TSTP Solution File: SWC204-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC204-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n005.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 22:02:27 EDT 2022
% Result : Unsatisfiable 58.03s 58.20s
% Output : Refutation 75.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC204-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n005.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 02:22:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 58.03/58.20
% 58.03/58.20 SPASS V 3.9
% 58.03/58.20 SPASS beiseite: Proof found.
% 58.03/58.20 % SZS status Theorem
% 58.03/58.20 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.03/58.20 SPASS derived 34269 clauses, backtracked 13513 clauses, performed 176 splits and kept 25224 clauses.
% 58.03/58.20 SPASS allocated 117940 KBytes.
% 58.03/58.20 SPASS spent 0:0:57.79 on the problem.
% 58.03/58.20 0:00:00.04 for the input.
% 58.03/58.20 0:00:00.00 for the FLOTTER CNF translation.
% 58.03/58.20 0:00:00.51 for inferences.
% 58.03/58.20 0:00:03.16 for the backtracking.
% 58.03/58.20 0:0:53.52 for the reduction.
% 58.03/58.20
% 58.03/58.20
% 58.03/58.20 Here is a proof with depth 4, length 310 :
% 58.03/58.20 % SZS output start Refutation
% 58.03/58.20 1[0:Inp] || -> ssList(sk1)*.
% 58.03/58.20 2[0:Inp] || -> ssList(sk2)*.
% 58.03/58.20 5[0:Inp] || -> equal(sk4,sk2)**.
% 58.03/58.20 6[0:Inp] || -> equal(sk3,sk1)**.
% 58.03/58.20 7[0:Inp] || -> neq(sk2,nil)* neq(sk2,nil)*.
% 58.03/58.20 11[0:Inp] ssList(u) ssList(v) || equal(tl(sk4),v) equal(app(sk3,v),u)* neq(nil,sk4) neq(sk4,nil) -> equal(sk4,u).
% 58.03/58.20 12[0:Inp] || neq(sk1,nil) neq(sk4,nil)* -> .
% 58.03/58.20 25[0:Inp] || -> ssList(skaf82(u))*.
% 58.03/58.20 44[0:Inp] || -> ssList(skaf63(u))*.
% 58.03/58.20 45[0:Inp] || -> ssList(skaf62(u))*.
% 58.03/58.20 46[0:Inp] || -> ssList(skaf61(u))*.
% 58.03/58.20 49[0:Inp] || -> ssList(skaf58(u))*.
% 58.03/58.20 50[0:Inp] || -> ssList(skaf57(u))*.
% 58.03/58.20 51[0:Inp] || -> ssList(skaf56(u))*.
% 58.03/58.20 59[0:Inp] || -> ssItem(skaf44(u))*.
% 58.03/58.20 66[0:Inp] || equal(skac2,skac3)** -> .
% 58.03/58.20 76[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 58.03/58.20 77[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 58.03/58.20 78[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 58.03/58.20 79[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 58.03/58.20 80[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 58.03/58.20 81[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 58.03/58.20 82[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 58.03/58.20 84[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 58.03/58.20 85[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 58.03/58.20 86[0:Inp] ssList(u) || -> equal(app(nil,u),u)**.
% 58.03/58.20 89[0:Inp] ssList(u) || -> ssList(tl(u))* equal(nil,u).
% 58.03/58.20 97[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 58.03/58.20 98[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 58.03/58.20 100[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 58.03/58.20 105[0:Inp] ssList(u) || lt(skaf59(u),skaf60(u))* -> strictorderP(u).
% 58.03/58.20 107[0:Inp] ssList(u) || leq(skaf54(u),skaf55(u))* -> totalorderP(u).
% 58.03/58.20 108[0:Inp] ssList(u) ssItem(v) || -> equal(tl(cons(v,u)),u)**.
% 58.03/58.20 109[0:Inp] ssList(u) ssItem(v) || -> equal(hd(cons(v,u)),v)**.
% 58.03/58.20 111[0:Inp] ssList(u) ssItem(v) || equal(cons(v,u),u)** -> .
% 58.03/58.20 113[0:Inp] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),nil),u)**.
% 58.03/58.20 114[0:Inp] ssItem(u) ssItem(v) || -> equal(u,v) neq(u,v)*.
% 58.03/58.20 116[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(hd(u),tl(u)),u)**.
% 58.03/58.20 121[0:Inp] ssList(u) || -> equal(nil,u) equal(cons(skaf83(u),skaf82(u)),u)**.
% 58.03/58.20 128[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)* -> singletonP(u)*.
% 58.03/58.20 129[0:Inp] ssItem(u) ssItem(v) || neq(u,v)* equal(u,v) -> .
% 58.03/58.20 135[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 58.03/58.20 136[0:Inp] ssItem(u) ssList(v) || strictorderedP(cons(u,v))* -> strictorderedP(v) equal(nil,v).
% 58.03/58.20 137[0:Inp] ssItem(u) ssList(v) || totalorderedP(cons(u,v))* -> totalorderedP(v) equal(nil,v).
% 58.03/58.20 169[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 58.03/58.20 175[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 58.03/58.20 176[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 58.03/58.20 177[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 58.03/58.20 178[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 58.03/58.20 182[0:Inp] ssList(u) ssList(v) ssItem(w) ssItem(x) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 58.03/58.20 189[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).
% 58.03/58.20 191[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)* -> .
% 58.03/58.20 193[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).
% 58.03/58.20 194[0:Inp] ssList(u) totalorderedP(u) ssItem(v) ssItem(w) ssList(x) ssList(y) ssList(z) || equal(app(app(x,cons(v,y)),cons(w,z)),u)* -> leq(v,w).
% 58.03/58.20 200[0:Obv:7.0] || -> neq(sk2,nil)*.
% 58.03/58.20 201[0:Rew:5.0,12.1] || neq(sk1,nil) neq(sk2,nil)* -> .
% 58.03/58.20 202[0:MRR:201.1,200.0] || neq(sk1,nil)* -> .
% 58.03/58.20 207[0:Rew:5.0,11.6,5.0,11.5,5.0,11.4,6.0,11.3,5.0,11.2] ssList(u) ssList(v) || equal(tl(sk2),v) equal(app(sk1,v),u)* neq(nil,sk2) neq(sk2,nil) -> equal(sk2,u).
% 58.03/58.20 208[0:MRR:207.5,200.0] ssList(u) ssList(v) || neq(nil,sk2) equal(tl(sk2),u) equal(app(sk1,u),v)* -> equal(sk2,v).
% 58.03/58.20 226[0:Res:2.0,178.0] || -> totalorderP(sk2) equal(app(app(skaf56(sk2),cons(skaf54(sk2),skaf57(sk2))),cons(skaf55(sk2),skaf58(sk2))),sk2)**.
% 58.03/58.20 227[0:Res:2.0,177.0] || -> strictorderP(sk2) equal(app(app(skaf61(sk2),cons(skaf59(sk2),skaf62(sk2))),cons(skaf60(sk2),skaf63(sk2))),sk2)**.
% 58.03/58.20 228[0:Res:2.0,176.0] || -> totalorderedP(sk2) equal(app(app(skaf66(sk2),cons(skaf64(sk2),skaf67(sk2))),cons(skaf65(sk2),skaf68(sk2))),sk2)**.
% 58.03/58.20 229[0:Res:2.0,175.0] || -> strictorderedP(sk2) equal(app(app(skaf71(sk2),cons(skaf69(sk2),skaf72(sk2))),cons(skaf70(sk2),skaf73(sk2))),sk2)**.
% 58.03/58.20 267[0:Res:2.0,116.0] || -> equal(nil,sk2) equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 58.03/58.20 268[0:Res:2.0,121.0] || -> equal(nil,sk2) equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 58.03/58.20 275[0:Res:2.0,105.0] || lt(skaf59(sk2),skaf60(sk2))* -> strictorderP(sk2).
% 58.03/58.20 277[0:Res:2.0,107.0] || leq(skaf54(sk2),skaf55(sk2))* -> totalorderP(sk2).
% 58.03/58.20 286[0:Res:2.0,100.0] || -> cyclefreeP(sk2) leq(skaf49(sk2),skaf50(sk2))*.
% 58.03/58.20 287[0:Res:2.0,89.0] || -> ssList(tl(sk2))* equal(nil,sk2).
% 58.03/58.20 341[0:Res:2.0,128.1] ssItem(u) || equal(cons(u,nil),sk2)** -> singletonP(sk2).
% 58.03/58.20 348[0:Res:2.0,98.1] ssItem(u) || -> ssList(cons(u,sk2))*.
% 58.03/58.20 389[0:Res:1.0,208.0] ssList(u) || neq(nil,sk2) equal(tl(sk2),u) equal(app(sk1,u),sk1)** -> equal(sk2,sk1).
% 58.03/58.20 480[0:Res:1.0,189.1] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u) equal(nil,sk1).
% 58.03/58.20 509[0:Res:1.0,135.1] ssList(u) || -> equal(nil,sk1) equal(hd(app(sk1,u)),hd(sk1))**.
% 58.03/58.20 516[0:Res:1.0,109.1] ssItem(u) || -> equal(hd(cons(u,sk1)),u)**.
% 58.03/58.20 521[0:Res:1.0,98.1] ssItem(u) || -> ssList(cons(u,sk1))*.
% 58.03/58.20 532[0:Res:1.0,169.2] ssList(u) ssItem(v) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 58.03/58.20 559[1:Spt:84.1] || -> ssItem(u)*.
% 58.03/58.20 562[1:MRR:521.0,559.0] || -> ssList(cons(u,sk1))*.
% 58.03/58.20 565[1:MRR:82.0,559.0] || -> cyclefreeP(cons(u,nil))*.
% 58.03/58.20 566[1:MRR:81.0,559.0] || -> totalorderP(cons(u,nil))*.
% 58.03/58.20 567[1:MRR:80.0,559.0] || -> strictorderP(cons(u,nil))*.
% 58.03/58.20 568[1:MRR:79.0,559.0] || -> totalorderedP(cons(u,nil))*.
% 58.03/58.20 569[1:MRR:78.0,559.0] || -> strictorderedP(cons(u,nil))*.
% 58.03/58.20 570[1:MRR:77.0,559.0] || -> duplicatefreeP(cons(u,nil))*.
% 58.03/58.20 571[1:MRR:76.0,559.0] || -> equalelemsP(cons(u,nil))*.
% 58.03/58.20 575[1:MRR:516.0,559.0] || -> equal(hd(cons(u,sk1)),u)**.
% 58.03/58.20 584[1:MRR:341.0,559.0] || equal(cons(u,nil),sk2)** -> singletonP(sk2).
% 58.03/58.20 589[1:MRR:114.1,114.0,559.0] || -> equal(u,v) neq(u,v)*.
% 58.03/58.20 599[1:MRR:129.1,129.0,559.0] || neq(u,v)* equal(u,v) -> .
% 58.03/58.20 625[1:MRR:137.0,559.0] ssList(u) || totalorderedP(cons(v,u))* -> totalorderedP(u) equal(nil,u).
% 58.03/58.20 626[1:MRR:136.0,559.0] ssList(u) || strictorderedP(cons(v,u))* -> strictorderedP(u) equal(nil,u).
% 58.03/58.20 685[1:MRR:111.1,559.0] ssList(u) || equal(cons(v,u),u)** -> .
% 58.03/58.20 687[1:MRR:109.1,559.0] ssList(u) || -> equal(hd(cons(v,u)),v)**.
% 58.03/58.20 688[1:MRR:108.1,559.0] ssList(u) || -> equal(tl(cons(v,u)),u)**.
% 58.03/58.20 691[1:MRR:532.1,559.0] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,app(u,sk1)))**.
% 58.03/58.20 741[1:MRR:194.3,194.2,559.0] ssList(u) totalorderedP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(z,x)),u)* -> leq(y,z).
% 58.03/58.20 742[1:MRR:193.3,193.2,559.0] ssList(u) strictorderedP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(z,x)),u)* -> lt(y,z).
% 58.03/58.20 754[1:MRR:182.3,182.2,559.0] ssList(u) ssList(v) || equal(cons(w,u),cons(x,v))* -> equal(w,x).
% 58.03/58.20 755[2:Spt:509.0,509.2] ssList(u) || -> equal(hd(app(sk1,u)),hd(sk1))**.
% 58.03/58.20 768[3:Spt:480.5] || -> equal(nil,sk1)**.
% 58.03/58.20 851[3:Rew:768.0,86.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 58.03/58.20 852[3:Rew:768.0,85.1] ssList(u) || -> equal(app(u,sk1),u)**.
% 58.03/58.20 857[3:Rew:768.0,565.0] || -> cyclefreeP(cons(u,sk1))*.
% 58.03/58.20 858[3:Rew:768.0,566.0] || -> totalorderP(cons(u,sk1))*.
% 58.03/58.20 859[3:Rew:768.0,567.0] || -> strictorderP(cons(u,sk1))*.
% 58.03/58.20 860[3:Rew:768.0,568.0] || -> totalorderedP(cons(u,sk1))*.
% 58.03/58.20 861[3:Rew:768.0,569.0] || -> strictorderedP(cons(u,sk1))*.
% 58.03/58.20 862[3:Rew:768.0,570.0] || -> duplicatefreeP(cons(u,sk1))*.
% 58.03/58.20 863[3:Rew:768.0,571.0] || -> equalelemsP(cons(u,sk1))*.
% 58.03/58.20 913[3:Rew:851.1,755.1] ssList(u) || -> equal(hd(u),hd(sk1))*.
% 58.03/58.20 937[3:Rew:852.1,691.1] ssList(u) || -> equal(app(cons(v,u),sk1),cons(v,u))**.
% 58.03/58.20 1241[3:SpR:913.1,575.0] ssList(cons(u,sk1)) || -> equal(hd(sk1),u)*.
% 58.03/58.20 1248[3:SSi:1241.0,562.0,857.0,858.0,859.0,860.0,861.0,862.0,863.0] || -> equal(hd(sk1),u)*.
% 58.03/58.20 1310[3:Rew:1248.0,937.1] ssList(u) || -> equal(cons(v,u),hd(sk1))**.
% 58.03/58.20 1467[3:Rew:1248.0,754.2] ssList(u) ssList(v) || equal(cons(w,u),hd(sk1))** -> equal(w,x)*.
% 58.03/58.20 1577[3:Con:1467.1] ssList(u) || equal(cons(v,u),hd(sk1))** -> equal(v,w)*.
% 58.03/58.20 1578[3:AED:66.0,1577.2] ssList(u) || equal(cons(v,u),hd(sk1))** -> .
% 58.03/58.20 1579[3:Rew:1310.1,1578.1] ssList(u) || equal(hd(sk1),hd(sk1))* -> .
% 58.03/58.20 1580[3:Obv:1579.1] ssList(u) || -> .
% 58.03/58.20 1581[3:UnC:1580.0,2.0] || -> .
% 58.03/58.20 1732[3:Spt:1581.0,480.5,768.0] || equal(nil,sk1)** -> .
% 58.03/58.20 1733[3:Spt:1581.0,480.0,480.1,480.2,480.3,480.4] ssList(u) || equal(hd(u),hd(sk1))* equal(tl(u),tl(sk1)) -> equal(u,sk1) equal(nil,u).
% 58.03/58.20 1976[1:Res:589.1,202.0] || -> equal(nil,sk1)**.
% 58.03/58.20 1977[3:MRR:1976.0,1732.0] || -> .
% 58.03/58.20 1978[2:Spt:1977.0,509.1] || -> equal(nil,sk1)**.
% 58.03/58.20 1993[1:Rew:1976.0,200.0] || -> neq(sk2,sk1)*.
% 58.03/58.20 1995[1:Rew:1976.0,202.0] || neq(sk1,sk1)* -> .
% 58.03/58.20 1997[1:Rew:1976.0,565.0] || -> cyclefreeP(cons(u,sk1))*.
% 58.03/58.20 2005[1:Rew:1976.0,584.0] || equal(cons(u,sk1),sk2)** -> singletonP(sk2).
% 58.03/58.20 2017[1:Rew:1976.0,86.1] ssList(u) || -> equal(app(sk1,u),u)**.
% 58.03/58.20 2028[1:Rew:1976.0,626.3] ssList(u) || strictorderedP(cons(v,u))* -> strictorderedP(u) equal(sk1,u).
% 58.03/58.20 2029[1:Rew:1976.0,625.3] ssList(u) || totalorderedP(cons(v,u))* -> totalorderedP(u) equal(sk1,u).
% 58.03/58.20 2048[1:Rew:1976.0,113.2] ssList(u) singletonP(u) || -> equal(cons(skaf44(u),sk1),u)**.
% 58.03/58.20 2058[1:Rew:1976.0,287.1] || -> ssList(tl(sk2))* equal(sk2,sk1).
% 58.03/58.20 2109[1:Rew:1976.0,268.0] || -> equal(sk2,sk1) equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 58.03/58.20 2110[1:Rew:1976.0,267.0] || -> equal(sk2,sk1) equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 58.03/58.20 2147[1:Rew:2017.1,389.3,1976.0,389.1] ssList(u) || neq(sk1,sk2)* equal(tl(sk2),u)* equal(u,sk1) -> equal(sk2,sk1).
% 58.03/58.20 2148[1:MRR:2147.1,589.1] ssList(u) || equal(tl(sk2),u)* equal(u,sk1) -> equal(sk2,sk1).
% 58.03/58.20 2151[1:Rew:2017.1,208.4,1976.0,208.2] ssList(u) ssList(v) || neq(sk1,sk2)* equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 58.03/58.20 2157[3:Spt:228.0] || -> totalorderedP(sk2)*.
% 58.03/58.20 2161[4:Spt:229.0] || -> strictorderedP(sk2)*.
% 58.03/58.20 2164[5:Spt:286.0] || -> cyclefreeP(sk2)*.
% 58.03/58.20 2166[6:Spt:226.0] || -> totalorderP(sk2)*.
% 58.03/58.20 2167[7:Spt:227.0] || -> strictorderP(sk2)*.
% 58.03/58.20 2173[8:Spt:2058.1] || -> equal(sk2,sk1)**.
% 58.03/58.20 2186[8:Rew:2173.0,1993.0] || -> neq(sk1,sk1)*.
% 58.03/58.20 2311[8:MRR:2186.0,1995.0] || -> .
% 58.03/58.20 2380[8:Spt:2311.0,2058.1,2173.0] || equal(sk2,sk1)** -> .
% 58.03/58.20 2381[8:Spt:2311.0,2058.0] || -> ssList(tl(sk2))*.
% 58.03/58.20 2385[8:MRR:2109.0,2380.0] || -> equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 58.03/58.20 2386[8:MRR:2110.0,2380.0] || -> equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 58.03/58.20 2393[8:MRR:2148.3,2380.0] ssList(u) || equal(tl(sk2),u)* equal(u,sk1) -> .
% 58.03/58.20 2418[1:Res:1993.0,599.0] || equal(sk2,sk1)** -> .
% 58.03/58.20 2444[8:SpL:2386.0,685.1] ssList(tl(sk2)) || equal(tl(sk2),sk2)** -> .
% 58.03/58.20 2446[8:SSi:2444.0,2381.0] || equal(tl(sk2),sk2)** -> .
% 58.03/58.20 2451[8:SpR:2385.0,687.1] ssList(skaf82(sk2)) || -> equal(hd(sk2),skaf83(sk2))**.
% 58.03/58.20 2453[8:SSi:2451.0,25.0,2167.0,2.0,2166.0,2164.0,2161.0,2157.0] || -> equal(hd(sk2),skaf83(sk2))**.
% 58.03/58.20 2454[8:Rew:2453.0,2386.0] || -> equal(cons(skaf83(sk2),tl(sk2)),sk2)**.
% 58.03/58.20 2478[8:SpR:2385.0,688.1] ssList(skaf82(sk2)) || -> equal(skaf82(sk2),tl(sk2))**.
% 58.03/58.20 2480[8:SSi:2478.0,25.0,2167.0,2.0,2166.0,2164.0,2161.0,2157.0] || -> equal(skaf82(sk2),tl(sk2))**.
% 58.03/58.20 2666[1:SpR:2048.2,1997.0] ssList(u) singletonP(u) || -> cyclefreeP(u)*.
% 58.03/58.20 2746[8:SpL:2454.0,2028.1] ssList(tl(sk2)) || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 58.03/58.20 2751[8:SSi:2746.0,2381.0] || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 58.03/58.20 2752[8:MRR:2751.0,2161.0] || -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 58.03/58.20 2753[9:Spt:2752.1] || -> equal(tl(sk2),sk1)**.
% 58.03/58.20 2757[9:Rew:2753.0,2480.0] || -> equal(skaf82(sk2),sk1)**.
% 58.03/58.20 2761[9:Rew:2753.0,2393.1] ssList(u) || equal(sk1,u)* equal(u,sk1)* -> .
% 58.03/58.20 2765[9:Obv:2761.1] ssList(u) || equal(u,sk1)* -> .
% 58.03/58.20 2911[9:EmS:2765.0,25.0] || equal(skaf82(u),sk1)** -> .
% 58.03/58.20 2934[9:UnC:2911.0,2757.0] || -> .
% 58.03/58.20 2935[9:Spt:2934.0,2752.1,2753.0] || equal(tl(sk2),sk1)** -> .
% 58.03/58.20 2936[9:Spt:2934.0,2752.0] || -> strictorderedP(tl(sk2))*.
% 58.03/58.20 2967[8:SpL:2454.0,2029.1] ssList(tl(sk2)) || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 58.03/58.20 2968[9:SSi:2967.0,2936.0,2381.0] || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 58.03/58.20 2969[9:MRR:2968.0,2968.2,2157.0,2935.0] || -> totalorderedP(tl(sk2))*.
% 58.03/58.20 5964[10:Spt:2151.0,2151.1,2151.3,2151.4,2151.5] ssList(u) ssList(v) || equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 58.03/58.20 5965[10:EqR:5964.2] ssList(tl(sk2)) ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 58.03/58.20 5967[10:SSi:5965.0,2936.0,2381.0,2969.0] ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 58.03/58.20 6018[10:EqR:5967.1] ssList(tl(sk2)) || -> equal(tl(sk2),sk2)**.
% 58.03/58.20 6020[10:SSi:6018.0,2936.0,2381.0,2969.0] || -> equal(tl(sk2),sk2)**.
% 58.03/58.20 6021[10:MRR:6020.0,2446.0] || -> .
% 58.03/58.20 6022[10:Spt:6021.0,2151.2] || neq(sk1,sk2)* -> .
% 58.03/58.20 6023[10:Res:589.1,6022.0] || -> equal(sk2,sk1)**.
% 58.03/58.20 6024[10:MRR:6023.0,2380.0] || -> .
% 58.03/58.20 6025[7:Spt:6024.0,227.0,2167.0] || strictorderP(sk2)* -> .
% 58.03/58.20 6026[7:Spt:6024.0,227.1] || -> equal(app(app(skaf61(sk2),cons(skaf59(sk2),skaf62(sk2))),cons(skaf60(sk2),skaf63(sk2))),sk2)**.
% 58.03/58.20 6027[1:MRR:2058.1,2418.0] || -> ssList(tl(sk2))*.
% 58.03/58.20 6032[7:MRR:275.1,6025.0] || lt(skaf59(sk2),skaf60(sk2))* -> .
% 58.03/58.20 6034[1:MRR:2109.0,2418.0] || -> equal(cons(skaf83(sk2),skaf82(sk2)),sk2)**.
% 58.03/58.20 6035[1:MRR:2110.0,2418.0] || -> equal(cons(hd(sk2),tl(sk2)),sk2)**.
% 58.03/58.20 6047[1:MRR:2148.3,2418.0] ssList(u) || equal(tl(sk2),u)* equal(u,sk1) -> .
% 58.03/58.20 6289[1:SpR:6034.0,687.1] ssList(skaf82(sk2)) || -> equal(hd(sk2),skaf83(sk2))**.
% 58.03/58.20 6290[1:SpR:6034.0,688.1] ssList(skaf82(sk2)) || -> equal(skaf82(sk2),tl(sk2))**.
% 58.03/58.20 6308[1:SpL:6034.0,685.1] ssList(skaf82(sk2)) || equal(skaf82(sk2),sk2)** -> .
% 58.03/58.20 6309[1:SpL:6034.0,2028.1] ssList(skaf82(sk2)) || strictorderedP(sk2) -> strictorderedP(skaf82(sk2))* equal(skaf82(sk2),sk1).
% 58.03/58.20 6310[1:SpL:6034.0,2029.1] ssList(skaf82(sk2)) || totalorderedP(sk2) -> totalorderedP(skaf82(sk2))* equal(skaf82(sk2),sk1).
% 58.03/58.20 6994[7:SpL:6026.0,742.5] ssList(u) strictorderedP(u) ssList(skaf61(sk2)) ssList(skaf62(sk2)) ssList(skaf63(sk2)) || equal(sk2,u)* -> lt(skaf59(sk2),skaf60(sk2))*.
% 58.03/58.20 7000[7:SSi:6994.4,6994.3,6994.2,44.0,2.0,2166.0,2164.0,2161.0,2157.0,45.0,2.0,2166.0,2164.0,2161.0,2157.0,46.0,2.0,2166.0,2164.0,2161.0,2157.0] ssList(u) strictorderedP(u) || equal(sk2,u)* -> lt(skaf59(sk2),skaf60(sk2))*.
% 58.03/58.20 7001[7:MRR:7000.3,6032.0] ssList(u) strictorderedP(u) || equal(sk2,u)* -> .
% 58.03/58.20 7304[7:EmS:7001.0,7001.1,2.0,2161.0] || equal(sk2,sk2)* -> .
% 58.03/58.20 7315[7:Obv:7304.0] || -> .
% 58.03/58.20 7320[6:Spt:7315.0,226.0,2166.0] || totalorderP(sk2)* -> .
% 58.03/58.20 7321[6:Spt:7315.0,226.1] || -> equal(app(app(skaf56(sk2),cons(skaf54(sk2),skaf57(sk2))),cons(skaf55(sk2),skaf58(sk2))),sk2)**.
% 58.03/58.20 7322[6:MRR:277.1,7320.0] || leq(skaf54(sk2),skaf55(sk2))* -> .
% 58.03/58.20 7412[6:SpL:7321.0,741.5] ssList(u) totalorderedP(u) ssList(skaf56(sk2)) ssList(skaf57(sk2)) ssList(skaf58(sk2)) || equal(sk2,u)* -> leq(skaf54(sk2),skaf55(sk2))*.
% 58.03/58.20 7419[6:SSi:7412.4,7412.3,7412.2,49.0,2.0,2164.0,2161.0,2157.0,50.0,2.0,2164.0,2161.0,2157.0,51.0,2.0,2164.0,2161.0,2157.0] ssList(u) totalorderedP(u) || equal(sk2,u)* -> leq(skaf54(sk2),skaf55(sk2))*.
% 58.03/58.20 7420[6:MRR:7419.3,7322.0] ssList(u) totalorderedP(u) || equal(sk2,u)* -> .
% 58.03/58.20 8213[6:EmS:7420.0,7420.1,2.0,2157.0] || equal(sk2,sk2)* -> .
% 58.03/58.20 8247[6:Obv:8213.0] || -> .
% 58.03/58.20 8257[5:Spt:8247.0,286.0,2164.0] || cyclefreeP(sk2)* -> .
% 58.03/58.20 8258[5:Spt:8247.0,286.1] || -> leq(skaf49(sk2),skaf50(sk2))*.
% 58.03/58.20 8261[4:SSi:6289.0,25.0,2.0,2161.0,2157.0] || -> equal(hd(sk2),skaf83(sk2))**.
% 58.03/58.20 8263[4:Rew:8261.0,6035.0] || -> equal(cons(skaf83(sk2),tl(sk2)),sk2)**.
% 75.17/75.33 8270[4:SSi:6290.0,25.0,2.0,2161.0,2157.0] || -> equal(skaf82(sk2),tl(sk2))**.
% 75.17/75.33 8273[4:Rew:8270.0,6308.1] ssList(skaf82(sk2)) || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 8274[4:SSi:8273.0,25.0,2.0,2161.0,2157.0] || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 8285[4:Rew:8270.0,6309.3,8270.0,6309.2] ssList(skaf82(sk2)) || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8286[4:SSi:8285.0,25.0,2.0,2161.0,2157.0] || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8287[4:MRR:8286.0,2161.0] || -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8288[4:Rew:8270.0,6310.3,8270.0,6310.2] ssList(skaf82(sk2)) || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8289[4:SSi:8288.0,25.0,2.0,2161.0,2157.0] || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8290[4:MRR:8289.0,2157.0] || -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 8332[6:Spt:227.0] || -> strictorderP(sk2)*.
% 75.17/75.33 8333[5:Res:2666.2,8257.0] ssList(sk2) singletonP(sk2) || -> .
% 75.17/75.33 8334[6:SSi:8333.0,2.0,2161.0,2157.0,8332.0] singletonP(sk2) || -> .
% 75.17/75.33 8335[6:MRR:2005.1,8334.0] || equal(cons(u,sk1),sk2)** -> .
% 75.17/75.33 8339[7:Spt:2151.0,2151.1,2151.3,2151.4,2151.5] ssList(u) ssList(v) || equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 75.17/75.33 8340[7:EqR:8339.2] ssList(tl(sk2)) ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 8342[7:SSi:8340.0,6027.0] ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 8434[8:Spt:8287.1] || -> equal(tl(sk2),sk1)**.
% 75.17/75.33 8441[8:Rew:8434.0,8263.0] || -> equal(cons(skaf83(sk2),sk1),sk2)**.
% 75.17/75.33 8456[8:MRR:8441.0,8335.0] || -> .
% 75.17/75.33 8468[8:Spt:8456.0,8287.1,8434.0] || equal(tl(sk2),sk1)** -> .
% 75.17/75.33 8469[8:Spt:8456.0,8287.0] || -> strictorderedP(tl(sk2))*.
% 75.17/75.33 8470[8:MRR:8290.1,8468.0] || -> totalorderedP(tl(sk2))*.
% 75.17/75.33 9204[1:EqR:6047.1] ssList(tl(sk2)) || equal(tl(sk2),sk1)** -> .
% 75.17/75.33 9406[7:EqR:8342.1] ssList(tl(sk2)) || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 9408[8:SSi:9406.0,8469.0,6027.0,8470.0] || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 9409[8:MRR:9408.0,8274.0] || -> .
% 75.17/75.33 9410[7:Spt:9409.0,2151.2] || neq(sk1,sk2)* -> .
% 75.17/75.33 9411[1:SSi:9204.0,6027.0] || equal(tl(sk2),sk1)** -> .
% 75.17/75.33 9484[7:Res:589.1,9410.0] || -> equal(sk2,sk1)**.
% 75.17/75.33 9485[7:MRR:9484.0,2418.0] || -> .
% 75.17/75.33 9486[6:Spt:9485.0,227.0,8332.0] || strictorderP(sk2)* -> .
% 75.17/75.33 9487[6:Spt:9485.0,227.1] || -> equal(app(app(skaf61(sk2),cons(skaf59(sk2),skaf62(sk2))),cons(skaf60(sk2),skaf63(sk2))),sk2)**.
% 75.17/75.33 9489[6:MRR:275.1,9486.0] || lt(skaf59(sk2),skaf60(sk2))* -> .
% 75.17/75.33 9538[6:SpL:9487.0,742.5] ssList(u) strictorderedP(u) ssList(skaf61(sk2)) ssList(skaf62(sk2)) ssList(skaf63(sk2)) || equal(sk2,u)* -> lt(skaf59(sk2),skaf60(sk2))*.
% 75.17/75.33 9543[6:SSi:9538.4,9538.3,9538.2,44.0,2.0,2161.0,2157.0,45.0,2.0,2161.0,2157.0,46.0,2.0,2161.0,2157.0] ssList(u) strictorderedP(u) || equal(sk2,u)* -> lt(skaf59(sk2),skaf60(sk2))*.
% 75.17/75.33 9544[6:MRR:9543.3,9489.0] ssList(u) strictorderedP(u) || equal(sk2,u)* -> .
% 75.17/75.33 9868[6:EmS:9544.0,9544.1,2.0,2161.0] || equal(sk2,sk2)* -> .
% 75.17/75.33 9881[6:Obv:9868.0] || -> .
% 75.17/75.33 9886[4:Spt:9881.0,229.0,2161.0] || strictorderedP(sk2)* -> .
% 75.17/75.33 9887[4:Spt:9881.0,229.1] || -> equal(app(app(skaf71(sk2),cons(skaf69(sk2),skaf72(sk2))),cons(skaf70(sk2),skaf73(sk2))),sk2)**.
% 75.17/75.33 9900[3:SSi:6290.0,25.0,2.0,2157.0] || -> equal(skaf82(sk2),tl(sk2))**.
% 75.17/75.33 9903[3:Rew:9900.0,6308.1] ssList(skaf82(sk2)) || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 9904[3:SSi:9903.0,25.0,2.0,2157.0] || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 9919[3:Rew:9900.0,6310.3,9900.0,6310.2] ssList(skaf82(sk2)) || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 9920[3:SSi:9919.0,25.0,2.0,2157.0] || totalorderedP(sk2) -> totalorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 9921[3:MRR:9920.0,9920.2,2157.0,9411.0] || -> totalorderedP(tl(sk2))*.
% 75.17/75.33 10039[5:Spt:2151.0,2151.1,2151.3,2151.4,2151.5] ssList(u) ssList(v) || equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 75.17/75.33 10040[5:EqR:10039.2] ssList(tl(sk2)) ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 10042[5:SSi:10040.0,6027.0,9921.0] ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 14808[5:EqR:10042.1] ssList(tl(sk2)) || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 14810[5:SSi:14808.0,6027.0,9921.0] || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 14811[5:MRR:14810.0,9904.0] || -> .
% 75.17/75.33 14812[5:Spt:14811.0,2151.2] || neq(sk1,sk2)* -> .
% 75.17/75.33 14896[5:Res:589.1,14812.0] || -> equal(sk2,sk1)**.
% 75.17/75.33 14897[5:MRR:14896.0,2418.0] || -> .
% 75.17/75.33 14898[3:Spt:14897.0,228.0,2157.0] || totalorderedP(sk2)* -> .
% 75.17/75.33 14899[3:Spt:14897.0,228.1] || -> equal(app(app(skaf66(sk2),cons(skaf64(sk2),skaf67(sk2))),cons(skaf65(sk2),skaf68(sk2))),sk2)**.
% 75.17/75.33 14908[1:SSi:6290.0,25.0,2.0] || -> equal(skaf82(sk2),tl(sk2))**.
% 75.17/75.33 14911[1:Rew:14908.0,6308.1] ssList(skaf82(sk2)) || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 14912[1:SSi:14911.0,25.0,2.0] || equal(tl(sk2),sk2)** -> .
% 75.17/75.33 14930[1:Rew:14908.0,6309.3,14908.0,6309.2] ssList(skaf82(sk2)) || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 14931[1:SSi:14930.0,25.0,2.0] || strictorderedP(sk2) -> strictorderedP(tl(sk2))* equal(tl(sk2),sk1).
% 75.17/75.33 14932[1:MRR:14931.2,9411.0] || strictorderedP(sk2) -> strictorderedP(tl(sk2))*.
% 75.17/75.33 15232[4:Spt:229.0] || -> strictorderedP(sk2)*.
% 75.17/75.33 15235[4:MRR:14932.0,15232.0] || -> strictorderedP(tl(sk2))*.
% 75.17/75.33 15250[5:Spt:2151.0,2151.1,2151.3,2151.4,2151.5] ssList(u) ssList(v) || equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 75.17/75.33 15251[5:EqR:15250.2] ssList(tl(sk2)) ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 15253[5:SSi:15251.0,6027.0,15235.0] ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 21842[5:EqR:15253.1] ssList(tl(sk2)) || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 21844[5:SSi:21842.0,6027.0,15235.0] || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 21845[5:MRR:21844.0,14912.0] || -> .
% 75.17/75.33 21846[5:Spt:21845.0,2151.2] || neq(sk1,sk2)* -> .
% 75.17/75.33 22038[5:Res:589.1,21846.0] || -> equal(sk2,sk1)**.
% 75.17/75.33 22039[5:MRR:22038.0,2418.0] || -> .
% 75.17/75.33 22040[4:Spt:22039.0,229.0,15232.0] || strictorderedP(sk2)* -> .
% 75.17/75.33 22041[4:Spt:22039.0,229.1] || -> equal(app(app(skaf71(sk2),cons(skaf69(sk2),skaf72(sk2))),cons(skaf70(sk2),skaf73(sk2))),sk2)**.
% 75.17/75.33 22328[5:Spt:2151.0,2151.1,2151.3,2151.4,2151.5] ssList(u) ssList(v) || equal(tl(sk2),u)*+ equal(u,v)* -> equal(sk2,v)*.
% 75.17/75.33 22329[5:EqR:22328.2] ssList(tl(sk2)) ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 22331[5:SSi:22329.0,6027.0] ssList(u) || equal(tl(sk2),u)* -> equal(sk2,u).
% 75.17/75.33 33613[5:EqR:22331.1] ssList(tl(sk2)) || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 34161[5:SSi:33613.0,6027.0] || -> equal(tl(sk2),sk2)**.
% 75.17/75.33 34162[5:MRR:34161.0,14912.0] || -> .
% 75.17/75.33 34298[5:Spt:34162.0,2151.2] || neq(sk1,sk2)* -> .
% 75.17/75.33 34764[5:Res:589.1,34298.0] || -> equal(sk2,sk1)**.
% 75.17/75.33 34765[5:MRR:34764.0,2418.0] || -> .
% 75.17/75.33 34766[1:Spt:34765.0,84.0,84.2] ssList(u) || -> duplicatefreeP(u)*.
% 75.17/75.33 34867[1:MRR:191.1,34766.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 75.17/75.33 53787[0:SpR:169.3,97.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 75.17/75.33 53839[0:Obv:53787.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 75.17/75.33 53840[0:SSi:53839.2,98.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 75.17/75.33 56009[1:EqR:34867.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 75.17/75.33 56034[1:SSi:56009.0,97.2,97.2,98.2,98.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 75.17/75.33 56035[1:MRR:53840.3,56034.1] ssList(u) ssItem(v) ssList(w) || -> .
% 75.17/75.33 56044[1:Con:56035.2] ssList(u) ssItem(v) || -> .
% 75.17/75.33 56046[1:MRR:348.1,56044.0] ssItem(u) || -> .
% 75.17/75.33 56048[1:UnC:56046.0,59.0] || -> .
% 75.17/75.33 % SZS output end Refutation
% 75.17/75.33 Formulae used in the proof : co1_1 co1_2 co1_5 co1_6 co1_7 co1_11 co1_12 clause13 clause32 clause33 clause34 clause37 clause38 clause39 clause47 clause54 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause72 clause73 clause74 clause77 clause85 clause86 clause88 clause93 clause95 clause96 clause97 clause99 clause101 clause102 clause104 clause109 clause116 clause117 clause123 clause124 clause125 clause157 clause163 clause164 clause165 clause166 clause170 clause177 clause179 clause181 clause182
% 75.17/75.33
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