TSTP Solution File: SWC065-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC065-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 22:01:28 EDT 2022
% Result : Unsatisfiable 26.63s 26.82s
% Output : Refutation 32.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC065-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n015.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 14:01:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 26.63/26.82
% 26.63/26.82 SPASS V 3.9
% 26.63/26.82 SPASS beiseite: Proof found.
% 26.63/26.82 % SZS status Theorem
% 26.63/26.82 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.63/26.82 SPASS derived 23232 clauses, backtracked 11675 clauses, performed 124 splits and kept 19307 clauses.
% 26.63/26.82 SPASS allocated 102398 KBytes.
% 26.63/26.82 SPASS spent 0:0:26.44 on the problem.
% 26.63/26.82 0:00:00.04 for the input.
% 26.63/26.82 0:00:00.00 for the FLOTTER CNF translation.
% 26.63/26.82 0:00:00.26 for inferences.
% 26.63/26.82 0:00:01.09 for the backtracking.
% 26.63/26.82 0:0:24.70 for the reduction.
% 26.63/26.82
% 26.63/26.82
% 26.63/26.82 Here is a proof with depth 4, length 320 :
% 26.63/26.82 % SZS output start Refutation
% 26.63/26.82 1[0:Inp] || -> ssList(sk1)*.
% 26.63/26.82 2[0:Inp] || -> ssList(sk2)*.
% 26.63/26.82 5[0:Inp] || -> equal(sk4,sk2)**.
% 26.63/26.82 6[0:Inp] || -> equal(sk3,sk1)**.
% 26.63/26.82 7[0:Inp] || -> ssList(sk5)*.
% 26.63/26.82 8[0:Inp] || -> equal(app(sk3,sk5),sk4)**.
% 26.63/26.82 9[0:Inp] || -> equalelemsP(sk3)*.
% 26.63/26.82 11[0:Inp] || equal(nil,sk3)** -> equal(nil,sk4).
% 26.63/26.82 12[0:Inp] || -> neq(sk2,nil)* equal(nil,sk2).
% 26.63/26.82 13[0:Inp] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk2,u)* -> equal(nil,sk2).
% 26.63/26.82 14[0:Inp] || equal(nil,sk1) -> neq(sk2,nil)*.
% 26.63/26.82 15[0:Inp] ssList(u) || equal(nil,sk1) neq(u,nil) segmentP(sk2,u)* segmentP(sk1,u) -> .
% 26.63/26.82 16[0:Inp] || -> equalelemsP(nil)*.
% 26.63/26.82 17[0:Inp] || -> duplicatefreeP(nil)*.
% 26.63/26.82 18[0:Inp] || -> strictorderedP(nil)*.
% 26.63/26.82 19[0:Inp] || -> totalorderedP(nil)*.
% 26.63/26.82 20[0:Inp] || -> strictorderP(nil)*.
% 26.63/26.82 21[0:Inp] || -> totalorderP(nil)*.
% 26.63/26.82 22[0:Inp] || -> cyclefreeP(nil)*.
% 26.63/26.82 23[0:Inp] || -> ssList(nil)*.
% 26.63/26.82 28[0:Inp] || -> ssList(skaf82(u))*.
% 26.63/26.82 33[0:Inp] || -> ssList(skaf77(u))*.
% 26.63/26.82 34[0:Inp] || -> ssList(skaf76(u))*.
% 26.63/26.82 35[0:Inp] || -> ssList(skaf75(u))*.
% 26.63/26.82 37[0:Inp] || -> ssList(skaf73(u))*.
% 26.63/26.82 38[0:Inp] || -> ssList(skaf72(u))*.
% 26.63/26.82 39[0:Inp] || -> ssList(skaf71(u))*.
% 26.63/26.82 42[0:Inp] || -> ssList(skaf68(u))*.
% 26.63/26.82 43[0:Inp] || -> ssList(skaf67(u))*.
% 26.63/26.82 44[0:Inp] || -> ssList(skaf66(u))*.
% 26.63/26.82 47[0:Inp] || -> ssList(skaf63(u))*.
% 26.63/26.82 48[0:Inp] || -> ssList(skaf62(u))*.
% 26.63/26.82 49[0:Inp] || -> ssList(skaf61(u))*.
% 26.63/26.82 57[0:Inp] || -> ssList(skaf53(u))*.
% 26.63/26.82 58[0:Inp] || -> ssList(skaf52(u))*.
% 26.63/26.82 59[0:Inp] || -> ssList(skaf51(u))*.
% 26.63/26.82 65[0:Inp] || -> ssList(skaf46(u,v))*.
% 26.63/26.82 69[0:Inp] || equal(skac2,skac3)** -> .
% 26.63/26.82 72[0:Inp] ssList(u) || -> segmentP(u,u)*.
% 26.63/26.82 73[0:Inp] ssList(u) || -> rearsegP(u,nil)*.
% 26.63/26.82 75[0:Inp] ssList(u) || -> frontsegP(u,nil)*.
% 26.63/26.82 79[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 26.63/26.82 80[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 26.63/26.82 81[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 26.63/26.82 82[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 26.63/26.82 83[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 26.63/26.82 84[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 26.63/26.82 85[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 26.63/26.82 86[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 26.63/26.82 87[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 26.63/26.82 88[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 26.63/26.82 89[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 26.63/26.82 100[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 26.63/26.82 101[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 26.63/26.82 102[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf50(u),skaf49(u))*.
% 26.63/26.82 103[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 26.63/26.82 112[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 26.63/26.82 115[0:Inp] ssList(u) ssList(v) || -> equal(u,v) neq(u,v)*.
% 26.63/26.82 117[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 26.63/26.82 135[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 26.63/26.82 138[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 26.63/26.82 143[0:Inp] ssList(u) ssList(v) || rearsegP(u,v)*+ rearsegP(v,u)* -> equal(u,v).
% 26.63/26.82 144[0:Inp] ssList(u) ssList(v) || frontsegP(u,v)*+ frontsegP(v,u)* -> equal(u,v).
% 26.63/26.82 145[0:Inp] ssItem(u) ssItem(v) || leq(u,v)* leq(v,u)* -> equal(u,v).
% 26.63/26.82 146[0:Inp] ssList(u) ssList(v) || rearsegP(u,v) -> equal(app(skaf46(u,v),v),u)**.
% 26.63/26.82 155[0:Inp] ssItem(u) ssList(v) ssList(w) || memberP(v,u) -> memberP(app(v,w),u)*.
% 26.63/26.82 158[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,v),u)*+ -> rearsegP(u,v)*.
% 26.63/26.82 159[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,w),u)*+ -> frontsegP(u,v)*.
% 26.63/26.82 164[0:Inp] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),app(u,app(v,w)))**.
% 26.63/26.82 165[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(v,w),app(v,u))* -> equal(w,u).
% 26.63/26.82 166[0:Inp] ssList(u) ssList(v) ssList(w) || equal(app(w,v),app(u,v))* -> equal(w,u).
% 26.63/26.82 177[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(app(app(skaf75(u),cons(skaf74(u),skaf76(u))),cons(skaf74(u),skaf77(u))),u)**.
% 26.63/26.82 178[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 26.63/26.82 179[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 26.63/26.82 180[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 26.63/26.82 182[0:Inp] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf49(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 26.63/26.82 185[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 26.63/26.82 187[0:Inp] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(x,w) -> segmentP(app(app(v,x),u),w)*.
% 26.63/26.82 190[0:Inp] ssList(u) ssItem(v) ssList(w) ssList(x) || equal(app(w,cons(v,x)),u)* -> memberP(u,v)*.
% 26.63/26.82 192[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).
% 26.63/26.82 201[0:Rew:6.0,9.0] || -> equalelemsP(sk1)*.
% 26.63/26.82 204[0:Rew:6.0,8.0,5.0,8.0] || -> equal(app(sk1,sk5),sk2)**.
% 26.63/26.82 205[0:Rew:12.0,14.0] || equal(sk2,sk1) -> neq(sk2,nil)*.
% 26.63/26.82 206[0:Rew:5.0,11.1,6.0,11.0] || equal(nil,sk1)** -> equal(nil,sk2).
% 26.63/26.82 207[0:Rew:13.4,15.1] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk2,u)* equal(sk2,sk1) -> .
% 26.63/26.82 210[0:Rew:164.3,187.5] ssList(u) ssList(v) ssList(w) ssList(x) || segmentP(u,v) -> segmentP(app(w,app(u,x)),v)*.
% 26.63/26.82 244[0:Res:7.0,207.0] || segmentP(sk1,sk5) segmentP(sk2,sk5)* neq(sk5,nil) equal(sk2,sk1) -> .
% 26.63/26.82 260[0:Res:7.0,143.0] ssList(u) || rearsegP(u,sk5)*+ rearsegP(sk5,u)* -> equal(u,sk5).
% 26.63/26.82 296[0:Res:7.0,87.0] || -> ssItem(u)* duplicatefreeP(sk5)*.
% 26.63/26.82 299[0:Res:7.0,73.0] || -> rearsegP(sk5,nil)*.
% 26.63/26.82 339[0:Res:7.0,146.1] ssList(u) || rearsegP(sk5,u) -> equal(app(skaf46(sk5,u),u),sk5)**.
% 26.63/26.82 418[0:Res:2.0,164.0] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,app(v,sk2)))**.
% 26.63/26.82 419[0:Res:2.0,207.0] || equal(sk2,sk1) neq(sk2,nil) segmentP(sk2,sk2)* segmentP(sk1,sk2) -> .
% 26.63/26.82 421[0:Res:2.0,13.0] || neq(sk2,nil) segmentP(sk2,sk2)* segmentP(sk1,sk2) -> equal(nil,sk2).
% 26.63/26.82 470[0:Res:2.0,89.0] || -> equal(app(nil,sk2),sk2)**.
% 26.63/26.82 471[0:Res:2.0,87.0] || -> ssItem(u)* duplicatefreeP(sk2)*.
% 26.63/26.82 473[0:Res:2.0,72.0] || -> segmentP(sk2,sk2)*.
% 26.63/26.82 486[0:Res:2.0,192.1] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u) equal(nil,sk2).
% 26.63/26.82 514[0:Res:2.0,146.1] ssList(u) || rearsegP(sk2,u) -> equal(app(skaf46(sk2,u),u),sk2)**.
% 26.63/26.82 516[0:Res:2.0,138.1] ssList(u) || -> equal(nil,sk2) equal(hd(app(sk2,u)),hd(sk2))**.
% 26.63/26.82 523[0:Res:2.0,112.1] ssItem(u) || -> equal(hd(cons(u,sk2)),u)**.
% 26.63/26.82 528[0:Res:2.0,101.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 26.63/26.82 567[0:MRR:421.0,421.1,12.1,473.0] || segmentP(sk1,sk2)* -> equal(nil,sk2).
% 26.63/26.82 568[0:Rew:567.1,419.1] || equal(sk2,sk1) neq(sk2,sk2) segmentP(sk2,sk2)* segmentP(sk1,sk2) -> .
% 26.63/26.82 569[0:MRR:568.2,473.0] || neq(sk2,sk2) segmentP(sk1,sk2)* equal(sk2,sk1) -> .
% 26.63/26.82 570[1:Spt:87.1] || -> ssItem(u)*.
% 26.63/26.82 573[1:MRR:528.0,570.0] || -> ssList(cons(u,sk2))*.
% 26.63/26.82 575[1:MRR:86.0,570.0] || memberP(nil,u)* -> .
% 26.63/26.82 576[1:MRR:85.0,570.0] || -> cyclefreeP(cons(u,nil))*.
% 26.63/26.82 577[1:MRR:84.0,570.0] || -> totalorderP(cons(u,nil))*.
% 26.63/26.82 578[1:MRR:83.0,570.0] || -> strictorderP(cons(u,nil))*.
% 26.63/26.82 579[1:MRR:82.0,570.0] || -> totalorderedP(cons(u,nil))*.
% 26.63/26.82 580[1:MRR:81.0,570.0] || -> strictorderedP(cons(u,nil))*.
% 26.63/26.82 581[1:MRR:80.0,570.0] || -> duplicatefreeP(cons(u,nil))*.
% 26.63/26.82 582[1:MRR:79.0,570.0] || -> equalelemsP(cons(u,nil))*.
% 26.63/26.82 586[1:MRR:523.0,570.0] || -> equal(hd(cons(u,sk2)),u)**.
% 26.63/26.82 600[1:MRR:117.1,117.0,570.0] || -> equal(u,v) neq(u,v)*.
% 26.63/26.82 639[1:MRR:145.1,145.0,570.0] || leq(u,v)*+ leq(v,u)* -> equal(u,v).
% 26.63/26.82 650[1:MRR:155.0,570.0] ssList(u) ssList(v) || memberP(u,w) -> memberP(app(u,v),w)*.
% 26.63/26.82 695[1:MRR:101.1,570.0] ssList(u) || -> ssList(cons(v,u))*.
% 26.63/26.82 701[1:MRR:135.1,570.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 26.63/26.82 718[1:MRR:190.1,570.0] ssList(u) ssList(v) ssList(w) || equal(app(v,cons(x,w)),u)*+ -> memberP(u,x)*.
% 26.63/26.82 769[1:MRR:185.3,185.2,570.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 26.63/26.82 770[2:Spt:516.0,516.2] ssList(u) || -> equal(hd(app(sk2,u)),hd(sk2))**.
% 26.63/26.82 778[3:Spt:486.5] || -> equal(nil,sk2)**.
% 26.63/26.82 860[3:Rew:778.0,89.1] ssList(u) || -> equal(app(sk2,u),u)**.
% 26.63/26.82 861[3:Rew:778.0,88.1] ssList(u) || -> equal(app(u,sk2),u)**.
% 26.63/26.82 866[3:Rew:778.0,576.0] || -> cyclefreeP(cons(u,sk2))*.
% 26.63/26.82 867[3:Rew:778.0,577.0] || -> totalorderP(cons(u,sk2))*.
% 26.63/26.82 868[3:Rew:778.0,578.0] || -> strictorderP(cons(u,sk2))*.
% 26.63/26.82 869[3:Rew:778.0,579.0] || -> totalorderedP(cons(u,sk2))*.
% 26.63/26.82 870[3:Rew:778.0,580.0] || -> strictorderedP(cons(u,sk2))*.
% 26.63/26.82 871[3:Rew:778.0,581.0] || -> duplicatefreeP(cons(u,sk2))*.
% 26.63/26.82 872[3:Rew:778.0,582.0] || -> equalelemsP(cons(u,sk2))*.
% 26.63/26.82 881[3:Rew:778.0,701.1] ssList(u) || -> equal(app(cons(v,sk2),u),cons(v,u))**.
% 26.63/26.82 927[3:Rew:860.1,770.1] ssList(u) || -> equal(hd(u),hd(sk2))*.
% 26.63/26.82 940[3:Rew:861.1,418.2] ssList(u) ssList(v) || -> equal(app(app(u,v),sk2),app(u,v))**.
% 26.63/26.82 1229[3:SpR:927.1,586.0] ssList(cons(u,sk2)) || -> equal(hd(sk2),u)*.
% 26.63/26.82 1234[3:SSi:1229.0,573.0,866.0,867.0,868.0,869.0,870.0,871.0,872.0] || -> equal(hd(sk2),u)*.
% 26.63/26.82 1297[3:Rew:1234.0,769.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk2))** -> equal(w,x)*.
% 26.63/26.82 1317[3:Rew:1234.0,881.1] ssList(u) || -> equal(app(hd(sk2),u),cons(v,u))*.
% 26.63/26.82 1342[3:Rew:1234.0,940.2] ssList(u) ssList(v) || -> equal(app(u,v),hd(sk2))**.
% 26.63/26.82 1347[3:Rew:1234.0,164.3] ssList(u) ssList(v) ssList(w) || -> equal(app(app(u,v),w),hd(sk2))**.
% 26.63/26.82 1425[3:Con:1297.1] ssList(u) || equal(cons(v,u),hd(sk2))** -> equal(v,w)*.
% 26.63/26.82 1426[3:AED:69.0,1425.2] ssList(u) || equal(cons(v,u),hd(sk2))** -> .
% 26.63/26.82 1431[3:Rew:1342.2,1347.3] ssList(u) ssList(v) ssList(w) || -> equal(app(hd(sk2),w),hd(sk2))**.
% 26.63/26.82 1432[3:Con:1431.0] ssList(u) || -> equal(app(hd(sk2),u),hd(sk2))**.
% 26.63/26.82 1433[3:Rew:1432.1,1317.1] ssList(u) || -> equal(cons(v,u),hd(sk2))**.
% 26.63/26.82 1434[3:MRR:1433.1,1426.1] ssList(u) || -> .
% 26.63/26.82 1435[3:UnC:1434.0,28.0] || -> .
% 26.63/26.82 1481[3:Spt:1435.0,486.5,778.0] || equal(nil,sk2)** -> .
% 26.63/26.82 1482[3:Spt:1435.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 26.63/26.82 1488[3:MRR:206.1,1481.0] || equal(nil,sk1)** -> .
% 26.63/26.82 1498[3:MRR:13.4,1481.0] ssList(u) || neq(u,nil) segmentP(sk1,u) segmentP(sk2,u)* -> .
% 26.63/26.82 2198[1:Res:103.2,639.0] ssList(u) || leq(skaf50(u),skaf49(u))* -> cyclefreeP(u) equal(skaf49(u),skaf50(u)).
% 26.63/26.82 2200[1:MRR:2198.1,102.2] ssList(u) || -> cyclefreeP(u) equal(skaf49(u),skaf50(u))**.
% 26.63/26.82 2205[1:Rew:2200.2,182.2] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf50(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 26.63/26.82 2724[1:SpR:204.0,650.3] ssList(sk1) ssList(sk5) || memberP(sk1,u) -> memberP(sk2,u)*.
% 26.63/26.82 3884[0:EqR:158.3] ssList(app(u,v)) ssList(v) ssList(u) || -> rearsegP(app(u,v),v)*.
% 26.63/26.82 3897[0:SSi:3884.0,100.2] ssList(u) ssList(v) || -> rearsegP(app(v,u),u)*.
% 26.63/26.82 3937[0:EqR:159.3] ssList(app(u,v)) ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 26.63/26.82 3950[0:SSi:3937.0,100.2] ssList(u) ssList(v) || -> frontsegP(app(u,v),u)*.
% 26.63/26.82 4405[1:EqR:718.3] ssList(app(u,cons(v,w))) ssList(u) ssList(w) || -> memberP(app(u,cons(v,w)),v)*.
% 26.63/26.82 4419[1:SSi:4405.0,100.1,695.2] ssList(u) ssList(v) || -> memberP(app(u,cons(w,v)),w)*.
% 26.63/26.82 5065[1:SSi:2724.0,201.0,1.0] ssList(sk5) || memberP(sk1,u) -> memberP(sk2,u)*.
% 26.63/26.82 5066[1:MRR:5065.0,7.0] || memberP(sk1,u) -> memberP(sk2,u)*.
% 26.63/26.82 5148[0:SpL:204.0,165.3] ssList(sk5) ssList(sk1) ssList(u) || equal(app(sk1,u),sk2)** -> equal(u,sk5).
% 26.63/26.82 5152[0:SpL:204.0,166.3] ssList(sk1) ssList(sk5) ssList(u) || equal(app(u,sk5),sk2)** -> equal(u,sk1).
% 26.63/26.82 5653[0:SpR:204.0,210.5] ssList(sk1) ssList(u) ssList(v) ssList(sk5) || segmentP(sk1,u) -> segmentP(app(v,sk2),u)*.
% 26.63/26.82 7450[0:SpR:204.0,3897.2] ssList(sk5) ssList(sk1) || -> rearsegP(sk2,sk5)*.
% 26.63/26.82 7526[0:SpR:204.0,3950.2] ssList(sk1) ssList(sk5) || -> frontsegP(sk2,sk1)*.
% 26.63/26.82 9336[1:SpR:180.2,4419.2] ssList(u) ssList(app(skaf61(u),cons(skaf59(u),skaf62(u)))) ssList(skaf63(u)) || -> strictorderP(u) memberP(u,skaf60(u))*.
% 26.63/26.82 9337[1:SpR:179.2,4419.2] ssList(u) ssList(app(skaf66(u),cons(skaf64(u),skaf67(u)))) ssList(skaf68(u)) || -> totalorderedP(u) memberP(u,skaf65(u))*.
% 26.63/26.82 9338[1:SpR:178.2,4419.2] ssList(u) ssList(app(skaf71(u),cons(skaf69(u),skaf72(u)))) ssList(skaf73(u)) || -> strictorderedP(u) memberP(u,skaf70(u))*.
% 26.63/26.82 9339[1:SpR:177.2,4419.2] ssList(u) ssList(app(skaf75(u),cons(skaf74(u),skaf76(u)))) ssList(skaf77(u)) || -> duplicatefreeP(u) memberP(u,skaf74(u))*.
% 26.63/26.82 9340[1:SpR:2205.2,4419.2] ssList(u) ssList(app(skaf51(u),cons(skaf50(u),skaf52(u)))) ssList(skaf53(u)) || -> cyclefreeP(u) memberP(u,skaf50(u))*.
% 26.63/26.82 9357[1:SSi:9340.2,9340.1,57.0,100.1,59.0,695.2,58.0] ssList(u) || -> cyclefreeP(u) memberP(u,skaf50(u))*.
% 26.63/26.82 9358[1:SSi:9339.2,9339.1,33.0,100.1,35.0,695.2,34.0] ssList(u) || -> duplicatefreeP(u) memberP(u,skaf74(u))*.
% 26.63/26.82 9359[1:SSi:9338.2,9338.1,37.0,100.1,39.0,695.2,38.0] ssList(u) || -> strictorderedP(u) memberP(u,skaf70(u))*.
% 26.63/26.82 9360[1:SSi:9337.2,9337.1,42.0,100.1,44.0,695.2,43.0] ssList(u) || -> totalorderedP(u) memberP(u,skaf65(u))*.
% 26.63/26.82 9361[1:SSi:9336.2,9336.1,47.0,100.1,49.0,695.2,48.0] ssList(u) || -> strictorderP(u) memberP(u,skaf60(u))*.
% 26.63/26.82 10012[0:SpR:339.2,88.1] ssList(nil) ssList(skaf46(sk5,nil)) || rearsegP(sk5,nil) -> equal(skaf46(sk5,nil),sk5)**.
% 26.63/26.82 23897[0:SSi:7450.1,7450.0,201.0,1.0,7.0] || -> rearsegP(sk2,sk5)*.
% 26.63/26.82 23898[0:SSi:7526.1,7526.0,7.0,201.0,1.0] || -> frontsegP(sk2,sk1)*.
% 26.63/26.82 23964[0:SSi:10012.1,10012.0,65.0,7.0,23.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0,23.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0] || rearsegP(sk5,nil) -> equal(skaf46(sk5,nil),sk5)**.
% 26.63/26.82 23965[0:MRR:23964.0,299.0] || -> equal(skaf46(sk5,nil),sk5)**.
% 26.63/26.82 23979[0:SSi:5148.1,5148.0,201.0,1.0,7.0] ssList(u) || equal(app(sk1,u),sk2)** -> equal(u,sk5).
% 26.63/26.82 23980[0:SSi:5152.1,5152.0,7.0,201.0,1.0] ssList(u) || equal(app(u,sk5),sk2)** -> equal(u,sk1).
% 26.63/26.82 24028[0:SSi:5653.3,5653.0,7.0,201.0,1.0] ssList(u) ssList(v) || segmentP(sk1,u) -> segmentP(app(v,sk2),u)*.
% 26.63/26.82 24288[0:Res:23897.0,260.1] ssList(sk2) || rearsegP(sk5,sk2)* -> equal(sk5,sk2).
% 26.63/26.82 24293[0:Res:23898.0,144.2] ssList(sk2) ssList(sk1) || frontsegP(sk1,sk2)* -> equal(sk2,sk1).
% 26.63/26.82 25314[0:SpL:88.1,23979.1] ssList(sk1) ssList(nil) || equal(sk2,sk1) -> equal(nil,sk5)**.
% 26.63/26.82 25376[0:SpL:514.2,23980.1] ssList(sk5) ssList(skaf46(sk2,sk5)) || rearsegP(sk2,sk5) equal(sk2,sk2) -> equal(skaf46(sk2,sk5),sk1)**.
% 26.63/26.82 25382[0:Obv:25376.3] ssList(sk5) ssList(skaf46(sk2,sk5)) || rearsegP(sk2,sk5) -> equal(skaf46(sk2,sk5),sk1)**.
% 26.63/26.82 25405[0:SpR:470.0,24028.3] ssList(u) ssList(nil) || segmentP(sk1,u) -> segmentP(sk2,u)*.
% 26.63/26.82 25425[0:SSi:25405.1,23.0,22.0,21.0,20.0,19.0,18.0,17.0,16.0] ssList(u) || segmentP(sk1,u) -> segmentP(sk2,u)*.
% 26.63/26.82 25426[3:MRR:1498.3,25425.2] ssList(u) || neq(u,nil) segmentP(sk1,u)* -> .
% 26.63/26.82 25474[3:Res:72.1,25426.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 26.63/26.82 25476[3:Obv:25474.0] ssList(sk1) || neq(sk1,nil)* -> .
% 26.63/26.82 25477[3:SSi:25476.0,201.0,1.0] || neq(sk1,nil)* -> .
% 26.63/26.82 25478[3:Res:600.1,25477.0] || -> equal(nil,sk1)**.
% 26.63/26.82 25479[3:MRR:25478.0,1488.0] || -> .
% 26.63/26.82 25480[2:Spt:25479.0,516.1] || -> equal(nil,sk2)**.
% 26.63/26.82 25533[2:Rew:25480.0,575.0] || memberP(sk2,u)* -> .
% 26.63/26.82 25550[2:Rew:25480.0,75.1] ssList(u) || -> frontsegP(u,sk2)*.
% 26.63/26.82 25919[2:MRR:5066.1,25533.0] || memberP(sk1,u)* -> .
% 26.63/26.82 25979[2:Rew:25480.0,205.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 26.63/26.82 26456[2:MRR:569.0,25979.1] || segmentP(sk1,sk2)* equal(sk2,sk1) -> .
% 26.63/26.82 26509[0:SSi:24293.1,24293.0,201.0,1.0,2.0] || frontsegP(sk1,sk2)* -> equal(sk2,sk1).
% 26.63/26.82 27247[2:Res:9357.2,25919.0] ssList(sk1) || -> cyclefreeP(sk1)*.
% 26.63/26.82 27248[2:Res:9358.2,25919.0] ssList(sk1) || -> duplicatefreeP(sk1)*.
% 26.63/26.82 27249[2:Res:9359.2,25919.0] ssList(sk1) || -> strictorderedP(sk1)*.
% 26.63/26.82 27250[2:Res:9360.2,25919.0] ssList(sk1) || -> totalorderedP(sk1)*.
% 26.63/26.82 27251[2:Res:9361.2,25919.0] ssList(sk1) || -> strictorderP(sk1)*.
% 26.63/26.82 27252[2:SSi:27247.0,201.0,1.0] || -> cyclefreeP(sk1)*.
% 26.63/26.82 27253[2:SSi:27248.0,201.0,1.0] || -> duplicatefreeP(sk1)*.
% 26.63/26.82 27254[2:SSi:27249.0,201.0,1.0] || -> strictorderedP(sk1)*.
% 26.63/26.82 27255[2:SSi:27250.0,201.0,1.0] || -> totalorderedP(sk1)*.
% 26.63/26.82 27256[2:SSi:27251.0,201.0,1.0] || -> strictorderP(sk1)*.
% 26.63/26.82 27359[3:Spt:25979.0] || equal(sk2,sk1)** -> .
% 26.63/26.82 27363[3:MRR:26509.1,27359.0] || frontsegP(sk1,sk2)* -> .
% 26.63/26.82 27368[3:Res:25550.1,27363.0] ssList(sk1) || -> .
% 26.63/26.82 27369[3:SSi:27368.0,201.0,1.0,27252.0,27253.0,27254.0,27255.0,27256.0] || -> .
% 32.13/32.33 27370[3:Spt:27369.0,25979.0,27359.0] || -> equal(sk2,sk1)**.
% 32.13/32.33 27371[3:Spt:27369.0,25979.1] || -> neq(sk2,sk2)*.
% 32.13/32.33 27375[3:Rew:27370.0,473.0] || -> segmentP(sk1,sk1)*.
% 32.13/32.33 27845[3:Rew:27370.0,26456.1,27370.0,26456.0] || segmentP(sk1,sk1)* equal(sk1,sk1) -> .
% 32.13/32.33 27846[3:Obv:27845.1] || segmentP(sk1,sk1)* -> .
% 32.13/32.33 27847[3:MRR:27846.0,27375.0] || -> .
% 32.13/32.33 28006[1:Spt:27847.0,87.0,87.2] ssList(u) || -> duplicatefreeP(u)*.
% 32.13/32.33 28008[0:MRR:24288.0,2.0] || rearsegP(sk5,sk2)* -> equal(sk5,sk2).
% 32.13/32.33 28010[0:SSi:25314.0,201.0,1.0] ssList(nil) || equal(sk2,sk1) -> equal(nil,sk5)**.
% 32.13/32.33 28011[0:MRR:28010.0,23.0] || equal(sk2,sk1) -> equal(nil,sk5)**.
% 32.13/32.33 28012[0:Rew:28011.1,205.1] || equal(sk2,sk1) -> neq(sk2,sk5)*.
% 32.13/32.33 28037[0:Rew:28011.1,244.2] || segmentP(sk1,sk5) segmentP(sk2,sk5)* neq(sk5,sk5) equal(sk2,sk1) -> .
% 32.13/32.33 28044[0:SSi:25382.1,65.0] ssList(sk5) || rearsegP(sk2,sk5) -> equal(skaf46(sk2,sk5),sk1)**.
% 32.13/32.33 28045[0:MRR:28044.0,28044.1,7.0,23897.0] || -> equal(skaf46(sk2,sk5),sk1)**.
% 32.13/32.33 28055[0:MRR:13.3,25425.2] ssList(u) || neq(u,nil) segmentP(sk1,u)* -> equal(nil,sk2).
% 32.13/32.33 28255[2:Spt:471.0] || -> ssItem(u)*.
% 32.13/32.33 28283[2:MRR:117.1,117.0,28255.0] || -> equal(u,v) neq(u,v)*.
% 32.13/32.33 28455[3:Spt:486.5] || -> equal(nil,sk2)**.
% 32.13/32.33 28465[3:Rew:28455.0,299.0] || -> rearsegP(sk5,sk2)*.
% 32.13/32.33 28472[3:Rew:28455.0,23965.0] || -> equal(skaf46(sk5,sk2),sk5)**.
% 32.13/32.33 28692[3:MRR:28008.0,28465.0] || -> equal(sk5,sk2)**.
% 32.13/32.33 28846[3:Rew:28692.0,28012.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 32.13/32.33 28869[3:Rew:28692.0,28037.0] || segmentP(sk1,sk2) segmentP(sk2,sk5)* neq(sk5,sk5) equal(sk2,sk1) -> .
% 32.13/32.33 28876[3:Rew:28692.0,28045.0] || -> equal(skaf46(sk2,sk2),sk1)**.
% 32.13/32.33 28937[3:Rew:28692.0,28472.0] || -> equal(skaf46(sk2,sk2),sk2)**.
% 32.13/32.33 28940[3:Rew:28937.0,28876.0] || -> equal(sk2,sk1)**.
% 32.13/32.33 28946[3:Rew:28940.0,473.0] || -> segmentP(sk1,sk1)*.
% 32.13/32.33 29156[3:Rew:28940.0,28692.0] || -> equal(sk5,sk1)**.
% 32.13/32.33 29201[3:Rew:28940.0,28846.1,28940.0,28846.0] || equal(sk1,sk1) -> neq(sk1,sk1)*.
% 32.13/32.33 29202[3:Obv:29201.0] || -> neq(sk1,sk1)*.
% 32.13/32.33 29487[3:Rew:28940.0,28869.3,29156.0,28869.2,28940.0,28869.1,29156.0,28869.1,28940.0,28869.0] || segmentP(sk1,sk1)* segmentP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 32.13/32.33 29488[3:Obv:29487.3] || segmentP(sk1,sk1)* neq(sk1,sk1) -> .
% 32.13/32.33 29489[3:MRR:29488.0,29488.1,28946.0,29202.0] || -> .
% 32.13/32.33 29783[3:Spt:29489.0,486.5,28455.0] || equal(nil,sk2)** -> .
% 32.13/32.33 29784[3:Spt:29489.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 32.13/32.33 29790[3:MRR:206.1,29783.0] || equal(nil,sk1)** -> .
% 32.13/32.33 29803[3:MRR:28055.3,29783.0] ssList(u) || neq(u,nil) segmentP(sk1,u)* -> .
% 32.13/32.33 31540[3:Res:72.1,29803.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 31542[3:Obv:31540.0] ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 31543[3:SSi:31542.0,201.0,1.0] || neq(sk1,nil)* -> .
% 32.13/32.33 31545[3:Res:28283.1,31543.0] || -> equal(nil,sk1)**.
% 32.13/32.33 31546[3:MRR:31545.0,29790.0] || -> .
% 32.13/32.33 31547[2:Spt:31546.0,471.1] || -> duplicatefreeP(sk2)*.
% 32.13/32.33 31557[3:Spt:296.0] || -> ssItem(u)*.
% 32.13/32.33 31587[3:MRR:117.1,117.0,31557.0] || -> equal(u,v) neq(u,v)*.
% 32.13/32.33 31757[4:Spt:486.5] || -> equal(nil,sk2)**.
% 32.13/32.33 31768[4:Rew:31757.0,299.0] || -> rearsegP(sk5,sk2)*.
% 32.13/32.33 31774[4:Rew:31757.0,23965.0] || -> equal(skaf46(sk5,sk2),sk5)**.
% 32.13/32.33 31994[4:MRR:28008.0,31768.0] || -> equal(sk5,sk2)**.
% 32.13/32.33 32002[4:Rew:31994.0,28045.0] || -> equal(skaf46(sk2,sk2),sk1)**.
% 32.13/32.33 32179[4:Rew:31994.0,28012.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 32.13/32.33 32188[4:Rew:31994.0,28037.0] || segmentP(sk1,sk2) segmentP(sk2,sk5)* neq(sk5,sk5) equal(sk2,sk1) -> .
% 32.13/32.33 32240[4:Rew:31994.0,31774.0] || -> equal(skaf46(sk2,sk2),sk2)**.
% 32.13/32.33 32244[4:Rew:32240.0,32002.0] || -> equal(sk2,sk1)**.
% 32.13/32.33 32249[4:Rew:32244.0,473.0] || -> segmentP(sk1,sk1)*.
% 32.13/32.33 32465[4:Rew:32244.0,31994.0] || -> equal(sk5,sk1)**.
% 32.13/32.33 32508[4:Rew:32244.0,32179.1,32244.0,32179.0] || equal(sk1,sk1) -> neq(sk1,sk1)*.
% 32.13/32.33 32509[4:Obv:32508.0] || -> neq(sk1,sk1)*.
% 32.13/32.33 32793[4:Rew:32244.0,32188.3,32465.0,32188.2,32244.0,32188.1,32465.0,32188.1,32244.0,32188.0] || segmentP(sk1,sk1)* segmentP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 32.13/32.33 32794[4:Obv:32793.3] || segmentP(sk1,sk1)* neq(sk1,sk1) -> .
% 32.13/32.33 32795[4:MRR:32794.0,32794.1,32249.0,32509.0] || -> .
% 32.13/32.33 33088[4:Spt:32795.0,486.5,31757.0] || equal(nil,sk2)** -> .
% 32.13/32.33 33089[4:Spt:32795.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 32.13/32.33 33095[4:MRR:206.1,33088.0] || equal(nil,sk1)** -> .
% 32.13/32.33 33108[4:MRR:28055.3,33088.0] ssList(u) || neq(u,nil) segmentP(sk1,u)* -> .
% 32.13/32.33 34813[4:Res:72.1,33108.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 34815[4:Obv:34813.0] ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 34816[4:SSi:34815.0,201.0,1.0] || neq(sk1,nil)* -> .
% 32.13/32.33 34818[4:Res:31587.1,34816.0] || -> equal(nil,sk1)**.
% 32.13/32.33 34819[4:MRR:34818.0,33095.0] || -> .
% 32.13/32.33 34820[3:Spt:34819.0,296.1] || -> duplicatefreeP(sk5)*.
% 32.13/32.33 34823[4:Spt:486.5] || -> equal(nil,sk2)**.
% 32.13/32.33 34834[4:Rew:34823.0,299.0] || -> rearsegP(sk5,sk2)*.
% 32.13/32.33 34841[4:Rew:34823.0,23965.0] || -> equal(skaf46(sk5,sk2),sk5)**.
% 32.13/32.33 35064[4:MRR:28008.0,34834.0] || -> equal(sk5,sk2)**.
% 32.13/32.33 35072[4:Rew:35064.0,28045.0] || -> equal(skaf46(sk2,sk2),sk1)**.
% 32.13/32.33 35249[4:Rew:35064.0,28012.1] || equal(sk2,sk1) -> neq(sk2,sk2)*.
% 32.13/32.33 35265[4:Rew:35064.0,28037.0] || segmentP(sk1,sk2) segmentP(sk2,sk5)* neq(sk5,sk5) equal(sk2,sk1) -> .
% 32.13/32.33 35311[4:Rew:35064.0,34841.0] || -> equal(skaf46(sk2,sk2),sk2)**.
% 32.13/32.33 35315[4:Rew:35311.0,35072.0] || -> equal(sk2,sk1)**.
% 32.13/32.33 35321[4:Rew:35315.0,473.0] || -> segmentP(sk1,sk1)*.
% 32.13/32.33 35541[4:Rew:35315.0,35064.0] || -> equal(sk5,sk1)**.
% 32.13/32.33 35587[4:Rew:35315.0,35249.1,35315.0,35249.0] || equal(sk1,sk1) -> neq(sk1,sk1)*.
% 32.13/32.33 35588[4:Obv:35587.0] || -> neq(sk1,sk1)*.
% 32.13/32.33 35868[4:Rew:35315.0,35265.3,35541.0,35265.2,35315.0,35265.1,35541.0,35265.1,35315.0,35265.0] || segmentP(sk1,sk1)* segmentP(sk1,sk1)* neq(sk1,sk1) equal(sk1,sk1) -> .
% 32.13/32.33 35869[4:Obv:35868.3] || segmentP(sk1,sk1)* neq(sk1,sk1) -> .
% 32.13/32.33 35870[4:MRR:35869.0,35869.1,35321.0,35588.0] || -> .
% 32.13/32.33 36185[4:Spt:35870.0,486.5,34823.0] || equal(nil,sk2)** -> .
% 32.13/32.33 36186[4:Spt:35870.0,486.0,486.1,486.2,486.3,486.4] ssList(u) || equal(hd(u),hd(sk2))* equal(tl(u),tl(sk2)) -> equal(u,sk2) equal(nil,u).
% 32.13/32.33 36194[4:MRR:206.1,36185.0] || equal(nil,sk1)** -> .
% 32.13/32.33 36205[4:MRR:28055.3,36185.0] ssList(u) || neq(u,nil) segmentP(sk1,u)* -> .
% 32.13/32.33 37587[4:Res:72.1,36205.2] ssList(sk1) ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 37589[4:Obv:37587.0] ssList(sk1) || neq(sk1,nil)* -> .
% 32.13/32.33 37590[4:SSi:37589.0,201.0,1.0] || neq(sk1,nil)* -> .
% 32.13/32.33 37725[4:Res:115.3,37590.0] ssList(sk1) ssList(nil) || -> equal(nil,sk1)**.
% 32.13/32.33 37727[4:SSi:37725.1,37725.0,16.0,17.0,18.0,19.0,20.0,21.0,22.0,23.0,201.0,1.0] || -> equal(nil,sk1)**.
% 32.13/32.33 37728[4:MRR:37727.0,36194.0] || -> .
% 32.13/32.33 % SZS output end Refutation
% 32.13/32.33 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_8 co1_9 co1_11 co1_12 co1_13 co1_14 co1_15 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause13 clause18 clause19 clause20 clause22 clause23 clause24 clause27 clause28 clause29 clause32 clause33 clause34 clause42 clause43 clause44 clause50 clause54 clause57 clause58 clause60 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause74 clause85 clause86 clause87 clause88 clause97 clause100 clause102 clause120 clause123 clause128 clause129 clause130 clause131 clause140 clause143 clause144 clause149 clause150 clause151 clause162 clause163 clause164 clause165 clause167 clause170 clause172 clause175 clause177
% 32.13/32.33
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