TSTP Solution File: SWC279-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWC279-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 22:03:01 EDT 2022
% Result : Unsatisfiable 15.42s 15.65s
% Output : Refutation 15.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC279-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 15:21:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 15.42/15.65
% 15.42/15.65 SPASS V 3.9
% 15.42/15.65 SPASS beiseite: Proof found.
% 15.42/15.65 % SZS status Theorem
% 15.42/15.65 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.42/15.65 SPASS derived 18845 clauses, backtracked 5008 clauses, performed 62 splits and kept 12249 clauses.
% 15.42/15.65 SPASS allocated 98648 KBytes.
% 15.42/15.65 SPASS spent 0:0:15.27 on the problem.
% 15.42/15.65 0:00:00.04 for the input.
% 15.42/15.65 0:00:00.00 for the FLOTTER CNF translation.
% 15.42/15.65 0:00:00.24 for inferences.
% 15.42/15.65 0:00:00.70 for the backtracking.
% 15.42/15.65 0:0:14.03 for the reduction.
% 15.42/15.65
% 15.42/15.65
% 15.42/15.65 Here is a proof with depth 4, length 215 :
% 15.42/15.65 % SZS output start Refutation
% 15.42/15.65 6[0:Inp] || -> equal(sk1,sk3)**.
% 15.42/15.65 7[0:Inp] ssItem(u) ssList(v) ssList(w) ssItem(x) || memberP(v,u)* equal(app(app(w,cons(x,nil)),v),sk3)** -> leq(x,u)*.
% 15.42/15.65 8[0:Inp] ssItem(u) ssList(v) ssList(w) ssItem(x) || memberP(w,u)* equal(app(app(w,cons(x,nil)),v),sk3)** -> leq(u,x)*.
% 15.42/15.65 10[0:Inp] || -> ssList(sk6)*.
% 15.42/15.65 11[0:Inp] || -> ssList(sk7)*.
% 15.42/15.65 12[0:Inp] || -> equal(app(app(sk6,cons(sk5,nil)),sk7),sk1)**.
% 15.42/15.65 14[0:Inp] || -> memberP(sk7,sk8)* memberP(sk6,sk8).
% 15.42/15.65 15[0:Inp] || leq(sk5,sk8) -> memberP(sk6,sk8)*.
% 15.42/15.65 16[0:Inp] || leq(sk8,sk5) -> memberP(sk7,sk8)*.
% 15.42/15.65 17[0:Inp] || leq(sk5,sk8) leq(sk8,sk5)* -> .
% 15.42/15.65 18[0:Inp] || -> equalelemsP(nil)*.
% 15.42/15.65 19[0:Inp] || -> duplicatefreeP(nil)*.
% 15.42/15.65 20[0:Inp] || -> strictorderedP(nil)*.
% 15.42/15.65 21[0:Inp] || -> totalorderedP(nil)*.
% 15.42/15.65 22[0:Inp] || -> strictorderP(nil)*.
% 15.42/15.65 23[0:Inp] || -> totalorderP(nil)*.
% 15.42/15.65 24[0:Inp] || -> cyclefreeP(nil)*.
% 15.42/15.65 25[0:Inp] || -> ssList(nil)*.
% 15.42/15.65 35[0:Inp] || -> ssList(skaf77(u))*.
% 15.42/15.65 36[0:Inp] || -> ssList(skaf76(u))*.
% 15.42/15.65 37[0:Inp] || -> ssList(skaf75(u))*.
% 15.42/15.65 49[0:Inp] || -> ssList(skaf63(u))*.
% 15.42/15.65 50[0:Inp] || -> ssList(skaf62(u))*.
% 15.42/15.65 51[0:Inp] || -> ssList(skaf61(u))*.
% 15.42/15.65 54[0:Inp] || -> ssList(skaf58(u))*.
% 15.42/15.65 55[0:Inp] || -> ssList(skaf57(u))*.
% 15.42/15.65 56[0:Inp] || -> ssList(skaf56(u))*.
% 15.42/15.65 59[0:Inp] || -> ssList(skaf53(u))*.
% 15.42/15.65 60[0:Inp] || -> ssList(skaf52(u))*.
% 15.42/15.65 61[0:Inp] || -> ssList(skaf51(u))*.
% 15.42/15.65 64[0:Inp] || -> ssItem(skaf44(u))*.
% 15.42/15.65 80[0:Inp] ssItem(u) || lt(u,u)* -> .
% 15.42/15.65 81[0:Inp] ssItem(u) || -> equalelemsP(cons(u,nil))*.
% 15.42/15.65 82[0:Inp] ssItem(u) || -> duplicatefreeP(cons(u,nil))*.
% 15.42/15.65 83[0:Inp] ssItem(u) || -> strictorderedP(cons(u,nil))*.
% 15.42/15.65 84[0:Inp] ssItem(u) || -> totalorderedP(cons(u,nil))*.
% 15.42/15.65 85[0:Inp] ssItem(u) || -> strictorderP(cons(u,nil))*.
% 15.42/15.65 86[0:Inp] ssItem(u) || -> totalorderP(cons(u,nil))*.
% 15.42/15.65 87[0:Inp] ssItem(u) || -> cyclefreeP(cons(u,nil))*.
% 15.42/15.65 88[0:Inp] ssItem(u) || memberP(nil,u)* -> .
% 15.42/15.65 89[0:Inp] ssList(u) || -> ssItem(v)* duplicatefreeP(u)*.
% 15.42/15.65 90[0:Inp] ssList(u) || -> equal(app(u,nil),u)**.
% 15.42/15.65 102[0:Inp] ssList(u) ssList(v) || -> ssList(app(u,v))*.
% 15.42/15.65 103[0:Inp] ssList(u) ssItem(v) || -> ssList(cons(v,u))*.
% 15.42/15.65 104[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf50(u),skaf49(u))*.
% 15.42/15.65 105[0:Inp] ssList(u) || -> cyclefreeP(u) leq(skaf49(u),skaf50(u))*.
% 15.42/15.65 110[0:Inp] ssList(u) || lt(skaf59(u),skaf60(u))* -> strictorderP(u).
% 15.42/15.65 112[0:Inp] ssList(u) || leq(skaf54(u),skaf55(u))* -> totalorderP(u).
% 15.42/15.65 133[0:Inp] ssList(u) ssItem(v) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 15.42/15.65 140[0:Inp] ssList(u) ssList(v) || -> equal(nil,u) equal(hd(app(u,v)),hd(u))**.
% 15.42/15.65 147[0:Inp] ssItem(u) ssItem(v) || leq(u,v)*+ leq(v,u)* -> equal(u,v).
% 15.42/15.65 174[0:Inp] ssList(u) ssList(v) ssItem(w) || -> equal(app(cons(w,v),u),cons(w,app(v,u)))**.
% 15.42/15.65 179[0:Inp] ssList(u) || -> duplicatefreeP(u) equal(app(app(skaf75(u),cons(skaf74(u),skaf76(u))),cons(skaf74(u),skaf77(u))),u)**.
% 15.42/15.65 180[0:Inp] ssList(u) || -> strictorderedP(u) equal(app(app(skaf71(u),cons(skaf69(u),skaf72(u))),cons(skaf70(u),skaf73(u))),u)**.
% 15.42/15.65 181[0:Inp] ssList(u) || -> totalorderedP(u) equal(app(app(skaf66(u),cons(skaf64(u),skaf67(u))),cons(skaf65(u),skaf68(u))),u)**.
% 15.42/15.65 182[0:Inp] ssList(u) || -> strictorderP(u) equal(app(app(skaf61(u),cons(skaf59(u),skaf62(u))),cons(skaf60(u),skaf63(u))),u)**.
% 15.42/15.65 183[0:Inp] ssList(u) || -> totalorderP(u) equal(app(app(skaf56(u),cons(skaf54(u),skaf57(u))),cons(skaf55(u),skaf58(u))),u)**.
% 15.42/15.65 184[0:Inp] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf49(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 15.42/15.65 196[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)* -> .
% 15.42/15.65 198[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).
% 15.42/15.65 199[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).
% 15.42/15.65 205[0:Rew:6.0,12.0] || -> equal(app(app(sk6,cons(sk5,nil)),sk7),sk3)**.
% 15.42/15.65 332[0:Res:11.0,183.0] || -> totalorderP(sk7) equal(app(app(skaf56(sk7),cons(skaf54(sk7),skaf57(sk7))),cons(skaf55(sk7),skaf58(sk7))),sk7)**.
% 15.42/15.65 333[0:Res:11.0,182.0] || -> strictorderP(sk7) equal(app(app(skaf61(sk7),cons(skaf59(sk7),skaf62(sk7))),cons(skaf60(sk7),skaf63(sk7))),sk7)**.
% 15.42/15.65 334[0:Res:11.0,181.0] || -> totalorderedP(sk7) equal(app(app(skaf66(sk7),cons(skaf64(sk7),skaf67(sk7))),cons(skaf65(sk7),skaf68(sk7))),sk7)**.
% 15.42/15.65 335[0:Res:11.0,180.0] || -> strictorderedP(sk7) equal(app(app(skaf71(sk7),cons(skaf69(sk7),skaf72(sk7))),cons(skaf70(sk7),skaf73(sk7))),sk7)**.
% 15.42/15.65 392[0:Res:11.0,105.0] || -> cyclefreeP(sk7) leq(skaf49(sk7),skaf50(sk7))*.
% 15.42/15.65 443[0:Res:11.0,140.1] ssList(u) || -> equal(sk7,nil) equal(hd(app(sk7,u)),hd(sk7))**.
% 15.42/15.65 455[0:Res:11.0,103.1] ssItem(u) || -> ssList(cons(u,sk7))*.
% 15.42/15.65 491[1:Spt:89.1] || -> ssItem(u)*.
% 15.42/15.65 494[1:MRR:455.0,491.0] || -> ssList(cons(u,sk7))*.
% 15.42/15.65 495[1:MRR:88.0,491.0] || memberP(nil,u)* -> .
% 15.42/15.65 496[1:MRR:87.0,491.0] || -> cyclefreeP(cons(u,nil))*.
% 15.42/15.65 497[1:MRR:86.0,491.0] || -> totalorderP(cons(u,nil))*.
% 15.42/15.65 498[1:MRR:85.0,491.0] || -> strictorderP(cons(u,nil))*.
% 15.42/15.65 499[1:MRR:84.0,491.0] || -> totalorderedP(cons(u,nil))*.
% 15.42/15.65 500[1:MRR:83.0,491.0] || -> strictorderedP(cons(u,nil))*.
% 15.42/15.65 501[1:MRR:82.0,491.0] || -> duplicatefreeP(cons(u,nil))*.
% 15.42/15.65 502[1:MRR:81.0,491.0] || -> equalelemsP(cons(u,nil))*.
% 15.42/15.65 503[1:MRR:80.0,491.0] || lt(u,u)* -> .
% 15.42/15.65 580[1:MRR:147.1,147.0,491.0] || leq(u,v)*+ leq(v,u)* -> equal(u,v).
% 15.42/15.65 627[1:MRR:8.3,8.0,491.0] ssList(u) ssList(v) || memberP(v,w)* equal(app(app(v,cons(x,nil)),u),sk3)**+ -> leq(w,x)*.
% 15.42/15.65 628[1:MRR:7.3,7.0,491.0] ssList(u) ssList(v) || memberP(u,w)* equal(app(app(v,cons(x,nil)),u),sk3)**+ -> leq(x,w)*.
% 15.42/15.65 634[1:MRR:103.1,491.0] ssList(u) || -> ssList(cons(v,u))*.
% 15.42/15.65 639[1:MRR:133.1,491.0] ssList(u) || equal(cons(v,nil),u)*+ -> singletonP(u)*.
% 15.42/15.65 656[1:MRR:196.2,491.0] ssList(u) duplicatefreeP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(y,x)),u)* -> .
% 15.42/15.65 678[1:MRR:199.3,199.2,491.0] ssList(u) totalorderedP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(z,x)),u)* -> leq(y,z).
% 15.42/15.65 679[1:MRR:198.3,198.2,491.0] ssList(u) strictorderedP(u) ssList(v) ssList(w) ssList(x) || equal(app(app(v,cons(y,w)),cons(z,x)),u)* -> lt(y,z).
% 15.42/15.65 695[2:Spt:443.1] || -> equal(sk7,nil)**.
% 15.42/15.65 696[2:Rew:695.0,16.1] || leq(sk8,sk5) -> memberP(nil,sk8)*.
% 15.42/15.65 697[2:Rew:695.0,14.0] || -> memberP(nil,sk8) memberP(sk6,sk8)*.
% 15.42/15.65 791[2:Rew:695.0,205.0] || -> equal(app(app(sk6,cons(sk5,nil)),nil),sk3)**.
% 15.42/15.65 797[2:Rew:695.0,494.0] || -> ssList(cons(u,nil))*.
% 15.42/15.65 846[2:MRR:697.0,495.0] || -> memberP(sk6,sk8)*.
% 15.42/15.65 847[2:MRR:696.1,495.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 959[2:SpR:791.0,90.1] ssList(app(sk6,cons(sk5,nil))) || -> equal(app(sk6,cons(sk5,nil)),sk3)**.
% 15.42/15.65 1042[1:EqR:639.1] ssList(cons(u,nil)) || -> singletonP(cons(u,nil))*.
% 15.42/15.65 1044[2:SSi:1042.0,496.0,497.0,498.0,499.0,500.0,501.0,502.0,797.0] || -> singletonP(cons(u,nil))*.
% 15.42/15.65 1046[1:Res:105.2,580.0] ssList(u) || leq(skaf50(u),skaf49(u))* -> cyclefreeP(u) equal(skaf49(u),skaf50(u)).
% 15.42/15.65 1048[1:MRR:1046.1,104.2] ssList(u) || -> cyclefreeP(u) equal(skaf49(u),skaf50(u))**.
% 15.42/15.65 1051[1:Rew:1048.2,184.2] ssList(u) || -> cyclefreeP(u) equal(app(app(skaf51(u),cons(skaf50(u),skaf52(u))),cons(skaf50(u),skaf53(u))),u)**.
% 15.42/15.65 2447[2:SoR:959.0,102.2] ssList(cons(sk5,nil)) ssList(sk6) || -> equal(app(sk6,cons(sk5,nil)),sk3)**.
% 15.42/15.65 2448[2:SSi:2447.1,2447.0,10.0,1044.0,502.0,501.0,500.0,499.0,498.0,497.0,496.1,634.0,25.0,20.0,21.0,22.0,23.0,24.0,18.0,19.0] || -> equal(app(sk6,cons(sk5,nil)),sk3)**.
% 15.42/15.65 4870[1:SpL:90.1,627.3] ssList(app(u,cons(v,nil))) ssList(nil) ssList(u) || memberP(u,w)* equal(app(u,cons(v,nil)),sk3)** -> leq(w,v)*.
% 15.42/15.65 4876[2:SSi:4870.1,4870.0,25.0,20.0,21.0,22.0,23.0,24.0,18.0,19.0,102.1,1044.0,502.0,501.0,500.0,499.0,498.0,497.0,496.0,634.2,25.0,20.0,21.0,22.0,23.0,24.0,18.0,19.0] ssList(u) || memberP(u,v)* equal(app(u,cons(w,nil)),sk3)**+ -> leq(v,w)*.
% 15.42/15.65 5378[1:SpL:1051.2,656.5] ssList(u) ssList(v) duplicatefreeP(v) ssList(skaf51(u)) ssList(skaf52(u)) ssList(skaf53(u)) || equal(u,v)* -> cyclefreeP(u)*.
% 15.42/15.65 5385[1:SSi:5378.5,5378.4,5378.3,59.0,60.0,61.0] ssList(u) ssList(v) duplicatefreeP(v) || equal(u,v)*+ -> cyclefreeP(u)*.
% 15.42/15.65 5442[1:SpL:183.2,678.5] ssList(u) ssList(v) totalorderedP(v) ssList(skaf56(u)) ssList(skaf57(u)) ssList(skaf58(u)) || equal(u,v)* -> totalorderP(u) leq(skaf54(u),skaf55(u))*.
% 15.42/15.65 5458[1:SSi:5442.5,5442.4,5442.3,54.0,55.0,56.0] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)* -> totalorderP(u) leq(skaf54(u),skaf55(u))*.
% 15.42/15.65 5459[1:MRR:5458.5,112.1] ssList(u) ssList(v) totalorderedP(v) || equal(u,v)*+ -> totalorderP(u)*.
% 15.42/15.65 5519[1:SpL:182.2,679.5] 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))*.
% 15.42/15.65 5522[1:SpL:179.2,679.5] 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))*.
% 15.42/15.65 5532[1:SSi:5522.5,5522.4,5522.3,35.0,36.0,37.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> duplicatefreeP(u) lt(skaf74(u),skaf74(u))*.
% 15.42/15.65 5533[1:MRR:5532.5,503.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> duplicatefreeP(u)*.
% 15.42/15.65 5537[1:SSi:5519.5,5519.4,5519.3,49.0,50.0,51.0] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)* -> strictorderP(u) lt(skaf59(u),skaf60(u))*.
% 15.42/15.65 5538[1:MRR:5537.5,110.1] ssList(u) ssList(v) strictorderedP(v) || equal(u,v)*+ -> strictorderP(u)*.
% 15.42/15.65 8483[1:EqR:5385.3] ssList(u) ssList(u) duplicatefreeP(u) || -> cyclefreeP(u)*.
% 15.42/15.65 8484[1:Obv:8483.0] ssList(u) duplicatefreeP(u) || -> cyclefreeP(u)*.
% 15.42/15.65 8852[1:EqR:5459.3] ssList(u) ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 15.42/15.65 8853[1:Obv:8852.0] ssList(u) totalorderedP(u) || -> totalorderP(u)*.
% 15.42/15.65 8856[1:EqR:5533.3] ssList(u) ssList(u) strictorderedP(u) || -> duplicatefreeP(u)*.
% 15.42/15.65 8857[1:Obv:8856.0] ssList(u) strictorderedP(u) || -> duplicatefreeP(u)*.
% 15.42/15.65 8859[1:EqR:5538.3] ssList(u) ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 15.42/15.65 8860[1:Obv:8859.0] ssList(u) strictorderedP(u) || -> strictorderP(u)*.
% 15.42/15.65 12872[2:SpL:2448.0,4876.2] ssList(sk6) || memberP(sk6,u)* equal(sk3,sk3) -> leq(u,sk5).
% 15.42/15.65 12874[2:Obv:12872.2] ssList(sk6) || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 13553[2:SSi:12874.0,10.0] || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 13989[2:Res:846.0,13553.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 14010[2:MRR:13989.0,847.0] || -> .
% 15.42/15.65 14027[2:Spt:14010.0,443.1,695.0] || equal(sk7,nil)** -> .
% 15.42/15.65 14028[2:Spt:14010.0,443.0,443.2] ssList(u) || -> equal(hd(app(sk7,u)),hd(sk7))**.
% 15.42/15.65 14188[3:Spt:334.0] || -> totalorderedP(sk7)*.
% 15.42/15.65 14192[4:Spt:335.0] || -> strictorderedP(sk7)*.
% 15.42/15.65 14197[5:Spt:392.0] || -> cyclefreeP(sk7)*.
% 15.42/15.65 14201[6:Spt:332.0] || -> totalorderP(sk7)*.
% 15.42/15.65 14206[7:Spt:333.0] || -> strictorderP(sk7)*.
% 15.42/15.65 14224[8:Spt:14.0] || -> memberP(sk7,sk8)*.
% 15.42/15.65 14357[9:Spt:17.0] || leq(sk5,sk8)* -> .
% 15.42/15.65 14425[1:SpL:205.0,627.3] ssList(sk7) ssList(sk6) || memberP(sk6,u)* equal(sk3,sk3) -> leq(u,sk5).
% 15.42/15.65 14426[1:SpL:205.0,628.3] ssList(sk7) ssList(sk6) || memberP(sk7,u)* equal(sk3,sk3) -> leq(sk5,u).
% 15.42/15.65 14439[1:Obv:14425.3] ssList(sk7) ssList(sk6) || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 14440[7:SSi:14439.1,14439.0,10.0,14188.0,11.0,14192.0,14197.0,14201.0,14206.0] || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 14441[1:Obv:14426.3] ssList(sk7) ssList(sk6) || memberP(sk7,u)* -> leq(sk5,u).
% 15.42/15.65 14442[7:SSi:14441.1,14441.0,10.0,14188.0,11.0,14192.0,14197.0,14201.0,14206.0] || memberP(sk7,u)* -> leq(sk5,u).
% 15.42/15.65 15286[8:Res:14224.0,14442.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 15288[9:MRR:15286.0,14357.0] || -> .
% 15.42/15.65 15299[9:Spt:15288.0,17.0,14357.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 15300[9:Spt:15288.0,17.1] || leq(sk8,sk5)* -> .
% 15.42/15.65 15301[8:MRR:15.0,15286.0] || -> memberP(sk6,sk8)*.
% 15.42/15.65 15469[8:Res:15301.0,14440.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 15471[9:MRR:15469.0,15300.0] || -> .
% 15.42/15.65 15490[8:Spt:15471.0,14.0,14224.0] || memberP(sk7,sk8)* -> .
% 15.42/15.65 15491[8:Spt:15471.0,14.1] || -> memberP(sk6,sk8)*.
% 15.42/15.65 15492[8:MRR:16.1,15490.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 15499[8:Res:15491.0,14440.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 15500[8:MRR:15499.0,15492.0] || -> .
% 15.42/15.65 15509[7:Spt:15500.0,333.0,14206.0] || strictorderP(sk7)* -> .
% 15.42/15.65 15510[7:Spt:15500.0,333.1] || -> equal(app(app(skaf61(sk7),cons(skaf59(sk7),skaf62(sk7))),cons(skaf60(sk7),skaf63(sk7))),sk7)**.
% 15.42/15.65 15695[7:Res:8860.2,15509.0] ssList(sk7) strictorderedP(sk7) || -> .
% 15.42/15.65 15697[7:SSi:15695.1,15695.0,14188.0,11.0,14192.0,14197.0,14201.0,14188.0,11.0,14192.0,14197.0,14201.0] || -> .
% 15.42/15.65 15700[6:Spt:15697.0,332.0,14201.0] || totalorderP(sk7)* -> .
% 15.42/15.65 15701[6:Spt:15697.0,332.1] || -> equal(app(app(skaf56(sk7),cons(skaf54(sk7),skaf57(sk7))),cons(skaf55(sk7),skaf58(sk7))),sk7)**.
% 15.42/15.65 15882[6:Res:8853.2,15700.0] ssList(sk7) totalorderedP(sk7) || -> .
% 15.42/15.65 15889[6:SSi:15882.1,15882.0,14188.0,11.0,14192.0,14197.0,14188.0,11.0,14192.0,14197.0] || -> .
% 15.42/15.65 15894[5:Spt:15889.0,392.0,14197.0] || cyclefreeP(sk7)* -> .
% 15.42/15.65 15895[5:Spt:15889.0,392.1] || -> leq(skaf49(sk7),skaf50(sk7))*.
% 15.42/15.65 16006[5:Res:8484.2,15894.0] ssList(sk7) duplicatefreeP(sk7) || -> .
% 15.42/15.65 16018[5:SSi:16006.1,16006.0,8857.0,14188.0,11.0,14192.0,14188.0,11.0,14192.2] || -> .
% 15.42/15.65 16023[4:Spt:16018.0,335.0,14192.0] || strictorderedP(sk7)* -> .
% 15.42/15.65 16024[4:Spt:16018.0,335.1] || -> equal(app(app(skaf71(sk7),cons(skaf69(sk7),skaf72(sk7))),cons(skaf70(sk7),skaf73(sk7))),sk7)**.
% 15.42/15.65 16047[3:SSi:14439.1,14439.0,10.0,14188.0,11.0] || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 16048[3:SSi:14441.1,14441.0,10.0,14188.0,11.0] || memberP(sk7,u)* -> leq(sk5,u).
% 15.42/15.65 16208[5:Spt:14.0] || -> memberP(sk7,sk8)*.
% 15.42/15.65 16225[6:Spt:15.0] || leq(sk5,sk8)* -> .
% 15.42/15.65 16610[5:Res:16208.0,16048.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 16613[6:MRR:16610.0,16225.0] || -> .
% 15.42/15.65 16627[6:Spt:16613.0,15.0,16225.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 16628[6:Spt:16613.0,15.1] || -> memberP(sk6,sk8)*.
% 15.42/15.65 16629[5:MRR:17.0,16610.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 16838[6:Res:16628.0,16047.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 16840[6:MRR:16838.0,16629.0] || -> .
% 15.42/15.65 16859[5:Spt:16840.0,14.0,16208.0] || memberP(sk7,sk8)* -> .
% 15.42/15.65 16860[5:Spt:16840.0,14.1] || -> memberP(sk6,sk8)*.
% 15.42/15.65 16861[5:MRR:16.1,16859.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 16935[5:Res:16860.0,16047.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 16936[5:MRR:16935.0,16861.0] || -> .
% 15.42/15.65 16945[3:Spt:16936.0,334.0,14188.0] || totalorderedP(sk7)* -> .
% 15.42/15.65 16946[3:Spt:16936.0,334.1] || -> equal(app(app(skaf66(sk7),cons(skaf64(sk7),skaf67(sk7))),cons(skaf65(sk7),skaf68(sk7))),sk7)**.
% 15.42/15.65 16971[1:SSi:14439.1,14439.0,10.0,11.0] || memberP(sk6,u)* -> leq(u,sk5).
% 15.42/15.65 16972[1:SSi:14441.1,14441.0,10.0,11.0] || memberP(sk7,u)* -> leq(sk5,u).
% 15.42/15.65 17149[4:Spt:14.0] || -> memberP(sk7,sk8)*.
% 15.42/15.65 17157[5:Spt:15.0] || leq(sk5,sk8)* -> .
% 15.42/15.65 17564[4:Res:17149.0,16972.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 17567[5:MRR:17564.0,17157.0] || -> .
% 15.42/15.65 17580[5:Spt:17567.0,15.0,17157.0] || -> leq(sk5,sk8)*.
% 15.42/15.65 17581[5:Spt:17567.0,15.1] || -> memberP(sk6,sk8)*.
% 15.42/15.65 17582[4:MRR:17.0,17564.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 17791[5:Res:17581.0,16971.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 17793[5:MRR:17791.0,17582.0] || -> .
% 15.42/15.65 17812[4:Spt:17793.0,14.0,17149.0] || memberP(sk7,sk8)* -> .
% 15.42/15.65 17813[4:Spt:17793.0,14.1] || -> memberP(sk6,sk8)*.
% 15.42/15.65 17814[4:MRR:16.1,17812.0] || leq(sk8,sk5)* -> .
% 15.42/15.65 17834[4:Res:17813.0,16971.0] || -> leq(sk8,sk5)*.
% 15.42/15.65 17835[4:MRR:17834.0,17814.0] || -> .
% 15.42/15.65 17844[1:Spt:17835.0,89.0,89.2] ssList(u) || -> duplicatefreeP(u)*.
% 15.42/15.65 17877[1:MRR:196.1,17844.1] ssList(u) ssItem(v) ssList(w) ssList(x) ssList(y) || equal(app(app(w,cons(v,x)),cons(v,y)),u)* -> .
% 15.42/15.65 28088[0:SpR:174.3,102.2] ssList(u) ssList(v) ssItem(w) ssList(cons(w,v)) ssList(u) || -> ssList(cons(w,app(v,u)))*.
% 15.42/15.65 28117[0:Obv:28088.0] ssList(u) ssItem(v) ssList(cons(v,u)) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 15.42/15.65 28118[0:SSi:28117.2,103.2] ssList(u) ssItem(v) ssList(w) || -> ssList(cons(v,app(u,w)))*.
% 15.42/15.65 29208[1:EqR:17877.5] ssList(app(app(u,cons(v,w)),cons(v,x))) ssItem(v) ssList(u) ssList(w) ssList(x) || -> .
% 15.42/15.65 29236[1:SSi:29208.0,102.2,102.2,103.2,103.2] ssItem(u) ssList(v) ssList(w) ssList(x) || -> .
% 15.42/15.65 29237[1:MRR:28118.3,29236.1] ssList(u) ssItem(v) ssList(w) || -> .
% 15.42/15.65 29240[1:Con:29237.2] ssList(u) ssItem(v) || -> .
% 15.42/15.65 29241[1:MRR:455.1,29240.0] ssItem(u) || -> .
% 15.42/15.65 29242[1:UnC:29241.0,64.0] || -> .
% 15.42/15.65 % SZS output end Refutation
% 15.42/15.65 Formulae used in the proof : co1_6 co1_7 co1_8 co1_10 co1_11 co1_12 co1_14 co1_15 co1_16 co1_17 clause1 clause2 clause3 clause4 clause5 clause6 clause7 clause8 clause18 clause19 clause20 clause32 clause33 clause34 clause37 clause38 clause39 clause42 clause43 clause44 clause47 clause63 clause64 clause65 clause66 clause67 clause68 clause69 clause70 clause71 clause72 clause73 clause85 clause86 clause87 clause88 clause93 clause95 clause116 clause123 clause130 clause157 clause162 clause163 clause164 clause165 clause166 clause167 clause179 clause181 clause182
% 18.83/19.01
%------------------------------------------------------------------------------