TSTP Solution File: SWC025-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC025-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 22:01:10 EDT 2022
% Result : Unsatisfiable 3.63s 3.88s
% Output : Refutation 4.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC025-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 03:45:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.63/3.88
% 3.63/3.88 SPASS V 3.9
% 3.63/3.88 SPASS beiseite: Proof found.
% 3.63/3.88 % SZS status Theorem
% 3.63/3.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.63/3.88 SPASS derived 7919 clauses, backtracked 4282 clauses, performed 83 splits and kept 7388 clauses.
% 3.63/3.88 SPASS allocated 85419 KBytes.
% 3.63/3.88 SPASS spent 0:00:03.53 on the problem.
% 3.63/3.88 0:00:00.04 for the input.
% 3.63/3.88 0:00:00.00 for the FLOTTER CNF translation.
% 3.63/3.88 0:00:00.07 for inferences.
% 3.63/3.88 0:00:00.11 for the backtracking.
% 3.63/3.88 0:00:03.10 for the reduction.
% 3.63/3.88
% 3.63/3.88
% 3.63/3.88 Here is a proof with depth 6, length 188 :
% 3.63/3.88 % SZS output start Refutation
% 3.63/3.88 3[0:Inp] || -> ssList(sk3)*.
% 3.63/3.88 4[0:Inp] || -> ssList(sk4)*.
% 3.63/3.88 5[0:Inp] || -> equal(sk2,sk4)**.
% 3.63/3.88 6[0:Inp] || -> equal(sk1,sk3)**.
% 3.63/3.88 7[0:Inp] || -> duplicatefreeP(sk3)*.
% 3.63/3.88 8[0:Inp] ssItem(u) || memberP(sk3,u) -> memberP(sk4,u)*.
% 3.63/3.88 9[0:Inp] ssItem(u) || memberP(sk4,u)* -> memberP(sk3,u).
% 3.63/3.88 10[0:Inp] || -> equal(nil,sk2)** equal(nil,sk1).
% 3.63/3.88 13[0:Inp] || equal(nil,sk1) equal(nil,sk2)** -> .
% 3.63/3.88 22[0:Inp] || -> ssItem(skac3)*.
% 3.63/3.88 23[0:Inp] || -> ssItem(skac2)*.
% 3.63/3.88 25[0:Inp] || -> ssItem(skaf83(u))*.
% 3.63/3.88 26[0:Inp] || -> ssList(skaf82(u))*.
% 3.63/3.88 67[0:Inp] || equal(skac2,skac3)** -> .
% 3.63/3.88 73[0:Inp] ssList(u) || -> frontsegP(u,nil)*.
% 3.63/3.88 77[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 3.63/3.88 78[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 3.63/3.88 79[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 3.63/3.88 80[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 3.63/3.88 81[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 3.63/3.88 82[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 3.63/3.88 83[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 3.63/3.88 84[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 3.63/3.88 85[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 3.63/3.88 86[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 3.63/3.88 87[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 3.63/3.88 90[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 3.63/3.88 99[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 3.63/3.88 110[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 3.63/3.88 122[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 3.63/3.88 133[0:Inp] ssList(u) ssItem(v) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.63/3.88 136[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 3.63/3.88 151[0:Inp] ssItem(u) ssItem(v) ssList(w) || equal(u,v) -> memberP(cons(v,w),u)*.
% 3.63/3.88 170[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 3.63/3.88 183[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.63/3.88 189[0:Inp] ssItem(u) ssItem(v) ssList(w) ssList(x) || frontsegP(cons(u,w),cons(v,x))* -> equal(u,v).
% 3.63/3.88 191[0:Inp] ssItem(u) ssItem(v) ssList(w) ssList(x) || equal(u,v) frontsegP(w,x) -> frontsegP(cons(u,w),cons(v,x))*.
% 3.63/3.88 201[0:Rew:6.0,10.1,5.0,10.0] || -> equal(nil,sk3) equal(nil,sk4)**.
% 3.63/3.88 202[0:Rew:5.0,13.1,6.0,13.0] || equal(nil,sk4)** equal(nil,sk3) -> .
% 3.63/3.88 215[0:Res:4.0,191.0] ssItem(u) ssItem(v) ssList(w) || equal(u,v) frontsegP(w,sk4) -> frontsegP(cons(u,w),cons(v,sk4))*.
% 3.63/3.88 266[0:Res:4.0,122.0] || -> equal(nil,sk4) equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 3.63/3.88 289[0:Res:4.0,85.0] || -> ssItem(u)* duplicatefreeP(sk4)*.
% 3.63/3.88 333[0:Res:4.0,136.1] ssList(u) || -> equal(nil,sk4) equal(hd(app(sk4,u)),hd(sk4))**.
% 3.63/3.88 340[0:Res:4.0,110.1] ssItem(u) || -> equal(hd(cons(u,sk4)),u)**.
% 3.63/3.88 437[0:Res:3.0,122.0] || -> equal(nil,sk3) equal(cons(skaf83(sk3),skaf82(sk3)),sk3)**.
% 3.63/3.88 456[0:Res:3.0,90.0] || -> ssList(tl(sk3))* equal(nil,sk3).
% 3.63/3.88 504[0:Res:3.0,136.1] ssList(u) || -> equal(nil,sk3) equal(hd(app(sk3,u)),hd(sk3))**.
% 3.63/3.88 511[0:Res:3.0,110.1] ssItem(u) || -> equal(hd(cons(u,sk3)),u)**.
% 3.63/3.88 516[0:Res:3.0,99.1] ssItem(u) || -> ssList(cons(u,sk3))*.
% 3.63/3.88 527[0:Res:3.0,170.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk3),cons(v,app(u,sk3)))**.
% 3.63/3.88 565[1:Spt:85.1] || -> ssItem(u)*.
% 3.63/3.88 568[1:MRR:516.0,565.0] || -> ssList(cons(u,sk3))*.
% 3.63/3.88 570[1:MRR:84.0,565.0] || memberP(nil,u)* -> .
% 3.63/3.88 571[1:MRR:83.0,565.0] || -> cyclefreeP(cons(u,nil))*.
% 3.63/3.88 572[1:MRR:82.0,565.0] || -> totalorderP(cons(u,nil))*.
% 3.63/3.88 573[1:MRR:81.0,565.0] || -> strictorderP(cons(u,nil))*.
% 3.63/3.88 574[1:MRR:80.0,565.0] || -> totalorderedP(cons(u,nil))*.
% 3.63/3.88 575[1:MRR:79.0,565.0] || -> strictorderedP(cons(u,nil))*.
% 3.63/3.88 576[1:MRR:78.0,565.0] || -> duplicatefreeP(cons(u,nil))*.
% 3.63/3.88 577[1:MRR:77.0,565.0] || -> equalelemsP(cons(u,nil))*.
% 3.63/3.88 581[1:MRR:511.0,565.0] || -> equal(hd(cons(u,sk3)),u)**.
% 3.63/3.88 585[1:MRR:340.0,565.0] || -> equal(hd(cons(u,sk4)),u)**.
% 3.63/3.88 587[1:MRR:9.0,565.0] || memberP(sk4,u)* -> memberP(sk3,u).
% 3.63/3.88 588[1:MRR:8.0,565.0] || memberP(sk3,u) -> memberP(sk4,u)*.
% 3.63/3.88 649[1:MRR:151.1,151.0,565.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 3.63/3.88 671[1:MRR:189.1,189.0,565.0] ssList(u) ssList(v) || frontsegP(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.63/3.88 674[1:MRR:215.1,215.0,565.0] ssList(u) || equal(v,w) frontsegP(u,sk4) -> frontsegP(cons(v,u),cons(w,sk4))*.
% 3.63/3.88 698[1:MRR:133.1,565.0] ssList(u) || -> equal(app(cons(v,nil),u),cons(v,u))**.
% 3.63/3.88 699[1:MRR:527.1,565.0] ssList(u) || -> equal(app(cons(v,u),sk3),cons(v,app(u,sk3)))**.
% 3.63/3.88 762[1:MRR:183.3,183.2,565.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 3.63/3.88 763[2:Spt:504.0,504.2] ssList(u) || -> equal(hd(app(sk3,u)),hd(sk3))**.
% 3.63/3.88 765[3:Spt:333.0,333.2] ssList(u) || -> equal(hd(app(sk4,u)),hd(sk4))**.
% 3.63/3.88 771[4:Spt:201.0] || -> equal(nil,sk3)**.
% 3.63/3.88 851[4:Rew:771.0,87.1] ssList(u) || -> equal(app(sk3,u),u)**.
% 3.63/3.88 852[4:Rew:771.0,86.1] ssList(u) || -> equal(app(u,sk3),u)**.
% 3.63/3.88 857[4:Rew:771.0,571.0] || -> cyclefreeP(cons(u,sk3))*.
% 3.63/3.88 858[4:Rew:771.0,572.0] || -> totalorderP(cons(u,sk3))*.
% 3.63/3.88 859[4:Rew:771.0,573.0] || -> strictorderP(cons(u,sk3))*.
% 3.63/3.88 860[4:Rew:771.0,574.0] || -> totalorderedP(cons(u,sk3))*.
% 3.63/3.88 861[4:Rew:771.0,575.0] || -> strictorderedP(cons(u,sk3))*.
% 3.63/3.88 862[4:Rew:771.0,576.0] || -> duplicatefreeP(cons(u,sk3))*.
% 3.63/3.88 863[4:Rew:771.0,577.0] || -> equalelemsP(cons(u,sk3))*.
% 3.63/3.88 920[4:Rew:851.1,763.1] ssList(u) || -> equal(hd(u),hd(sk3))*.
% 3.63/3.88 943[4:Rew:852.1,699.1] ssList(u) || -> equal(app(cons(v,u),sk3),cons(v,u))**.
% 3.63/3.88 1021[4:SpR:920.1,581.0] ssList(cons(u,sk3)) || -> equal(hd(sk3),u)*.
% 3.63/3.88 1027[4:SSi:1021.0,568.0,857.0,858.0,859.0,860.0,861.0,862.0,863.0] || -> equal(hd(sk3),u)*.
% 3.63/3.88 1079[4:Rew:1027.0,943.1] ssList(u) || -> equal(cons(v,u),hd(sk3))**.
% 3.63/3.88 1244[4:Rew:1027.0,762.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk3))** -> equal(w,x)*.
% 3.63/3.88 1371[4:Con:1244.1] ssList(u) || equal(cons(v,u),hd(sk3))** -> equal(v,w)*.
% 3.63/3.88 1372[4:AED:67.0,1371.2] ssList(u) || equal(cons(v,u),hd(sk3))** -> .
% 3.63/3.88 1373[4:Rew:1079.1,1372.1] ssList(u) || equal(hd(sk3),hd(sk3))* -> .
% 3.63/3.88 1374[4:Obv:1373.1] ssList(u) || -> .
% 3.63/3.88 1375[4:UnC:1374.0,26.0] || -> .
% 3.63/3.88 1540[4:Spt:1375.0,201.0,771.0] || equal(nil,sk3)** -> .
% 3.63/3.88 1541[4:Spt:1375.0,201.1] || -> equal(nil,sk4)**.
% 3.63/3.88 1565[4:Rew:1541.0,1540.0] || equal(sk4,sk3)** -> .
% 3.63/3.88 1570[4:Rew:1541.0,456.1] || -> ssList(tl(sk3))* equal(sk4,sk3).
% 3.63/3.88 1571[4:MRR:1570.1,1565.0] || -> ssList(tl(sk3))*.
% 3.63/3.88 1578[4:Rew:1541.0,73.1] ssList(u) || -> frontsegP(u,sk4)*.
% 3.63/3.88 1599[4:Rew:1541.0,87.1] ssList(u) || -> equal(app(sk4,u),u)**.
% 3.63/3.88 1626[4:Rew:1599.1,765.1] ssList(u) || -> equal(hd(u),hd(sk4))*.
% 3.63/3.88 1639[4:Rew:1541.0,698.1] ssList(u) || -> equal(app(cons(v,sk4),u),cons(v,u))**.
% 3.63/3.88 1695[4:MRR:674.2,1578.1] ssList(u) || equal(v,w) -> frontsegP(cons(v,u),cons(w,sk4))*.
% 3.63/3.88 1741[4:SpR:1626.1,581.0] ssList(cons(u,sk3)) || -> equal(hd(sk4),u)*.
% 3.63/3.88 1747[4:SSi:1741.0,568.0] || -> equal(hd(sk4),u)*.
% 3.63/3.88 1929[4:Rew:1747.0,1639.1] ssList(u) || -> equal(cons(v,u),hd(sk4))**.
% 3.63/3.88 1954[4:Rew:1747.0,671.2] ssList(u) ssList(v) || frontsegP(cons(w,u),hd(sk4))* -> equal(w,x)*.
% 3.63/3.88 1955[4:Rew:1747.0,1695.2] ssList(u) || equal(v,w)* -> frontsegP(cons(v,u),hd(sk4))*.
% 3.63/3.88 2026[4:AED:67.0,1955.1] ssList(u) || -> frontsegP(cons(v,u),hd(sk4))*.
% 3.63/3.88 2027[4:Rew:1929.1,2026.1] ssList(u) || -> frontsegP(hd(sk4),hd(sk4))*.
% 3.63/3.88 2090[4:Con:1954.1] ssList(u) || frontsegP(cons(v,u),hd(sk4))* -> equal(v,w)*.
% 3.63/3.88 2091[4:AED:67.0,2090.2] ssList(u) || frontsegP(cons(v,u),hd(sk4))* -> .
% 3.63/3.88 2092[4:Rew:1929.1,2091.1] ssList(u) || frontsegP(hd(sk4),hd(sk4))* -> .
% 3.63/3.88 2093[4:MRR:2092.1,2027.1] ssList(u) || -> .
% 3.63/3.88 2094[4:UnC:2093.0,1571.0] || -> .
% 3.63/3.88 2274[3:Spt:2094.0,333.1] || -> equal(nil,sk4)**.
% 3.63/3.88 2297[3:Rew:2274.0,570.0] || memberP(sk4,u)* -> .
% 3.63/3.88 2320[3:MRR:588.1,2297.0] || memberP(sk3,u)* -> .
% 3.63/3.88 2329[3:Rew:2274.0,202.1,2274.0,202.0] || equal(sk4,sk4)* equal(sk4,sk3) -> .
% 3.63/3.88 2330[3:Obv:2329.0] || equal(sk4,sk3)** -> .
% 3.63/3.88 2342[3:Rew:2274.0,437.0] || -> equal(sk4,sk3) equal(cons(skaf83(sk3),skaf82(sk3)),sk3)**.
% 4.16/4.39 2343[3:MRR:2342.0,2330.0] || -> equal(cons(skaf83(sk3),skaf82(sk3)),sk3)**.
% 4.16/4.39 2786[3:SpR:2343.0,649.2] ssList(skaf82(sk3)) || equal(u,skaf83(sk3)) -> memberP(sk3,u)*.
% 4.16/4.39 2943[3:SSi:2786.0,26.0,7.0,3.0] || equal(u,skaf83(sk3)) -> memberP(sk3,u)*.
% 4.16/4.39 2944[3:MRR:2943.1,2320.0] || equal(u,skaf83(sk3))* -> .
% 4.16/4.39 2945[3:UnC:2944.0,585.0] || -> .
% 4.16/4.39 2948[2:Spt:2945.0,504.1] || -> equal(nil,sk3)**.
% 4.16/4.39 2977[2:Rew:2948.0,570.0] || memberP(sk3,u)* -> .
% 4.16/4.39 3013[2:MRR:587.1,2977.0] || memberP(sk4,u)* -> .
% 4.16/4.39 3040[2:Rew:2948.0,202.1,2948.0,202.0] || equal(sk4,sk3)** equal(sk3,sk3) -> .
% 4.16/4.39 3041[2:Obv:3040.1] || equal(sk4,sk3)** -> .
% 4.16/4.39 3061[2:Rew:2948.0,266.0] || -> equal(sk4,sk3) equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 4.16/4.39 3062[2:MRR:3061.0,3041.0] || -> equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 4.16/4.39 3149[2:SpR:3062.0,649.2] ssList(skaf82(sk4)) || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 3276[2:SSi:3149.0,26.0,4.0] || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 3277[2:MRR:3276.1,3013.0] || equal(u,skaf83(sk4))* -> .
% 4.16/4.39 3278[2:UnC:3277.0,585.0] || -> .
% 4.16/4.39 3282[1:Spt:3278.0,85.0,85.2] ssList(u) || -> duplicatefreeP(u)*.
% 4.16/4.39 3290[2:Spt:504.0,504.2] ssList(u) || -> equal(hd(app(sk3,u)),hd(sk3))**.
% 4.16/4.39 3292[3:Spt:201.0] || -> equal(nil,sk3)**.
% 4.16/4.39 3346[3:Rew:3292.0,77.1] ssItem(u) || -> equalelemsP(cons(u,sk3))*.
% 4.16/4.39 3347[3:Rew:3292.0,78.1] ssItem(u) || -> duplicatefreeP(cons(u,sk3))*.
% 4.16/4.39 3348[3:Rew:3292.0,79.1] ssItem(u) || -> strictorderedP(cons(u,sk3))*.
% 4.16/4.39 3349[3:Rew:3292.0,80.1] ssItem(u) || -> totalorderedP(cons(u,sk3))*.
% 4.16/4.39 3350[3:Rew:3292.0,81.1] ssItem(u) || -> strictorderP(cons(u,sk3))*.
% 4.16/4.39 3351[3:Rew:3292.0,82.1] ssItem(u) || -> totalorderP(cons(u,sk3))*.
% 4.16/4.39 3352[3:Rew:3292.0,83.1] ssItem(u) || -> cyclefreeP(cons(u,sk3))*.
% 4.16/4.39 3359[3:Rew:3292.0,87.1] ssList(u) || -> equal(app(sk3,u),u)**.
% 4.16/4.39 3456[3:Rew:3359.1,3290.1] ssList(u) || -> equal(hd(u),hd(sk3))*.
% 4.16/4.39 4271[3:SpR:511.1,3456.1] ssItem(u) ssList(cons(u,sk3)) || -> equal(u,hd(sk3))*.
% 4.16/4.39 4274[3:SSi:4271.1,3352.1,3351.1,3350.1,3349.1,3348.1,3347.1,3346.1,516.1] ssItem(u) || -> equal(u,hd(sk3))*.
% 4.16/4.39 4354[3:SpR:4274.1,4274.1] ssItem(u) ssItem(v) || -> equal(v,u)*.
% 4.16/4.39 4448[3:EmS:4354.0,22.0] ssItem(u) || -> equal(u,skac3)*.
% 4.16/4.39 4469[3:EmS:4448.0,23.0] || -> equal(skac2,skac3)**.
% 4.16/4.39 4470[3:MRR:4469.0,67.0] || -> .
% 4.16/4.39 4664[3:Spt:4470.0,201.0,3292.0] || equal(nil,sk3)** -> .
% 4.16/4.39 4665[3:Spt:4470.0,201.1] || -> equal(nil,sk4)**.
% 4.16/4.39 4681[3:Rew:4665.0,4664.0] || equal(sk4,sk3)** -> .
% 4.16/4.39 4712[3:Rew:4665.0,84.1] ssItem(u) || memberP(sk4,u)* -> .
% 4.16/4.39 4761[3:Rew:4665.0,437.0] || -> equal(sk4,sk3) equal(cons(skaf83(sk3),skaf82(sk3)),sk3)**.
% 4.16/4.39 4762[3:MRR:4761.0,4681.0] || -> equal(cons(skaf83(sk3),skaf82(sk3)),sk3)**.
% 4.16/4.39 4771[3:MRR:8.2,4712.1] ssItem(u) || memberP(sk3,u)* -> .
% 4.16/4.39 6829[3:SpR:4762.0,151.4] ssItem(u) ssItem(skaf83(sk3)) ssList(skaf82(sk3)) || equal(u,skaf83(sk3)) -> memberP(sk3,u)*.
% 4.16/4.39 8253[3:SSi:6829.2,6829.1,26.0,7.0,3.0,25.0,7.0,3.0] ssItem(u) || equal(u,skaf83(sk3)) -> memberP(sk3,u)*.
% 4.16/4.39 8254[3:MRR:8253.2,4771.1] ssItem(u) || equal(u,skaf83(sk3))* -> .
% 4.16/4.39 8456[3:EqR:8254.1] ssItem(skaf83(sk3)) || -> .
% 4.16/4.39 8478[3:SSi:8456.0,25.0,7.0,3.0] || -> .
% 4.16/4.39 8486[2:Spt:8478.0,504.1] || -> equal(nil,sk3)**.
% 4.16/4.39 8530[2:Rew:8486.0,84.1] ssItem(u) || memberP(sk3,u)* -> .
% 4.16/4.39 8576[2:Rew:8486.0,202.1,8486.0,202.0] || equal(sk4,sk3)** equal(sk3,sk3) -> .
% 4.16/4.39 8577[2:Obv:8576.1] || equal(sk4,sk3)** -> .
% 4.16/4.39 8595[2:Rew:8486.0,266.0] || -> equal(sk4,sk3) equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 4.16/4.39 8596[2:MRR:8595.0,8577.0] || -> equal(cons(skaf83(sk4),skaf82(sk4)),sk4)**.
% 4.16/4.39 8599[2:MRR:9.2,8530.1] ssItem(u) || memberP(sk4,u)* -> .
% 4.16/4.39 8673[3:Spt:289.0] || -> ssItem(u)*.
% 4.16/4.39 8684[3:MRR:340.0,8673.0] || -> equal(hd(cons(u,sk4)),u)**.
% 4.16/4.39 8703[3:MRR:151.1,151.0,8673.0] ssList(u) || equal(v,w) -> memberP(cons(w,u),v)*.
% 4.16/4.39 8746[3:MRR:8599.0,8673.0] || memberP(sk4,u)* -> .
% 4.16/4.39 9602[3:SpR:8596.0,8703.2] ssList(skaf82(sk4)) || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 9786[3:SSi:9602.0,26.0,4.0] || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 9787[3:MRR:9786.1,8746.0] || equal(u,skaf83(sk4))* -> .
% 4.16/4.39 9788[3:UnC:9787.0,8684.0] || -> .
% 4.16/4.39 9797[3:Spt:9788.0,289.1] || -> duplicatefreeP(sk4)*.
% 4.16/4.39 11484[2:SpR:8596.0,151.4] ssItem(u) ssItem(skaf83(sk4)) ssList(skaf82(sk4)) || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 12908[3:SSi:11484.2,11484.1,26.0,4.0,9797.0,25.0,4.0,9797.0] ssItem(u) || equal(u,skaf83(sk4)) -> memberP(sk4,u)*.
% 4.16/4.39 12909[3:MRR:12908.2,8599.1] ssItem(u) || equal(u,skaf83(sk4))* -> .
% 4.16/4.39 13079[3:EqR:12909.1] ssItem(skaf83(sk4)) || -> .
% 4.16/4.39 13132[3:SSi:13079.0,25.0,4.0,9797.0] || -> .
% 4.16/4.39 % SZS output end Refutation
% 4.16/4.39 Formulae used in the proof : co1_3 co1_4 co1_5 co1_6 co1_7 co1_8 co1_9 co1_10 co1_13 clause9 clause10 clause12 clause13 clause54 clause60 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause74 clause77 clause86 clause97 clause109 clause120 clause123 clause138 clause157 clause170 clause176 clause178
% 4.16/4.39
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