(u) || segmentP(nil,u)* -> equal(nil,u).
% 65.28/65.45 106[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 65.28/65.45 109[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 65.28/65.45 137[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 65.28/65.45 155[0:Inp] ssItem(u) ssList(v) || strictorderedP(cons(u,v))* -> lt(u,hd(v)) equal(nil,v).
% 65.28/65.45 170[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 65.28/65.45 184[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 65.28/65.45 185[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 65.28/65.45 186[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 65.28/65.45 187[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 65.28/65.45 193[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(x,w) -> segmentP(app(app(v,x),u),w)*.
% 65.28/65.45 194[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,w),u),x)* -> segmentP(x,w)*.
% 65.28/65.45 198[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).
% 65.28/65.45 209[0:Rew:6.0,16.1] || -> ssList(sk7)* equal(nil,sk1).
% 65.28/65.45 210[0:Rew:6.0,15.1] || -> ssList(sk6)* equal(nil,sk1).
% 65.28/65.45 213[0:Rew:6.0,8.1] || -> ssItem(sk5)* equal(nil,sk1).
% 65.28/65.45 215[0:Rew:6.0,17.1,6.0,17.0] || -> equal(nil,sk1) equal(cons(sk5,nil),sk1)**.
% 65.28/65.45 217[0:Rew:6.0,18.1,6.0,18.0,5.0,18.0] || -> equal(nil,sk1) equal(app(app(sk6,sk1),sk7),sk2)**.
% 65.28/65.45 225[0:Rew:170.3,193.5] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(u,v) -> segmentP(app(w,app(u,x)),v)*.
% 65.28/65.45 226[0:Rew:170.3,194.4] ssList(u) ssList(v) ssList(w) ssList(x) || equal(app(w,app(v,x)),u)*+ -> segmentP(u,v)*.
% 65.28/65.45 260[0:Res:2.0,155.0] ssItem(u) || strictorderedP(cons(u,sk2))* -> lt(u,hd(sk2)) equal(nil,sk2).
% 65.28/65.45 304[0:Res:2.0,98.0] || -> ssList(tl(sk2))* equal(nil,sk2).
% 65.28/65.45 307[0:Res:2.0,95.0] || -> equal(app(nil,sk2),sk2)**.
% 65.28/65.45 308[0:Res:2.0,93.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 65.28/65.45 309[0:Res:2.0,77.0] || -> segmentP(sk2,nil)*.
% 65.28/65.45 414[0:Res:1.0,187.0] || -> totalorderP(sk1) equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 65.28/65.45 415[0:Res:1.0,186.0] || -> strictorderP(sk1) equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 65.28/65.45 416[0:Res:1.0,185.0] || -> totalorderedP(sk1) equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 65.28/65.45 417[0:Res:1.0,184.0] || -> strictorderedP(sk1) equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 65.28/65.45 467[0:Res:1.0,101.0] || segmentP(nil,sk1)* -> equal(nil,sk1).
% 65.28/65.45 472[0:Res:1.0,106.0] ssList(u) || -> ssList(app(u,sk1))*.
% 65.28/65.45 474[0:Res:1.0,109.0] || -> cyclefreeP(sk1) leq(skaf49(sk1),skaf50(sk1))*.
% 65.28/65.45 477[0:Res:1.0,94.0] || -> equal(app(sk1,nil),sk1)**.
% 65.28/65.45 479[0:Res:1.0,93.0] || -> ssItem(u)* duplicatefreeP(sk1)*.
% 65.28/65.45 494[0:Res:1.0,198.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 65.28/65.45 528[0:Res:1.0,137.1] ssItem(u) || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 65.28/65.45 573[1:Spt:93.1] || -> ssItem(u)*.
% 65.28/65.45 579[1:MRR:91.0,573.0] || -> cyclefreeP(cons(u,nil))*.
% 65.28/65.45 580[1:MRR:90.0,573.0] || -> totalorderP(cons(u,nil))*.
% 65.28/65.45 581[1:MRR:89.0,573.0] || -> strictorderP(cons(u,nil))*.
% 65.28/65.45 582[1:MRR:88.0,573.0] || -> totalorderedP(cons(u,nil))*.
% 65.28/65.45 583[1:MRR:87.0,573.0] || -> strictorderedP(cons(u,nil))*.
% 65.28/65.45 584[1:MRR:86.0,573.0] || -> duplicatefreeP(cons(u,nil))*.
% 65.28/65.45 585[1:MRR:85.0,573.0] || -> equalelemsP(cons(u,nil))*.
% 65.28/65.45 595[1:MRR:528.0,573.0] || equal(cons(u,nil),sk1)** -> singletonP(sk1).
% 65.28/65.45 781[2:Spt:494.5] || -> equal(nil,sk1)**.
% 65.28/65.45 844[2:Rew:781.0,24.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 852[2:Rew:781.0,309.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 888[2:MRR:21.0,844.0] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 897[2:MRR:888.0,852.0] || -> .
% 65.28/65.45 1197[2:Spt:897.0,494.5,781.0] || equal(nil,sk1)** -> .
% 65.28/65.45 1198[2:Spt:897.0,494.0,494.1,494.2,494.3,494.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 65.28/65.45 1199[2:MRR:209.1,1197.0] || -> ssList(sk7)*.
% 65.28/65.45 1200[2:MRR:210.1,1197.0] || -> ssList(sk6)*.
% 65.28/65.45 1205[2:MRR:215.0,1197.0] || -> equal(cons(sk5,nil),sk1)**.
% 65.28/65.45 1208[2:MRR:217.0,1197.0] || -> equal(app(app(sk6,sk1),sk7),sk2)**.
% 65.28/65.45 2014[3:Spt:21.0] || strictorderedP(sk1)* -> .
% 65.28/65.45 2039[2:SpR:1205.0,579.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 2040[2:SpR:1205.0,580.0] || -> totalorderP(sk1)*.
% 65.28/65.45 2041[2:SpR:1205.0,581.0] || -> strictorderP(sk1)*.
% 65.28/65.45 2042[2:SpR:1205.0,582.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 2043[2:SpR:1205.0,583.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 2044[2:SpR:1205.0,584.0] || -> duplicatefreeP(sk1)*.
% 65.28/65.45 2045[2:SpR:1205.0,585.0] || -> equalelemsP(sk1)*.
% 65.28/65.45 2047[3:MRR:2043.0,2014.0] || -> .
% 65.28/65.45 2050[3:Spt:2047.0,21.0,2014.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 2051[3:Spt:2047.0,21.1] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 2109[2:SpL:1205.0,595.0] || equal(sk1,sk1) -> singletonP(sk1)*.
% 65.28/65.45 2110[2:Obv:2109.0] || -> singletonP(sk1)*.
% 65.28/65.45 8055[0:EqR:226.4] ssList(app(u,app(v,w))) ssList(v) ssList(u) ssList(w) || -> segmentP(app(u,app(v,w)),v)*.
% 65.28/65.45 8098[0:SSi:8055.0,106.2,106.2] ssList(u) ssList(v) ssList(w) || -> segmentP(app(v,app(u,w)),u)*.
% 65.28/65.45 17728[2:SpR:1208.0,225.5] ssList(app(sk6,sk1)) ssList(u) ssList(v) ssList(sk7) || segmentP(app(sk6,sk1),u)* -> segmentP(app(v,sk2),u)*.
% 65.28/65.45 17756[2:SSi:17728.3,17728.0,1199.0,472.1,1200.0] ssList(u) ssList(v) || segmentP(app(sk6,sk1),u)*+ -> segmentP(app(v,sk2),u)*.
% 65.28/65.45 35964[0:SpR:477.0,8098.3] ssList(sk1) ssList(u) ssList(nil) || -> segmentP(app(u,sk1),sk1)*.
% 65.28/65.45 35987[2:SSi:35964.2,35964.0,29.0,28.0,27.0,26.0,25.0,24.0,23.0,22.0,1.0,2044.0,2045.0,2040.0,2041.0,2039.0,2042.0,2043.0,2110.0] ssList(u) || -> segmentP(app(u,sk1),sk1)*.
% 65.28/65.45 41584[2:Res:35987.1,17756.2] ssList(sk6) ssList(sk1) ssList(u) || -> segmentP(app(u,sk2),sk1)*.
% 65.28/65.45 44888[2:SSi:41584.1,41584.0,1.0,2044.0,2045.0,2040.0,2041.0,2039.0,2042.0,2043.0,2110.0,1200.0] ssList(u) || -> segmentP(app(u,sk2),sk1)*.
% 65.28/65.45 48788[2:SpR:307.0,44888.1] ssList(nil) || -> segmentP(sk2,sk1)*.
% 65.28/65.45 48795[2:SSi:48788.0,22.0,23.0,24.0,25.0,26.0,27.0,28.0,29.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 48796[3:MRR:48795.0,2051.0] || -> .
% 65.28/65.45 48811[1:Spt:48796.0,93.0,93.2] ssList(u) || -> duplicatefreeP(u)*.
% 65.28/65.45 49474[2:Spt:479.0] || -> ssItem(u)*.
% 65.28/65.45 49478[2:MRR:85.0,49474.0] || -> equalelemsP(cons(u,nil))*.
% 65.28/65.45 49479[2:MRR:86.0,49474.0] || -> duplicatefreeP(cons(u,nil))*.
% 65.28/65.45 49480[2:MRR:87.0,49474.0] || -> strictorderedP(cons(u,nil))*.
% 65.28/65.45 49481[2:MRR:88.0,49474.0] || -> totalorderedP(cons(u,nil))*.
% 65.28/65.45 49482[2:MRR:89.0,49474.0] || -> strictorderP(cons(u,nil))*.
% 65.28/65.45 49483[2:MRR:90.0,49474.0] || -> totalorderP(cons(u,nil))*.
% 65.28/65.45 49484[2:MRR:91.0,49474.0] || -> cyclefreeP(cons(u,nil))*.
% 65.28/65.45 49676[3:Spt:494.5] || -> equal(nil,sk1)**.
% 65.28/65.45 49680[3:Rew:49676.0,24.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 49688[3:Rew:49676.0,309.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 49959[3:MRR:21.0,49680.0] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 49980[3:MRR:49959.0,49688.0] || -> .
% 65.28/65.45 51158[3:Spt:49980.0,494.5,49676.0] || equal(nil,sk1)** -> .
% 65.28/65.45 51159[3:Spt:49980.0,494.0,494.1,494.2,494.3,494.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 65.28/65.45 51160[3:MRR:209.1,51158.0] || -> ssList(sk7)*.
% 65.28/65.45 51161[3:MRR:210.1,51158.0] || -> ssList(sk6)*.
% 65.28/65.45 51166[3:MRR:467.1,51158.0] || segmentP(nil,sk1)* -> .
% 65.28/65.45 51167[3:MRR:215.0,51158.0] || -> equal(cons(sk5,nil),sk1)**.
% 65.28/65.45 51172[3:MRR:217.0,51158.0] || -> equal(app(app(sk6,sk1),sk7),sk2)**.
% 65.28/65.45 51238[4:Spt:304.1] || -> equal(nil,sk2)**.
% 65.28/65.45 51257[4:Rew:51238.0,49484.0] || -> cyclefreeP(cons(u,sk2))*.
% 65.28/65.45 51258[4:Rew:51238.0,49483.0] || -> totalorderP(cons(u,sk2))*.
% 65.28/65.45 51259[4:Rew:51238.0,49482.0] || -> strictorderP(cons(u,sk2))*.
% 65.28/65.45 51260[4:Rew:51238.0,49481.0] || -> totalorderedP(cons(u,sk2))*.
% 65.28/65.45 51261[4:Rew:51238.0,49480.0] || -> strictorderedP(cons(u,sk2))*.
% 65.28/65.45 51262[4:Rew:51238.0,49479.0] || -> duplicatefreeP(cons(u,sk2))*.
% 65.28/65.45 51263[4:Rew:51238.0,49478.0] || -> equalelemsP(cons(u,sk2))*.
% 65.28/65.45 51300[4:Rew:51238.0,51166.0] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 51307[4:Rew:51238.0,51167.0] || -> equal(cons(sk5,sk2),sk1)**.
% 65.28/65.45 52032[5:Spt:417.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 52035[6:Spt:416.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 52039[7:Spt:474.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 52041[8:Spt:415.0] || -> strictorderP(sk1)*.
% 65.28/65.45 52042[9:Spt:414.0] || -> totalorderP(sk1)*.
% 65.28/65.45 52064[4:SpR:51307.0,51257.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 52066[4:SpR:51307.0,51258.0] || -> totalorderP(sk1)*.
% 65.28/65.45 52067[4:SpR:51307.0,51259.0] || -> strictorderP(sk1)*.
% 65.28/65.45 52068[4:SpR:51307.0,51260.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 52069[4:SpR:51307.0,51261.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 52070[4:SpR:51307.0,51262.0] || -> duplicatefreeP(sk1)*.
% 65.28/65.45 52071[4:SpR:51307.0,51263.0] || -> equalelemsP(sk1)*.
% 65.28/65.45 52307[3:SpR:51172.0,170.3] ssList(sk6) ssList(sk1) ssList(sk7) || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 65.28/65.45 52322[9:SSi:52307.2,52307.1,52307.0,51160.0,1.0,52032.0,52035.0,52039.0,52041.0,52042.0,52070.0,52071.0,51161.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 65.28/65.45 52406[9:SpR:52322.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 65.28/65.45 52419[9:SSi:52406.2,52406.1,52406.0,51160.0,51161.0,1.0,52032.0,52035.0,52039.0,52041.0,52042.0,52070.0,52071.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 52420[9:MRR:52419.0,51300.0] || -> .
% 65.28/65.45 52437[9:Spt:52420.0,414.0,52042.0] || totalorderP(sk1)* -> .
% 65.28/65.45 52438[9:Spt:52420.0,414.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 65.28/65.45 52439[9:MRR:52437.0,52066.0] || -> .
% 65.28/65.45 52474[8:Spt:52439.0,415.0,52041.0] || strictorderP(sk1)* -> .
% 65.28/65.45 52475[8:Spt:52439.0,415.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 65.28/65.45 52476[8:MRR:52474.0,52067.0] || -> .
% 65.28/65.45 52490[7:Spt:52476.0,474.0,52039.0] || cyclefreeP(sk1)* -> .
% 65.28/65.45 52491[7:Spt:52476.0,474.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 65.28/65.45 52492[7:MRR:52490.0,52064.0] || -> .
% 65.28/65.45 52507[6:Spt:52492.0,416.0,52035.0] || totalorderedP(sk1)* -> .
% 65.28/65.45 52508[6:Spt:52492.0,416.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 65.28/65.45 52509[6:MRR:52507.0,52068.0] || -> .
% 65.28/65.45 52527[5:Spt:52509.0,417.0,52032.0] || strictorderedP(sk1)* -> .
% 65.28/65.45 52528[5:Spt:52509.0,417.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 65.28/65.45 52529[5:MRR:52527.0,52069.0] || -> .
% 65.28/65.45 52546[4:Spt:52529.0,304.1,51238.0] || equal(nil,sk2)** -> .
% 65.28/65.45 52547[4:Spt:52529.0,304.0] || -> ssList(tl(sk2))*.
% 65.28/65.45 52573[3:SSi:52307.2,52307.1,52307.0,51160.0,1.0,51161.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 65.28/65.45 52699[5:Spt:21.0] || strictorderedP(sk1)* -> .
% 65.28/65.45 52751[3:SpR:51167.0,49478.0] || -> equalelemsP(sk1)*.
% 65.28/65.45 52752[3:SpR:51167.0,49479.0] || -> duplicatefreeP(sk1)*.
% 65.28/65.45 52753[3:SpR:51167.0,49480.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 52754[3:SpR:51167.0,49481.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 52755[3:SpR:51167.0,49482.0] || -> strictorderP(sk1)*.
% 65.28/65.45 52756[3:SpR:51167.0,49483.0] || -> totalorderP(sk1)*.
% 65.28/65.45 52757[3:SpR:51167.0,49484.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 52761[5:MRR:52753.0,52699.0] || -> .
% 65.28/65.45 52762[5:Spt:52761.0,21.0,52699.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 52763[5:Spt:52761.0,21.1] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 52998[3:SpR:52573.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 65.28/65.45 53011[3:SSi:52998.2,52998.1,52998.0,51160.0,51161.0,1.0,52751.0,52752.0,52755.0,52756.0,52757.0,52754.0,52753.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 53012[5:MRR:53011.0,52763.0] || -> .
% 65.28/65.45 53028[2:Spt:53012.0,479.1] || -> duplicatefreeP(sk1)*.
% 65.28/65.45 53031[3:Spt:308.0] || -> ssItem(u)*.
% 65.28/65.45 53037[3:MRR:91.0,53031.0] || -> cyclefreeP(cons(u,nil))*.
% 65.28/65.45 53038[3:MRR:90.0,53031.0] || -> totalorderP(cons(u,nil))*.
% 65.28/65.45 53039[3:MRR:89.0,53031.0] || -> strictorderP(cons(u,nil))*.
% 65.28/65.45 53040[3:MRR:88.0,53031.0] || -> totalorderedP(cons(u,nil))*.
% 65.28/65.45 53041[3:MRR:87.0,53031.0] || -> strictorderedP(cons(u,nil))*.
% 65.28/65.45 53043[3:MRR:85.0,53031.0] || -> equalelemsP(cons(u,nil))*.
% 65.28/65.45 53231[4:Spt:494.5] || -> equal(nil,sk1)**.
% 65.28/65.45 53234[4:Rew:53231.0,24.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 53243[4:Rew:53231.0,309.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 53514[4:MRR:21.0,53234.0] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 53535[4:MRR:53514.0,53243.0] || -> .
% 65.28/65.45 54706[4:Spt:53535.0,494.5,53231.0] || equal(nil,sk1)** -> .
% 65.28/65.45 54707[4:Spt:53535.0,494.0,494.1,494.2,494.3,494.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 65.28/65.45 54708[4:MRR:209.1,54706.0] || -> ssList(sk7)*.
% 65.28/65.45 54709[4:MRR:210.1,54706.0] || -> ssList(sk6)*.
% 65.28/65.45 54714[4:MRR:467.1,54706.0] || segmentP(nil,sk1)* -> .
% 65.28/65.45 54715[4:MRR:215.0,54706.0] || -> equal(cons(sk5,nil),sk1)**.
% 65.28/65.45 54720[4:MRR:217.0,54706.0] || -> equal(app(app(sk6,sk1),sk7),sk2)**.
% 65.28/65.45 54786[5:Spt:304.1] || -> equal(nil,sk2)**.
% 65.28/65.45 54804[5:Rew:54786.0,53043.0] || -> equalelemsP(cons(u,sk2))*.
% 65.28/65.45 54806[5:Rew:54786.0,53041.0] || -> strictorderedP(cons(u,sk2))*.
% 65.28/65.45 54807[5:Rew:54786.0,53040.0] || -> totalorderedP(cons(u,sk2))*.
% 65.28/65.45 54808[5:Rew:54786.0,53039.0] || -> strictorderP(cons(u,sk2))*.
% 65.28/65.45 54809[5:Rew:54786.0,53038.0] || -> totalorderP(cons(u,sk2))*.
% 65.28/65.45 54810[5:Rew:54786.0,53037.0] || -> cyclefreeP(cons(u,sk2))*.
% 65.28/65.45 54848[5:Rew:54786.0,54714.0] || segmentP(sk2,sk1)* -> .
% 65.28/65.45 54855[5:Rew:54786.0,54715.0] || -> equal(cons(sk5,sk2),sk1)**.
% 65.28/65.45 55580[6:Spt:417.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 55583[7:Spt:416.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 55587[8:Spt:474.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 55589[9:Spt:415.0] || -> strictorderP(sk1)*.
% 65.28/65.45 55590[10:Spt:414.0] || -> totalorderP(sk1)*.
% 65.28/65.45 55612[5:SpR:54855.0,54804.0] || -> equalelemsP(sk1)*.
% 65.28/65.45 55615[5:SpR:54855.0,54806.0] || -> strictorderedP(sk1)*.
% 65.28/65.45 55616[5:SpR:54855.0,54807.0] || -> totalorderedP(sk1)*.
% 65.28/65.45 55617[5:SpR:54855.0,54808.0] || -> strictorderP(sk1)*.
% 65.28/65.45 55618[5:SpR:54855.0,54809.0] || -> totalorderP(sk1)*.
% 65.28/65.45 55619[5:SpR:54855.0,54810.0] || -> cyclefreeP(sk1)*.
% 65.28/65.45 55856[4:SpR:54720.0,170.3] ssList(sk6) ssList(sk1) ssList(sk7) || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 65.28/65.45 55871[10:SSi:55856.2,55856.1,55856.0,54708.0,1.0,53028.0,55580.0,55583.0,55587.0,55589.0,55590.0,55612.0,54709.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 65.28/65.45 55952[10:SpR:55871.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 65.28/65.45 55965[10:SSi:55952.2,55952.1,55952.0,54708.0,54709.0,1.0,53028.0,55580.0,55583.0,55587.0,55589.0,55590.0,55612.0] || -> segmentP(sk2,sk1)*.
% 65.28/65.45 55966[10:MRR:55965.0,54848.0] || -> .
% 65.28/65.45 55983[10:Spt:55966.0,414.0,55590.0] || totalorderP(sk1)* -> .
% 65.28/65.45 55984[10:Spt:55966.0,414.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 65.28/65.45 55985[10:MRR:55983.0,55618.0] || -> .
% 65.28/65.45 56020[9:Spt:55985.0,415.0,55589.0] || strictorderP(sk1)* -> .
% 105.79/106.09 56021[9:Spt:55985.0,415.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 105.79/106.09 56022[9:MRR:56020.0,55617.0] || -> .
% 105.79/106.09 56036[8:Spt:56022.0,474.0,55587.0] || cyclefreeP(sk1)* -> .
% 105.79/106.09 56037[8:Spt:56022.0,474.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 105.79/106.09 56038[8:MRR:56036.0,55619.0] || -> .
% 105.79/106.09 56053[7:Spt:56038.0,416.0,55583.0] || totalorderedP(sk1)* -> .
% 105.79/106.09 56054[7:Spt:56038.0,416.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 105.79/106.09 56055[7:MRR:56053.0,55616.0] || -> .
% 105.79/106.09 56073[6:Spt:56055.0,417.0,55580.0] || strictorderedP(sk1)* -> .
% 105.79/106.09 56074[6:Spt:56055.0,417.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 105.79/106.09 56075[6:MRR:56073.0,55615.0] || -> .
% 105.79/106.09 56092[5:Spt:56075.0,304.1,54786.0] || equal(nil,sk2)** -> .
% 105.79/106.09 56093[5:Spt:56075.0,304.0] || -> ssList(tl(sk2))*.
% 105.79/106.09 56119[4:SSi:55856.2,55856.1,55856.0,54708.0,1.0,53028.0,54709.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 105.79/106.09 56245[6:Spt:21.0] || strictorderedP(sk1)* -> .
% 105.79/106.09 56297[4:SpR:54715.0,53037.0] || -> cyclefreeP(sk1)*.
% 105.79/106.09 56298[4:SpR:54715.0,53038.0] || -> totalorderP(sk1)*.
% 105.79/106.09 56299[4:SpR:54715.0,53039.0] || -> strictorderP(sk1)*.
% 105.79/106.09 56300[4:SpR:54715.0,53040.0] || -> totalorderedP(sk1)*.
% 105.79/106.09 56301[4:SpR:54715.0,53041.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 56303[4:SpR:54715.0,53043.0] || -> equalelemsP(sk1)*.
% 105.79/106.09 56306[6:MRR:56301.0,56245.0] || -> .
% 105.79/106.09 56308[6:Spt:56306.0,21.0,56245.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 56309[6:Spt:56306.0,21.1] || segmentP(sk2,sk1)* -> .
% 105.79/106.09 56546[4:SpR:56119.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 105.79/106.09 56559[4:SSi:56546.2,56546.1,56546.0,54708.0,54709.0,1.0,53028.0,56303.0,56299.0,56298.0,56297.0,56300.0,56301.0] || -> segmentP(sk2,sk1)*.
% 105.79/106.09 56560[6:MRR:56559.0,56309.0] || -> .
% 105.79/106.09 56576[3:Spt:56560.0,308.1] || -> duplicatefreeP(sk2)*.
% 105.79/106.09 56577[4:Spt:494.5] || -> equal(nil,sk1)**.
% 105.79/106.09 56580[4:Rew:56577.0,24.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 56589[4:Rew:56577.0,309.0] || -> segmentP(sk2,sk1)*.
% 105.79/106.09 56862[4:MRR:21.0,56580.0] || segmentP(sk2,sk1)* -> .
% 105.79/106.09 56879[4:MRR:56862.0,56589.0] || -> .
% 105.79/106.09 57311[4:Spt:56879.0,494.5,56577.0] || equal(nil,sk1)** -> .
% 105.79/106.09 57312[4:Spt:56879.0,494.0,494.1,494.2,494.3,494.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 105.79/106.09 57313[4:MRR:209.1,57311.0] || -> ssList(sk7)*.
% 105.79/106.09 57314[4:MRR:210.1,57311.0] || -> ssList(sk6)*.
% 105.79/106.09 57315[4:MRR:213.1,57311.0] || -> ssItem(sk5)*.
% 105.79/106.09 57322[4:MRR:467.1,57311.0] || segmentP(nil,sk1)* -> .
% 105.79/106.09 57323[4:MRR:215.0,57311.0] || -> equal(cons(sk5,nil),sk1)**.
% 105.79/106.09 57328[4:MRR:217.0,57311.0] || -> equal(app(app(sk6,sk1),sk7),sk2)**.
% 105.79/106.09 57393[5:Spt:260.3] || -> equal(nil,sk2)**.
% 105.79/106.09 57441[5:Rew:57393.0,57322.0] || segmentP(sk2,sk1)* -> .
% 105.79/106.09 57443[5:Rew:57393.0,91.1] ssItem(u) || -> cyclefreeP(cons(u,sk2))*.
% 105.79/106.09 57444[5:Rew:57393.0,90.1] ssItem(u) || -> totalorderP(cons(u,sk2))*.
% 105.79/106.09 57445[5:Rew:57393.0,89.1] ssItem(u) || -> strictorderP(cons(u,sk2))*.
% 105.79/106.09 57446[5:Rew:57393.0,88.1] ssItem(u) || -> totalorderedP(cons(u,sk2))*.
% 105.79/106.09 57447[5:Rew:57393.0,87.1] ssItem(u) || -> strictorderedP(cons(u,sk2))*.
% 105.79/106.09 57460[5:Rew:57393.0,57323.0] || -> equal(cons(sk5,sk2),sk1)**.
% 105.79/106.09 58187[6:Spt:417.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 58190[7:Spt:416.0] || -> totalorderedP(sk1)*.
% 105.79/106.09 58194[8:Spt:474.0] || -> cyclefreeP(sk1)*.
% 105.79/106.09 58196[9:Spt:415.0] || -> strictorderP(sk1)*.
% 105.79/106.09 58197[10:Spt:414.0] || -> totalorderP(sk1)*.
% 105.79/106.09 58348[4:SpR:57328.0,170.3] ssList(sk6) ssList(sk1) ssList(sk7) || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 105.79/106.09 58363[10:SSi:58348.2,58348.1,58348.0,57313.0,1.0,53028.0,58187.0,58190.0,58194.0,58196.0,58197.0,57314.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 105.79/106.09 58414[10:SpR:58363.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 105.79/106.09 58427[10:SSi:58414.2,58414.1,58414.0,57313.0,57314.0,1.0,53028.0,58187.0,58190.0,58194.0,58196.0,58197.0] || -> segmentP(sk2,sk1)*.
% 105.79/106.09 58428[10:MRR:58427.0,57441.0] || -> .
% 105.79/106.09 58445[10:Spt:58428.0,414.0,58197.0] || totalorderP(sk1)* -> .
% 105.79/106.09 58446[10:Spt:58428.0,414.1] || -> equal(app(app(skaf56(sk1),cons(skaf54(sk1),skaf57(sk1))),cons(skaf55(sk1),skaf58(sk1))),sk1)**.
% 105.79/106.09 58495[5:SpR:57460.0,57443.1] ssItem(sk5) || -> cyclefreeP(sk1)*.
% 105.79/106.09 58512[5:SpR:57460.0,57444.1] ssItem(sk5) || -> totalorderP(sk1)*.
% 105.79/106.09 58513[5:SSi:58512.0,57315.0] || -> totalorderP(sk1)*.
% 105.79/106.09 58514[10:MRR:58513.0,58445.0] || -> .
% 105.79/106.09 58515[9:Spt:58514.0,415.0,58196.0] || strictorderP(sk1)* -> .
% 105.79/106.09 58516[9:Spt:58514.0,415.1] || -> equal(app(app(skaf61(sk1),cons(skaf59(sk1),skaf62(sk1))),cons(skaf60(sk1),skaf63(sk1))),sk1)**.
% 105.79/106.09 58568[5:SpR:57460.0,57445.1] ssItem(sk5) || -> strictorderP(sk1)*.
% 105.79/106.09 58569[5:SSi:58568.0,57315.0] || -> strictorderP(sk1)*.
% 105.79/106.09 58570[9:MRR:58569.0,58515.0] || -> .
% 105.79/106.09 58571[8:Spt:58570.0,474.0,58194.0] || cyclefreeP(sk1)* -> .
% 105.79/106.09 58572[8:Spt:58570.0,474.1] || -> leq(skaf49(sk1),skaf50(sk1))*.
% 105.79/106.09 58573[5:SSi:58495.0,57315.0] || -> cyclefreeP(sk1)*.
% 105.79/106.09 58574[8:MRR:58573.0,58571.0] || -> .
% 105.79/106.09 58591[7:Spt:58574.0,416.0,58190.0] || totalorderedP(sk1)* -> .
% 105.79/106.09 58592[7:Spt:58574.0,416.1] || -> equal(app(app(skaf66(sk1),cons(skaf64(sk1),skaf67(sk1))),cons(skaf65(sk1),skaf68(sk1))),sk1)**.
% 105.79/106.09 58642[5:SpR:57460.0,57446.1] ssItem(sk5) || -> totalorderedP(sk1)*.
% 105.79/106.09 58643[5:SSi:58642.0,57315.0] || -> totalorderedP(sk1)*.
% 105.79/106.09 58644[7:MRR:58643.0,58591.0] || -> .
% 105.79/106.09 58645[6:Spt:58644.0,417.0,58187.0] || strictorderedP(sk1)* -> .
% 105.79/106.09 58646[6:Spt:58644.0,417.1] || -> equal(app(app(skaf71(sk1),cons(skaf69(sk1),skaf72(sk1))),cons(skaf70(sk1),skaf73(sk1))),sk1)**.
% 105.79/106.09 58703[5:SpR:57460.0,57447.1] ssItem(sk5) || -> strictorderedP(sk1)*.
% 105.79/106.09 58704[5:SSi:58703.0,57315.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 58705[6:MRR:58704.0,58645.0] || -> .
% 105.79/106.09 58706[5:Spt:58705.0,260.3,57393.0] || equal(nil,sk2)** -> .
% 105.79/106.09 58707[5:Spt:58705.0,260.0,260.1,260.2] ssItem(u) || strictorderedP(cons(u,sk2))* -> lt(u,hd(sk2)).
% 105.79/106.09 58736[4:SSi:58348.2,58348.1,58348.0,57313.0,1.0,53028.0,57314.0] || -> equal(app(sk6,app(sk1,sk7)),sk2)**.
% 105.79/106.09 58796[6:Spt:21.0] || strictorderedP(sk1)* -> .
% 105.79/106.09 58974[4:SpR:57323.0,85.1] ssItem(sk5) || -> equalelemsP(sk1)*.
% 105.79/106.09 58975[4:SSi:58974.0,57315.0] || -> equalelemsP(sk1)*.
% 105.79/106.09 59027[4:SpR:57323.0,87.1] ssItem(sk5) || -> strictorderedP(sk1)*.
% 105.79/106.09 59028[4:SSi:59027.0,57315.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 59029[6:MRR:59028.0,58796.0] || -> .
% 105.79/106.09 59030[6:Spt:59029.0,21.0,58796.0] || -> strictorderedP(sk1)*.
% 105.79/106.09 59031[6:Spt:59029.0,21.1] || segmentP(sk2,sk1)* -> .
% 105.79/106.09 59080[4:SpR:58736.0,8098.3] ssList(sk1) ssList(sk6) ssList(sk7) || -> segmentP(sk2,sk1)*.
% 105.79/106.09 59187[4:SSi:59080.2,59080.1,59080.0,57313.0,57314.0,1.0,53028.0,58975.0,59028.0] || -> segmentP(sk2,sk1)*.
% 105.79/106.09 59188[6:MRR:59187.0,59031.0] || -> .
% 105.79/106.09 % SZS output end Refutation
% 105.79/106.09 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_8 co1_15 co1_16 co1_17 co1_18 co1_21 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause56 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause77 clause80 clause85 clause88 clause116 clause134 clause149 clause163 clause164 clause165 clause166 clause172 clause173 clause177
% 105.79/106.09
%------------------------------------------------------------------------------