TSTP Solution File: SWC022-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC022-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 22:01:09 EDT 2022
% Result : Unsatisfiable 77.53s 77.77s
% Output : Refutation 98.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC022-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 12 01:02:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 77.53/77.77
% 77.53/77.77 SPASS V 3.9
% 77.53/77.77 SPASS beiseite: Proof found.
% 77.53/77.77 % SZS status Theorem
% 77.53/77.77 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.53/77.77 SPASS derived 40338 clauses, backtracked 15441 clauses, performed 150 splits and kept 28053 clauses.
% 77.53/77.77 SPASS allocated 124534 KBytes.
% 77.53/77.77 SPASS spent 0:1:17.33 on the problem.
% 77.53/77.77 0:00:00.04 for the input.
% 77.53/77.77 0:00:00.00 for the FLOTTER CNF translation.
% 77.53/77.77 0:00:00.58 for inferences.
% 77.53/77.77 0:00:03.59 for the backtracking.
% 77.53/77.77 0:1:12.40 for the reduction.
% 77.53/77.77
% 77.53/77.77
% 77.53/77.77 Here is a proof with depth 6, length 272 :
% 77.53/77.77 % SZS output start Refutation
% 77.53/77.77 1[0:Inp] || -> ssList(sk1)*.
% 77.53/77.77 2[0:Inp] || -> ssList(sk2)*.
% 77.53/77.77 5[0:Inp] || -> equal(sk4,sk2)**.
% 77.53/77.77 6[0:Inp] || -> equal(sk3,sk1)**.
% 77.53/77.77 7[0:Inp] || -> neq(sk2,nil)* neq(sk2,nil)*.
% 77.53/77.77 11[0:Inp] ssList(u) || neq(u,nil)* frontsegP(sk2,u) frontsegP(sk1,u) neq(sk4,nil)* -> .
% 77.53/77.77 12[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* equal(hd(sk4),v) neq(nil,sk4) neq(sk4,nil) -> equal(sk3,u).
% 77.53/77.77 13[0:Inp] || -> equalelemsP(nil)*.
% 77.53/77.77 14[0:Inp] || -> duplicatefreeP(nil)*.
% 77.53/77.77 15[0:Inp] || -> strictorderedP(nil)*.
% 77.53/77.77 16[0:Inp] || -> totalorderedP(nil)*.
% 77.53/77.77 17[0:Inp] || -> strictorderP(nil)*.
% 77.53/77.77 18[0:Inp] || -> totalorderP(nil)*.
% 77.53/77.77 19[0:Inp] || -> cyclefreeP(nil)*.
% 77.53/77.77 20[0:Inp] || -> ssList(nil)*.
% 77.53/77.77 25[0:Inp] || -> ssList(skaf82(u))*.
% 77.53/77.77 30[0:Inp] || -> ssList(skaf77(u))*.
% 77.53/77.77 31[0:Inp] || -> ssList(skaf76(u))*.
% 77.53/77.77 32[0:Inp] || -> ssList(skaf75(u))*.
% 77.53/77.77 44[0:Inp] || -> ssList(skaf63(u))*.
% 77.53/77.77 45[0:Inp] || -> ssList(skaf62(u))*.
% 77.53/77.77 46[0:Inp] || -> ssList(skaf61(u))*.
% 77.53/77.77 54[0:Inp] || -> ssList(skaf53(u))*.
% 77.53/77.77 55[0:Inp] || -> ssList(skaf52(u))*.
% 77.53/77.77 56[0:Inp] || -> ssList(skaf51(u))*.
% 77.53/77.77 59[0:Inp] || -> ssItem(skaf44(u))*.
% 77.53/77.77 60[0:Inp] || -> ssList(skaf48(u,v))*.
% 77.53/77.77 61[0:Inp] || -> ssList(skaf47(u,v))*.
% 77.53/77.77 68[0:Inp] ssList(u) || -> segmentP(u,nil)*.
% 77.53/77.77 72[0:Inp] ssList(u) || -> frontsegP(u,nil)*.
% 77.53/77.77 73[0:Inp] ssList(u) || -> frontsegP(u,u)*.
% 77.53/77.77 75[0:Inp] ssItem(u) || lt(u,u)* -> .
% 77.53/77.77 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 77.53/77.77 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 77.53/77.77 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 77.53/77.77 79[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 77.53/77.77 80[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 77.53/77.77 81[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 77.53/77.77 82[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 77.53/77.77 84[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 77.53/77.77 85[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 77.53/77.77 86[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 77.53/77.77 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 77.53/77.77 96[0:Inp] ssList(u) || frontsegP(nil,u)* -> equal(nil,u).
% 77.53/77.77 97[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 77.53/77.77 98[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 77.53/77.77 99[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf50(u),skaf49(u))*.
% 77.53/77.77 100[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 77.53/77.77 105[0:Inp] ssList(u) || lt(skaf59(u),skaf60(u))* -> strictorderP(u).
% 77.53/77.77 108[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 77.53/77.77 109[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 77.53/77.77 110[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),nil)** -> .
% 77.53/77.77 111[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 77.53/77.77 113[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 77.53/77.77 114[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 77.53/77.77 116[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 77.53/77.77 121[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 77.53/77.77 128[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 77.53/77.77 132[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 77.53/77.77 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 77.53/77.77 140[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(u,v).
% 77.53/77.77 142[0:Inp] ssItem(u) ssItem(v) || leq(u,v)*+ leq(v,u)* -> equal(u,v).
% 77.53/77.77 155[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,v),u)*+ -> rearsegP(u,v)*.
% 77.53/77.77 156[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,w),u)*+ -> frontsegP(u,v)*.
% 77.53/77.77 169[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 77.53/77.77 174[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(app(app(skaf75(u),cons(skaf74(u),skaf76(u))),cons(skaf74(u),skaf77(u))),u)**.
% 77.53/77.77 175[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 77.53/77.77 176[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 77.53/77.77 177[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 77.53/77.77 179[0:Inp] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf49(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 77.53/77.77 180[0:Inp] ssList(u) ssList(v) || segmentP(u,v) -> equal(app(app(skaf47(u,v),v),skaf48(v,u)),u)**.
% 77.53/77.77 189[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).
% 77.53/77.77 191[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)* -> .
% 77.53/77.77 193[0:Inp] ssList(u) strictorderedP(u) ssItem(v) ssItem(w) ssList(x) ssList(y) ssList(z) || equal(app(app(x,cons(v,y)),cons(w,z)),u)* -> lt(v,w).
% 77.53/77.77 200[0:Obv:7.0] || -> neq(sk2,nil)*.
% 77.53/77.77 201[0:Rew:5.0,11.4] ssList(u) || neq(u,nil)* frontsegP(sk2,u) frontsegP(sk1,u) neq(sk2,nil)* -> .
% 77.53/77.77 202[0:MRR:201.4,200.0] ssList(u) || neq(u,nil)* frontsegP(sk1,u) frontsegP(sk2,u) -> .
% 77.53/77.77 207[0:Rew:6.0,12.6,5.0,12.5,5.0,12.4,5.0,12.3] ssList(u) ssItem(v) || equal(cons(v,nil),u)* equal(hd(sk2),v) neq(nil,sk2) neq(sk2,nil) -> equal(sk1,u).
% 77.53/77.77 208[0:MRR:207.5,200.0] ssItem(u) ssList(v) || neq(nil,sk2) equal(hd(sk2),u) equal(cons(u,nil),v)* -> equal(sk1,v).
% 77.53/77.77 227[0:Res:2.0,177.0] || -> strictorderP(sk2) equal(app(app(skaf61(sk2),cons(skaf59(sk2),skaf62(sk2))),cons(skaf60(sk2),skaf63(sk2))),sk2)**.
% 77.53/77.77 228[0:Res:2.0,176.0] || -> totalorderedP(sk2) equal(app(app(skaf66(sk2),cons(skaf64(sk2),skaf67(sk2))),cons(skaf65(sk2),skaf68(sk2))),sk2)**.
% 77.53/77.77 229[0:Res:2.0,175.0] || -> strictorderedP(sk2) equal(app(app(skaf71(sk2),cons(skaf69(sk2),skaf72(sk2))),cons(skaf70(sk2),skaf73(sk2))),sk2)**.
% 77.53/77.77 241[0:Res:2.0,202.0] || neq(sk2,nil)* frontsegP(sk2,sk2) frontsegP(sk1,sk2) -> .
% 77.53/77.77 268[0:Res:2.0,116.0] || -> equal(nil,sk2) equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 77.53/77.77 269[0:Res:2.0,121.0] || -> equal(nil,sk2) equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 77.53/77.77 286[0:Res:2.0,99.0] || -> cyclefreeP(sk2) leq(skaf50(sk2),skaf49(sk2))*.
% 77.53/77.77 288[0:Res:2.0,89.0] || -> ssList(tl(sk2))* equal(nil,sk2).
% 77.53/77.77 298[0:Res:2.0,73.0] || -> frontsegP(sk2,sk2)*.
% 77.53/77.77 307[0:Res:2.0,189.1] ssList(u) || equal(hd(u),hd(sk2)) equal(tl(u),tl(sk2))* -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 77.53/77.77 470[0:Res:1.0,72.0] || -> frontsegP(sk1,nil)*.
% 77.53/77.77 471[0:Res:1.0,73.0] || -> frontsegP(sk1,sk1)*.
% 77.53/77.77 521[0:Res:1.0,98.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 77.53/77.77 555[0:MRR:241.0,241.1,200.0,298.0] || frontsegP(sk1,sk2)* -> .
% 77.53/77.77 561[1:Spt:84.1] || -> ssItem(u)*.
% 77.53/77.77 567[1:MRR:82.0,561.0] || -> cyclefreeP(cons(u,nil))*.
% 77.53/77.77 568[1:MRR:81.0,561.0] || -> totalorderP(cons(u,nil))*.
% 77.53/77.77 569[1:MRR:80.0,561.0] || -> strictorderP(cons(u,nil))*.
% 77.53/77.77 570[1:MRR:79.0,561.0] || -> totalorderedP(cons(u,nil))*.
% 77.53/77.77 571[1:MRR:78.0,561.0] || -> strictorderedP(cons(u,nil))*.
% 77.53/77.77 572[1:MRR:77.0,561.0] || -> duplicatefreeP(cons(u,nil))*.
% 77.53/77.77 573[1:MRR:76.0,561.0] || -> equalelemsP(cons(u,nil))*.
% 77.53/77.77 574[1:MRR:75.0,561.0] || lt(u,u)* -> .
% 77.53/77.77 591[1:MRR:114.1,114.0,561.0] || -> equal(u,v) neq(u,v)*.
% 77.53/77.77 630[1:MRR:142.1,142.0,561.0] || leq(u,v)*+ leq(v,u)* -> equal(u,v).
% 77.53/77.77 672[1:MRR:208.0,561.0] ssList(u) || neq(nil,sk2) equal(hd(sk2),v) equal(cons(v,nil),u)* -> equal(sk1,u).
% 77.53/77.77 688[1:MRR:98.1,561.0] ssList(u) || -> ssList(cons(v,u))*.
% 77.53/77.77 689[1:MRR:111.1,561.0] ssList(u) || equal(cons(v,u),u)** -> .
% 77.53/77.77 690[1:MRR:110.1,561.0] ssList(u) || equal(cons(v,u),nil)** -> .
% 77.53/77.77 691[1:MRR:109.1,561.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 77.53/77.77 692[1:MRR:108.1,561.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 77.53/77.77 693[1:MRR:128.1,561.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 77.53/77.77 694[1:MRR:132.1,561.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 77.53/77.77 719[1:MRR:191.2,561.0] ssList(u) duplicatefreeP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(y,x)),u)* -> .
% 77.53/77.77 746[1:MRR:193.3,193.2,561.0] ssList(u) strictorderedP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(z,x)),u)* -> lt(y,z).
% 77.53/77.77 767[2:Spt:307.5] || -> equal(nil,sk2)**.
% 77.53/77.77 832[2:Rew:767.0,470.0] || -> frontsegP(sk1,sk2)*.
% 77.53/77.77 882[2:MRR:832.0,555.0] || -> .
% 77.53/77.77 973[2:Spt:882.0,307.5,767.0] || equal(nil,sk2)** -> .
% 77.53/77.77 974[2:Spt:882.0,307.0,307.1,307.2,307.3,307.4] ssList(u) || equal(hd(u),hd(sk2)) equal(tl(u),tl(sk2))* -> equal(u,sk2) equal(nil,u).
% 77.53/77.77 975[2:MRR:288.1,973.0] || -> ssList(tl(sk2))*.
% 77.53/77.77 979[2:MRR:269.0,973.0] || -> equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 77.53/77.77 980[2:MRR:268.0,973.0] || -> equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 77.53/77.77 1787[3:Spt:229.0] || -> strictorderedP(sk2)*.
% 77.53/77.77 1790[4:Spt:228.0] || -> totalorderedP(sk2)*.
% 77.53/77.77 1801[5:Spt:286.0] || -> cyclefreeP(sk2)*.
% 77.53/77.77 1805[6:Spt:227.0] || -> strictorderP(sk2)*.
% 77.53/77.77 1893[2:SpR:979.0,691.1] ssList(skaf82(sk2)) || -> equal(skaf83(sk2),hd(sk2))**.
% 77.53/77.77 2011[1:EqR:693.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 77.53/77.77 2012[1:SSi:2011.0,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.1] || -> singletonP(cons(u,nil))*.
% 77.53/77.77 2037[1:Res:99.2,630.0] ssList(u) || leq(skaf49(u),skaf50(u))* -> cyclefreeP(u) equal(skaf49(u),skaf50(u)).
% 77.53/77.77 2039[1:MRR:2037.1,100.2] ssList(u) || -> cyclefreeP(u) equal(skaf49(u),skaf50(u))**.
% 77.53/77.77 2044[1:Rew:2039.2,179.2] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf50(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 77.53/77.77 2103[1:SpR:113.2,691.1] ssList(u) singletonP(u) ssList(nil) || -> equal(skaf44(u),hd(u))**.
% 77.53/77.77 2115[1:SSi:2103.2,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] ssList(u) singletonP(u) || -> equal(skaf44(u),hd(u))**.
% 77.53/77.77 2116[1:Rew:2115.2,113.2] ssList(u) singletonP(u) || -> equal(cons(hd(u),nil),u)**.
% 77.53/77.77 2218[1:SpR:121.2,691.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(skaf83(u),hd(u))**.
% 77.53/77.77 2219[1:SpR:121.2,692.1] ssList(u) ssList(skaf82(u)) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 77.53/77.77 2230[1:SSi:2218.1,25.0] ssList(u) || -> equal(nil,u) equal(skaf83(u),hd(u))**.
% 77.53/77.77 2231[1:Rew:2230.2,121.2] ssList(u) || -> equal(nil,u) equal(cons(hd(u),skaf82(u)),u)**.
% 77.53/77.77 2232[1:SSi:2219.1,25.0] ssList(u) || -> equal(nil,u) equal(tl(u),skaf82(u))**.
% 77.53/77.77 2395[1:Res:591.1,202.1] ssList(u) || frontsegP(sk1,u) frontsegP(sk2,u)* -> equal(u,nil).
% 77.53/77.77 2817[1:SpR:694.1,135.3] ssList(u) ssList(cons(v,nil)) ssList(u) || -> equal(cons(v,nil),nil) equal(hd(cons(v,u)),hd(cons(v,nil)))*.
% 77.53/77.77 2825[1:Obv:2817.0] ssList(cons(u,nil)) ssList(v) || -> equal(cons(u,nil),nil) equal(hd(cons(u,v)),hd(cons(u,nil)))*.
% 77.53/77.77 2826[1:Rew:691.1,2825.3] ssList(cons(u,nil)) ssList(v) || -> equal(cons(u,nil),nil) equal(hd(cons(u,nil)),u)**.
% 77.53/77.77 2827[1:Con:2826.1] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(hd(cons(u,nil)),u)**.
% 77.53/77.77 3586[0:EqR:155.3] ssList(app(u,v)) ssList(v) ssList(u) || -> rearsegP(app(u,v),v)*.
% 77.53/77.77 3601[0:SSi:3586.0,97.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 77.53/77.77 3620[0:EqR:156.3] ssList(app(u,v)) ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 77.53/77.77 3635[0:SSi:3620.0,97.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 77.53/77.77 4786[1:SSi:2827.0,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.1] || -> equal(cons(u,nil),nil) equal(hd(cons(u,nil)),u)**.
% 77.53/77.77 5412[0:SpR:85.1,180.3] ssList(skaf47(u,nil)) ssList(u) ssList(nil) || segmentP(u,nil) -> equal(app(skaf47(u,nil),skaf48(nil,u)),u)**.
% 77.53/77.77 5423[0:SSi:5412.2,5412.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,61.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] ssList(u) || segmentP(u,nil) -> equal(app(skaf47(u,nil),skaf48(nil,u)),u)**.
% 77.53/77.77 5424[0:MRR:5423.1,68.1] ssList(u) || -> equal(app(skaf47(u,nil),skaf48(nil,u)),u)**.
% 77.53/77.77 6053[1:SpL:2044.2,719.5] ssList(u) ssList(v) duplicatefreeP(v) ssList(skaf51(u)) ssList(skaf52(u)) ssList(skaf53(u)) || equal(u,v)* -> cyclefreeP(u)*.
% 77.53/77.77 6059[1:SSi:6053.5,6053.4,6053.3,54.0,55.0,56.0] ssList(u) ssList(v) duplicatefreeP(v) || equal(u,v)*+ -> cyclefreeP(u)*.
% 77.53/77.77 6155[1:SpL:177.2,746.5] ssList(u) ssList(v) strictorderedP(v) ssList(skaf61(u)) ssList(skaf62(u)) ssList(skaf63(u)) || equal(u,v)* -> strictorderP(u) lt(skaf59(u),skaf60(u))*.
% 77.53/77.77 6157[1:SpL:174.2,746.5] ssList(u) ssList(v) strictorderedP(v) ssList(skaf75(u)) ssList(skaf76(u)) ssList(skaf77(u)) || equal(u,v)* -> duplicatefreeP(u) lt(skaf74(u),skaf74(u))*.
% 77.53/77.77 6173[1:SSi:6157.5,6157.4,6157.3,30.0,31.0,32.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> duplicatefreeP(u) lt(skaf74(u),skaf74(u))*.
% 77.53/77.77 6174[1:MRR:6173.5,574.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> duplicatefreeP(u)*.
% 77.53/77.77 6176[1:SSi:6155.5,6155.4,6155.3,44.0,45.0,46.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skaf59(u),skaf60(u))*.
% 77.53/77.77 6177[1:MRR:6176.5,105.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> strictorderP(u)*.
% 77.53/77.77 6556[1:SpR:4786.1,2231.2] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 77.53/77.77 6569[1:Obv:6556.1] ssList(cons(u,nil)) || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 77.53/77.77 6570[1:SSi:6569.0,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.1] || -> equal(cons(u,nil),nil) equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 77.53/77.77 6597[1:SpR:2232.2,692.1] ssList(cons(u,v)) ssList(v) || -> equal(cons(u,v),nil) equal(skaf82(cons(u,v)),v)**.
% 77.53/77.77 6604[1:SSi:6597.0,688.1] ssList(u) || -> equal(cons(v,u),nil) equal(skaf82(cons(v,u)),u)**.
% 77.53/77.77 6605[1:MRR:6604.1,690.1] ssList(u) || -> equal(skaf82(cons(v,u)),u)**.
% 77.53/77.77 7065[1:SpR:694.1,3601.2] ssList(u) ssList(u) ssList(cons(v,nil)) || -> rearsegP(cons(v,u),u)*.
% 77.53/77.77 7088[1:Obv:7065.0] ssList(u) ssList(cons(v,nil)) || -> rearsegP(cons(v,u),u)*.
% 77.53/77.77 7089[1:SSi:7088.1,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.1] ssList(u) || -> rearsegP(cons(v,u),u)*.
% 77.53/77.77 7140[1:SpR:694.1,3635.2] ssList(u) ssList(cons(v,nil)) ssList(u) || -> frontsegP(cons(v,u),cons(v,nil))*.
% 77.53/77.77 7163[1:Obv:7140.0] ssList(cons(u,nil)) ssList(v) || -> frontsegP(cons(u,v),cons(u,nil))*.
% 77.53/77.77 7164[1:SSi:7163.0,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.1] ssList(u) || -> frontsegP(cons(v,u),cons(v,nil))*.
% 77.53/77.77 7287[1:Res:7089.1,140.2] ssList(u) ssList(cons(v,u)) ssList(u) || rearsegP(u,cons(v,u))* -> equal(cons(v,u),u).
% 77.53/77.77 7291[1:Obv:7287.0] ssList(cons(u,v)) ssList(v) || rearsegP(v,cons(u,v))* -> equal(cons(u,v),v).
% 77.53/77.77 7292[1:SSi:7291.0,688.1] ssList(u) || rearsegP(u,cons(v,u))* -> equal(cons(v,u),u).
% 77.53/77.77 7293[1:MRR:7292.2,689.1] ssList(u) || rearsegP(u,cons(v,u))* -> .
% 77.53/77.77 7315[1:SpL:2116.2,7293.1] ssList(u) singletonP(u) ssList(nil) || rearsegP(nil,u)* -> .
% 77.53/77.77 7324[1:SSi:7315.2,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] ssList(u) singletonP(u) || rearsegP(nil,u)* -> .
% 77.53/77.77 7404[0:SpR:5424.1,3635.2] ssList(u) ssList(skaf47(u,nil)) ssList(skaf48(nil,u)) || -> frontsegP(u,skaf47(u,nil))*.
% 77.53/77.77 7407[0:SpR:5424.1,3601.2] ssList(u) ssList(skaf48(nil,u)) ssList(skaf47(u,nil)) || -> rearsegP(u,skaf48(nil,u))*.
% 77.53/77.77 7420[0:SSi:7404.2,7404.1,60.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,61.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] ssList(u) || -> frontsegP(u,skaf47(u,nil))*.
% 77.53/77.77 7421[0:SSi:7407.2,7407.1,61.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,60.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] ssList(u) || -> rearsegP(u,skaf48(nil,u))*.
% 77.53/77.77 7509[0:Res:7420.1,96.1] ssList(nil) ssList(skaf47(nil,nil)) || -> equal(skaf47(nil,nil),nil)**.
% 77.53/77.77 7510[0:SSi:7509.1,7509.0,61.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] || -> equal(skaf47(nil,nil),nil)**.
% 77.53/77.77 7516[0:SpR:7510.0,5424.1] ssList(nil) || -> equal(app(nil,skaf48(nil,nil)),nil)**.
% 77.53/77.77 7519[0:SSi:7516.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] || -> equal(app(nil,skaf48(nil,nil)),nil)**.
% 77.53/77.77 7522[0:SpR:7519.0,86.1] ssList(skaf48(nil,nil)) || -> equal(skaf48(nil,nil),nil)**.
% 77.53/77.77 7545[0:SSi:7522.0,60.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] || -> equal(skaf48(nil,nil),nil)**.
% 77.53/77.77 7942[1:Res:7421.1,7324.2] ssList(nil) ssList(skaf48(nil,nil)) singletonP(skaf48(nil,nil)) || -> .
% 77.53/77.77 7947[1:SSi:7942.1,7942.0,60.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] singletonP(skaf48(nil,nil)) || -> .
% 98.00/98.19 7963[1:SoR:7947.0,693.2] ssList(skaf48(nil,nil)) || equal(cons(u,nil),skaf48(nil,nil))* -> .
% 98.00/98.19 7966[1:Rew:7545.0,7963.1] ssList(skaf48(nil,nil)) || equal(cons(u,nil),nil)** -> .
% 98.00/98.19 7967[1:SSi:7966.0,60.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0] || equal(cons(u,nil),nil)** -> .
% 98.00/98.19 7973[1:MRR:6570.0,7967.0] || -> equal(cons(u,skaf82(cons(u,nil))),cons(u,nil))**.
% 98.00/98.19 8049[1:SpR:7973.0,688.1] ssList(skaf82(cons(u,nil))) || -> ssList(cons(u,nil))*.
% 98.00/98.19 8096[1:SSi:8049.0,25.0,688.0,20.0,19.0,18.0,17.0,16.0,15.0,14.0,13.0,567.0,568.0,569.0,570.0,571.0,572.0,573.1,2012.0] || -> ssList(cons(u,nil))*.
% 98.00/98.19 8745[6:SSi:1893.0,25.0,2.0,1787.0,1790.0,1801.0,1805.0] || -> equal(skaf83(sk2),hd(sk2))**.
% 98.00/98.19 8746[6:Rew:8745.0,979.0] || -> equal(cons(hd(sk2),skaf82(sk2)),sk2)**.
% 98.00/98.19 8849[7:Spt:672.0,672.2,672.3,672.4] ssList(u) || equal(hd(sk2),v) equal(cons(v,nil),u)* -> equal(sk1,u).
% 98.00/98.19 8850[7:EqR:8849.2] ssList(cons(u,nil)) || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 8852[7:SSi:8850.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 9037[2:SpR:980.0,6605.1] ssList(tl(sk2)) || -> equal(tl(sk2),skaf82(sk2))**.
% 98.00/98.19 9078[2:SSi:9037.0,975.0] || -> equal(tl(sk2),skaf82(sk2))**.
% 98.00/98.19 9081[2:Rew:9078.0,980.0] || -> equal(cons(hd(sk2),skaf82(sk2)),sk2)**.
% 98.00/98.19 9115[6:SpR:8746.0,7164.1] ssList(skaf82(sk2)) || -> frontsegP(sk2,cons(hd(sk2),nil))*.
% 98.00/98.19 9153[6:SSi:9115.0,25.0,2.0,1787.0,1790.0,1801.0,1805.0] || -> frontsegP(sk2,cons(hd(sk2),nil))*.
% 98.00/98.19 11093[6:Res:9153.0,2395.2] ssList(cons(hd(sk2),nil)) || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 11101[6:SSi:11093.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 11102[6:MRR:11101.1,7967.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> .
% 98.00/98.19 12991[7:SpL:8852.1,11102.0] || equal(hd(sk2),hd(sk2)) frontsegP(sk1,sk1)* -> .
% 98.00/98.19 13050[7:Obv:12991.0] || frontsegP(sk1,sk1)* -> .
% 98.00/98.19 13051[7:MRR:13050.0,471.0] || -> .
% 98.00/98.19 13117[7:Spt:13051.0,672.1] || neq(nil,sk2)* -> .
% 98.00/98.19 13309[7:Res:591.1,13117.0] || -> equal(nil,sk2)**.
% 98.00/98.19 13310[7:MRR:13309.0,973.0] || -> .
% 98.00/98.19 13311[6:Spt:13310.0,227.0,1805.0] || strictorderP(sk2)* -> .
% 98.00/98.19 13312[6:Spt:13310.0,227.1] || -> equal(app(app(skaf61(sk2),cons(skaf59(sk2),skaf62(sk2))),cons(skaf60(sk2),skaf63(sk2))),sk2)**.
% 98.00/98.19 13808[2:SpR:9081.0,7164.1] ssList(skaf82(sk2)) || -> frontsegP(sk2,cons(hd(sk2),nil))*.
% 98.00/98.19 18572[1:EqR:6059.3] ssList(u) ssList(u) duplicatefreeP(u) || -> cyclefreeP(u)*.
% 98.00/98.19 18573[1:Obv:18572.0] ssList(u) duplicatefreeP(u) || -> cyclefreeP(u)*.
% 98.00/98.19 20028[1:EqR:6174.3] ssList(u) ssList(u) strictorderedP(u) || -> duplicatefreeP(u)*.
% 98.00/98.19 20029[1:Obv:20028.0] ssList(u) strictorderedP(u) || -> duplicatefreeP(u)*.
% 98.00/98.19 20038[1:EqR:6177.3] ssList(u) ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 98.00/98.19 20039[1:Obv:20038.0] ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 98.00/98.19 20634[6:Res:20039.2,13311.0] ssList(sk2) strictorderedP(sk2) || -> .
% 98.00/98.19 20638[6:SSi:20634.1,20634.0,2.0,1787.0,1790.0,1801.0,2.0,1787.0,1790.0,1801.0] || -> .
% 98.00/98.19 20690[5:Spt:20638.0,286.0,1801.0] || cyclefreeP(sk2)* -> .
% 98.00/98.19 20691[5:Spt:20638.0,286.1] || -> leq(skaf50(sk2),skaf49(sk2))*.
% 98.00/98.19 21089[5:Res:18573.2,20690.0] ssList(sk2) duplicatefreeP(sk2) || -> .
% 98.00/98.19 21093[5:SSi:21089.1,21089.0,20029.0,2.0,1787.0,1790.0,2.0,1787.0,1790.2] || -> .
% 98.00/98.19 21097[4:Spt:21093.0,228.0,1790.0] || totalorderedP(sk2)* -> .
% 98.00/98.19 21098[4:Spt:21093.0,228.1] || -> equal(app(app(skaf66(sk2),cons(skaf64(sk2),skaf67(sk2))),cons(skaf65(sk2),skaf68(sk2))),sk2)**.
% 98.00/98.19 21109[3:SSi:13808.0,25.0,2.0,1787.0] || -> frontsegP(sk2,cons(hd(sk2),nil))*.
% 98.00/98.19 21581[5:Spt:672.0,672.2,672.3,672.4] ssList(u) || equal(hd(sk2),v) equal(cons(v,nil),u)* -> equal(sk1,u).
% 98.00/98.19 21582[5:EqR:21581.2] ssList(cons(u,nil)) || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 21584[5:SSi:21582.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 21768[3:Res:21109.0,2395.2] ssList(cons(hd(sk2),nil)) || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 21771[3:SSi:21768.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 21772[3:MRR:21771.1,7967.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> .
% 98.00/98.19 28713[5:SpL:21584.1,21772.0] || equal(hd(sk2),hd(sk2)) frontsegP(sk1,sk1)* -> .
% 98.00/98.19 28779[5:Obv:28713.0] || frontsegP(sk1,sk1)* -> .
% 98.00/98.19 28780[5:MRR:28779.0,471.0] || -> .
% 98.00/98.19 28858[5:Spt:28780.0,672.1] || neq(nil,sk2)* -> .
% 98.00/98.19 29394[5:Res:591.1,28858.0] || -> equal(nil,sk2)**.
% 98.00/98.19 29395[5:MRR:29394.0,973.0] || -> .
% 98.00/98.19 29396[3:Spt:29395.0,229.0,1787.0] || strictorderedP(sk2)* -> .
% 98.00/98.19 29397[3:Spt:29395.0,229.1] || -> equal(app(app(skaf71(sk2),cons(skaf69(sk2),skaf72(sk2))),cons(skaf70(sk2),skaf73(sk2))),sk2)**.
% 98.00/98.19 29408[2:SSi:13808.0,25.0,2.0] || -> frontsegP(sk2,cons(hd(sk2),nil))*.
% 98.00/98.19 30071[4:Spt:672.0,672.2,672.3,672.4] ssList(u) || equal(hd(sk2),v) equal(cons(v,nil),u)* -> equal(sk1,u).
% 98.00/98.19 30072[4:EqR:30071.2] ssList(cons(u,nil)) || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 30074[4:SSi:30072.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || equal(hd(sk2),u) -> equal(cons(u,nil),sk1)**.
% 98.00/98.19 30223[2:Res:29408.0,2395.2] ssList(cons(hd(sk2),nil)) || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 30231[2:SSi:30223.0,567.0,568.0,569.0,570.0,571.0,572.0,573.0,2012.0,8096.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> equal(cons(hd(sk2),nil),nil).
% 98.00/98.19 30232[2:MRR:30231.1,7967.0] || frontsegP(sk1,cons(hd(sk2),nil))* -> .
% 98.00/98.19 39125[4:SpL:30074.1,30232.0] || equal(hd(sk2),hd(sk2)) frontsegP(sk1,sk1)* -> .
% 98.00/98.19 39203[4:Obv:39125.0] || frontsegP(sk1,sk1)* -> .
% 98.00/98.19 39204[4:MRR:39203.0,471.0] || -> .
% 98.00/98.19 39303[4:Spt:39204.0,672.1] || neq(nil,sk2)* -> .
% 98.00/98.19 39919[4:Res:591.1,39303.0] || -> equal(nil,sk2)**.
% 98.00/98.19 39920[4:MRR:39919.0,973.0] || -> .
% 98.00/98.19 39921[1:Spt:39920.0,84.0,84.2] ssList(u) || -> duplicatefreeP(u)*.
% 98.00/98.19 40133[1:MRR:191.1,39921.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 98.00/98.19 62565[0:SpR:169.3,97.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 98.00/98.19 62619[0:Obv:62565.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 98.00/98.19 62620[0:SSi:62619.2,98.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 98.00/98.19 64723[1:EqR:40133.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 98.00/98.19 64755[1:SSi:64723.0,97.2,97.2,98.2,98.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 98.00/98.19 64756[1:MRR:62620.3,64755.1] ssList(u) ssItem(v) ssList(w) || -> .
% 98.00/98.19 64759[1:Con:64756.2] ssList(u) ssItem(v) || -> .
% 98.00/98.19 64768[1:MRR:521.1,64759.0] ssItem(u) || -> .
% 98.00/98.19 64780[1:UnC:64768.0,59.0] || -> .
% 98.00/98.19 % SZS output end Refutation
% 98.00/98.19 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_11 co1_12 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause18 clause19 clause20 clause32 clause33 clause34 clause42 clause43 clause44 clause47 clause48 clause49 clause56 clause60 clause61 clause63 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause77 clause84 clause85 clause86 clause87 clause88 clause93 clause96 clause97 clause98 clause99 clause101 clause102 clause104 clause109 clause116 clause120 clause123 clause128 clause130 clause143 clause144 clause157 clause162 clause163 clause164 clause165 clause167 clause168 clause177 clause179 clause181
% 98.00/98.19
%------------------------------------------------------------------------------