%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC052-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:39:45 PM UTC 2026
% Result : Unsatisfiable 14.92s 2.39s
% Output : CNFRefutation 14.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 913
% Syntax : Number of formulae : 2958 ( 126 unt; 792 def)
% Number of atoms : 12271 (1179 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 17620 (8307 ~;8521 |; 0 &)
% ( 792 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 811 ( 809 usr; 793 prp; 0-2 aty)
% Number of functors : 47 ( 47 usr; 8 con; 0-2 aty)
% Number of variables : 3239 (3239 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] : ssItem(skaf79(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [U] : ssItem(skaf78(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] : ssItem(skaf74(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] : ssList(skaf71(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] : ssItem(skaf70(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] : ssItem(skaf69(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] : ssItem(skaf64(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U] : ssList(skaf63(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U] : ssList(skaf62(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U] : ssList(skaf61(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [U] : ssItem(skaf60(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] : ssItem(skaf59(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] : ssList(skaf58(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] : ssList(skaf57(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U] : ssList(skaf56(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] : ssItem(skaf55(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] : ssItem(skaf54(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] : ssList(skaf53(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] : ssList(skaf52(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] : ssList(skaf51(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] : ssItem(skaf50(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] : ssItem(skaf49(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,V] : ssList(skaf46(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U,V] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [U] :
( equalelemsP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( duplicatefreeP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( strictorderP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [U] :
( totalorderP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [U] :
( cyclefreeP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( nil = U
| ssItem(hd(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( rearsegP(nil,U)
| ~ ssList(U)
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ rearsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ frontsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [U] :
( cons(skaf44(U),nil) = U
| ~ ssList(U)
| ~ singletonP(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [U] :
( nil = U
| cons(skaf83(U),skaf82(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [U,V] :
( hd(app(V,U)) = hd(V)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [U,V] :
( app(skaf46(U,V),V) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f133,axiom,
! [U,V] :
( tl(app(V,U)) = app(tl(V),U)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f134,axiom,
! [U,V] :
( nil = V
| lt(U,hd(V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ strictorderedP(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f135,axiom,
! [U,V] :
( nil = V
| leq(U,hd(V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ totalorderedP(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f136,axiom,
! [U,V,W] :
( rearsegP(app(W,U),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f137,axiom,
! [U,V,W] :
( frontsegP(app(U,W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,axiom,
! [U,V,W] :
( memberP(cons(V,W),U)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
! [U,V,W] :
( memberP(cons(W,U),V)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [U,V,W] :
( memberP(app(U,W),V)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [U,V,W] :
( memberP(app(W,U),V)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,axiom,
! [U,V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [U,V,W] :
( app(app(W,V),U) = app(W,app(V,U))
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [U,V,W] :
( V = W
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [U,V,W] :
( segmentP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [U,V,W] :
( rearsegP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,axiom,
! [U,V,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f158,axiom,
! [U,V,W] :
( memberP(U,W)
| memberP(V,W)
| ~ ssItem(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,axiom,
! [U,V] :
( nil = V
| totalorderedP(cons(U,V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ totalorderedP(V)
| ~ leq(U,hd(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,axiom,
! [U,V] :
( nil = V
| strictorderedP(cons(U,V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ strictorderedP(V)
| ~ lt(U,hd(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [U,V,W] :
( W = U
| memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f168,axiom,
! [U,V] :
( app(app(skaf47(U,V),V),skaf48(V,U)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f169,axiom,
! [U,V] :
( app(skaf42(U,V),cons(V,skaf43(V,U))) = U
| ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,axiom,
! [U,V,W,X] :
( segmentP(app(app(X,U),W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| ~ ssList(W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,axiom,
! [U,V,W,X] :
( frontsegP(V,X)
| ~ ssItem(U)
| ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f175,axiom,
! [U,V,W,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| app(U,cons(V,W)) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f176,axiom,
! [U,V,W,X] :
( U = W
| ~ ssItem(U)
| ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f177,axiom,
! [U,V] :
( nil = U
| U = V
| nil = V
| ~ ssList(V)
| ~ ssList(U)
| hd(U) != hd(V)
| tl(U) != tl(V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [U,V,W,X] :
( frontsegP(cons(W,U),cons(X,V))
| ~ ssItem(W)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(V)
| W != X
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f179,axiom,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f180,axiom,
! [U,V,W,X,Y] :
( V = W
| ~ ssList(Y)
| ~ equalelemsP(Y)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ ssList(U)
| ~ ssList(X)
| app(U,cons(V,cons(W,X))) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f181,axiom,
! [U,V,W,X,Y,Z] :
( lt(V,X)
| ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f182,axiom,
! [U,V,W,X,Y,Z] :
( leq(V,X)
| ~ ssList(Z)
| ~ totalorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f183,axiom,
! [U,V,W,X,Y,Z] :
( lt(X,V)
| lt(V,X)
| ~ ssList(Z)
| ~ strictorderP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f184,axiom,
! [U,V,W,X,Y,Z] :
( leq(X,V)
| leq(V,X)
| ~ ssList(Z)
| ~ totalorderP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f185,axiom,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( nil != sk4
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
! [A] :
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f209,plain,
ssItem(skac3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f210,plain,
ssItem(skac2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f212,plain,
! [X0] : ssItem(skaf83(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f213,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f216,plain,
! [X0] : ssItem(skaf79(X0)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f217,plain,
! [X0] : ssItem(skaf78(X0)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f221,plain,
! [X0] : ssItem(skaf74(X0)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f224,plain,
! [X0] : ssList(skaf71(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f225,plain,
! [X0] : ssItem(skaf70(X0)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f226,plain,
! [X0] : ssItem(skaf69(X0)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f227,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f228,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f229,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f230,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f231,plain,
! [X0] : ssItem(skaf64(X0)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f232,plain,
! [X0] : ssList(skaf63(X0)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f233,plain,
! [X0] : ssList(skaf62(X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f234,plain,
! [X0] : ssList(skaf61(X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f235,plain,
! [X0] : ssItem(skaf60(X0)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f236,plain,
! [X0] : ssItem(skaf59(X0)),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f237,plain,
! [X0] : ssList(skaf58(X0)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f238,plain,
! [X0] : ssList(skaf57(X0)),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f239,plain,
! [X0] : ssList(skaf56(X0)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f240,plain,
! [X0] : ssItem(skaf55(X0)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f241,plain,
! [X0] : ssItem(skaf54(X0)),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f242,plain,
! [X0] : ssList(skaf53(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f243,plain,
! [X0] : ssList(skaf52(X0)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f244,plain,
! [X0] : ssList(skaf51(X0)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f245,plain,
! [X0] : ssItem(skaf50(X0)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f246,plain,
! [X0] : ssItem(skaf49(X0)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f247,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f250,plain,
! [X0,X1] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f251,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f256,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f257,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f258,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f260,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f261,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f264,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f265,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f266,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f267,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f268,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f269,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f270,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f271,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f272,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f273,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f274,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f275,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f276,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f277,plain,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f281,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f282,plain,
! [X0] :
( rearsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f283,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f285,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f287,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f297,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f298,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f304,plain,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f307,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f323,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f324,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f327,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f328,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f329,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f330,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f334,plain,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f340,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f341,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f342,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f344,plain,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f345,plain,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f346,plain,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f347,plain,
! [V] :
( nil = V
| ! [U] :
( lt(U,hd(V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ strictorderedP(cons(U,V)) ) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f348,plain,
! [X0,X1] :
( nil = X1
| lt(X0,hd(X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(cons(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f349,plain,
! [V] :
( nil = V
| ! [U] :
( leq(U,hd(V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ totalorderedP(cons(U,V)) ) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f350,plain,
! [X0,X1] :
( nil = X1
| leq(X0,hd(X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(cons(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f349]) ).
fof(f351,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f352,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f353,plain,
! [X0,X1,X2] :
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f354,plain,
! [X0,X1,X2] :
( memberP(cons(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f355,plain,
! [X0,X1,X2] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f356,plain,
! [X0,X1,X2] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f358,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f359,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f358]) ).
fof(f360,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f361,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f369,plain,
! [X0,X1,X2] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f370,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f371,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f374,plain,
! [U,W] :
( segmentP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f375,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f376,plain,
! [U,W] :
( rearsegP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V) ) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f377,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f378,plain,
! [U,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f379,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f378]) ).
fof(f385,plain,
! [U,W] :
( memberP(U,W)
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ memberP(app(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f386,plain,
! [X0,X1,X2] :
( memberP(X0,X2)
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ memberP(app(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f387,plain,
! [V] :
( nil = V
| ! [U] :
( totalorderedP(cons(U,V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ totalorderedP(V)
| ~ leq(U,hd(V)) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f388,plain,
! [X0,X1] :
( nil = X1
| totalorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ leq(X0,hd(X1)) ),
inference(cnf_transformation,[status(thm)],[f387]) ).
fof(f389,plain,
! [V] :
( nil = V
| ! [U] :
( strictorderedP(cons(U,V))
| ~ ssItem(U)
| ~ ssList(V)
| ~ strictorderedP(V)
| ~ lt(U,hd(V)) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f390,plain,
! [X0,X1] :
( nil = X1
| strictorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| ~ lt(X0,hd(X1)) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f391,plain,
! [U,W] :
( W = U
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f392,plain,
! [X0,X1,X2] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f391]) ).
fof(f399,plain,
! [X0,X1] :
( app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f400,plain,
! [X0,X1] :
( app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f405,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f406,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f408,plain,
! [V,X] :
( frontsegP(V,X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ) ),
inference(miniscoping,[status(thm)],[f174]) ).
fof(f409,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f410,plain,
! [V,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(U,cons(V,W)) != X ) ) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f411,plain,
! [X0,X1,X2,X3] :
( memberP(X3,X1)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(X0,cons(X1,X2)) != X3 ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f412,plain,
! [U,W] :
( U = W
| ~ ssItem(U)
| ~ ssItem(W)
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f413,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f412]) ).
fof(f414,plain,
! [U] :
( nil = U
| ! [V] :
( U = V
| nil = V
| ~ ssList(V)
| ~ ssList(U)
| hd(U) != hd(V)
| tl(U) != tl(V) ) ),
inference(miniscoping,[status(thm)],[f177]) ).
fof(f415,plain,
! [X0,X1] :
( nil = X0
| X0 = X1
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| hd(X0) != hd(X1)
| tl(X0) != tl(X1) ),
inference(cnf_transformation,[status(thm)],[f414]) ).
fof(f416,plain,
! [X0,X1,X2,X3] :
( frontsegP(cons(X2,X0),cons(X3,X1))
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| X2 != X3
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f417,plain,
! [Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f418,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f419,plain,
! [V,W] :
( V = W
| ! [Y] :
( ~ ssList(Y)
| ~ equalelemsP(Y)
| ~ ssItem(V)
| ~ ssItem(W)
| ! [U] :
( ~ ssList(U)
| ! [X] :
( ~ ssList(X)
| app(U,cons(V,cons(W,X))) != Y ) ) ) ),
inference(miniscoping,[status(thm)],[f180]) ).
fof(f420,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X2
| ~ ssList(X4)
| ~ equalelemsP(X4)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X3)
| app(X0,cons(X1,cons(X2,X3))) != X4 ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f421,plain,
! [V,X] :
( lt(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ strictorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f181]) ).
fof(f422,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X3)
| ~ ssList(X5)
| ~ strictorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f423,plain,
! [V,X] :
( leq(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ totalorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f182]) ).
fof(f424,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X1,X3)
| ~ ssList(X5)
| ~ totalorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f425,plain,
! [V,X] :
( lt(X,V)
| lt(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ strictorderP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f426,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X3,X1)
| lt(X1,X3)
| ~ ssList(X5)
| ~ strictorderP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f427,plain,
! [V,X] :
( leq(X,V)
| leq(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ totalorderP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f428,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X5)
| ~ totalorderP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f427]) ).
fof(f429,plain,
! [Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| ! [Y] :
( ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f185]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ ssList(X5)
| ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f432,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f435,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f436,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f437,plain,
( nil != sk4
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f438,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f439,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f441,plain,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f442,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f443,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f444,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f445,plain,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f446,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f447,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f450,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f273,f446,f449]) ).
fof(f453,definition,
( sQ2_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ2_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
( sQ3_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( sQ3_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f453,f456]) ).
fof(f460,definition,
( sQ4_spl
<=> ssList(sk5) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ4_spl
| ssList(sk5) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,definition,
( sQ5_spl
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ5_spl
| ~ neq(sk4,nil) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f438,f460,f463]) ).
fof(f467,definition,
( sQ6_spl
<=> neq(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ6_spl
| neq(sk5,nil) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f439,f467,f463]) ).
fof(f471,definition,
( sQ7_spl
<=> frontsegP(sk4,sk5) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ7_spl
| frontsegP(sk4,sk5) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f440,f471,f463]) ).
fof(f475,definition,
( sQ8_spl
<=> frontsegP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ8_spl
| frontsegP(sk3,sk5) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f441,f475,f463]) ).
fof(f479,definition,
( sQ9_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ9_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ10_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ10_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f442,f479,f482]) ).
fof(f486,definition,
! [X0] :
( sQ11_spl
<=> ( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f487,plain,
! [X0] :
( ~ sQ11_spl
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f443,f479,f486]) ).
fof(f490,definition,
( sQ12_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ12_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f444,f490,f482]) ).
fof(f494,plain,
( sQ11_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f445,f490,f486]) ).
fof(f496,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f282]) ).
fof(f504,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f324]) ).
fof(f507,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f353]) ).
fof(f508,plain,
! [X0,X1] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f507]) ).
fof(f509,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f359]) ).
fof(f510,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f361]) ).
fof(f513,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f407]) ).
fof(f514,plain,
! [X0,X1,X2] :
( memberP(app(X1,cons(X2,X0)),X2)
| ~ ssList(app(X1,cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f411]) ).
fof(f515,plain,
! [X0,X1,X3] :
( frontsegP(cons(X3,X0),cons(X3,X1))
| ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f416]) ).
fof(f516,plain,
! [X0,X1,X2] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f515]) ).
fof(f517,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f418]) ).
fof(f518,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ ssList(app(X1,cons(X3,cons(X2,X0))))
| ~ equalelemsP(app(X1,cons(X3,cons(X2,X0))))
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f420]) ).
fof(f519,plain,
! [X0,X1,X2,X3,X4] :
( lt(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ strictorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f422]) ).
fof(f520,plain,
! [X0,X1,X2,X3,X4] :
( leq(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ totalorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f424]) ).
fof(f521,plain,
! [X0,X1,X2,X3,X4] :
( lt(X3,X4)
| lt(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ strictorderP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f426]) ).
fof(f522,plain,
! [X0,X1,X2,X3,X4] :
( leq(X3,X4)
| leq(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ totalorderP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f428]) ).
fof(f523,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(app(app(X4,cons(X0,X3)),cons(X1,X2)))
| ~ cyclefreeP(app(app(X4,cons(X0,X3)),cons(X1,X2)))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f430]) ).
fof(f528,plain,
( ~ sQ2_spl
| sk1 = nil ),
inference(backward_demodulation,[status(thm)],[f454,f436]) ).
fof(f529,plain,
( ~ sQ2_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f492]) ).
fof(f530,plain,
( ~ sQ2_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
( sQ5_spl
| ~ neq(sk2,nil) ),
inference(backward_demodulation,[status(thm)],[f435,f465]) ).
fof(f532,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f281,f256]) ).
fof(f534,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,definition,
( sQ14_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f532,f534,f537]) ).
fof(f542,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f208]) ).
fof(f543,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ3_spl
| nil != sk2 ),
inference(forward_demodulation,[status(thm)],[f435,f458]) ).
fof(f547,plain,
( ~ sQ9_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f544]) ).
fof(f548,plain,
( ~ sQ9_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f553,plain,
( sQ5_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f483]) ).
fof(f554,plain,
( sQ5_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f555,plain,
( ~ sQ7_spl
| frontsegP(sk2,sk5) ),
inference(forward_demodulation,[status(thm)],[f435,f472]) ).
fof(f560,definition,
( sQ15_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( sQ15_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,definition,
( sQ16_spl
<=> segmentP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( ~ sQ16_spl
| segmentP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f578,definition,
( sQ19_spl
<=> ssItem(nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ19_spl
| ~ ssItem(nil) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f589,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| frontsegP(nil,sk5) ),
inference(forward_demodulation,[status(thm)],[f480,f555]) ).
fof(f590,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| nil = sk5
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f589,f285]) ).
fof(f591,definition,
( sQ21_spl
<=> nil = sk5 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ21_spl
| nil = sk5 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f590,f460,f591,f479,f471]) ).
fof(f596,plain,
( ~ sQ6_spl
| ~ sQ21_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f592,f468]) ).
fof(f611,definition,
! [X0] :
( sQ23_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f615,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f340,f256]) ).
fof(f617,plain,
( ~ sQ13_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f615,f611,f534]) ).
fof(f619,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f342,f260]) ).
fof(f621,definition,
! [X0] :
( sQ24_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ13_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f619,f621,f534]) ).
fof(f627,plain,
! [X0,X1,X2] :
( app(X0,X2) = X1
| ~ ssList(app(X0,X2))
| ~ ssList(X1)
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f352,f342]) ).
fof(f628,plain,
! [X0,X1,X2] :
( app(X0,X2) = X1
| ~ ssList(app(X0,X2))
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f627]) ).
fof(f629,plain,
( ~ sQ8_spl
| frontsegP(sk1,sk5) ),
inference(forward_demodulation,[status(thm)],[f436,f476]) ).
fof(f634,definition,
( sQ26_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ26_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f641,plain,
( ~ sQ11_spl
| ~ ssList(sk1)
| ~ segmentP(sk2,nil)
| ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f487,f256]) ).
fof(f643,definition,
( sQ28_spl
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( sQ28_spl
| ~ neq(nil,nil) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,definition,
( sQ29_spl
<=> segmentP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( ~ sQ29_spl
| segmentP(sk2,nil) ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f648,plain,
( sQ29_spl
| ~ segmentP(sk2,nil) ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f649,plain,
( ~ sQ11_spl
| ~ sQ26_spl
| ~ sQ29_spl
| ~ sQ28_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f641,f534,f643,f646,f634,f486]) ).
fof(f657,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f431]) ).
fof(f658,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f657]) ).
fof(f663,definition,
( sQ33_spl
<=> sk2 = sk5 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( ~ sQ33_spl
| sk2 = sk5 ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f667,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f432]) ).
fof(f668,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f669,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f375,f256]) ).
fof(f671,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ13_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f669,f671,f534]) ).
fof(f676,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f379,f285]) ).
fof(f677,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X0)
| ~ ssList(X2)
| ~ frontsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f379,f342]) ).
fof(f678,definition,
! [X0,X1] :
( sQ35_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f679,plain,
! [X0,X1] :
( ~ sQ35_spl
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( ~ sQ13_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f676,f678,f534]) ).
fof(f682,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ frontsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f677]) ).
fof(f683,plain,
! [X0,X1] :
( ~ sQ35_spl
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f679]) ).
fof(f705,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ ssList(X4)
| ~ ssList(app(app(X3,X0),X2))
| ~ ssList(X1)
| ~ segmentP(X4,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f405,f375]) ).
fof(f706,plain,
! [X0,X1,X2,X3] :
( app(app(X3,X0),X2) = X1
| ~ ssList(app(app(X3,X0),X2))
| ~ ssList(X1)
| ~ segmentP(X1,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f405,f340]) ).
fof(f707,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ ssList(X4)
| ~ ssList(app(app(X3,X0),X2))
| ~ segmentP(X4,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f705]) ).
fof(f708,plain,
! [X0,X1,X2,X3] :
( app(app(X3,X0),X2) = X1
| ~ ssList(app(app(X3,X0),X2))
| ~ segmentP(X1,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f706]) ).
fof(f722,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X3,X1))
| ~ ssList(X4)
| ~ ssList(cons(X2,X0))
| ~ frontsegP(X4,cons(X2,X0))
| ~ frontsegP(cons(X3,X1),X4)
| frontsegP(X1,X0)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f409,f379]) ).
fof(f725,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X3,X1))
| ~ ssList(X4)
| ~ ssList(cons(X2,X0))
| ~ frontsegP(X4,cons(X2,X0))
| ~ frontsegP(cons(X3,X1),X4)
| X3 = X2
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f413,f379]) ).
fof(f742,plain,
! [X0,X1,X2] :
( X2 = X2
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f516,f413]) ).
fof(f743,plain,
! [X0,X1,X2] :
( frontsegP(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f516,f409]) ).
fof(f744,plain,
! [X0,X1,X2] :
( cons(X2,X0) = cons(X2,X1)
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ frontsegP(cons(X2,X1),cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f516,f342]) ).
fof(f745,definition,
! [X0,X1] :
( sQ41_spl
<=> ( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f746,plain,
! [X0,X1] :
( ~ sQ41_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f748,definition,
! [X2] :
( sQ42_spl
<=> ( X2 = X2
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f742,f745,f748]) ).
fof(f752,definition,
! [X0,X1] :
( sQ43_spl
<=> ( frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f755,definition,
! [X2] :
( sQ44_spl
<=> ( ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f756,plain,
! [X0] :
( ~ sQ44_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f755]) ).
fof(f758,plain,
( sQ44_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f743,f752,f755]) ).
fof(f759,plain,
! [X0,X1] :
( ~ sQ41_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f746]) ).
fof(f760,plain,
! [X0] :
( ~ sQ44_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f756]) ).
fof(f761,plain,
( ~ sQ44_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f247,f760]) ).
fof(f778,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f761]) ).
fof(f779,plain,
( sQ29_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f648,f256]) ).
fof(f780,plain,
( sQ29_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f779,f560,f646]) ).
fof(f785,definition,
( sQ45_spl
<=> frontsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f787,plain,
( sQ45_spl
| ~ frontsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f785]) ).
fof(f788,definition,
( sQ46_spl
<=> sk2 = sk2 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f799,plain,
! [X0,X1,X2] :
( X0 = skac3
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(skac3,X2)) ),
inference(resolution,[status(thm)],[f413,f209]) ).
fof(f800,plain,
! [X0,X1,X2] :
( X0 = skac2
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(skac2,X2)) ),
inference(resolution,[status(thm)],[f413,f210]) ).
fof(f801,plain,
! [X0,X1,X2] :
( frontsegP(X1,X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(skac3,X2)) ),
inference(resolution,[status(thm)],[f409,f209]) ).
fof(f802,plain,
! [X0,X1,X2] :
( frontsegP(X1,X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(skac2,X2)) ),
inference(resolution,[status(thm)],[f409,f210]) ).
fof(f803,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf44(X2),X3)) ),
inference(resolution,[status(thm)],[f247,f409]) ).
fof(f804,plain,
! [X0,X1,X2,X3] :
( X0 = skaf44(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf44(X2),X3)) ),
inference(resolution,[status(thm)],[f247,f413]) ).
fof(f805,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf49(X2),X3)) ),
inference(resolution,[status(thm)],[f246,f409]) ).
fof(f806,plain,
! [X0,X1,X2,X3] :
( X0 = skaf49(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf49(X2),X3)) ),
inference(resolution,[status(thm)],[f246,f413]) ).
fof(f807,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf50(X2),X3)) ),
inference(resolution,[status(thm)],[f245,f409]) ).
fof(f808,plain,
! [X0,X1,X2,X3] :
( X0 = skaf50(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf50(X2),X3)) ),
inference(resolution,[status(thm)],[f245,f413]) ).
fof(f811,plain,
! [X0] :
( ~ sQ29_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ segmentP(X0,sk2) ),
inference(resolution,[status(thm)],[f647,f375]) ).
fof(f813,definition,
! [X0] :
( sQ47_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f816,plain,
( ~ sQ29_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f811,f813,f534,f560,f646]) ).
fof(f823,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf54(X2),X3)) ),
inference(resolution,[status(thm)],[f241,f409]) ).
fof(f824,plain,
! [X0,X1,X2,X3] :
( X0 = skaf54(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf54(X2),X3)) ),
inference(resolution,[status(thm)],[f241,f413]) ).
fof(f825,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf55(X2),X3)) ),
inference(resolution,[status(thm)],[f240,f409]) ).
fof(f826,plain,
! [X0,X1,X2,X3] :
( X0 = skaf55(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf55(X2),X3)) ),
inference(resolution,[status(thm)],[f240,f413]) ).
fof(f827,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf59(X2),X3)) ),
inference(resolution,[status(thm)],[f236,f409]) ).
fof(f828,plain,
! [X0,X1,X2,X3] :
( X0 = skaf59(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf59(X2),X3)) ),
inference(resolution,[status(thm)],[f236,f413]) ).
fof(f842,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f759,f260]) ).
fof(f846,definition,
! [X0] :
( sQ49_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f847,plain,
! [X0] :
( ~ sQ49_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f846]) ).
fof(f849,plain,
( ~ sQ41_spl
| sQ49_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f842,f534,f846,f745]) ).
fof(f851,plain,
! [X0] :
( ~ sQ49_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f847]) ).
fof(f858,plain,
( ~ sQ4_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f461,f851]) ).
fof(f889,plain,
( ~ sQ4_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f858]) ).
fof(f897,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f274,f208]) ).
fof(f898,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[f274,f432]) ).
fof(f899,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[f274,f431]) ).
fof(f900,plain,
( ~ sQ4_spl
| app(sk5,nil) = sk5 ),
inference(resolution,[status(thm)],[f274,f461]) ).
fof(f902,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[f275,f432]) ).
fof(f903,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[f275,f431]) ).
fof(f904,plain,
( ~ sQ4_spl
| app(nil,sk5) = sk5 ),
inference(resolution,[status(thm)],[f275,f461]) ).
fof(f906,plain,
! [X0] :
( app(tl(X0),nil) = tl(X0)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f276,f274]) ).
fof(f907,plain,
! [X0] :
( frontsegP(sk2,X0)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f898,f352]) ).
fof(f908,definition,
! [X0] :
( sQ50_spl
<=> ( frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f911,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f907,f908,f534,f560]) ).
fof(f912,plain,
! [X0] :
( frontsegP(sk1,X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f899,f352]) ).
fof(f913,definition,
! [X0] :
( sQ51_spl
<=> ( frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f912,f913,f534,f634]) ).
fof(f920,plain,
( frontsegP(app(sk1,nil),sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f899,f510]) ).
fof(f921,plain,
( frontsegP(app(sk2,nil),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f898,f510]) ).
fof(f922,definition,
( sQ52_spl
<=> frontsegP(app(sk1,nil),sk1) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f923,plain,
( ~ sQ52_spl
| frontsegP(app(sk1,nil),sk1) ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f925,plain,
( sQ52_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f920,f534,f634,f922]) ).
fof(f926,definition,
( sQ53_spl
<=> frontsegP(app(sk2,nil),sk2) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( ~ sQ53_spl
| frontsegP(app(sk2,nil),sk2) ),
inference(component_clause,[status(thm)],[f926]) ).
fof(f929,plain,
( sQ53_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f921,f534,f560,f926]) ).
fof(f930,plain,
( ~ sQ52_spl
| frontsegP(sk1,sk1) ),
inference(forward_demodulation,[status(thm)],[f899,f923]) ).
fof(f931,plain,
( ~ sQ53_spl
| frontsegP(sk2,sk2) ),
inference(forward_demodulation,[status(thm)],[f898,f927]) ).
fof(f935,definition,
( sQ54_spl
<=> frontsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f937,plain,
( sQ54_spl
| ~ frontsegP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f938,definition,
( sQ55_spl
<=> sk1 = sk1 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( sQ54_spl
| ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f937,f930]) ).
fof(f943,plain,
( sQ54_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f942]) ).
fof(f944,plain,
( ~ sQ4_spl
| frontsegP(app(sk5,nil),sk5)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f900,f510]) ).
fof(f945,plain,
! [X0] :
( ~ sQ4_spl
| frontsegP(sk5,X0)
| ~ ssList(sk5)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk5,X0) ),
inference(paramodulation,[status(thm)],[f900,f352]) ).
fof(f946,definition,
( sQ56_spl
<=> frontsegP(app(sk5,nil),sk5) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( ~ sQ56_spl
| frontsegP(app(sk5,nil),sk5) ),
inference(component_clause,[status(thm)],[f946]) ).
fof(f949,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f944,f534,f460,f946]) ).
fof(f950,definition,
! [X0] :
( sQ57_spl
<=> ( frontsegP(sk5,X0)
| ~ ssList(X0)
| ~ frontsegP(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f945,f950,f534,f460]) ).
fof(f954,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| frontsegP(sk5,sk5) ),
inference(forward_demodulation,[status(thm)],[f900,f947]) ).
fof(f957,plain,
( sQ45_spl
| ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f931]) ).
fof(f958,plain,
( sQ45_spl
| ~ sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f957]) ).
fof(f960,definition,
( sQ58_spl
<=> frontsegP(sk5,sk5) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( sQ58_spl
| ~ frontsegP(sk5,sk5) ),
inference(component_clause,[status(thm)],[f960]) ).
fof(f963,definition,
( sQ59_spl
<=> sk5 = sk5 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f967,plain,
( sQ58_spl
| ~ sQ56_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f962,f954]) ).
fof(f968,plain,
( sQ58_spl
| ~ sQ56_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f967]) ).
fof(f979,plain,
rearsegP(nil,nil),
inference(forward_subsumption_resolution,[status(thm)],[f496,f208]) ).
fof(f982,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f510,f286]) ).
fof(f983,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ssList(app(tl(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f286,f276]) ).
fof(f984,plain,
! [X0] :
( ssList(app(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f286,f208]) ).
fof(f985,plain,
! [X0] :
( ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f286,f432]) ).
fof(f986,plain,
! [X0] :
( ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f286,f431]) ).
fof(f988,plain,
! [X0] :
( frontsegP(sk2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f902,f352]) ).
fof(f989,definition,
! [X0] :
( sQ60_spl
<=> ( frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f990,plain,
! [X0] :
( ~ sQ60_spl
| frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f989]) ).
fof(f992,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f988,f989,f560,f534]) ).
fof(f993,plain,
! [X0] :
( frontsegP(sk1,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f903,f352]) ).
fof(f994,definition,
! [X0] :
( sQ61_spl
<=> ( frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f995,plain,
! [X0] :
( ~ sQ61_spl
| frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f993,f994,f634,f534]) ).
fof(f1006,plain,
! [X0] :
( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f903,f513]) ).
fof(f1007,plain,
! [X0] :
( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f902,f513]) ).
fof(f1008,plain,
! [X0] :
( ~ sQ4_spl
| segmentP(app(app(sk5,nil),X0),nil)
| ~ ssList(app(sk5,X0))
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f900,f513]) ).
fof(f1009,plain,
! [X0] :
( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f899,f513]) ).
fof(f1010,plain,
! [X0] :
( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f898,f513]) ).
fof(f1011,definition,
! [X0] :
( sQ62_spl
<=> ( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1012,plain,
! [X0] :
( ~ sQ62_spl
| segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1011]) ).
fof(f1014,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1006,f1011,f534,f634]) ).
fof(f1015,definition,
! [X0] :
( sQ63_spl
<=> ( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1016,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1007,f1015,f534,f560]) ).
fof(f1019,definition,
! [X0] :
( sQ64_spl
<=> ( segmentP(app(app(sk5,nil),X0),nil)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1022,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f1008,f1019,f460,f534]) ).
fof(f1023,definition,
! [X0] :
( sQ65_spl
<=> ( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1009,f1023,f634,f534]) ).
fof(f1027,definition,
! [X0] :
( sQ66_spl
<=> ( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1010,f1027,f560,f534]) ).
fof(f1031,plain,
! [X0] :
( ~ sQ62_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f903,f1012]) ).
fof(f1032,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f902,f1016]) ).
fof(f1036,plain,
! [X0,X1] :
( ssList(app(skaf51(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f244,f286]) ).
fof(f1037,plain,
! [X0] : app(nil,skaf51(X0)) = skaf51(X0),
inference(resolution,[status(thm)],[f244,f275]) ).
fof(f1038,plain,
! [X0] : app(skaf51(X0),nil) = skaf51(X0),
inference(resolution,[status(thm)],[f244,f274]) ).
fof(f1039,plain,
! [X0,X1] :
( ssList(app(skaf52(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f243,f286]) ).
fof(f1040,plain,
! [X0] : app(nil,skaf52(X0)) = skaf52(X0),
inference(resolution,[status(thm)],[f243,f275]) ).
fof(f1041,plain,
! [X0] : app(skaf52(X0),nil) = skaf52(X0),
inference(resolution,[status(thm)],[f243,f274]) ).
fof(f1042,plain,
! [X0,X1] :
( ssList(app(skaf53(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f242,f286]) ).
fof(f1043,plain,
! [X0] : app(nil,skaf53(X0)) = skaf53(X0),
inference(resolution,[status(thm)],[f242,f275]) ).
fof(f1044,plain,
! [X0] : app(skaf53(X0),nil) = skaf53(X0),
inference(resolution,[status(thm)],[f242,f274]) ).
fof(f1048,plain,
! [X0] :
( ~ sQ4_spl
| segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f904,f513]) ).
fof(f1049,plain,
! [X0] :
( ~ sQ4_spl
| frontsegP(sk5,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f904,f352]) ).
fof(f1050,definition,
! [X0] :
( sQ67_spl
<=> ( segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1051,plain,
! [X0] :
( ~ sQ67_spl
| segmentP(app(app(nil,sk5),X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1050]) ).
fof(f1053,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1048,f1050,f534,f460]) ).
fof(f1054,definition,
! [X0] :
( sQ68_spl
<=> ( frontsegP(sk5,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1055,plain,
! [X0] :
( ~ sQ68_spl
| frontsegP(sk5,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1054]) ).
fof(f1057,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1049,f1054,f460,f534]) ).
fof(f1058,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ4_spl
| segmentP(app(sk5,X0),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f904,f1051]) ).
fof(f1064,plain,
! [X0] :
( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f897,f513]) ).
fof(f1065,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f897,f352]) ).
fof(f1066,definition,
! [X0] :
( sQ69_spl
<=> ( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1069,plain,
( ~ sQ13_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1064,f1066,f534]) ).
fof(f1070,definition,
! [X0] :
( sQ70_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1073,plain,
( ~ sQ13_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1065,f1070,f534]) ).
fof(f1075,plain,
! [X0,X1] :
( ~ sQ29_spl
| segmentP(app(app(X1,sk2),X0),nil)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f405,f647]) ).
fof(f1076,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f405,f256]) ).
fof(f1077,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f405,f257]) ).
fof(f1078,definition,
! [X0,X1] :
( sQ71_spl
<=> ( segmentP(app(app(X1,sk2),X0),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1081,plain,
( ~ sQ29_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1075,f1078,f534,f560,f646]) ).
fof(f1082,definition,
! [X0,X1,X2] :
( sQ72_spl
<=> ( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1083,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1082]) ).
fof(f1085,plain,
( ~ sQ13_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1076,f1082,f534]) ).
fof(f1086,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1077]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1083]) ).
fof(f1093,plain,
! [X0,X1] :
( ssList(app(skaf56(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f239,f286]) ).
fof(f1094,plain,
! [X0] : app(nil,skaf56(X0)) = skaf56(X0),
inference(resolution,[status(thm)],[f239,f275]) ).
fof(f1095,plain,
! [X0] : app(skaf56(X0),nil) = skaf56(X0),
inference(resolution,[status(thm)],[f239,f274]) ).
fof(f1096,plain,
! [X0,X1] :
( ssList(app(skaf57(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f238,f286]) ).
fof(f1097,plain,
! [X0] : app(nil,skaf57(X0)) = skaf57(X0),
inference(resolution,[status(thm)],[f238,f275]) ).
fof(f1098,plain,
! [X0] : app(skaf57(X0),nil) = skaf57(X0),
inference(resolution,[status(thm)],[f238,f274]) ).
fof(f1099,plain,
! [X0,X1] :
( ssList(app(skaf58(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f237,f286]) ).
fof(f1100,plain,
! [X0] : app(nil,skaf58(X0)) = skaf58(X0),
inference(resolution,[status(thm)],[f237,f275]) ).
fof(f1101,plain,
! [X0] : app(skaf58(X0),nil) = skaf58(X0),
inference(resolution,[status(thm)],[f237,f274]) ).
fof(f1138,plain,
! [X0,X1] :
( ssList(app(skaf61(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f234,f286]) ).
fof(f1139,plain,
! [X0] : app(nil,skaf61(X0)) = skaf61(X0),
inference(resolution,[status(thm)],[f234,f275]) ).
fof(f1140,plain,
! [X0] : app(skaf61(X0),nil) = skaf61(X0),
inference(resolution,[status(thm)],[f234,f274]) ).
fof(f1141,plain,
! [X0,X1] :
( ssList(app(skaf62(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f233,f286]) ).
fof(f1142,plain,
! [X0] : app(nil,skaf62(X0)) = skaf62(X0),
inference(resolution,[status(thm)],[f233,f275]) ).
fof(f1143,plain,
! [X0] : app(skaf62(X0),nil) = skaf62(X0),
inference(resolution,[status(thm)],[f233,f274]) ).
fof(f1144,plain,
! [X0,X1] :
( ssList(app(skaf63(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f232,f286]) ).
fof(f1145,plain,
! [X0] : app(nil,skaf63(X0)) = skaf63(X0),
inference(resolution,[status(thm)],[f232,f275]) ).
fof(f1146,plain,
! [X0] : app(skaf63(X0),nil) = skaf63(X0),
inference(resolution,[status(thm)],[f232,f274]) ).
fof(f1183,plain,
! [X0,X1] :
( app(X1,X0) = X1
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ frontsegP(X1,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f982,f342]) ).
fof(f1184,plain,
( frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f897,f982]) ).
fof(f1187,plain,
( frontsegP(sk2,nil)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f902,f982]) ).
fof(f1191,plain,
! [X0,X1] :
( app(X1,X0) = X1
| ~ ssList(app(X1,X0))
| ~ frontsegP(X1,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1183]) ).
fof(f1192,plain,
! [X0,X1] :
( app(X1,X0) = X1
| ~ frontsegP(X1,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1191,f286]) ).
fof(f1193,definition,
( sQ77_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1194,plain,
( ~ sQ77_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1193]) ).
fof(f1196,plain,
( sQ77_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1184,f534,f1193]) ).
fof(f1197,definition,
( sQ78_spl
<=> frontsegP(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1198,plain,
( ~ sQ78_spl
| frontsegP(sk5,nil) ),
inference(component_clause,[status(thm)],[f1197]) ).
fof(f1201,definition,
( sQ79_spl
<=> frontsegP(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( ~ sQ79_spl
| frontsegP(sk1,nil) ),
inference(component_clause,[status(thm)],[f1201]) ).
fof(f1205,definition,
( sQ80_spl
<=> frontsegP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( ~ sQ80_spl
| frontsegP(sk2,nil) ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1208,plain,
( sQ80_spl
| ~ sQ13_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1187,f560,f534,f1205]) ).
fof(f1212,plain,
! [X0,X1] :
( ssList(app(skaf66(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f229,f286]) ).
fof(f1213,plain,
! [X0] : app(nil,skaf66(X0)) = skaf66(X0),
inference(resolution,[status(thm)],[f229,f275]) ).
fof(f1214,plain,
! [X0] : app(skaf66(X0),nil) = skaf66(X0),
inference(resolution,[status(thm)],[f229,f274]) ).
fof(f1215,plain,
! [X0,X1] :
( ssList(app(skaf67(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f228,f286]) ).
fof(f1216,plain,
! [X0] : app(nil,skaf67(X0)) = skaf67(X0),
inference(resolution,[status(thm)],[f228,f275]) ).
fof(f1217,plain,
! [X0] : app(skaf67(X0),nil) = skaf67(X0),
inference(resolution,[status(thm)],[f228,f274]) ).
fof(f1218,plain,
! [X0,X1] :
( ssList(app(skaf68(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f227,f286]) ).
fof(f1219,plain,
! [X0] : app(nil,skaf68(X0)) = skaf68(X0),
inference(resolution,[status(thm)],[f227,f275]) ).
fof(f1220,plain,
! [X0] : app(skaf68(X0),nil) = skaf68(X0),
inference(resolution,[status(thm)],[f227,f274]) ).
fof(f1224,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| tl(cons(hd(X1),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f297,f277]) ).
fof(f1239,plain,
! [X0,X1] :
( hd(cons(skaf83(X1),X0)) = skaf83(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f212]) ).
fof(f1242,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| hd(cons(hd(X1),X0)) = hd(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f277]) ).
fof(f1279,plain,
! [X0,X1,X2] :
( app(X0,X2) = X1
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f286]) ).
fof(f1284,plain,
! [X0] :
( app(nil,nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f897,f1279]) ).
fof(f1285,plain,
! [X0] :
( ~ sQ4_spl
| app(nil,sk5) = X0
| ~ frontsegP(X0,sk5)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f904,f1279]) ).
fof(f1286,plain,
! [X0] :
( app(nil,sk1) = X0
| ~ frontsegP(X0,sk1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f903,f1279]) ).
fof(f1287,plain,
! [X0] :
( app(nil,sk2) = X0
| ~ frontsegP(X0,sk2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f902,f1279]) ).
fof(f1288,plain,
! [X0] :
( ~ sQ4_spl
| app(sk5,nil) = X0
| ~ frontsegP(X0,sk5)
| ~ ssList(sk5)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk5,X0) ),
inference(paramodulation,[status(thm)],[f900,f1279]) ).
fof(f1289,plain,
! [X0] :
( app(sk1,nil) = X0
| ~ frontsegP(X0,sk1)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f899,f1279]) ).
fof(f1290,plain,
! [X0] :
( app(sk2,nil) = X0
| ~ frontsegP(X0,sk2)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f898,f1279]) ).
fof(f1295,definition,
! [X0] :
( sQ82_spl
<=> ( app(nil,nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1298,plain,
( ~ sQ13_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1284,f1295,f534]) ).
fof(f1299,definition,
! [X0] :
( sQ83_spl
<=> ( app(nil,sk5) = X0
| ~ frontsegP(X0,sk5)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1285,f1299,f460,f534]) ).
fof(f1303,definition,
! [X0] :
( sQ84_spl
<=> ( app(nil,sk1) = X0
| ~ frontsegP(X0,sk1)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1286,f1303,f634,f534]) ).
fof(f1307,definition,
! [X0] :
( sQ85_spl
<=> ( app(nil,sk2) = X0
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1310,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1287,f1307,f560,f534]) ).
fof(f1311,definition,
! [X0] :
( sQ86_spl
<=> ( app(sk5,nil) = X0
| ~ frontsegP(X0,sk5)
| ~ ssList(X0)
| ~ frontsegP(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1314,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1288,f1311,f534,f460]) ).
fof(f1315,definition,
! [X0] :
( sQ87_spl
<=> ( app(sk1,nil) = X0
| ~ frontsegP(X0,sk1)
| ~ ssList(X0)
| ~ frontsegP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1318,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1289,f1315,f534,f634]) ).
fof(f1319,definition,
! [X0] :
( sQ88_spl
<=> ( app(sk2,nil) = X0
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1290,f1319,f534,f560]) ).
fof(f1331,plain,
! [X0] :
( ~ sQ77_spl
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f682,f1194]) ).
fof(f1335,plain,
! [X0] :
( ~ sQ56_spl
| ~ sQ4_spl
| X0 = sk5
| ~ frontsegP(sk5,X0)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ frontsegP(X0,sk5) ),
inference(resolution,[status(thm)],[f682,f954]) ).
fof(f1339,plain,
! [X0] :
( ~ sQ79_spl
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f682,f1202]) ).
fof(f1341,plain,
! [X0] :
( ~ sQ52_spl
| X0 = sk1
| ~ frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ frontsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f682,f930]) ).
fof(f1343,plain,
! [X0] :
( ~ sQ80_spl
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f682,f1206]) ).
fof(f1345,plain,
! [X0] :
( ~ sQ53_spl
| X0 = sk2
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f682,f931]) ).
fof(f1348,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f682,f260]) ).
fof(f1368,definition,
! [X0] :
( sQ89_spl
<=> ( X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1371,plain,
( ~ sQ77_spl
| ~ sQ13_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1331,f1368,f534,f1193]) ).
fof(f1374,definition,
! [X0] :
( sQ90_spl
<=> ( X0 = sk5
| ~ frontsegP(sk5,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1335,f1374,f460,f946]) ).
fof(f1382,definition,
! [X0] :
( sQ91_spl
<=> ( X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1385,plain,
( ~ sQ79_spl
| ~ sQ26_spl
| ~ sQ13_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1339,f1382,f534,f634,f1201]) ).
fof(f1387,definition,
! [X0] :
( sQ92_spl
<=> ( X0 = sk1
| ~ frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1390,plain,
( ~ sQ52_spl
| ~ sQ26_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1341,f1387,f634,f922]) ).
fof(f1395,definition,
! [X0] :
( sQ94_spl
<=> ( X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1343,f1395,f534,f560,f1205]) ).
fof(f1400,definition,
! [X0] :
( sQ95_spl
<=> ( X0 = sk2
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1403,plain,
( ~ sQ53_spl
| ~ sQ15_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1345,f1400,f560,f926]) ).
fof(f1409,definition,
! [X0,X1] :
( sQ97_spl
<=> ( ~ ssList(X1)
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ13_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1348,f1409,f534]) ).
fof(f1444,plain,
! [X0] : app(nil,skaf71(X0)) = skaf71(X0),
inference(resolution,[status(thm)],[f224,f275]) ).
fof(f1445,plain,
! [X0] : app(skaf71(X0),nil) = skaf71(X0),
inference(resolution,[status(thm)],[f224,f274]) ).
fof(f1490,plain,
! [X0] :
( ~ sQ78_spl
| nil = sk5
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ frontsegP(X0,sk5)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f1198,f682]) ).
fof(f1491,plain,
! [X0] :
( ~ sQ78_spl
| X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ frontsegP(X0,sk5) ),
inference(resolution,[status(thm)],[f1198,f682]) ).
fof(f1492,plain,
( ~ sQ78_spl
| sk5 = nil
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ frontsegP(nil,sk5) ),
inference(resolution,[status(thm)],[f1198,f342]) ).
fof(f1495,definition,
! [X0] :
( sQ102_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(X0,sk5)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1498,plain,
( ~ sQ78_spl
| sQ21_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1490,f1495,f460,f534,f591,f1197]) ).
fof(f1499,definition,
! [X0] :
( sQ103_spl
<=> ( X0 = nil
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1502,plain,
( ~ sQ78_spl
| ~ sQ4_spl
| ~ sQ13_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1491,f1499,f534,f460,f1197]) ).
fof(f1503,definition,
( sQ104_spl
<=> frontsegP(nil,sk5) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
( ~ sQ78_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f1492,f1503,f534,f460,f591,f1197]) ).
fof(f1507,plain,
( ~ sQ6_spl
| ~ sQ21_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f645]) ).
fof(f1508,plain,
( ~ sQ6_spl
| ~ sQ21_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1507]) ).
fof(f1511,plain,
! [X0,X1] :
( ~ sQ60_spl
| app(X0,X1) = sk2
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ frontsegP(X0,sk2)
| ~ ssList(app(X0,X1))
| ~ frontsegP(nil,app(X0,X1)) ),
inference(resolution,[status(thm)],[f990,f1279]) ).
fof(f1513,plain,
! [X0,X1] :
( ~ sQ60_spl
| X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ frontsegP(X1,sk2)
| ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f990,f682]) ).
fof(f1515,plain,
! [X0,X1] :
( ~ sQ60_spl
| X1 = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ frontsegP(X1,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f990,f682]) ).
fof(f1516,plain,
! [X0] :
( ~ sQ60_spl
| sk2 = X0
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f990,f342]) ).
fof(f1517,definition,
! [X0,X1] :
( sQ105_spl
<=> ( app(X0,X1) = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk2)
| ~ ssList(app(X0,X1))
| ~ frontsegP(nil,app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1520,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1511,f1517,f560,f989]) ).
fof(f1522,definition,
! [X0,X1] :
( sQ106_spl
<=> ( X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,sk2)
| ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1513,f1522,f560,f989]) ).
fof(f1527,definition,
! [X0,X1] :
( sQ107_spl
<=> ( X1 = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1515,f1527,f560,f989]) ).
fof(f1531,definition,
! [X0] :
( sQ108_spl
<=> ( sk2 = X0
| ~ ssList(X0)
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1534,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1516,f1531,f560,f989]) ).
fof(f1540,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(nil)
| nil = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f683,f260]) ).
fof(f1541,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ frontsegP(X2,X0)
| ~ frontsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f683,f379]) ).
fof(f1543,definition,
! [X0] :
( sQ109_spl
<=> ( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1547,plain,
( ~ sQ35_spl
| ~ sQ13_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1540,f1543,f534,f678]) ).
fof(f1548,definition,
! [X0,X1,X2] :
( sQ110_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ frontsegP(X2,X0)
| ~ frontsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1551,plain,
( ~ sQ35_spl
| ~ sQ13_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1541,f1548,f534,f678]) ).
fof(f1554,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| segmentP(X2,nil)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(X2,app(app(X1,sk2),X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f707,f647]) ).
fof(f1555,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| segmentP(X3,nil)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f707,f256]) ).
fof(f1557,definition,
! [X0,X1,X2] :
( sQ111_spl
<=> ( segmentP(X2,nil)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(X2,app(app(X1,sk2),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
( ~ sQ29_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1554,f1557,f534,f560,f646]) ).
fof(f1561,definition,
! [X0,X1,X2,X3] :
( sQ112_spl
<=> ( ~ ssList(X2)
| segmentP(X3,nil)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1564,plain,
( ~ sQ13_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1555,f1561,f534]) ).
fof(f1601,plain,
( nil = sk2
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(resolution,[status(thm)],[f307,f432]) ).
fof(f1603,plain,
( ~ sQ4_spl
| nil = sk5
| cons(hd(sk5),tl(sk5)) = sk5 ),
inference(resolution,[status(thm)],[f307,f461]) ).
fof(f1609,definition,
( sQ114_spl
<=> cons(hd(sk2),tl(sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1610,plain,
( ~ sQ114_spl
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(component_clause,[status(thm)],[f1609]) ).
fof(f1612,plain,
( sQ9_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1601,f1609,f479]) ).
fof(f1617,definition,
( sQ116_spl
<=> cons(hd(sk5),tl(sk5)) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1618,plain,
( ~ sQ116_spl
| cons(hd(sk5),tl(sk5)) = sk5 ),
inference(component_clause,[status(thm)],[f1617]) ).
fof(f1620,plain,
( ~ sQ4_spl
| sQ21_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1603,f1617,f591,f460]) ).
fof(f1625,plain,
! [X0,X1] :
( ~ sQ29_spl
| app(app(X1,sk2),X0) = nil
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(nil,app(app(X1,sk2),X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f708,f647]) ).
fof(f1626,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| app(app(X1,X2),X0) = nil
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(nil,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f708,f256]) ).
fof(f1628,definition,
! [X0,X1] :
( sQ117_spl
<=> ( app(app(X1,sk2),X0) = nil
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(nil,app(app(X1,sk2),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1631,plain,
( ~ sQ29_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1625,f1628,f534,f560,f646]) ).
fof(f1632,definition,
! [X0,X1,X2] :
( sQ118_spl
<=> ( ~ ssList(X2)
| app(app(X1,X2),X0) = nil
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(nil,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1635,plain,
( ~ sQ13_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1626,f1632,f534]) ).
fof(f1638,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X3,X1))
| ~ ssList(X4)
| ~ frontsegP(X4,cons(X2,X0))
| ~ frontsegP(cons(X3,X1),X4)
| frontsegP(X1,X0)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f722,f287]) ).
fof(f1658,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),tl(sk5)),X2)
| frontsegP(tl(sk5),X0)
| ~ ssItem(hd(sk5))
| ~ ssItem(X1)
| ~ ssList(tl(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1618,f1638]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ sQ116_spl
| X0 = hd(sk5)
| ~ ssItem(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(X1)
| ~ ssList(tl(sk5))
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f1618,f413]) ).
fof(f1661,plain,
! [X0,X1] :
( ~ sQ116_spl
| hd(sk5) = X0
| ~ ssItem(hd(sk5))
| ~ ssItem(X0)
| ~ ssList(tl(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1618,f413]) ).
fof(f1662,plain,
! [X0] :
( ~ sQ116_spl
| frontsegP(cons(hd(sk5),X0),sk5)
| ~ ssItem(hd(sk5))
| ~ ssList(X0)
| ~ ssList(tl(sk5))
| ~ frontsegP(X0,tl(sk5)) ),
inference(paramodulation,[status(thm)],[f1618,f516]) ).
fof(f1663,plain,
! [X0] :
( ~ sQ116_spl
| frontsegP(sk5,cons(hd(sk5),X0))
| ~ ssItem(hd(sk5))
| ~ ssList(tl(sk5))
| ~ ssList(X0)
| ~ frontsegP(tl(sk5),X0) ),
inference(paramodulation,[status(thm)],[f1618,f516]) ).
fof(f1664,plain,
! [X0,X1] :
( ~ sQ116_spl
| frontsegP(X1,tl(sk5))
| ~ ssItem(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(X1)
| ~ ssList(tl(sk5))
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f1618,f409]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ sQ116_spl
| frontsegP(tl(sk5),X1)
| ~ ssItem(hd(sk5))
| ~ ssItem(X0)
| ~ ssList(tl(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1618,f409]) ).
fof(f1666,definition,
! [X0,X1,X2] :
( sQ119_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),tl(sk5)),X2)
| frontsegP(tl(sk5),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1669,definition,
( sQ120_spl
<=> ssList(tl(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1670,plain,
( ~ sQ120_spl
| ssList(tl(sk5)) ),
inference(component_clause,[status(thm)],[f1669]) ).
fof(f1671,plain,
( sQ120_spl
| ~ ssList(tl(sk5)) ),
inference(component_clause,[status(thm)],[f1669]) ).
fof(f1672,definition,
( sQ121_spl
<=> ssItem(hd(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1674,plain,
( sQ121_spl
| ~ ssItem(hd(sk5)) ),
inference(component_clause,[status(thm)],[f1672]) ).
fof(f1675,plain,
( ~ sQ116_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1658,f1666,f1669,f1672,f460,f1617]) ).
fof(f1677,definition,
! [X0,X1] :
( sQ122_spl
<=> ( X0 = hd(sk5)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1680,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1660,f1677,f1669,f1672,f1617]) ).
fof(f1681,definition,
! [X0,X1] :
( sQ123_spl
<=> ( hd(sk5) = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1684,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1661,f1681,f1669,f1672,f1617]) ).
fof(f1685,definition,
! [X0] :
( sQ124_spl
<=> ( frontsegP(cons(hd(sk5),X0),sk5)
| ~ ssList(X0)
| ~ frontsegP(X0,tl(sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1688,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1662,f1685,f1669,f1672,f1617]) ).
fof(f1689,definition,
! [X0] :
( sQ125_spl
<=> ( frontsegP(sk5,cons(hd(sk5),X0))
| ~ ssList(X0)
| ~ frontsegP(tl(sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1692,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1663,f1689,f1669,f1672,f1617]) ).
fof(f1693,definition,
! [X0,X1] :
( sQ126_spl
<=> ( frontsegP(X1,tl(sk5))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1696,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1664,f1693,f1669,f1672,f1617]) ).
fof(f1697,definition,
! [X0,X1] :
( sQ127_spl
<=> ( frontsegP(tl(sk5),X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1700,plain,
( ~ sQ116_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1665,f1697,f1669,f1672,f1617]) ).
fof(f1701,plain,
( sQ121_spl
| nil = sk5
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f1674,f277]) ).
fof(f1702,plain,
( sQ121_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1701,f460,f591,f1672]) ).
fof(f1703,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(cons(X3,X1))
| ~ ssList(X4)
| ~ frontsegP(X4,cons(X2,X0))
| ~ frontsegP(cons(X3,X1),X4)
| X3 = X2
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f725,f287]) ).
fof(f1705,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),tl(sk5)),X2)
| hd(sk5) = X1
| ~ ssItem(hd(sk5))
| ~ ssItem(X1)
| ~ ssList(tl(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1618,f1703]) ).
fof(f1707,definition,
! [X0,X1,X2] :
( sQ128_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),tl(sk5)),X2)
| hd(sk5) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( ~ sQ116_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f1705,f1707,f1669,f1672,f460,f1617]) ).
fof(f1711,plain,
! [X0,X1,X2] :
( cons(X2,X0) = cons(X2,X1)
| ~ ssList(cons(X2,X0))
| ~ frontsegP(cons(X2,X1),cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f744,f287]) ).
fof(f1713,plain,
! [X0] :
( ~ sQ116_spl
| cons(hd(sk5),tl(sk5)) = cons(hd(sk5),X0)
| ~ ssList(sk5)
| ~ frontsegP(cons(hd(sk5),X0),cons(hd(sk5),tl(sk5)))
| ~ ssItem(hd(sk5))
| ~ ssList(tl(sk5))
| ~ ssList(X0)
| ~ frontsegP(tl(sk5),X0) ),
inference(paramodulation,[status(thm)],[f1618,f1711]) ).
fof(f1715,definition,
! [X0] :
( sQ129_spl
<=> ( cons(hd(sk5),tl(sk5)) = cons(hd(sk5),X0)
| ~ frontsegP(cons(hd(sk5),X0),cons(hd(sk5),tl(sk5)))
| ~ ssList(X0)
| ~ frontsegP(tl(sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1718,plain,
( ~ sQ116_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ120_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1713,f1715,f1669,f1672,f460,f1617]) ).
fof(f1757,plain,
( nil = sk2
| cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
inference(resolution,[status(thm)],[f312,f432]) ).
fof(f1759,plain,
( ~ sQ4_spl
| nil = sk5
| cons(skaf83(sk5),skaf82(sk5)) = sk5 ),
inference(resolution,[status(thm)],[f312,f461]) ).
fof(f1765,definition,
( sQ131_spl
<=> cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1766,plain,
( ~ sQ131_spl
| cons(skaf83(sk2),skaf82(sk2)) = sk2 ),
inference(component_clause,[status(thm)],[f1765]) ).
fof(f1768,plain,
( sQ9_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1757,f1765,f479]) ).
fof(f1773,definition,
( sQ133_spl
<=> cons(skaf83(sk5),skaf82(sk5)) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1774,plain,
( ~ sQ133_spl
| cons(skaf83(sk5),skaf82(sk5)) = sk5 ),
inference(component_clause,[status(thm)],[f1773]) ).
fof(f1776,plain,
( ~ sQ4_spl
| sQ21_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1759,f1773,f591,f460]) ).
fof(f1777,plain,
( sQ120_spl
| nil = sk5
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f1671,f276]) ).
fof(f1778,plain,
( sQ120_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1777,f460,f591,f1669]) ).
fof(f1796,definition,
( sQ135_spl
<=> ssList(tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1798,plain,
( sQ135_spl
| ~ ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f1796]) ).
fof(f1799,definition,
( sQ136_spl
<=> ssItem(hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1840,plain,
( ~ sQ120_spl
| nil = tl(sk5)
| cons(skaf83(tl(sk5)),skaf82(tl(sk5))) = tl(sk5) ),
inference(resolution,[status(thm)],[f1670,f312]) ).
fof(f1841,plain,
( ~ sQ120_spl
| nil = tl(sk5)
| cons(hd(tl(sk5)),tl(tl(sk5))) = tl(sk5) ),
inference(resolution,[status(thm)],[f1670,f307]) ).
fof(f1845,definition,
( sQ145_spl
<=> cons(skaf83(tl(sk5)),skaf82(tl(sk5))) = tl(sk5) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1848,definition,
( sQ146_spl
<=> nil = tl(sk5) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1849,plain,
( ~ sQ146_spl
| nil = tl(sk5) ),
inference(component_clause,[status(thm)],[f1848]) ).
fof(f1851,plain,
( ~ sQ120_spl
| sQ146_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1840,f1845,f1848,f1669]) ).
fof(f1852,definition,
( sQ147_spl
<=> cons(hd(tl(sk5)),tl(tl(sk5))) = tl(sk5) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1855,plain,
( ~ sQ120_spl
| sQ146_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1841,f1852,f1848,f1669]) ).
fof(f1856,plain,
! [X0,X1] :
( ~ ssItem(skac3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skac3 = skac3
| ~ ssItem(skac3)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f799,f516]) ).
fof(f1861,definition,
( sQ148_spl
<=> ssItem(skac3) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1863,plain,
( sQ148_spl
| ~ ssItem(skac3) ),
inference(component_clause,[status(thm)],[f1861]) ).
fof(f1864,definition,
( sQ149_spl
<=> skac3 = skac3 ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1867,plain,
( sQ149_spl
| ~ sQ148_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1856,f745,f1861,f1864]) ).
fof(f1887,plain,
( sQ148_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1863,f209]) ).
fof(f1888,plain,
sQ148_spl,
inference(contradiction_clause,[status(thm)],[f1887]) ).
fof(f1971,plain,
( sQ135_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f1798,f276]) ).
fof(f1972,plain,
( sQ135_spl
| sQ9_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1971,f560,f479,f1796]) ).
fof(f1977,plain,
! [X0,X1] :
( ~ ssItem(skac2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skac2 = skac2
| ~ ssItem(skac2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f800,f516]) ).
fof(f1982,definition,
( sQ168_spl
<=> ssItem(skac2) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1984,plain,
( sQ168_spl
| ~ ssItem(skac2) ),
inference(component_clause,[status(thm)],[f1982]) ).
fof(f1985,definition,
( sQ169_spl
<=> skac2 = skac2 ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1988,plain,
( sQ169_spl
| ~ sQ168_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1977,f745,f1982,f1985]) ).
fof(f2008,plain,
( sQ168_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1984,f210]) ).
fof(f2009,plain,
sQ168_spl,
inference(contradiction_clause,[status(thm)],[f2008]) ).
fof(f2012,plain,
! [X0] :
( ~ ssList(cons(skac3,X0))
| frontsegP(X0,X0)
| ~ ssItem(skac3)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f801,f261]) ).
fof(f2017,definition,
! [X0] :
( sQ175_spl
<=> ( ~ ssList(cons(skac3,X0))
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2020,plain,
( ~ sQ148_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f2012,f2017,f1861]) ).
fof(f2076,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| app(X0,nil) != nil ),
inference(resolution,[status(thm)],[f328,f208]) ).
fof(f2077,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| app(X0,sk2) != nil ),
inference(resolution,[status(thm)],[f328,f432]) ).
fof(f2078,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| app(X0,sk1) != nil ),
inference(resolution,[status(thm)],[f328,f431]) ).
fof(f2116,plain,
! [X0] :
( ~ sQ4_spl
| nil = sk5
| ~ ssList(X0)
| app(X0,sk5) != nil ),
inference(resolution,[status(thm)],[f330,f461]) ).
fof(f2130,definition,
! [X0] :
( sQ181_spl
<=> ( ~ ssList(X0)
| app(X0,sk5) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2133,plain,
( ~ sQ4_spl
| sQ21_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f2116,f2130,f591,f460]) ).
fof(f2134,plain,
! [X0] :
( ~ sQ120_spl
| nil = tl(sk5)
| ~ ssList(X0)
| app(X0,tl(sk5)) != nil ),
inference(resolution,[status(thm)],[f1670,f330]) ).
fof(f2141,definition,
! [X0] :
( sQ182_spl
<=> ( ~ ssList(X0)
| app(X0,tl(sk5)) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2144,plain,
( ~ sQ120_spl
| sQ146_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f2134,f2141,f1848,f1669]) ).
fof(f2147,plain,
! [X0] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac3,X0)) ),
inference(paramodulation,[status(thm)],[f1774,f801]) ).
fof(f2150,plain,
! [X0] :
( ~ sQ133_spl
| cons(skaf83(sk5),skaf82(sk5)) = cons(skaf83(sk5),X0)
| ~ ssList(sk5)
| ~ frontsegP(cons(skaf83(sk5),X0),cons(skaf83(sk5),skaf82(sk5)))
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk5),X0) ),
inference(paramodulation,[status(thm)],[f1774,f1711]) ).
fof(f2151,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk5),skaf82(sk5)),X2)
| skaf83(sk5) = X1
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f1703]) ).
fof(f2152,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk5),skaf82(sk5)),X2)
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f1638]) ).
fof(f2155,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = X0
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X0)
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1774,f413]) ).
fof(f2158,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(X1,skaf82(sk5))
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(skaf82(sk5))
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f1774,f409]) ).
fof(f2159,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X0)
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1774,f409]) ).
fof(f2160,definition,
! [X0] :
( sQ183_spl
<=> ( frontsegP(skaf82(sk5),X0)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac3,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2163,definition,
( sQ184_spl
<=> ssList(skaf82(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2165,plain,
( sQ184_spl
| ~ ssList(skaf82(sk5)) ),
inference(component_clause,[status(thm)],[f2163]) ).
fof(f2166,definition,
( sQ185_spl
<=> ssItem(skaf83(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2168,plain,
( sQ185_spl
| ~ ssItem(skaf83(sk5)) ),
inference(component_clause,[status(thm)],[f2166]) ).
fof(f2169,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2147,f2160,f2163,f2166,f1773]) ).
fof(f2181,definition,
! [X0] :
( sQ189_spl
<=> ( cons(skaf83(sk5),skaf82(sk5)) = cons(skaf83(sk5),X0)
| ~ frontsegP(cons(skaf83(sk5),X0),cons(skaf83(sk5),skaf82(sk5)))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2184,plain,
( ~ sQ133_spl
| ~ sQ4_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f2150,f2181,f2163,f2166,f460,f1773]) ).
fof(f2185,definition,
! [X0,X1,X2] :
( sQ190_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk5),skaf82(sk5)),X2)
| skaf83(sk5) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2188,plain,
( ~ sQ133_spl
| ~ sQ4_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f2151,f2185,f2163,f2166,f460,f1773]) ).
fof(f2189,definition,
! [X0,X1,X2] :
( sQ191_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk5),skaf82(sk5)),X2)
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2192,plain,
( ~ sQ133_spl
| ~ sQ4_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f2152,f2189,f2163,f2166,f460,f1773]) ).
fof(f2194,definition,
! [X0,X1] :
( sQ192_spl
<=> ( X0 = skaf83(sk5)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2198,definition,
! [X0,X1] :
( sQ193_spl
<=> ( skaf83(sk5) = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2201,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f2155,f2198,f2163,f2166,f1773]) ).
fof(f2202,definition,
! [X0] :
( sQ194_spl
<=> ( frontsegP(cons(skaf83(sk5),X0),sk5)
| ~ ssList(X0)
| ~ frontsegP(X0,skaf82(sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2206,definition,
! [X0] :
( sQ195_spl
<=> ( frontsegP(sk5,cons(skaf83(sk5),X0))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2210,definition,
! [X0,X1] :
( sQ196_spl
<=> ( frontsegP(X1,skaf82(sk5))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2213,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ196_spl ),
inference(split_clause,[status(thm)],[f2158,f2210,f2163,f2166,f1773]) ).
fof(f2214,definition,
! [X0,X1] :
( sQ197_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2217,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f2159,f2214,f2163,f2166,f1773]) ).
fof(f2218,plain,
( sQ185_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2168,f212]) ).
fof(f2219,plain,
sQ185_spl,
inference(contradiction_clause,[status(thm)],[f2218]) ).
fof(f2220,plain,
( sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2165,f213]) ).
fof(f2221,plain,
sQ184_spl,
inference(contradiction_clause,[status(thm)],[f2220]) ).
fof(f2256,plain,
! [X0] :
( ~ ssList(cons(skac2,X0))
| frontsegP(X0,X0)
| ~ ssItem(skac2)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f802,f261]) ).
fof(f2257,plain,
! [X0] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac2,X0)) ),
inference(paramodulation,[status(thm)],[f1774,f802]) ).
fof(f2262,definition,
! [X0] :
( sQ202_spl
<=> ( ~ ssList(cons(skac2,X0))
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2265,plain,
( ~ sQ168_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2256,f2262,f1982]) ).
fof(f2266,definition,
! [X0] :
( sQ203_spl
<=> ( frontsegP(skaf82(sk5),X0)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac2,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2269,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2257,f2266,f2163,f2166,f1773]) ).
fof(f2282,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f803]) ).
fof(f2291,definition,
! [X0,X1] :
( sQ207_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2294,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2282,f2291,f2163,f2166,f1773]) ).
fof(f2362,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f803]) ).
fof(f2363,plain,
! [X0] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X0)
| ~ frontsegP(sk2,cons(skac2,X0)) ),
inference(paramodulation,[status(thm)],[f1766,f802]) ).
fof(f2364,plain,
! [X0] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X0)
| ~ frontsegP(sk2,cons(skac3,X0)) ),
inference(paramodulation,[status(thm)],[f1766,f801]) ).
fof(f2367,plain,
! [X0] :
( ~ sQ131_spl
| cons(skaf83(sk2),skaf82(sk2)) = cons(skaf83(sk2),X0)
| ~ ssList(sk2)
| ~ frontsegP(cons(skaf83(sk2),X0),cons(skaf83(sk2),skaf82(sk2)))
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk2),X0) ),
inference(paramodulation,[status(thm)],[f1766,f1711]) ).
fof(f2368,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ ssList(sk2)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk2),skaf82(sk2)),X2)
| skaf83(sk2) = X1
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f1703]) ).
fof(f2369,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ ssList(sk2)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk2),skaf82(sk2)),X2)
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f1638]) ).
fof(f2372,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = X0
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X0)
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1766,f413]) ).
fof(f2375,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(X1,skaf82(sk2))
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ frontsegP(cons(X0,X1),sk2) ),
inference(paramodulation,[status(thm)],[f1766,f409]) ).
fof(f2376,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X0)
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1766,f409]) ).
fof(f2377,definition,
! [X0,X1] :
( sQ214_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2380,definition,
( sQ215_spl
<=> ssList(skaf82(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( sQ215_spl
| ~ ssList(skaf82(sk2)) ),
inference(component_clause,[status(thm)],[f2380]) ).
fof(f2383,definition,
( sQ216_spl
<=> ssItem(skaf83(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2385,plain,
( sQ216_spl
| ~ ssItem(skaf83(sk2)) ),
inference(component_clause,[status(thm)],[f2383]) ).
fof(f2386,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f2362,f2377,f2380,f2383,f1765]) ).
fof(f2387,definition,
! [X0] :
( sQ217_spl
<=> ( frontsegP(skaf82(sk2),X0)
| ~ ssList(X0)
| ~ frontsegP(sk2,cons(skac2,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2390,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f2363,f2387,f2380,f2383,f1765]) ).
fof(f2391,definition,
! [X0] :
( sQ218_spl
<=> ( frontsegP(skaf82(sk2),X0)
| ~ ssList(X0)
| ~ frontsegP(sk2,cons(skac3,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2394,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2364,f2391,f2380,f2383,f1765]) ).
fof(f2403,definition,
! [X0] :
( sQ221_spl
<=> ( cons(skaf83(sk2),skaf82(sk2)) = cons(skaf83(sk2),X0)
| ~ frontsegP(cons(skaf83(sk2),X0),cons(skaf83(sk2),skaf82(sk2)))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk2),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2406,plain,
( ~ sQ131_spl
| ~ sQ15_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2367,f2403,f2380,f2383,f560,f1765]) ).
fof(f2407,definition,
! [X0,X1,X2] :
( sQ222_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk2),skaf82(sk2)),X2)
| skaf83(sk2) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2410,plain,
( ~ sQ131_spl
| ~ sQ15_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f2368,f2407,f2380,f2383,f560,f1765]) ).
fof(f2411,definition,
! [X0,X1,X2] :
( sQ223_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(skaf83(sk2),skaf82(sk2)),X2)
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2414,plain,
( ~ sQ131_spl
| ~ sQ15_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f2369,f2411,f2380,f2383,f560,f1765]) ).
fof(f2416,definition,
! [X0,X1] :
( sQ224_spl
<=> ( X0 = skaf83(sk2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2420,definition,
! [X0,X1] :
( sQ225_spl
<=> ( skaf83(sk2) = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2372,f2420,f2380,f2383,f1765]) ).
fof(f2424,definition,
! [X0] :
( sQ226_spl
<=> ( frontsegP(cons(skaf83(sk2),X0),sk2)
| ~ ssList(X0)
| ~ frontsegP(X0,skaf82(sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2428,definition,
! [X0] :
( sQ227_spl
<=> ( frontsegP(sk2,cons(skaf83(sk2),X0))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk2),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2432,definition,
! [X0,X1] :
( sQ228_spl
<=> ( frontsegP(X1,skaf82(sk2))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2375,f2432,f2380,f2383,f1765]) ).
fof(f2436,definition,
! [X0,X1] :
( sQ229_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2439,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2376,f2436,f2380,f2383,f1765]) ).
fof(f2440,plain,
( sQ216_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2385,f212]) ).
fof(f2441,plain,
sQ216_spl,
inference(contradiction_clause,[status(thm)],[f2440]) ).
fof(f2442,plain,
( sQ215_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2382,f213]) ).
fof(f2443,plain,
sQ215_spl,
inference(contradiction_clause,[status(thm)],[f2442]) ).
fof(f2490,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf44(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf44(X2) = skaf44(X2)
| ~ ssItem(skaf44(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f804,f516]) ).
fof(f2493,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf44(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f804]) ).
fof(f2494,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf44(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f804]) ).
fof(f2495,definition,
! [X2] :
( sQ230_spl
<=> ( ~ ssItem(skaf44(X2))
| skaf44(X2) = skaf44(X2)
| ~ ssItem(skaf44(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2498,plain,
( sQ230_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2490,f745,f2495]) ).
fof(f2500,definition,
! [X0,X1] :
( sQ231_spl
<=> ( skaf83(sk2) = skaf44(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2503,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2493,f2500,f2380,f2383,f1765]) ).
fof(f2504,definition,
! [X0,X1] :
( sQ232_spl
<=> ( skaf83(sk5) = skaf44(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2507,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2494,f2504,f2163,f2166,f1773]) ).
fof(f2511,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f805]) ).
fof(f2512,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f805]) ).
fof(f2519,definition,
! [X0,X1] :
( sQ234_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2522,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2511,f2519,f2380,f2383,f1765]) ).
fof(f2523,definition,
! [X0,X1] :
( sQ235_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2526,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2512,f2523,f2163,f2166,f1773]) ).
fof(f2535,plain,
( ~ sQ4_spl
| hd(sk5) = hd(sk5)
| nil = sk5
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f900,f334]) ).
fof(f2554,definition,
( sQ240_spl
<=> hd(sk5) = hd(sk5) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2557,plain,
( sQ240_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2535,f534,f460,f591,f2554]) ).
fof(f2586,definition,
( sQ244_spl
<=> ssList(skaf82(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2588,plain,
( sQ244_spl
| ~ ssList(skaf82(sk1)) ),
inference(component_clause,[status(thm)],[f2586]) ).
fof(f2589,definition,
( sQ245_spl
<=> ssItem(skaf83(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2591,plain,
( sQ245_spl
| ~ ssItem(skaf83(sk1)) ),
inference(component_clause,[status(thm)],[f2589]) ).
fof(f2654,plain,
( sQ245_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2591,f212]) ).
fof(f2655,plain,
sQ245_spl,
inference(contradiction_clause,[status(thm)],[f2654]) ).
fof(f2656,plain,
( sQ244_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2588,f213]) ).
fof(f2657,plain,
sQ244_spl,
inference(contradiction_clause,[status(thm)],[f2656]) ).
fof(f2662,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf49(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf49(X2) = skaf49(X2)
| ~ ssItem(skaf49(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f806,f516]) ).
fof(f2666,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf49(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f806]) ).
fof(f2667,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf49(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f806]) ).
fof(f2668,definition,
! [X2] :
( sQ261_spl
<=> ( ~ ssItem(skaf49(X2))
| skaf49(X2) = skaf49(X2)
| ~ ssItem(skaf49(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2671,plain,
( sQ261_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2662,f745,f2668]) ).
fof(f2677,definition,
! [X0,X1] :
( sQ263_spl
<=> ( skaf83(sk2) = skaf49(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2680,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f2666,f2677,f2380,f2383,f1765]) ).
fof(f2681,definition,
! [X0,X1] :
( sQ264_spl
<=> ( skaf83(sk5) = skaf49(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2684,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f2667,f2681,f2163,f2166,f1773]) ).
fof(f2689,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f807]) ).
fof(f2690,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f807]) ).
fof(f2701,definition,
! [X0,X1] :
( sQ267_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2704,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f2689,f2701,f2380,f2383,f1765]) ).
fof(f2705,definition,
! [X0,X1] :
( sQ268_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f2708,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f2690,f2705,f2163,f2166,f1773]) ).
fof(f2750,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f341,f258]) ).
fof(f2752,definition,
( sQ269_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2756,definition,
! [X0] :
( sQ270_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2759,plain,
( ~ sQ13_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2750,f2756,f534]) ).
fof(f2766,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| cons(hd(sk5),nil) = sk5 ),
inference(forward_demodulation,[status(thm)],[f1849,f1618]) ).
fof(f2767,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| singletonP(sk5)
| ~ ssList(cons(hd(sk5),nil))
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f504]) ).
fof(f2768,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| cyclefreeP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f270]) ).
fof(f2769,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| totalorderP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f269]) ).
fof(f2770,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| strictorderP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f268]) ).
fof(f2771,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| totalorderedP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f267]) ).
fof(f2772,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| strictorderedP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f266]) ).
fof(f2773,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| duplicatefreeP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f265]) ).
fof(f2774,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| equalelemsP(sk5)
| ~ ssItem(hd(sk5)) ),
inference(paramodulation,[status(thm)],[f2766,f264]) ).
fof(f2775,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f807]) ).
fof(f2776,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf49(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f806]) ).
fof(f2777,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f805]) ).
fof(f2778,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf44(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f804]) ).
fof(f2779,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f803]) ).
fof(f2780,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac2,X0)) ),
inference(paramodulation,[status(thm)],[f2766,f802]) ).
fof(f2781,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac3,X0)) ),
inference(paramodulation,[status(thm)],[f2766,f801]) ).
fof(f2784,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| cons(hd(sk5),nil) = cons(hd(sk5),X0)
| ~ ssList(sk5)
| ~ frontsegP(cons(hd(sk5),X0),cons(hd(sk5),nil))
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f2766,f1711]) ).
fof(f2785,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),nil),X2)
| hd(sk5) = X1
| ~ ssItem(hd(sk5))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2766,f1703]) ).
fof(f2786,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),nil),X2)
| frontsegP(nil,X0)
| ~ ssItem(hd(sk5))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2766,f1638]) ).
fof(f2790,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(cons(hd(sk5),X0),sk5)
| ~ ssItem(hd(sk5))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f2766,f516]) ).
fof(f2791,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(sk5,cons(hd(sk5),X0))
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f2766,f516]) ).
fof(f2792,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(X1,nil)
| ~ ssItem(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f2766,f409]) ).
fof(f2793,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2766,f409]) ).
fof(f2794,definition,
( sQ271_spl
<=> ssList(cons(hd(sk5),nil)) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2796,plain,
( sQ271_spl
| ~ ssList(cons(hd(sk5),nil)) ),
inference(component_clause,[status(thm)],[f2794]) ).
fof(f2797,definition,
( sQ272_spl
<=> singletonP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2798,plain,
( ~ sQ272_spl
| singletonP(sk5) ),
inference(component_clause,[status(thm)],[f2797]) ).
fof(f2800,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ272_spl
| ~ sQ271_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2767,f1672,f2794,f2797,f1848,f1617]) ).
fof(f2801,definition,
( sQ273_spl
<=> cyclefreeP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2804,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ273_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2768,f1672,f2801,f1848,f1617]) ).
fof(f2805,definition,
( sQ274_spl
<=> totalorderP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2808,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ274_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2769,f1672,f2805,f1848,f1617]) ).
fof(f2809,definition,
( sQ275_spl
<=> strictorderP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2812,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ275_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2770,f1672,f2809,f1848,f1617]) ).
fof(f2813,definition,
( sQ276_spl
<=> totalorderedP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2814,plain,
( ~ sQ276_spl
| totalorderedP(sk5) ),
inference(component_clause,[status(thm)],[f2813]) ).
fof(f2816,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ276_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2771,f1672,f2813,f1848,f1617]) ).
fof(f2817,definition,
( sQ277_spl
<=> strictorderedP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2818,plain,
( ~ sQ277_spl
| strictorderedP(sk5) ),
inference(component_clause,[status(thm)],[f2817]) ).
fof(f2820,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ277_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2772,f1672,f2817,f1848,f1617]) ).
fof(f2821,definition,
( sQ278_spl
<=> duplicatefreeP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2824,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ278_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2773,f1672,f2821,f1848,f1617]) ).
fof(f2825,definition,
( sQ279_spl
<=> equalelemsP(sk5) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2828,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ279_spl
| ~ sQ121_spl ),
inference(split_clause,[status(thm)],[f2774,f1672,f2825,f1848,f1617]) ).
fof(f2829,definition,
! [X0,X1] :
( sQ280_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2832,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f2775,f2829,f534,f1672,f1848,f1617]) ).
fof(f2833,definition,
! [X0,X1] :
( sQ281_spl
<=> ( hd(sk5) = skaf49(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2836,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f2776,f2833,f534,f1672,f1848,f1617]) ).
fof(f2837,definition,
! [X0,X1] :
( sQ282_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f2840,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f2777,f2837,f534,f1672,f1848,f1617]) ).
fof(f2841,definition,
! [X0,X1] :
( sQ283_spl
<=> ( hd(sk5) = skaf44(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f2844,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f2778,f2841,f534,f1672,f1848,f1617]) ).
fof(f2845,definition,
! [X0,X1] :
( sQ284_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2848,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f2779,f2845,f534,f1672,f1848,f1617]) ).
fof(f2849,definition,
! [X0] :
( sQ285_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac2,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2852,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f2780,f2849,f534,f1672,f1848,f1617]) ).
fof(f2853,definition,
! [X0] :
( sQ286_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac3,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2856,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f2781,f2853,f534,f1672,f1848,f1617]) ).
fof(f2862,definition,
! [X0] :
( sQ288_spl
<=> ( cons(hd(sk5),nil) = cons(hd(sk5),X0)
| ~ frontsegP(cons(hd(sk5),X0),cons(hd(sk5),nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f2865,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f2784,f2862,f534,f1672,f460,f1848,f1617]) ).
fof(f2866,definition,
! [X0,X1,X2] :
( sQ289_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),nil),X2)
| hd(sk5) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f2869,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f2785,f2866,f534,f1672,f460,f1848,f1617]) ).
fof(f2870,definition,
! [X0,X1,X2] :
( sQ290_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk5),nil),X2)
| frontsegP(nil,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f2873,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ4_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f2786,f2870,f534,f1672,f460,f1848,f1617]) ).
fof(f2877,definition,
! [X0] :
( sQ291_spl
<=> ( frontsegP(cons(hd(sk5),X0),sk5)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2880,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2790,f2877,f534,f1672,f1848,f1617]) ).
fof(f2881,definition,
! [X0] :
( sQ292_spl
<=> ( frontsegP(sk5,cons(hd(sk5),X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2884,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f2791,f2881,f534,f1672,f1848,f1617]) ).
fof(f2885,definition,
! [X0,X1] :
( sQ293_spl
<=> ( frontsegP(X1,nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2888,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f2792,f2885,f534,f1672,f1848,f1617]) ).
fof(f2889,definition,
! [X0,X1] :
( sQ294_spl
<=> ( frontsegP(nil,X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2892,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2793,f2889,f534,f1672,f1848,f1617]) ).
fof(f2898,plain,
( sQ271_spl
| ~ sQ116_spl
| ~ sQ146_spl
| ~ ssList(sk5) ),
inference(forward_demodulation,[status(thm)],[f2766,f2796]) ).
fof(f2899,plain,
( sQ271_spl
| ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2898,f461]) ).
fof(f2900,plain,
( sQ271_spl
| ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f2899]) ).
fof(f2902,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf50(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf50(X2) = skaf50(X2)
| ~ ssItem(skaf50(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f808,f516]) ).
fof(f2905,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf50(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f808]) ).
fof(f2907,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf50(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f808]) ).
fof(f2908,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf50(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f808]) ).
fof(f2909,definition,
! [X2] :
( sQ295_spl
<=> ( ~ ssItem(skaf50(X2))
| skaf50(X2) = skaf50(X2)
| ~ ssItem(skaf50(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f2912,plain,
( sQ295_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2902,f745,f2909]) ).
fof(f2914,definition,
! [X0,X1] :
( sQ296_spl
<=> ( hd(sk5) = skaf50(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2917,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f2905,f2914,f534,f1672,f1848,f1617]) ).
fof(f2922,definition,
! [X0,X1] :
( sQ298_spl
<=> ( skaf83(sk2) = skaf50(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2925,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f2907,f2922,f2380,f2383,f1765]) ).
fof(f2926,definition,
! [X0,X1] :
( sQ299_spl
<=> ( skaf83(sk5) = skaf50(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2929,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f2908,f2926,f2163,f2166,f1773]) ).
fof(f2933,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f823]) ).
fof(f2935,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f823]) ).
fof(f2936,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f823]) ).
fof(f2943,definition,
! [X0,X1] :
( sQ301_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f2946,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f2933,f2943,f534,f1672,f1848,f1617]) ).
fof(f2951,definition,
! [X0,X1] :
( sQ303_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2954,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f2935,f2951,f2380,f2383,f1765]) ).
fof(f2955,definition,
! [X0,X1] :
( sQ304_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f2958,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f2936,f2955,f2163,f2166,f1773]) ).
fof(f2959,plain,
( app(skaf46(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f344,f979]) ).
fof(f2960,plain,
! [X0] :
( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f344,f258]) ).
fof(f2962,definition,
( sQ305_spl
<=> app(skaf46(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f2963,plain,
( ~ sQ305_spl
| app(skaf46(nil,nil),nil) = nil ),
inference(component_clause,[status(thm)],[f2962]) ).
fof(f2965,plain,
( sQ305_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2959,f534,f2962]) ).
fof(f2966,definition,
! [X0] :
( sQ306_spl
<=> ( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f2969,plain,
( sQ306_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2960,f534,f2966]) ).
fof(f2972,plain,
( ~ sQ77_spl
| app(nil,skaf45(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f345,f1194]) ).
fof(f2973,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(cons(X0,X1),skaf45(cons(X0,X2),cons(X0,X1))) = cons(X0,X2)
| ~ ssList(cons(X0,X2))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f345,f516]) ).
fof(f2974,plain,
( ~ sQ78_spl
| app(nil,skaf45(sk5,nil)) = sk5
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f345,f1198]) ).
fof(f2975,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| app(sk5,skaf45(sk5,sk5)) = sk5
| ~ ssList(sk5)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f345,f954]) ).
fof(f2977,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ frontsegP(X1,X0)
| app(X0,skaf45(app(X1,X2),X0)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f345,f352]) ).
fof(f2978,plain,
( ~ sQ79_spl
| app(nil,skaf45(sk1,nil)) = sk1
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f345,f1202]) ).
fof(f2979,plain,
( ~ sQ52_spl
| app(sk1,skaf45(sk1,sk1)) = sk1
| ~ ssList(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f345,f930]) ).
fof(f2980,plain,
( ~ sQ8_spl
| app(sk5,skaf45(sk1,sk5)) = sk1
| ~ ssList(sk1)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f345,f629]) ).
fof(f2981,plain,
( ~ sQ80_spl
| app(nil,skaf45(sk2,nil)) = sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f345,f1206]) ).
fof(f2982,plain,
( ~ sQ53_spl
| app(sk2,skaf45(sk2,sk2)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f345,f931]) ).
fof(f2983,plain,
( ~ sQ7_spl
| app(sk5,skaf45(sk2,sk5)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f345,f555]) ).
fof(f2984,plain,
! [X0] :
( ~ sQ60_spl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| app(X0,skaf45(sk2,X0)) = sk2
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f345,f990]) ).
fof(f2985,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f345,f260]) ).
fof(f2986,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| app(X0,skaf45(X1,X0)) = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f345,f379]) ).
fof(f2988,definition,
( sQ307_spl
<=> app(nil,skaf45(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f2991,plain,
( ~ sQ77_spl
| sQ307_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2972,f534,f2988,f1193]) ).
fof(f2992,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| app(cons(X0,X2),skaf45(cons(X0,X1),cons(X0,X2))) = cons(X0,X1)
| ~ ssList(cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2973,f287]) ).
fof(f2993,definition,
( sQ308_spl
<=> app(nil,skaf45(sk5,nil)) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f2996,plain,
( ~ sQ78_spl
| sQ308_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2974,f534,f460,f2993,f1197]) ).
fof(f2997,definition,
( sQ309_spl
<=> app(sk5,skaf45(sk5,sk5)) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f3000,plain,
( ~ sQ56_spl
| sQ309_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2975,f460,f2997,f946]) ).
fof(f3003,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X0)
| app(X0,skaf45(app(X1,X2),X0)) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2977]) ).
fof(f3004,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X0)
| app(X0,skaf45(app(X1,X2),X0)) = app(X1,X2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3003,f286]) ).
fof(f3005,definition,
( sQ310_spl
<=> app(nil,skaf45(sk1,nil)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f3008,plain,
( ~ sQ79_spl
| sQ310_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2978,f534,f634,f3005,f1201]) ).
fof(f3009,definition,
( sQ311_spl
<=> app(sk1,skaf45(sk1,sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f3012,plain,
( ~ sQ52_spl
| sQ311_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f2979,f634,f3009,f922]) ).
fof(f3013,definition,
( sQ312_spl
<=> app(sk5,skaf45(sk1,sk5)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f3014,plain,
( ~ sQ312_spl
| app(sk5,skaf45(sk1,sk5)) = sk1 ),
inference(component_clause,[status(thm)],[f3013]) ).
fof(f3016,plain,
( ~ sQ8_spl
| sQ312_spl
| ~ sQ26_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2980,f460,f634,f3013,f475]) ).
fof(f3017,definition,
( sQ313_spl
<=> app(nil,skaf45(sk2,nil)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f3020,plain,
( ~ sQ80_spl
| sQ313_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2981,f534,f560,f3017,f1205]) ).
fof(f3021,definition,
( sQ314_spl
<=> app(sk2,skaf45(sk2,sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f3024,plain,
( ~ sQ53_spl
| sQ314_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2982,f560,f3021,f926]) ).
fof(f3025,definition,
( sQ315_spl
<=> app(sk5,skaf45(sk2,sk5)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f3026,plain,
( ~ sQ315_spl
| app(sk5,skaf45(sk2,sk5)) = sk2 ),
inference(component_clause,[status(thm)],[f3025]) ).
fof(f3028,plain,
( ~ sQ7_spl
| sQ315_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2983,f460,f560,f3025,f471]) ).
fof(f3029,definition,
! [X0] :
( sQ316_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| app(X0,skaf45(sk2,X0)) = sk2
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f3032,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ316_spl ),
inference(split_clause,[status(thm)],[f2984,f3029,f560,f989]) ).
fof(f3033,definition,
! [X0] :
( sQ317_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f3036,plain,
( sQ317_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2985,f534,f3033]) ).
fof(f3037,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| app(X0,skaf45(X1,X0)) = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2986]) ).
fof(f3045,plain,
( ~ sQ4_spl
| tl(sk5) = app(tl(sk5),nil)
| nil = sk5
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f900,f346]) ).
fof(f3064,definition,
( sQ322_spl
<=> tl(sk5) = app(tl(sk5),nil) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3067,plain,
( sQ322_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3045,f534,f460,f591,f3064]) ).
fof(f3118,plain,
( ~ sQ4_spl
| nil = sk5
| app(sk5,sk2) != nil ),
inference(resolution,[status(thm)],[f2077,f461]) ).
fof(f3132,definition,
( sQ328_spl
<=> app(sk5,sk2) = nil ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3135,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ328_spl ),
inference(split_clause,[status(thm)],[f3118,f3132,f591,f460]) ).
fof(f3136,plain,
( ~ sQ272_spl
| cons(skaf44(sk5),nil) = sk5
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f2798,f304]) ).
fof(f3137,definition,
( sQ329_spl
<=> cons(skaf44(sk5),nil) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3140,plain,
( ~ sQ272_spl
| sQ329_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3136,f460,f3137,f2797]) ).
fof(f3141,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf54(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf54(X2) = skaf54(X2)
| ~ ssItem(skaf54(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f824,f516]) ).
fof(f3144,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf54(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f824]) ).
fof(f3146,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf54(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f824]) ).
fof(f3147,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf54(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f824]) ).
fof(f3148,definition,
! [X2] :
( sQ330_spl
<=> ( ~ ssItem(skaf54(X2))
| skaf54(X2) = skaf54(X2)
| ~ ssItem(skaf54(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3151,plain,
( sQ330_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f3141,f745,f3148]) ).
fof(f3153,definition,
! [X0,X1] :
( sQ331_spl
<=> ( hd(sk5) = skaf54(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f3156,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ331_spl ),
inference(split_clause,[status(thm)],[f3144,f3153,f534,f1672,f1848,f1617]) ).
fof(f3161,definition,
! [X0,X1] :
( sQ333_spl
<=> ( skaf83(sk2) = skaf54(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3164,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f3146,f3161,f2380,f2383,f1765]) ).
fof(f3165,definition,
! [X0,X1] :
( sQ334_spl
<=> ( skaf83(sk5) = skaf54(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f3168,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f3147,f3165,f2163,f2166,f1773]) ).
fof(f3172,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f825]) ).
fof(f3174,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f825]) ).
fof(f3175,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f825]) ).
fof(f3182,definition,
! [X0,X1] :
( sQ336_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f3185,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f3172,f3182,f534,f1672,f1848,f1617]) ).
fof(f3190,definition,
! [X0,X1] :
( sQ338_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f3193,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f3174,f3190,f2380,f2383,f1765]) ).
fof(f3194,definition,
! [X0,X1] :
( sQ339_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f3197,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f3175,f3194,f2163,f2166,f1773]) ).
fof(f3216,plain,
! [X0] :
( rearsegP(app(X0,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f351,f979]) ).
fof(f3217,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X0,X1),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f351,f258]) ).
fof(f3219,definition,
! [X0] :
( sQ340_spl
<=> ( rearsegP(app(X0,nil),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f3220,plain,
! [X0] :
( ~ sQ340_spl
| rearsegP(app(X0,nil),nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3219]) ).
fof(f3222,plain,
( ~ sQ13_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f3216,f3219,f534]) ).
fof(f3223,definition,
! [X0,X1] :
( sQ341_spl
<=> ( ~ ssList(X1)
| rearsegP(app(X0,X1),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f3226,plain,
( ~ sQ13_spl
| sQ341_spl ),
inference(split_clause,[status(thm)],[f3217,f3223,f534]) ).
fof(f3265,plain,
( ~ sQ4_spl
| nil = sk5
| app(sk5,sk1) != nil ),
inference(resolution,[status(thm)],[f2078,f461]) ).
fof(f3279,definition,
( sQ345_spl
<=> app(sk5,sk1) = nil ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f3282,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ345_spl ),
inference(split_clause,[status(thm)],[f3265,f3279,f591,f460]) ).
fof(f3283,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf55(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf55(X2) = skaf55(X2)
| ~ ssItem(skaf55(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f826,f516]) ).
fof(f3286,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf55(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f826]) ).
fof(f3288,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf55(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f826]) ).
fof(f3289,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf55(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f826]) ).
fof(f3290,definition,
! [X2] :
( sQ346_spl
<=> ( ~ ssItem(skaf55(X2))
| skaf55(X2) = skaf55(X2)
| ~ ssItem(skaf55(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f3293,plain,
( sQ346_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f3283,f745,f3290]) ).
fof(f3295,definition,
! [X0,X1] :
( sQ347_spl
<=> ( hd(sk5) = skaf55(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f3298,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ347_spl ),
inference(split_clause,[status(thm)],[f3286,f3295,f534,f1672,f1848,f1617]) ).
fof(f3303,definition,
! [X0,X1] :
( sQ349_spl
<=> ( skaf83(sk2) = skaf55(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f3306,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ349_spl ),
inference(split_clause,[status(thm)],[f3288,f3303,f2380,f2383,f1765]) ).
fof(f3307,definition,
! [X0,X1] :
( sQ350_spl
<=> ( skaf83(sk5) = skaf55(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f3310,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f3289,f3307,f2163,f2166,f1773]) ).
fof(f3314,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| frontsegP(nil,X1)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f827]) ).
fof(f3316,plain,
! [X0,X1] :
( ~ sQ131_spl
| frontsegP(skaf82(sk2),X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f827]) ).
fof(f3317,plain,
! [X0,X1] :
( ~ sQ133_spl
| frontsegP(skaf82(sk5),X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f827]) ).
fof(f3324,definition,
! [X0,X1] :
( sQ352_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f3327,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f3314,f3324,f534,f1672,f1848,f1617]) ).
fof(f3332,definition,
! [X0,X1] :
( sQ354_spl
<=> ( frontsegP(skaf82(sk2),X1)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3335,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f3316,f3332,f2380,f2383,f1765]) ).
fof(f3336,definition,
! [X0,X1] :
( sQ355_spl
<=> ( frontsegP(skaf82(sk5),X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f3339,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f3317,f3336,f2163,f2166,f1773]) ).
fof(f3377,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| memberP(sk5,hd(sk5))
| ~ ssItem(hd(sk5))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2766,f508]) ).
fof(f3379,plain,
( ~ sQ131_spl
| memberP(sk2,skaf83(sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f508]) ).
fof(f3380,plain,
( ~ sQ133_spl
| memberP(sk5,skaf83(sk5))
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f508]) ).
fof(f3381,definition,
( sQ356_spl
<=> memberP(sk5,hd(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f3382,plain,
( ~ sQ356_spl
| memberP(sk5,hd(sk5)) ),
inference(component_clause,[status(thm)],[f3381]) ).
fof(f3384,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| sQ356_spl
| ~ sQ121_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3377,f534,f1672,f3381,f1848,f1617]) ).
fof(f3389,definition,
( sQ358_spl
<=> memberP(sk2,skaf83(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f3390,plain,
( ~ sQ358_spl
| memberP(sk2,skaf83(sk2)) ),
inference(component_clause,[status(thm)],[f3389]) ).
fof(f3392,plain,
( ~ sQ131_spl
| sQ358_spl
| ~ sQ216_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f3379,f2380,f2383,f3389,f1765]) ).
fof(f3393,definition,
( sQ359_spl
<=> memberP(sk5,skaf83(sk5)) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f3394,plain,
( ~ sQ359_spl
| memberP(sk5,skaf83(sk5)) ),
inference(component_clause,[status(thm)],[f3393]) ).
fof(f3396,plain,
( ~ sQ133_spl
| sQ359_spl
| ~ sQ185_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f3380,f2163,f2166,f3393,f1773]) ).
fof(f3403,plain,
! [X0,X1,X2] :
( ~ ssItem(skaf59(X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf59(X2) = skaf59(X2)
| ~ ssItem(skaf59(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f828,f516]) ).
fof(f3406,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| hd(sk5) = skaf59(X0)
| ~ ssItem(hd(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2766,f828]) ).
fof(f3408,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf59(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f828]) ).
fof(f3409,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf59(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f828]) ).
fof(f3410,definition,
! [X2] :
( sQ360_spl
<=> ( ~ ssItem(skaf59(X2))
| skaf59(X2) = skaf59(X2)
| ~ ssItem(skaf59(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f3413,plain,
( sQ360_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f3403,f745,f3410]) ).
fof(f3415,definition,
! [X0,X1] :
( sQ361_spl
<=> ( hd(sk5) = skaf59(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f3418,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ121_spl
| ~ sQ13_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f3406,f3415,f534,f1672,f1848,f1617]) ).
fof(f3423,definition,
! [X0,X1] :
( sQ363_spl
<=> ( skaf83(sk2) = skaf59(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f3426,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ363_spl ),
inference(split_clause,[status(thm)],[f3408,f3423,f2380,f2383,f1765]) ).
fof(f3427,definition,
! [X0,X1] :
( sQ364_spl
<=> ( skaf83(sk5) = skaf59(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f3430,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f3409,f3427,f2163,f2166,f1773]) ).
fof(f3431,plain,
! [X0] :
( ~ sQ359_spl
| memberP(app(sk5,X0),skaf83(sk5))
| ~ ssItem(skaf83(sk5))
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3394,f355]) ).
fof(f3432,plain,
! [X0] :
( ~ sQ359_spl
| memberP(cons(X0,sk5),skaf83(sk5))
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f3394,f354]) ).
fof(f3433,definition,
! [X0] :
( sQ365_spl
<=> ( memberP(app(sk5,X0),skaf83(sk5))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f3436,plain,
( ~ sQ359_spl
| ~ sQ185_spl
| ~ sQ4_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f3431,f3433,f460,f2166,f3393]) ).
fof(f3437,definition,
! [X0] :
( sQ366_spl
<=> ( memberP(cons(X0,sk5),skaf83(sk5))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f3440,plain,
( ~ sQ359_spl
| ~ sQ185_spl
| sQ366_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3432,f460,f3437,f2166,f3393]) ).
fof(f3441,plain,
! [X0] :
( ~ sQ356_spl
| memberP(app(sk5,X0),hd(sk5))
| ~ ssItem(hd(sk5))
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3382,f355]) ).
fof(f3442,plain,
! [X0] :
( ~ sQ356_spl
| memberP(cons(X0,sk5),hd(sk5))
| ~ ssItem(hd(sk5))
| ~ ssItem(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f3382,f354]) ).
fof(f3443,definition,
! [X0] :
( sQ367_spl
<=> ( memberP(app(sk5,X0),hd(sk5))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f3446,plain,
( ~ sQ356_spl
| ~ sQ121_spl
| ~ sQ4_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f3441,f3443,f460,f1672,f3381]) ).
fof(f3447,definition,
! [X0] :
( sQ368_spl
<=> ( memberP(cons(X0,sk5),hd(sk5))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f3450,plain,
( ~ sQ356_spl
| ~ sQ121_spl
| sQ368_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3442,f460,f3447,f1672,f3381]) ).
fof(f3451,plain,
! [X0] :
( ~ sQ358_spl
| memberP(app(sk2,X0),skaf83(sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3390,f355]) ).
fof(f3452,plain,
! [X0] :
( ~ sQ358_spl
| memberP(cons(X0,sk2),skaf83(sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f3390,f354]) ).
fof(f3453,definition,
! [X0] :
( sQ369_spl
<=> ( memberP(app(sk2,X0),skaf83(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3456,plain,
( ~ sQ358_spl
| ~ sQ216_spl
| ~ sQ15_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f3451,f3453,f560,f2383,f3389]) ).
fof(f3457,definition,
! [X0] :
( sQ370_spl
<=> ( memberP(cons(X0,sk2),skaf83(sk2))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f3460,plain,
( ~ sQ358_spl
| ~ sQ216_spl
| sQ370_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3452,f560,f3457,f2383,f3389]) ).
fof(f3461,plain,
! [X0] :
( ~ sQ358_spl
| memberP(app(X0,sk2),skaf83(sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssList(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f356,f3390]) ).
fof(f3462,plain,
! [X0] :
( ~ sQ356_spl
| memberP(app(X0,sk5),hd(sk5))
| ~ ssItem(hd(sk5))
| ~ ssList(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f356,f3382]) ).
fof(f3463,plain,
! [X0] :
( ~ sQ359_spl
| memberP(app(X0,sk5),skaf83(sk5))
| ~ ssItem(skaf83(sk5))
| ~ ssList(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f356,f3394]) ).
fof(f3465,definition,
! [X0] :
( sQ371_spl
<=> ( memberP(app(X0,sk2),skaf83(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f3468,plain,
( ~ sQ358_spl
| ~ sQ216_spl
| sQ371_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3461,f560,f3465,f2383,f3389]) ).
fof(f3469,definition,
! [X0] :
( sQ372_spl
<=> ( memberP(app(X0,sk5),hd(sk5))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f3472,plain,
( ~ sQ356_spl
| ~ sQ121_spl
| sQ372_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3462,f460,f3469,f1672,f3381]) ).
fof(f3473,definition,
! [X0] :
( sQ373_spl
<=> ( memberP(app(X0,sk5),skaf83(sk5))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3476,plain,
( ~ sQ359_spl
| ~ sQ185_spl
| sQ373_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3463,f460,f3473,f2166,f3393]) ).
fof(f3479,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f286]) ).
fof(f3484,plain,
( ~ sQ4_spl
| rearsegP(sk5,sk5)
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f904,f3479]) ).
fof(f3485,plain,
( rearsegP(sk1,sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f903,f3479]) ).
fof(f3486,plain,
( rearsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f902,f3479]) ).
fof(f3487,plain,
( ~ sQ4_spl
| rearsegP(sk5,nil)
| ~ ssList(nil)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f900,f3479]) ).
fof(f3497,definition,
( sQ374_spl
<=> rearsegP(sk5,sk5) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3498,plain,
( ~ sQ374_spl
| rearsegP(sk5,sk5) ),
inference(component_clause,[status(thm)],[f3497]) ).
fof(f3500,plain,
( sQ374_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3484,f534,f460,f3497]) ).
fof(f3501,definition,
( sQ375_spl
<=> rearsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f3502,plain,
( ~ sQ375_spl
| rearsegP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f3501]) ).
fof(f3504,plain,
( sQ375_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3485,f534,f634,f3501]) ).
fof(f3505,definition,
( sQ376_spl
<=> rearsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f3506,plain,
( ~ sQ376_spl
| rearsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f3505]) ).
fof(f3508,plain,
( sQ376_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3486,f534,f560,f3505]) ).
fof(f3509,definition,
( sQ377_spl
<=> rearsegP(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f3510,plain,
( ~ sQ377_spl
| rearsegP(sk5,nil) ),
inference(component_clause,[status(thm)],[f3509]) ).
fof(f3512,plain,
( sQ377_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3487,f460,f534,f3509]) ).
fof(f3513,definition,
( sQ378_spl
<=> rearsegP(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f3514,plain,
( ~ sQ378_spl
| rearsegP(sk1,nil) ),
inference(component_clause,[status(thm)],[f3513]) ).
fof(f3517,definition,
( sQ379_spl
<=> rearsegP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f3518,plain,
( ~ sQ379_spl
| rearsegP(sk2,nil) ),
inference(component_clause,[status(thm)],[f3517]) ).
fof(f3521,plain,
! [X0] :
( ~ sQ375_spl
| rearsegP(app(X0,sk1),sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3502,f351]) ).
fof(f3522,plain,
( ~ sQ375_spl
| app(skaf46(sk1,sk1),sk1) = sk1
| ~ ssList(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f3502,f344]) ).
fof(f3524,definition,
! [X0] :
( sQ380_spl
<=> ( rearsegP(app(X0,sk1),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f3527,plain,
( ~ sQ375_spl
| ~ sQ26_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f3521,f3524,f634,f3501]) ).
fof(f3528,definition,
( sQ381_spl
<=> app(skaf46(sk1,sk1),sk1) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3531,plain,
( ~ sQ375_spl
| sQ381_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3522,f634,f3528,f3501]) ).
fof(f3571,plain,
! [X0] :
( ~ sQ376_spl
| rearsegP(app(X0,sk2),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3506,f351]) ).
fof(f3572,plain,
( ~ sQ376_spl
| app(skaf46(sk2,sk2),sk2) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f3506,f344]) ).
fof(f3574,definition,
! [X0] :
( sQ382_spl
<=> ( rearsegP(app(X0,sk2),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f3577,plain,
( ~ sQ376_spl
| ~ sQ15_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f3571,f3574,f560,f3505]) ).
fof(f3578,definition,
( sQ383_spl
<=> app(skaf46(sk2,sk2),sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f3581,plain,
( ~ sQ376_spl
| sQ383_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3572,f560,f3578,f3505]) ).
fof(f3583,plain,
! [X0] :
( ~ sQ378_spl
| rearsegP(app(X0,sk1),nil)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3514,f351]) ).
fof(f3584,plain,
( ~ sQ378_spl
| app(skaf46(sk1,nil),nil) = sk1
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3514,f344]) ).
fof(f3586,definition,
! [X0] :
( sQ384_spl
<=> ( rearsegP(app(X0,sk1),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f3589,plain,
( ~ sQ378_spl
| ~ sQ26_spl
| ~ sQ13_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f3583,f3586,f534,f634,f3513]) ).
fof(f3590,definition,
( sQ385_spl
<=> app(skaf46(sk1,nil),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f3593,plain,
( ~ sQ378_spl
| sQ385_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3584,f534,f634,f3590,f3513]) ).
fof(f3598,plain,
! [X0] :
( ~ sQ379_spl
| rearsegP(app(X0,sk2),nil)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3518,f351]) ).
fof(f3599,plain,
( ~ sQ379_spl
| app(skaf46(sk2,nil),nil) = sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3518,f344]) ).
fof(f3601,definition,
! [X0] :
( sQ387_spl
<=> ( rearsegP(app(X0,sk2),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f3604,plain,
( ~ sQ379_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ387_spl ),
inference(split_clause,[status(thm)],[f3598,f3601,f534,f560,f3517]) ).
fof(f3605,definition,
( sQ388_spl
<=> app(skaf46(sk2,nil),nil) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f3608,plain,
( ~ sQ379_spl
| sQ388_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3599,f534,f560,f3605,f3517]) ).
fof(f3613,plain,
! [X0] :
( ~ sQ374_spl
| rearsegP(app(X0,sk5),sk5)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3498,f351]) ).
fof(f3614,plain,
( ~ sQ374_spl
| app(skaf46(sk5,sk5),sk5) = sk5
| ~ ssList(sk5)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f3498,f344]) ).
fof(f3616,definition,
! [X0] :
( sQ390_spl
<=> ( rearsegP(app(X0,sk5),sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f3619,plain,
( ~ sQ374_spl
| ~ sQ4_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f3613,f3616,f460,f3497]) ).
fof(f3620,definition,
( sQ391_spl
<=> app(skaf46(sk5,sk5),sk5) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f3623,plain,
( ~ sQ374_spl
| sQ391_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3614,f460,f3620,f3497]) ).
fof(f3625,plain,
! [X0] :
( ~ sQ377_spl
| rearsegP(app(X0,sk5),nil)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3510,f351]) ).
fof(f3626,plain,
( ~ sQ377_spl
| app(skaf46(sk5,nil),nil) = sk5
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3510,f344]) ).
fof(f3627,plain,
( ~ sQ377_spl
| sk5 = nil
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ rearsegP(nil,sk5) ),
inference(resolution,[status(thm)],[f3510,f341]) ).
fof(f3628,definition,
! [X0] :
( sQ392_spl
<=> ( rearsegP(app(X0,sk5),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f3631,plain,
( ~ sQ377_spl
| ~ sQ4_spl
| ~ sQ13_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f3625,f3628,f534,f460,f3509]) ).
fof(f3632,definition,
( sQ393_spl
<=> app(skaf46(sk5,nil),nil) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f3635,plain,
( ~ sQ377_spl
| sQ393_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3626,f534,f460,f3632,f3509]) ).
fof(f3636,definition,
( sQ394_spl
<=> rearsegP(nil,sk5) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f3638,plain,
( sQ394_spl
| ~ rearsegP(nil,sk5) ),
inference(component_clause,[status(thm)],[f3636]) ).
fof(f3639,plain,
( ~ sQ377_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ394_spl ),
inference(split_clause,[status(thm)],[f3627,f3636,f534,f460,f591,f3509]) ).
fof(f3707,plain,
! [X0] :
( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f897,f369]) ).
fof(f3708,plain,
! [X0] :
( ~ sQ4_spl
| app(sk5,X0) = app(nil,app(sk5,X0))
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f904,f369]) ).
fof(f3709,plain,
! [X0] :
( app(sk1,X0) = app(nil,app(sk1,X0))
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f903,f369]) ).
fof(f3710,plain,
! [X0] :
( app(sk2,X0) = app(nil,app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f902,f369]) ).
fof(f3711,plain,
! [X0] :
( app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f897,f369]) ).
fof(f3712,plain,
! [X0] :
( ~ sQ4_spl
| app(app(X0,nil),sk5) = app(X0,sk5)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f904,f369]) ).
fof(f3713,plain,
! [X0] :
( app(app(X0,nil),sk1) = app(X0,sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f903,f369]) ).
fof(f3714,plain,
! [X0] :
( app(app(X0,nil),sk2) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f902,f369]) ).
fof(f3715,plain,
! [X0] :
( ~ sQ4_spl
| app(app(X0,sk5),nil) = app(X0,sk5)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f900,f369]) ).
fof(f3716,plain,
! [X0] :
( app(app(X0,sk1),nil) = app(X0,sk1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f899,f369]) ).
fof(f3717,plain,
! [X0] :
( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f898,f369]) ).
fof(f3718,definition,
! [X0] :
( sQ398_spl
<=> ( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f3721,plain,
( ~ sQ13_spl
| sQ398_spl ),
inference(split_clause,[status(thm)],[f3707,f3718,f534]) ).
fof(f3722,definition,
! [X0] :
( sQ399_spl
<=> ( app(sk5,X0) = app(nil,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f3725,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f3708,f3722,f460,f534]) ).
fof(f3726,definition,
! [X0] :
( sQ400_spl
<=> ( app(sk1,X0) = app(nil,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f3729,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f3709,f3726,f634,f534]) ).
fof(f3730,definition,
! [X0] :
( sQ401_spl
<=> ( app(sk2,X0) = app(nil,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f3733,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f3710,f3730,f560,f534]) ).
fof(f3734,definition,
! [X0] :
( sQ402_spl
<=> ( app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f3737,plain,
( sQ402_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3711,f534,f3734]) ).
fof(f3738,definition,
! [X0] :
( sQ403_spl
<=> ( app(app(X0,nil),sk5) = app(X0,sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f3741,plain,
( sQ403_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3712,f460,f534,f3738]) ).
fof(f3742,definition,
! [X0] :
( sQ404_spl
<=> ( app(app(X0,nil),sk1) = app(X0,sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f3745,plain,
( sQ404_spl
| ~ sQ13_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f3713,f634,f534,f3742]) ).
fof(f3746,definition,
! [X0] :
( sQ405_spl
<=> ( app(app(X0,nil),sk2) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f3749,plain,
( sQ405_spl
| ~ sQ13_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3714,f560,f534,f3746]) ).
fof(f3750,definition,
! [X0] :
( sQ406_spl
<=> ( app(app(X0,sk5),nil) = app(X0,sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f3753,plain,
( sQ406_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3715,f534,f460,f3750]) ).
fof(f3754,definition,
! [X0] :
( sQ407_spl
<=> ( app(app(X0,sk1),nil) = app(X0,sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f3757,plain,
( sQ407_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3716,f534,f634,f3754]) ).
fof(f3758,definition,
! [X0] :
( sQ408_spl
<=> ( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f3761,plain,
( sQ408_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3717,f534,f560,f3758]) ).
fof(f3795,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,nil) ),
inference(resolution,[status(thm)],[f371,f208]) ).
fof(f3796,plain,
! [X0,X1] :
( X1 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,sk2) ),
inference(resolution,[status(thm)],[f371,f432]) ).
fof(f3804,plain,
! [X0] :
( segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f897,f1086]) ).
fof(f3805,plain,
! [X0] :
( ~ sQ4_spl
| segmentP(app(sk5,X0),sk5)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f904,f1086]) ).
fof(f3806,plain,
! [X0] :
( segmentP(app(sk1,X0),sk1)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f903,f1086]) ).
fof(f3807,plain,
! [X0] :
( segmentP(app(sk2,X0),sk2)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f902,f1086]) ).
fof(f3808,plain,
! [X0] :
( ~ sQ4_spl
| segmentP(app(sk5,X0),nil)
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f900,f1086]) ).
fof(f3809,plain,
! [X0] :
( segmentP(app(sk1,X0),nil)
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f899,f1086]) ).
fof(f3810,plain,
! [X0] :
( segmentP(app(sk2,X0),nil)
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f898,f1086]) ).
fof(f3816,definition,
! [X0] :
( sQ409_spl
<=> ( segmentP(app(nil,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f3819,plain,
( ~ sQ13_spl
| sQ409_spl ),
inference(split_clause,[status(thm)],[f3804,f3816,f534]) ).
fof(f3820,definition,
! [X0] :
( sQ410_spl
<=> ( segmentP(app(sk5,X0),sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f3823,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| sQ410_spl ),
inference(split_clause,[status(thm)],[f3805,f3820,f534,f460]) ).
fof(f3824,definition,
! [X0] :
( sQ411_spl
<=> ( segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f3827,plain,
( ~ sQ26_spl
| ~ sQ13_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f3806,f3824,f534,f634]) ).
fof(f3828,definition,
! [X0] :
( sQ412_spl
<=> ( segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f3831,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| sQ412_spl ),
inference(split_clause,[status(thm)],[f3807,f3828,f534,f560]) ).
fof(f3832,definition,
! [X0] :
( sQ413_spl
<=> ( segmentP(app(sk5,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f3835,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| sQ413_spl ),
inference(split_clause,[status(thm)],[f3808,f3832,f460,f534]) ).
fof(f3836,definition,
! [X0] :
( sQ414_spl
<=> ( segmentP(app(sk1,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3839,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| sQ414_spl ),
inference(split_clause,[status(thm)],[f3809,f3836,f634,f534]) ).
fof(f3840,definition,
! [X0] :
( sQ415_spl
<=> ( segmentP(app(sk2,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f3843,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f3810,f3840,f560,f534]) ).
fof(f3844,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ72_spl
| app(app(X4,app(app(X1,X2),X0)),X3) = nil
| ~ ssList(app(app(X4,app(app(X1,X2),X0)),X3))
| ~ segmentP(nil,app(app(X4,app(app(X1,X2),X0)),X3))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(nil)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1087,f708]) ).
fof(f3845,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ72_spl
| segmentP(X5,nil)
| ~ ssList(X5)
| ~ ssList(app(app(X4,app(app(X1,X2),X0)),X3))
| ~ segmentP(X5,app(app(X4,app(app(X1,X2),X0)),X3))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(nil)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1087,f707]) ).
fof(f3846,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| app(app(X1,X2),X0) = nil
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1087,f340]) ).
fof(f3847,plain,
! [X0,X1,X2,X3] :
( ~ sQ72_spl
| segmentP(X3,nil)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(nil)
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1087,f375]) ).
fof(f3848,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ72_spl
| segmentP(app(app(X4,app(app(X1,X2),X0)),X3),nil)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(nil)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1087,f405]) ).
fof(f3856,definition,
! [X0,X1,X2,X3,X4] :
( sQ416_spl
<=> ( app(app(X4,app(app(X1,X2),X0)),X3) = nil
| ~ ssList(app(app(X4,app(app(X1,X2),X0)),X3))
| ~ segmentP(nil,app(app(X4,app(app(X1,X2),X0)),X3))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f3859,plain,
( ~ sQ72_spl
| ~ sQ13_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f3844,f3856,f534,f1082]) ).
fof(f3860,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ417_spl
<=> ( segmentP(X5,nil)
| ~ ssList(X5)
| ~ ssList(app(app(X4,app(app(X1,X2),X0)),X3))
| ~ segmentP(X5,app(app(X4,app(app(X1,X2),X0)),X3))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f3863,plain,
( ~ sQ72_spl
| ~ sQ13_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f3845,f3860,f534,f1082]) ).
fof(f3864,definition,
! [X0,X1,X2] :
( sQ418_spl
<=> ( app(app(X1,X2),X0) = nil
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(nil,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f3867,plain,
( ~ sQ72_spl
| ~ sQ13_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f3846,f3864,f534,f1082]) ).
fof(f3868,definition,
! [X0,X1,X2,X3] :
( sQ419_spl
<=> ( segmentP(X3,nil)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X0))
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f3871,plain,
( ~ sQ72_spl
| ~ sQ13_spl
| sQ419_spl ),
inference(split_clause,[status(thm)],[f3847,f3868,f534,f1082]) ).
fof(f3872,definition,
! [X0,X1,X2,X3,X4] :
( sQ420_spl
<=> ( segmentP(app(app(X4,app(app(X1,X2),X0)),X3),nil)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f3875,plain,
( ~ sQ72_spl
| ~ sQ13_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f3848,f3872,f534,f1082]) ).
fof(f3995,plain,
! [X0] :
( sQ394_spl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ rearsegP(X0,sk5)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f377,f3638]) ).
fof(f3998,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f377,f283]) ).
fof(f4002,definition,
! [X0] :
( sQ421_spl
<=> ( ~ ssList(X0)
| ~ rearsegP(X0,sk5)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4005,plain,
( sQ394_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sQ421_spl ),
inference(split_clause,[status(thm)],[f3995,f4002,f460,f534,f3636]) ).
fof(f4014,definition,
! [X0,X1] :
( sQ424_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f4017,plain,
( ~ sQ13_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f3998,f4014,f534]) ).
fof(f4095,definition,
! [X0,X1] :
( sQ434_spl
<=> ( hd(sk2) = skaf59(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f4099,definition,
( sQ435_spl
<=> memberP(sk2,hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f4100,plain,
( ~ sQ435_spl
| memberP(sk2,hd(sk2)) ),
inference(component_clause,[status(thm)],[f4099]) ).
fof(f4107,definition,
! [X0,X1] :
( sQ437_spl
<=> ( hd(sk2) = skaf55(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f4115,definition,
! [X0,X1] :
( sQ439_spl
<=> ( hd(sk2) = skaf54(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f4123,definition,
! [X0,X1] :
( sQ441_spl
<=> ( hd(sk2) = skaf50(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f4131,definition,
! [X0,X1] :
( sQ443_spl
<=> ( hd(sk2) = skaf49(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f4139,definition,
! [X0,X1] :
( sQ445_spl
<=> ( hd(sk2) = skaf44(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f4157,definition,
! [X0] :
( sQ449_spl
<=> ( cons(hd(sk2),nil) = cons(hd(sk2),X0)
| ~ frontsegP(cons(hd(sk2),X0),cons(hd(sk2),nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4161,definition,
! [X0,X1,X2] :
( sQ450_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk2),nil),X2)
| hd(sk2) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f4165,definition,
! [X0,X1,X2] :
( sQ451_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk2),nil),X2)
| frontsegP(nil,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f4198,plain,
! [X0] :
( ~ sQ60_spl
| ~ ssList(app(sk2,X0))
| ~ frontsegP(nil,app(sk2,X0))
| app(sk2,X0) = sk2
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1192,f990]) ).
fof(f4200,plain,
( app(nil,nil) = nil
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f897,f1192]) ).
fof(f4204,plain,
( ~ sQ4_spl
| app(sk5,nil) = sk5
| ~ frontsegP(sk5,sk5)
| ~ ssList(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f900,f1192]) ).
fof(f4205,plain,
( app(sk1,nil) = sk1
| ~ frontsegP(sk1,sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f899,f1192]) ).
fof(f4206,plain,
( app(sk2,nil) = sk2
| ~ frontsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f898,f1192]) ).
fof(f4208,definition,
! [X0] :
( sQ456_spl
<=> ( ~ ssList(app(sk2,X0))
| ~ frontsegP(nil,app(sk2,X0))
| app(sk2,X0) = sk2
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f4211,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ456_spl ),
inference(split_clause,[status(thm)],[f4198,f4208,f560,f989]) ).
fof(f4214,definition,
( sQ457_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f4217,plain,
( sQ457_spl
| ~ sQ77_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4200,f534,f1193,f4214]) ).
fof(f4224,definition,
( sQ459_spl
<=> app(sk5,nil) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f4227,plain,
( sQ459_spl
| ~ sQ58_spl
| ~ sQ4_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4204,f534,f460,f960,f4224]) ).
fof(f4228,definition,
( sQ460_spl
<=> app(sk1,nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f4231,plain,
( sQ460_spl
| ~ sQ54_spl
| ~ sQ26_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4205,f534,f634,f935,f4228]) ).
fof(f4232,definition,
( sQ461_spl
<=> app(sk2,nil) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f4235,plain,
( sQ461_spl
| ~ sQ45_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4206,f534,f560,f785,f4232]) ).
fof(f4273,plain,
( ~ sQ4_spl
| nil = sk5
| app(sk5,nil) != nil ),
inference(resolution,[status(thm)],[f2076,f461]) ).
fof(f4284,definition,
( sQ464_spl
<=> app(sk5,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f4287,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ464_spl ),
inference(split_clause,[status(thm)],[f4273,f4284,f591,f460]) ).
fof(f4320,plain,
! [X0,X1] :
( ~ ssItem(X1)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ memberP(app(X0,nil),X1) ),
inference(resolution,[status(thm)],[f386,f271]) ).
fof(f4324,definition,
! [X0,X1] :
( sQ465_spl
<=> ( ~ ssItem(X1)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(app(X0,nil),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f4327,plain,
( ~ sQ13_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f4320,f4324,f534]) ).
fof(f4512,plain,
! [X0] :
( ~ sQ305_spl
| app(app(X0,skaf46(nil,nil)),nil) = app(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2963,f369]) ).
fof(f4513,plain,
( ~ sQ305_spl
| rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(skaf46(nil,nil)) ),
inference(paramodulation,[status(thm)],[f2963,f3479]) ).
fof(f4516,plain,
! [X0] :
( ~ sQ305_spl
| app(skaf46(nil,nil),nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(skaf46(nil,nil),X0) ),
inference(paramodulation,[status(thm)],[f2963,f1279]) ).
fof(f4517,plain,
( ~ sQ305_spl
| frontsegP(nil,skaf46(nil,nil))
| ~ ssList(skaf46(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2963,f982]) ).
fof(f4518,plain,
! [X0] :
( ~ sQ305_spl
| frontsegP(nil,X0)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(skaf46(nil,nil),X0) ),
inference(paramodulation,[status(thm)],[f2963,f352]) ).
fof(f4519,definition,
( sQ498_spl
<=> ssList(skaf46(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f4521,plain,
( sQ498_spl
| ~ ssList(skaf46(nil,nil)) ),
inference(component_clause,[status(thm)],[f4519]) ).
fof(f4531,definition,
! [X0] :
( sQ501_spl
<=> ( app(app(X0,skaf46(nil,nil)),nil) = app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f4534,plain,
( ~ sQ305_spl
| sQ501_spl
| ~ sQ498_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4512,f534,f4519,f4531,f2962]) ).
fof(f4535,plain,
( ~ sQ305_spl
| sQ269_spl
| ~ sQ13_spl
| ~ sQ498_spl ),
inference(split_clause,[status(thm)],[f4513,f4519,f534,f2752,f2962]) ).
fof(f4547,definition,
! [X0] :
( sQ505_spl
<=> ( app(skaf46(nil,nil),nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(skaf46(nil,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f4550,plain,
( ~ sQ305_spl
| ~ sQ498_spl
| ~ sQ13_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f4516,f4547,f534,f4519,f2962]) ).
fof(f4551,definition,
( sQ506_spl
<=> frontsegP(nil,skaf46(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f4554,plain,
( ~ sQ305_spl
| sQ506_spl
| ~ sQ498_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4517,f534,f4519,f4551,f2962]) ).
fof(f4555,definition,
! [X0] :
( sQ507_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(skaf46(nil,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f4558,plain,
( ~ sQ305_spl
| ~ sQ498_spl
| ~ sQ13_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f4518,f4555,f534,f4519,f2962]) ).
fof(f4559,plain,
( sQ498_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4521,f250]) ).
fof(f4560,plain,
sQ498_spl,
inference(contradiction_clause,[status(thm)],[f4559]) ).
fof(f4563,plain,
! [X0,X1,X2] :
( ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| app(cons(X0,X1),skaf45(cons(X0,X2),cons(X0,X1))) = cons(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f2992,f287]) ).
fof(f4564,plain,
! [X0] :
( ~ sQ77_spl
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| app(cons(X0,nil),skaf45(cons(X0,nil),cons(X0,nil))) = cons(X0,nil) ),
inference(resolution,[status(thm)],[f4563,f1194]) ).
fof(f4566,plain,
! [X0] :
( ~ sQ78_spl
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ ssList(nil)
| app(cons(X0,nil),skaf45(cons(X0,sk5),cons(X0,nil))) = cons(X0,sk5) ),
inference(resolution,[status(thm)],[f4563,f1198]) ).
fof(f4567,plain,
! [X0] :
( ~ sQ56_spl
| ~ sQ4_spl
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ ssList(sk5)
| app(cons(X0,sk5),skaf45(cons(X0,sk5),cons(X0,sk5))) = cons(X0,sk5) ),
inference(resolution,[status(thm)],[f4563,f954]) ).
fof(f4570,plain,
! [X0] :
( ~ sQ79_spl
| ~ ssItem(X0)
| ~ ssList(sk1)
| ~ ssList(nil)
| app(cons(X0,nil),skaf45(cons(X0,sk1),cons(X0,nil))) = cons(X0,sk1) ),
inference(resolution,[status(thm)],[f4563,f1202]) ).
fof(f4571,plain,
! [X0] :
( ~ sQ52_spl
| ~ ssItem(X0)
| ~ ssList(sk1)
| ~ ssList(sk1)
| app(cons(X0,sk1),skaf45(cons(X0,sk1),cons(X0,sk1))) = cons(X0,sk1) ),
inference(resolution,[status(thm)],[f4563,f930]) ).
fof(f4573,plain,
! [X0] :
( ~ sQ80_spl
| ~ ssItem(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| app(cons(X0,nil),skaf45(cons(X0,sk2),cons(X0,nil))) = cons(X0,sk2) ),
inference(resolution,[status(thm)],[f4563,f1206]) ).
fof(f4574,plain,
! [X0] :
( ~ sQ53_spl
| ~ ssItem(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| app(cons(X0,sk2),skaf45(cons(X0,sk2),cons(X0,sk2))) = cons(X0,sk2) ),
inference(resolution,[status(thm)],[f4563,f931]) ).
fof(f4576,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ ssList(X1)
| ~ frontsegP(nil,X1)
| ~ ssItem(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| app(cons(X0,X1),skaf45(cons(X0,sk2),cons(X0,X1))) = cons(X0,sk2) ),
inference(resolution,[status(thm)],[f4563,f990]) ).
fof(f4577,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| app(cons(X0,nil),skaf45(cons(X0,X1),cons(X0,nil))) = cons(X0,X1) ),
inference(resolution,[status(thm)],[f4563,f260]) ).
fof(f4580,definition,
! [X0] :
( sQ508_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,nil),skaf45(cons(X0,nil),cons(X0,nil))) = cons(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f4583,plain,
( ~ sQ77_spl
| ~ sQ13_spl
| sQ508_spl ),
inference(split_clause,[status(thm)],[f4564,f4580,f534,f1193]) ).
fof(f4585,definition,
! [X0] :
( sQ509_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,nil),skaf45(cons(X0,sk5),cons(X0,nil))) = cons(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f4588,plain,
( ~ sQ78_spl
| ~ sQ4_spl
| ~ sQ13_spl
| sQ509_spl ),
inference(split_clause,[status(thm)],[f4566,f4585,f534,f460,f1197]) ).
fof(f4589,definition,
! [X0] :
( sQ510_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,sk5),skaf45(cons(X0,sk5),cons(X0,sk5))) = cons(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f4592,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| sQ510_spl ),
inference(split_clause,[status(thm)],[f4567,f4589,f460,f946]) ).
fof(f4597,definition,
! [X0] :
( sQ511_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,nil),skaf45(cons(X0,sk1),cons(X0,nil))) = cons(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f4600,plain,
( ~ sQ79_spl
| ~ sQ26_spl
| ~ sQ13_spl
| sQ511_spl ),
inference(split_clause,[status(thm)],[f4570,f4597,f534,f634,f1201]) ).
fof(f4601,definition,
! [X0] :
( sQ512_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,sk1),skaf45(cons(X0,sk1),cons(X0,sk1))) = cons(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f4604,plain,
( ~ sQ52_spl
| ~ sQ26_spl
| sQ512_spl ),
inference(split_clause,[status(thm)],[f4571,f4601,f634,f922]) ).
fof(f4609,definition,
! [X0] :
( sQ514_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,nil),skaf45(cons(X0,sk2),cons(X0,nil))) = cons(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f4612,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ514_spl ),
inference(split_clause,[status(thm)],[f4573,f4609,f534,f560,f1205]) ).
fof(f4613,definition,
! [X0] :
( sQ515_spl
<=> ( ~ ssItem(X0)
| app(cons(X0,sk2),skaf45(cons(X0,sk2),cons(X0,sk2))) = cons(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f4616,plain,
( ~ sQ53_spl
| ~ sQ15_spl
| sQ515_spl ),
inference(split_clause,[status(thm)],[f4574,f4613,f560,f926]) ).
fof(f4621,definition,
! [X0,X1] :
( sQ517_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,X1),skaf45(cons(X0,sk2),cons(X0,X1))) = cons(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f4624,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ517_spl ),
inference(split_clause,[status(thm)],[f4576,f4621,f560,f989]) ).
fof(f4625,definition,
! [X0,X1] :
( sQ518_spl
<=> ( ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),skaf45(cons(X0,X1),cons(X0,nil))) = cons(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f4628,plain,
( ~ sQ13_spl
| sQ518_spl ),
inference(split_clause,[status(thm)],[f4577,f4625,f534]) ).
fof(f4638,plain,
! [X0,X1] :
( ~ ssItem(X1)
| X1 = X0
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ memberP(cons(X0,nil),X1) ),
inference(resolution,[status(thm)],[f392,f271]) ).
fof(f4642,definition,
! [X0,X1] :
( sQ519_spl
<=> ( ~ ssItem(X1)
| X1 = X0
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ memberP(cons(X0,nil),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f4645,plain,
( ~ sQ13_spl
| sQ519_spl ),
inference(split_clause,[status(thm)],[f4638,f4642,f534]) ).
fof(f4657,plain,
( ~ sQ315_spl
| hd(sk2) = hd(sk5)
| nil = sk5
| ~ ssList(sk5)
| ~ ssList(skaf45(sk2,sk5)) ),
inference(paramodulation,[status(thm)],[f3026,f334]) ).
fof(f4661,definition,
( sQ520_spl
<=> ssList(skaf45(sk2,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f4663,plain,
( sQ520_spl
| ~ ssList(skaf45(sk2,sk5)) ),
inference(component_clause,[status(thm)],[f4661]) ).
fof(f4686,definition,
( sQ526_spl
<=> hd(sk2) = hd(sk5) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f4687,plain,
( ~ sQ526_spl
| hd(sk2) = hd(sk5) ),
inference(component_clause,[status(thm)],[f4686]) ).
fof(f4689,plain,
( ~ sQ315_spl
| sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ520_spl ),
inference(split_clause,[status(thm)],[f4657,f4661,f460,f591,f4686,f3025]) ).
fof(f4702,plain,
( sQ520_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4663,f251]) ).
fof(f4703,plain,
sQ520_spl,
inference(contradiction_clause,[status(thm)],[f4702]) ).
fof(f4744,plain,
! [X0] :
( ~ sQ77_spl
| ~ ssList(nil)
| ~ ssList(X0)
| app(nil,skaf45(app(nil,X0),nil)) = app(nil,X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3004,f1194]) ).
fof(f4746,plain,
! [X0] :
( ~ sQ78_spl
| ~ ssList(sk5)
| ~ ssList(X0)
| app(nil,skaf45(app(sk5,X0),nil)) = app(sk5,X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3004,f1198]) ).
fof(f4747,plain,
! [X0] :
( ~ sQ56_spl
| ~ sQ4_spl
| ~ ssList(sk5)
| ~ ssList(X0)
| app(sk5,skaf45(app(sk5,X0),sk5)) = app(sk5,X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f3004,f954]) ).
fof(f4750,plain,
! [X0] :
( ~ sQ79_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| app(nil,skaf45(app(sk1,X0),nil)) = app(sk1,X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3004,f1202]) ).
fof(f4751,plain,
! [X0] :
( ~ sQ52_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| app(sk1,skaf45(app(sk1,X0),sk1)) = app(sk1,X0)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f3004,f930]) ).
fof(f4753,plain,
! [X0] :
( ~ sQ80_spl
| ~ ssList(sk2)
| ~ ssList(X0)
| app(nil,skaf45(app(sk2,X0),nil)) = app(sk2,X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3004,f1206]) ).
fof(f4754,plain,
! [X0] :
( ~ sQ53_spl
| ~ ssList(sk2)
| ~ ssList(X0)
| app(sk2,skaf45(app(sk2,X0),sk2)) = app(sk2,X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f3004,f931]) ).
fof(f4756,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| app(X0,skaf45(app(sk2,X1),X0)) = app(sk2,X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3004,f990]) ).
fof(f4757,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X1)
| app(nil,skaf45(app(X0,X1),nil)) = app(X0,X1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3004,f260]) ).
fof(f4760,definition,
! [X0] :
( sQ530_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(app(nil,X0),nil)) = app(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f4763,plain,
( ~ sQ77_spl
| sQ530_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4744,f534,f4760,f1193]) ).
fof(f4765,definition,
! [X0] :
( sQ531_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(app(sk5,X0),nil)) = app(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f4768,plain,
( ~ sQ78_spl
| ~ sQ4_spl
| sQ531_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4746,f534,f4765,f460,f1197]) ).
fof(f4769,definition,
! [X0] :
( sQ532_spl
<=> ( ~ ssList(X0)
| app(sk5,skaf45(app(sk5,X0),sk5)) = app(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f4772,plain,
( ~ sQ56_spl
| sQ532_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4747,f460,f4769,f946]) ).
fof(f4777,definition,
! [X0] :
( sQ533_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(app(sk1,X0),nil)) = app(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f4780,plain,
( ~ sQ79_spl
| ~ sQ26_spl
| sQ533_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4750,f534,f4777,f634,f1201]) ).
fof(f4781,definition,
! [X0] :
( sQ534_spl
<=> ( ~ ssList(X0)
| app(sk1,skaf45(app(sk1,X0),sk1)) = app(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f4784,plain,
( ~ sQ52_spl
| sQ534_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4751,f634,f4781,f922]) ).
fof(f4789,definition,
! [X0] :
( sQ536_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(app(sk2,X0),nil)) = app(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f4792,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| sQ536_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4753,f534,f4789,f560,f1205]) ).
fof(f4793,definition,
! [X0] :
( sQ537_spl
<=> ( ~ ssList(X0)
| app(sk2,skaf45(app(sk2,X0),sk2)) = app(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f4796,plain,
( ~ sQ53_spl
| sQ537_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4754,f560,f4793,f926]) ).
fof(f4801,definition,
! [X0,X1] :
( sQ539_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| app(X0,skaf45(app(sk2,X1),X0)) = app(sk2,X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f4804,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ539_spl ),
inference(split_clause,[status(thm)],[f4756,f4801,f560,f989]) ).
fof(f4805,definition,
! [X0,X1] :
( sQ540_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X1)
| app(nil,skaf45(app(X0,X1),nil)) = app(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f4808,plain,
( sQ540_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4757,f534,f4805]) ).
fof(f4818,plain,
! [X0] :
( ~ sQ435_spl
| memberP(app(X0,sk2),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f4100,f356]) ).
fof(f4819,plain,
! [X0] :
( ~ sQ435_spl
| memberP(app(sk2,X0),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4100,f355]) ).
fof(f4820,plain,
! [X0] :
( ~ sQ435_spl
| memberP(cons(X0,sk2),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssItem(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f4100,f354]) ).
fof(f4821,definition,
! [X0] :
( sQ542_spl
<=> ( memberP(app(X0,sk2),hd(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f4824,plain,
( ~ sQ435_spl
| ~ sQ136_spl
| sQ542_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4818,f560,f4821,f1799,f4099]) ).
fof(f4825,definition,
! [X0] :
( sQ543_spl
<=> ( memberP(app(sk2,X0),hd(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f4828,plain,
( ~ sQ435_spl
| ~ sQ136_spl
| ~ sQ15_spl
| sQ543_spl ),
inference(split_clause,[status(thm)],[f4819,f4825,f560,f1799,f4099]) ).
fof(f4829,definition,
! [X0] :
( sQ544_spl
<=> ( memberP(cons(X0,sk2),hd(sk2))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f4832,plain,
( ~ sQ435_spl
| ~ sQ136_spl
| sQ544_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4820,f560,f4829,f1799,f4099]) ).
fof(f4859,definition,
( sQ548_spl
<=> ssList(skaf45(sk1,sk5)) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f4861,plain,
( sQ548_spl
| ~ ssList(skaf45(sk1,sk5)) ),
inference(component_clause,[status(thm)],[f4859]) ).
fof(f4900,plain,
( sQ548_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4861,f251]) ).
fof(f4901,plain,
sQ548_spl,
inference(contradiction_clause,[status(thm)],[f4900]) ).
fof(f4907,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| memberP(sk5,hd(sk2)) ),
inference(backward_demodulation,[status(thm)],[f4687,f3382]) ).
fof(f4908,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| cons(hd(sk2),nil) = sk5 ),
inference(backward_demodulation,[status(thm)],[f4687,f2766]) ).
fof(f4910,plain,
! [X0] :
( ~ sQ526_spl
| nil = sk5
| strictorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ strictorderedP(sk5)
| ~ lt(X0,hd(sk2)) ),
inference(paramodulation,[status(thm)],[f4687,f390]) ).
fof(f4911,plain,
! [X0] :
( ~ sQ526_spl
| nil = sk5
| totalorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ totalorderedP(sk5)
| ~ leq(X0,hd(sk2)) ),
inference(paramodulation,[status(thm)],[f4687,f388]) ).
fof(f4912,plain,
! [X0] :
( ~ sQ526_spl
| nil = sk5
| leq(X0,hd(sk2))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ totalorderedP(cons(X0,sk5)) ),
inference(paramodulation,[status(thm)],[f4687,f350]) ).
fof(f4913,plain,
! [X0] :
( ~ sQ526_spl
| nil = sk5
| lt(X0,hd(sk2))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ strictorderedP(cons(X0,sk5)) ),
inference(paramodulation,[status(thm)],[f4687,f348]) ).
fof(f4914,plain,
( ~ sQ526_spl
| nil = sk5
| ssItem(hd(sk2))
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f4687,f277]) ).
fof(f4916,definition,
! [X0] :
( sQ558_spl
<=> ( strictorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ lt(X0,hd(sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f4919,plain,
( ~ sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ277_spl
| sQ558_spl ),
inference(split_clause,[status(thm)],[f4910,f4916,f2817,f460,f591,f4686]) ).
fof(f4920,definition,
! [X0] :
( sQ559_spl
<=> ( totalorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ leq(X0,hd(sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f4923,plain,
( ~ sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ276_spl
| sQ559_spl ),
inference(split_clause,[status(thm)],[f4911,f4920,f2813,f460,f591,f4686]) ).
fof(f4924,definition,
! [X0] :
( sQ560_spl
<=> ( leq(X0,hd(sk2))
| ~ ssItem(X0)
| ~ totalorderedP(cons(X0,sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f4927,plain,
( ~ sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| sQ560_spl ),
inference(split_clause,[status(thm)],[f4912,f4924,f460,f591,f4686]) ).
fof(f4928,definition,
! [X0] :
( sQ561_spl
<=> ( lt(X0,hd(sk2))
| ~ ssItem(X0)
| ~ strictorderedP(cons(X0,sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f4931,plain,
( ~ sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| sQ561_spl ),
inference(split_clause,[status(thm)],[f4913,f4928,f460,f591,f4686]) ).
fof(f4932,plain,
( ~ sQ526_spl
| sQ21_spl
| sQ136_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4914,f460,f1799,f591,f4686]) ).
fof(f4934,plain,
! [X0] :
( ~ sQ77_spl
| ~ ssList(nil)
| ~ frontsegP(X0,nil)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3037,f1194]) ).
fof(f4936,plain,
! [X0] :
( ~ sQ78_spl
| ~ ssList(sk5)
| ~ frontsegP(X0,sk5)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3037,f1198]) ).
fof(f4937,plain,
! [X0] :
( ~ sQ56_spl
| ~ sQ4_spl
| ~ ssList(sk5)
| ~ frontsegP(X0,sk5)
| app(sk5,skaf45(X0,sk5)) = X0
| ~ ssList(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f3037,f954]) ).
fof(f4940,plain,
! [X0] :
( ~ sQ79_spl
| ~ ssList(sk1)
| ~ frontsegP(X0,sk1)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3037,f1202]) ).
fof(f4941,plain,
! [X0] :
( ~ sQ52_spl
| ~ ssList(sk1)
| ~ frontsegP(X0,sk1)
| app(sk1,skaf45(X0,sk1)) = X0
| ~ ssList(X0)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f3037,f930]) ).
fof(f4943,plain,
! [X0] :
( ~ sQ80_spl
| ~ ssList(sk2)
| ~ frontsegP(X0,sk2)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3037,f1206]) ).
fof(f4944,plain,
! [X0] :
( ~ sQ53_spl
| ~ ssList(sk2)
| ~ frontsegP(X0,sk2)
| app(sk2,skaf45(X0,sk2)) = X0
| ~ ssList(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f3037,f931]) ).
fof(f4946,plain,
! [X0,X1] :
( ~ sQ60_spl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sk2)
| ~ frontsegP(X1,sk2)
| app(X0,skaf45(X1,X0)) = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3037,f990]) ).
fof(f4947,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3037,f260]) ).
fof(f4950,definition,
! [X0] :
( sQ562_spl
<=> ( ~ frontsegP(X0,nil)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f4953,plain,
( ~ sQ77_spl
| sQ562_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4934,f534,f4950,f1193]) ).
fof(f4955,definition,
! [X0] :
( sQ563_spl
<=> ( ~ frontsegP(X0,sk5)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f4958,plain,
( ~ sQ78_spl
| ~ sQ4_spl
| sQ563_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4936,f534,f4955,f460,f1197]) ).
fof(f4959,definition,
! [X0] :
( sQ564_spl
<=> ( ~ frontsegP(X0,sk5)
| app(sk5,skaf45(X0,sk5)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f4962,plain,
( ~ sQ56_spl
| sQ564_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f4937,f460,f4959,f946]) ).
fof(f4967,definition,
! [X0] :
( sQ565_spl
<=> ( ~ frontsegP(X0,sk1)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f4970,plain,
( ~ sQ79_spl
| ~ sQ26_spl
| sQ565_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4940,f534,f4967,f634,f1201]) ).
fof(f4971,definition,
! [X0] :
( sQ566_spl
<=> ( ~ frontsegP(X0,sk1)
| app(sk1,skaf45(X0,sk1)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f4974,plain,
( ~ sQ52_spl
| sQ566_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4941,f634,f4971,f922]) ).
fof(f4979,definition,
! [X0] :
( sQ568_spl
<=> ( ~ frontsegP(X0,sk2)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f4982,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| sQ568_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4943,f534,f4979,f560,f1205]) ).
fof(f4983,definition,
! [X0] :
( sQ569_spl
<=> ( ~ frontsegP(X0,sk2)
| app(sk2,skaf45(X0,sk2)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f4986,plain,
( ~ sQ53_spl
| sQ569_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4944,f560,f4983,f926]) ).
fof(f4991,definition,
! [X0,X1] :
( sQ571_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ frontsegP(X1,sk2)
| app(X0,skaf45(X1,X0)) = X1
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f4994,plain,
( ~ sQ60_spl
| ~ sQ15_spl
| sQ571_spl ),
inference(split_clause,[status(thm)],[f4946,f4991,f560,f989]) ).
fof(f4995,definition,
! [X0,X1] :
( sQ572_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ572_spl])],[split_symbol_definition]) ).
fof(f4998,plain,
( sQ572_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4947,f534,f4995]) ).
fof(f5094,plain,
! [X0] :
( ~ sQ356_spl
| ~ sQ526_spl
| memberP(app(X0,sk5),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f4907,f356]) ).
fof(f5095,plain,
! [X0] :
( ~ sQ356_spl
| ~ sQ526_spl
| memberP(app(sk5,X0),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4907,f355]) ).
fof(f5096,plain,
! [X0] :
( ~ sQ356_spl
| ~ sQ526_spl
| memberP(cons(X0,sk5),hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssItem(X0)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f4907,f354]) ).
fof(f5097,definition,
! [X0] :
( sQ578_spl
<=> ( memberP(app(X0,sk5),hd(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ578_spl])],[split_symbol_definition]) ).
fof(f5100,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ578_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5094,f460,f5097,f1799,f4686,f3381]) ).
fof(f5101,definition,
! [X0] :
( sQ579_spl
<=> ( memberP(app(sk5,X0),hd(sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f5104,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ4_spl
| sQ579_spl ),
inference(split_clause,[status(thm)],[f5095,f5101,f460,f1799,f4686,f3381]) ).
fof(f5105,definition,
! [X0] :
( sQ580_spl
<=> ( memberP(cons(X0,sk5),hd(sk2))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ580_spl])],[split_symbol_definition]) ).
fof(f5108,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ580_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5096,f460,f5105,f1799,f4686,f3381]) ).
fof(f5146,plain,
! [X0] :
( ~ sQ4_spl
| sk5 = sk2
| ~ ssList(X0)
| app(X0,sk5) != app(X0,sk2) ),
inference(resolution,[status(thm)],[f3796,f461]) ).
fof(f5169,definition,
! [X0] :
( sQ587_spl
<=> ( ~ ssList(X0)
| app(X0,sk5) != app(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ587_spl])],[split_symbol_definition]) ).
fof(f5172,plain,
( ~ sQ4_spl
| sQ33_spl
| sQ587_spl ),
inference(split_clause,[status(thm)],[f5146,f5169,f663,f460]) ).
fof(f5173,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| ~ sQ33_spl
| memberP(sk2,hd(sk2)) ),
inference(backward_demodulation,[status(thm)],[f664,f4907]) ).
fof(f5223,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| ~ sQ33_spl
| sQ435_spl ),
inference(split_clause,[status(thm)],[f5173,f4099,f663,f4686,f3381]) ).
fof(f5280,plain,
! [X0,X1,X2] :
( ~ sQ72_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(skaf47(app(app(X0,X1),X2),nil),nil),skaf48(nil,app(app(X0,X1),X2))) = app(app(X0,X1),X2)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f399,f1087]) ).
fof(f5282,plain,
( ~ sQ29_spl
| app(app(skaf47(sk2,nil),nil),skaf48(nil,sk2)) = sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f399,f647]) ).
fof(f5283,plain,
! [X0] :
( ~ ssList(X0)
| app(app(skaf47(X0,nil),nil),skaf48(nil,X0)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f399,f256]) ).
fof(f5285,definition,
! [X0,X1,X2] :
( sQ588_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(skaf47(app(app(X0,X1),X2),nil),nil),skaf48(nil,app(app(X0,X1),X2))) = app(app(X0,X1),X2)
| ~ ssList(app(app(X0,X1),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ588_spl])],[split_symbol_definition]) ).
fof(f5288,plain,
( ~ sQ72_spl
| sQ588_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5280,f534,f5285,f1082]) ).
fof(f5290,definition,
( sQ589_spl
<=> app(app(skaf47(sk2,nil),nil),skaf48(nil,sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f5293,plain,
( ~ sQ29_spl
| sQ589_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5282,f534,f560,f5290,f646]) ).
fof(f5294,definition,
! [X0] :
( sQ590_spl
<=> ( ~ ssList(X0)
| app(app(skaf47(X0,nil),nil),skaf48(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ590_spl])],[split_symbol_definition]) ).
fof(f5297,plain,
( sQ590_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f5283,f534,f5294]) ).
fof(f5301,plain,
( ~ sQ358_spl
| app(skaf42(sk2,skaf83(sk2)),cons(skaf83(sk2),skaf43(skaf83(sk2),sk2))) = sk2
| ~ ssList(sk2)
| ~ ssItem(skaf83(sk2)) ),
inference(resolution,[status(thm)],[f400,f3390]) ).
fof(f5309,definition,
( sQ592_spl
<=> app(skaf42(sk2,skaf83(sk2)),cons(skaf83(sk2),skaf43(skaf83(sk2),sk2))) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f5312,plain,
( ~ sQ358_spl
| sQ592_spl
| ~ sQ15_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f5301,f2383,f560,f5309,f3389]) ).
fof(f5406,plain,
! [X0,X1] :
( ~ ssList(cons(X1,X0))
| memberP(app(nil,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f514,f984]) ).
fof(f5407,plain,
! [X0,X1] :
( ~ ssList(cons(X1,X0))
| memberP(app(sk1,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f514,f986]) ).
fof(f5408,plain,
! [X0,X1] :
( ~ ssList(cons(X1,X0))
| memberP(app(sk2,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f514,f985]) ).
fof(f5410,plain,
! [X0] :
( ~ sQ131_spl
| memberP(app(X0,cons(skaf83(sk2),skaf82(sk2))),skaf83(sk2))
| ~ ssList(app(X0,sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f514]) ).
fof(f5411,definition,
! [X0,X1] :
( sQ593_spl
<=> ( ~ ssList(cons(X1,X0))
| memberP(app(nil,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f5414,plain,
( ~ sQ13_spl
| sQ593_spl ),
inference(split_clause,[status(thm)],[f5406,f5411,f534]) ).
fof(f5415,definition,
! [X0,X1] :
( sQ594_spl
<=> ( ~ ssList(cons(X1,X0))
| memberP(app(sk1,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f5418,plain,
( ~ sQ26_spl
| sQ594_spl ),
inference(split_clause,[status(thm)],[f5407,f5415,f634]) ).
fof(f5419,definition,
! [X0,X1] :
( sQ595_spl
<=> ( ~ ssList(cons(X1,X0))
| memberP(app(sk2,cons(X1,X0)),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f5422,plain,
( ~ sQ15_spl
| sQ595_spl ),
inference(split_clause,[status(thm)],[f5408,f5419,f560]) ).
fof(f5427,definition,
! [X0] :
( sQ597_spl
<=> ( memberP(app(X0,cons(skaf83(sk2),skaf82(sk2))),skaf83(sk2))
| ~ ssList(app(X0,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f5430,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ597_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5410,f2380,f5427,f2383,f1765]) ).
fof(f5619,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f447]) ).
fof(f5620,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,sk2),cons(skaf83(sk2),X0)))
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f5619]) ).
fof(f5621,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,cons(skaf83(sk2),X0)),sk2))
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f5619]) ).
fof(f5622,definition,
! [X0,X1] :
( sQ611_spl
<=> ( ~ ssList(app(app(X1,sk2),cons(skaf83(sk2),X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f5625,plain,
( ~ sQ131_spl
| ~ sQ0_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ611_spl ),
inference(split_clause,[status(thm)],[f5620,f5622,f2380,f2383,f446,f1765]) ).
fof(f5626,definition,
! [X0,X1] :
( sQ612_spl
<=> ( ~ ssList(app(app(X1,cons(skaf83(sk2),X0)),sk2))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f5629,plain,
( ~ sQ131_spl
| ~ sQ0_spl
| ~ sQ216_spl
| sQ612_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5621,f2380,f5626,f2383,f446,f1765]) ).
fof(f5632,plain,
! [X0,X1] :
( ~ sQ131_spl
| X1 = skaf83(sk2)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk2),skaf82(sk2)))))
| ~ equalelemsP(app(X0,cons(X1,sk2)))
| ~ ssItem(X1)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f518]) ).
fof(f5635,definition,
! [X0,X1] :
( sQ613_spl
<=> ( X1 = skaf83(sk2)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk2),skaf82(sk2)))))
| ~ equalelemsP(app(X0,cons(X1,sk2)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f5638,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ613_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5632,f2380,f5635,f2383,f1765]) ).
fof(f5640,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| lt(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f519]) ).
fof(f5641,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| lt(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f519]) ).
fof(f5642,definition,
! [X0,X1,X2] :
( sQ614_spl
<=> ( lt(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f5645,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ614_spl ),
inference(split_clause,[status(thm)],[f5640,f5642,f2380,f2383,f1765]) ).
fof(f5646,definition,
! [X0,X1,X2] :
( sQ615_spl
<=> ( lt(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f5649,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ615_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5641,f2380,f5646,f2383,f1765]) ).
fof(f5681,plain,
! [X0] :
( ~ sQ4_spl
| nil = X0
| ~ ssList(X0)
| app(X0,sk5) != nil ),
inference(resolution,[status(thm)],[f461,f328]) ).
fof(f5684,plain,
! [X0] :
( ~ sQ4_spl
| ssList(app(sk5,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f461,f286]) ).
fof(f5686,plain,
( ~ sQ4_spl
| app(sk5,nil) = sk5 ),
inference(resolution,[status(thm)],[f461,f274]) ).
fof(f5692,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| leq(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f520]) ).
fof(f5693,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| leq(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f520]) ).
fof(f5694,definition,
! [X0,X1,X2] :
( sQ616_spl
<=> ( leq(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f5697,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ616_spl ),
inference(split_clause,[status(thm)],[f5692,f5694,f2380,f2383,f1765]) ).
fof(f5698,definition,
! [X0,X1,X2] :
( sQ617_spl
<=> ( leq(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f5701,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ617_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5693,f2380,f5698,f2383,f1765]) ).
fof(f5704,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| lt(X2,skaf83(sk2))
| lt(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f521]) ).
fof(f5705,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| lt(skaf83(sk2),X2)
| lt(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f521]) ).
fof(f5706,definition,
! [X0,X1,X2] :
( sQ618_spl
<=> ( lt(X2,skaf83(sk2))
| lt(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f5709,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ618_spl ),
inference(split_clause,[status(thm)],[f5704,f5706,f2380,f2383,f1765]) ).
fof(f5710,definition,
! [X0,X1,X2] :
( sQ619_spl
<=> ( lt(skaf83(sk2),X2)
| lt(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f5713,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ619_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5705,f2380,f5710,f2383,f1765]) ).
fof(f5716,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| leq(X2,skaf83(sk2))
| leq(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f522]) ).
fof(f5717,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| leq(skaf83(sk2),X2)
| leq(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f522]) ).
fof(f5718,definition,
! [X0,X1,X2] :
( sQ620_spl
<=> ( leq(X2,skaf83(sk2))
| leq(skaf83(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f5721,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ620_spl ),
inference(split_clause,[status(thm)],[f5716,f5718,f2380,f2383,f1765]) ).
fof(f5722,definition,
! [X0,X1,X2] :
( sQ621_spl
<=> ( leq(skaf83(sk2),X2)
| leq(X2,skaf83(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f5725,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ621_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f5717,f2380,f5722,f2383,f1765]) ).
fof(f5752,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ ssList(app(app(X2,sk2),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,cons(skaf83(sk2),skaf82(sk2))),cons(X0,X1)))
| ~ ssItem(skaf83(sk2))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ leq(X0,skaf83(sk2))
| ~ leq(skaf83(sk2),X0) ),
inference(paramodulation,[status(thm)],[f1766,f523]) ).
fof(f5753,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ ssList(app(app(X2,cons(X0,X1)),sk2))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ leq(skaf83(sk2),X0)
| ~ leq(X0,skaf83(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f523]) ).
fof(f5754,definition,
! [X0,X1,X2] :
( sQ622_spl
<=> ( ~ ssList(app(app(X2,sk2),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,cons(skaf83(sk2),skaf82(sk2))),cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,skaf83(sk2))
| ~ leq(skaf83(sk2),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ622_spl])],[split_symbol_definition]) ).
fof(f5757,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ622_spl ),
inference(split_clause,[status(thm)],[f5752,f5754,f2380,f2383,f1765]) ).
fof(f5758,definition,
! [X0,X1,X2] :
( sQ623_spl
<=> ( ~ ssList(app(app(X2,cons(X0,X1)),sk2))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(skaf83(sk2),X0)
| ~ leq(X0,skaf83(sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f5761,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ623_spl ),
inference(split_clause,[status(thm)],[f5753,f5758,f2380,f2383,f1765]) ).
fof(f5793,plain,
! [X0,X1] :
( ~ sQ340_spl
| rearsegP(app(X1,app(X0,nil)),nil)
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3220,f351]) ).
fof(f5794,plain,
! [X0] :
( ~ sQ340_spl
| app(skaf46(app(X0,nil),nil),nil) = app(X0,nil)
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3220,f344]) ).
fof(f5795,plain,
! [X0] :
( ~ sQ340_spl
| app(X0,nil) = nil
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ rearsegP(nil,app(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3220,f341]) ).
fof(f5797,plain,
( ~ sQ340_spl
| rearsegP(sk2,nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f898,f3220]) ).
fof(f5798,definition,
! [X0,X1] :
( sQ624_spl
<=> ( rearsegP(app(X1,app(X0,nil)),nil)
| ~ ssList(app(X0,nil))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ624_spl])],[split_symbol_definition]) ).
fof(f5801,plain,
( ~ sQ340_spl
| ~ sQ13_spl
| sQ624_spl ),
inference(split_clause,[status(thm)],[f5793,f5798,f534,f3219]) ).
fof(f5802,definition,
! [X0] :
( sQ625_spl
<=> ( app(skaf46(app(X0,nil),nil),nil) = app(X0,nil)
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ625_spl])],[split_symbol_definition]) ).
fof(f5805,plain,
( ~ sQ340_spl
| ~ sQ13_spl
| sQ625_spl ),
inference(split_clause,[status(thm)],[f5794,f5802,f534,f3219]) ).
fof(f5806,definition,
! [X0] :
( sQ626_spl
<=> ( app(X0,nil) = nil
| ~ ssList(app(X0,nil))
| ~ rearsegP(nil,app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ626_spl])],[split_symbol_definition]) ).
fof(f5809,plain,
( ~ sQ340_spl
| ~ sQ13_spl
| sQ626_spl ),
inference(split_clause,[status(thm)],[f5795,f5806,f534,f3219]) ).
fof(f5811,plain,
( ~ sQ340_spl
| sQ379_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5797,f560,f3517,f3219]) ).
fof(f5813,plain,
! [X0] :
( ~ sQ4_spl
| sk5 = nil
| ~ ssList(X0)
| app(X0,sk5) != app(X0,nil) ),
inference(resolution,[status(thm)],[f3795,f461]) ).
fof(f5849,definition,
! [X0] :
( sQ627_spl
<=> ( ~ ssList(X0)
| app(X0,sk5) != app(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ627_spl])],[split_symbol_definition]) ).
fof(f5852,plain,
( ~ sQ4_spl
| sQ21_spl
| sQ627_spl ),
inference(split_clause,[status(thm)],[f5813,f5849,f591,f460]) ).
fof(f5949,plain,
! [X0] :
( ~ sQ146_spl
| nil = sk5
| ~ ssList(sk5)
| ssList(app(nil,X0))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1849,f983]) ).
fof(f5950,plain,
( ~ sQ146_spl
| app(nil,nil) = tl(sk5)
| nil = sk5
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f1849,f906]) ).
fof(f5952,plain,
! [X0] :
( ~ sQ146_spl
| nil = X0
| X0 = sk5
| nil = sk5
| ~ ssList(sk5)
| ~ ssList(X0)
| hd(X0) != hd(sk5)
| tl(X0) != nil ),
inference(paramodulation,[status(thm)],[f1849,f415]) ).
fof(f5955,definition,
! [X0] :
( sQ633_spl
<=> ( ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ633_spl])],[split_symbol_definition]) ).
fof(f5958,plain,
( ~ sQ146_spl
| sQ21_spl
| ~ sQ4_spl
| sQ633_spl ),
inference(split_clause,[status(thm)],[f5949,f5955,f460,f591,f1848]) ).
fof(f5959,definition,
( sQ634_spl
<=> app(nil,nil) = tl(sk5) ),
introduced(definition,[new_symbols(definition,[sQ634_spl])],[split_symbol_definition]) ).
fof(f5962,plain,
( ~ sQ146_spl
| sQ634_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5950,f460,f591,f5959,f1848]) ).
fof(f5964,definition,
! [X0] :
( sQ635_spl
<=> ( nil = X0
| X0 = sk5
| ~ ssList(X0)
| hd(X0) != hd(sk5)
| tl(X0) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f5967,plain,
( ~ sQ146_spl
| sQ21_spl
| ~ sQ4_spl
| sQ635_spl ),
inference(split_clause,[status(thm)],[f5952,f5964,f460,f591,f1848]) ).
fof(f6054,plain,
! [X0] :
( app(nil,skaf51(X0)) = nil
| ~ frontsegP(nil,skaf51(X0))
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1037,f1192]) ).
fof(f6056,plain,
! [X0,X1] :
( segmentP(app(skaf51(X1),X0),skaf51(X1))
| ~ ssList(skaf51(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1037,f1086]) ).
fof(f6057,plain,
! [X0,X1] :
( app(app(X1,nil),skaf51(X0)) = app(X1,skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1037,f369]) ).
fof(f6058,plain,
! [X0,X1] :
( app(skaf51(X1),X0) = app(nil,app(skaf51(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1037,f369]) ).
fof(f6059,plain,
! [X0] :
( rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1037,f3479]) ).
fof(f6062,plain,
! [X0,X1] :
( app(nil,skaf51(X1)) = X0
| ~ frontsegP(X0,skaf51(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f1279]) ).
fof(f6063,plain,
! [X0] :
( frontsegP(skaf51(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1037,f982]) ).
fof(f6064,plain,
! [X0,X1] :
( frontsegP(skaf51(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f352]) ).
fof(f6065,definition,
! [X0] :
( sQ636_spl
<=> ( app(nil,skaf51(X0)) = nil
| ~ frontsegP(nil,skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f6068,plain,
( ~ sQ13_spl
| sQ636_spl ),
inference(split_clause,[status(thm)],[f6054,f6065,f534]) ).
fof(f6069,definition,
! [X0,X1] :
( sQ637_spl
<=> ( segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f6073,definition,
! [X0,X1] :
( sQ638_spl
<=> ( segmentP(app(skaf51(X1),X0),skaf51(X1))
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f6076,plain,
( ~ sQ13_spl
| sQ638_spl ),
inference(split_clause,[status(thm)],[f6056,f6073,f534]) ).
fof(f6077,definition,
! [X0,X1] :
( sQ639_spl
<=> ( app(app(X1,nil),skaf51(X0)) = app(X1,skaf51(X0))
| ~ ssList(X1)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f6080,plain,
( ~ sQ13_spl
| sQ639_spl ),
inference(split_clause,[status(thm)],[f6057,f6077,f534]) ).
fof(f6081,definition,
! [X0,X1] :
( sQ640_spl
<=> ( app(skaf51(X1),X0) = app(nil,app(skaf51(X1),X0))
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f6084,plain,
( ~ sQ13_spl
| sQ640_spl ),
inference(split_clause,[status(thm)],[f6058,f6081,f534]) ).
fof(f6085,definition,
! [X0] :
( sQ641_spl
<=> ( rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f6088,plain,
( sQ641_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6059,f534,f6085]) ).
fof(f6097,definition,
! [X0,X1] :
( sQ644_spl
<=> ( app(nil,skaf51(X1)) = X0
| ~ frontsegP(X0,skaf51(X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ644_spl])],[split_symbol_definition]) ).
fof(f6100,plain,
( ~ sQ13_spl
| sQ644_spl ),
inference(split_clause,[status(thm)],[f6062,f6097,f534]) ).
fof(f6101,definition,
! [X0] :
( sQ645_spl
<=> ( frontsegP(skaf51(X0),nil)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f6104,plain,
( ~ sQ13_spl
| sQ645_spl ),
inference(split_clause,[status(thm)],[f6063,f6101,f534]) ).
fof(f6105,definition,
! [X0,X1] :
( sQ646_spl
<=> ( frontsegP(skaf51(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f6108,plain,
( ~ sQ13_spl
| sQ646_spl ),
inference(split_clause,[status(thm)],[f6064,f6105,f534]) ).
fof(f6117,plain,
! [X0] :
( ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f1036]) ).
fof(f6119,plain,
! [X0] :
( app(skaf51(X0),nil) = skaf51(X0)
| ~ frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f1192]) ).
fof(f6121,plain,
! [X0,X1] :
( segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1038,f1086]) ).
fof(f6122,plain,
! [X0,X1] :
( app(app(X1,skaf51(X0)),nil) = app(X1,skaf51(X0))
| ~ ssList(X1)
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f369]) ).
fof(f6123,plain,
! [X0] :
( rearsegP(skaf51(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1038,f3479]) ).
fof(f6124,plain,
! [X0] :
( tl(skaf51(X0)) = app(tl(skaf51(X0)),nil)
| nil = skaf51(X0)
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f346]) ).
fof(f6125,plain,
! [X0] :
( hd(skaf51(X0)) = hd(skaf51(X0))
| nil = skaf51(X0)
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f334]) ).
fof(f6126,plain,
! [X0,X1] :
( app(skaf51(X0),nil) = X1
| ~ frontsegP(X1,skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1038,f1279]) ).
fof(f6127,plain,
! [X0] :
( frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f982]) ).
fof(f6128,plain,
! [X0,X1] :
( frontsegP(skaf51(X0),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1038,f352]) ).
fof(f6129,definition,
! [X0] :
( sQ647_spl
<=> ssList(skaf51(X0)) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f6132,plain,
( sQ647_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6117,f534,f6129]) ).
fof(f6133,definition,
! [X0] :
( sQ648_spl
<=> ( app(skaf51(X0),nil) = skaf51(X0)
| ~ frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f6136,plain,
( sQ648_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6119,f534,f6133]) ).
fof(f6138,plain,
( ~ sQ13_spl
| sQ637_spl ),
inference(split_clause,[status(thm)],[f6121,f6069,f534]) ).
fof(f6139,definition,
! [X0,X1] :
( sQ649_spl
<=> ( app(app(X1,skaf51(X0)),nil) = app(X1,skaf51(X0))
| ~ ssList(X1)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f6142,plain,
( sQ649_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6122,f534,f6139]) ).
fof(f6143,definition,
! [X0] :
( sQ650_spl
<=> ( rearsegP(skaf51(X0),nil)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f6146,plain,
( ~ sQ13_spl
| sQ650_spl ),
inference(split_clause,[status(thm)],[f6123,f6143,f534]) ).
fof(f6147,definition,
! [X0] :
( sQ651_spl
<=> ( tl(skaf51(X0)) = app(tl(skaf51(X0)),nil)
| nil = skaf51(X0)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f6150,plain,
( sQ651_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6124,f534,f6147]) ).
fof(f6151,definition,
! [X0] :
( sQ652_spl
<=> ( hd(skaf51(X0)) = hd(skaf51(X0))
| nil = skaf51(X0)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f6154,plain,
( sQ652_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6125,f534,f6151]) ).
fof(f6155,definition,
! [X0,X1] :
( sQ653_spl
<=> ( app(skaf51(X0),nil) = X1
| ~ frontsegP(X1,skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f6158,plain,
( ~ sQ13_spl
| sQ653_spl ),
inference(split_clause,[status(thm)],[f6126,f6155,f534]) ).
fof(f6159,definition,
! [X0] :
( sQ654_spl
<=> ( frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f6162,plain,
( sQ654_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6127,f534,f6159]) ).
fof(f6163,definition,
! [X0,X1] :
( sQ655_spl
<=> ( frontsegP(skaf51(X0),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f6166,plain,
( ~ sQ13_spl
| sQ655_spl ),
inference(split_clause,[status(thm)],[f6128,f6163,f534]) ).
fof(f6312,plain,
! [X0] :
( app(nil,skaf52(X0)) = nil
| ~ frontsegP(nil,skaf52(X0))
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1040,f1192]) ).
fof(f6314,plain,
! [X0,X1] :
( segmentP(app(skaf52(X1),X0),skaf52(X1))
| ~ ssList(skaf52(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1040,f1086]) ).
fof(f6315,plain,
! [X0,X1] :
( app(app(X1,nil),skaf52(X0)) = app(X1,skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1040,f369]) ).
fof(f6316,plain,
! [X0,X1] :
( app(skaf52(X1),X0) = app(nil,app(skaf52(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1040,f369]) ).
fof(f6317,plain,
! [X0] :
( rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1040,f3479]) ).
fof(f6320,plain,
! [X0,X1] :
( app(nil,skaf52(X1)) = X0
| ~ frontsegP(X0,skaf52(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f1279]) ).
fof(f6321,plain,
! [X0] :
( frontsegP(skaf52(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1040,f982]) ).
fof(f6322,plain,
! [X0,X1] :
( frontsegP(skaf52(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f352]) ).
fof(f6323,definition,
! [X0] :
( sQ662_spl
<=> ( app(nil,skaf52(X0)) = nil
| ~ frontsegP(nil,skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ662_spl])],[split_symbol_definition]) ).
fof(f6326,plain,
( ~ sQ13_spl
| sQ662_spl ),
inference(split_clause,[status(thm)],[f6312,f6323,f534]) ).
fof(f6327,definition,
! [X0,X1] :
( sQ663_spl
<=> ( segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f6331,definition,
! [X0,X1] :
( sQ664_spl
<=> ( segmentP(app(skaf52(X1),X0),skaf52(X1))
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f6334,plain,
( ~ sQ13_spl
| sQ664_spl ),
inference(split_clause,[status(thm)],[f6314,f6331,f534]) ).
fof(f6335,definition,
! [X0,X1] :
( sQ665_spl
<=> ( app(app(X1,nil),skaf52(X0)) = app(X1,skaf52(X0))
| ~ ssList(X1)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f6338,plain,
( ~ sQ13_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f6315,f6335,f534]) ).
fof(f6339,definition,
! [X0,X1] :
( sQ666_spl
<=> ( app(skaf52(X1),X0) = app(nil,app(skaf52(X1),X0))
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f6342,plain,
( ~ sQ13_spl
| sQ666_spl ),
inference(split_clause,[status(thm)],[f6316,f6339,f534]) ).
fof(f6343,definition,
! [X0] :
( sQ667_spl
<=> ( rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f6346,plain,
( sQ667_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6317,f534,f6343]) ).
fof(f6355,definition,
! [X0,X1] :
( sQ670_spl
<=> ( app(nil,skaf52(X1)) = X0
| ~ frontsegP(X0,skaf52(X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f6358,plain,
( ~ sQ13_spl
| sQ670_spl ),
inference(split_clause,[status(thm)],[f6320,f6355,f534]) ).
fof(f6359,definition,
! [X0] :
( sQ671_spl
<=> ( frontsegP(skaf52(X0),nil)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f6362,plain,
( ~ sQ13_spl
| sQ671_spl ),
inference(split_clause,[status(thm)],[f6321,f6359,f534]) ).
fof(f6363,definition,
! [X0,X1] :
( sQ672_spl
<=> ( frontsegP(skaf52(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f6366,plain,
( ~ sQ13_spl
| sQ672_spl ),
inference(split_clause,[status(thm)],[f6322,f6363,f534]) ).
fof(f6375,plain,
! [X0] :
( ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f1039]) ).
fof(f6377,plain,
! [X0] :
( app(skaf52(X0),nil) = skaf52(X0)
| ~ frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f1192]) ).
fof(f6379,plain,
! [X0,X1] :
( segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1041,f1086]) ).
fof(f6380,plain,
! [X0,X1] :
( app(app(X1,skaf52(X0)),nil) = app(X1,skaf52(X0))
| ~ ssList(X1)
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f369]) ).
fof(f6381,plain,
! [X0] :
( rearsegP(skaf52(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1041,f3479]) ).
fof(f6382,plain,
! [X0] :
( tl(skaf52(X0)) = app(tl(skaf52(X0)),nil)
| nil = skaf52(X0)
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f346]) ).
fof(f6383,plain,
! [X0] :
( hd(skaf52(X0)) = hd(skaf52(X0))
| nil = skaf52(X0)
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f334]) ).
fof(f6384,plain,
! [X0,X1] :
( app(skaf52(X0),nil) = X1
| ~ frontsegP(X1,skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1041,f1279]) ).
fof(f6385,plain,
! [X0] :
( frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f982]) ).
fof(f6386,plain,
! [X0,X1] :
( frontsegP(skaf52(X0),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1041,f352]) ).
fof(f6387,definition,
! [X0] :
( sQ673_spl
<=> ssList(skaf52(X0)) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f6390,plain,
( sQ673_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6375,f534,f6387]) ).
fof(f6391,definition,
! [X0] :
( sQ674_spl
<=> ( app(skaf52(X0),nil) = skaf52(X0)
| ~ frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f6394,plain,
( sQ674_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6377,f534,f6391]) ).
fof(f6396,plain,
( ~ sQ13_spl
| sQ663_spl ),
inference(split_clause,[status(thm)],[f6379,f6327,f534]) ).
fof(f6397,definition,
! [X0,X1] :
( sQ675_spl
<=> ( app(app(X1,skaf52(X0)),nil) = app(X1,skaf52(X0))
| ~ ssList(X1)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f6400,plain,
( sQ675_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6380,f534,f6397]) ).
fof(f6401,definition,
! [X0] :
( sQ676_spl
<=> ( rearsegP(skaf52(X0),nil)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f6404,plain,
( ~ sQ13_spl
| sQ676_spl ),
inference(split_clause,[status(thm)],[f6381,f6401,f534]) ).
fof(f6405,definition,
! [X0] :
( sQ677_spl
<=> ( tl(skaf52(X0)) = app(tl(skaf52(X0)),nil)
| nil = skaf52(X0)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f6408,plain,
( sQ677_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6382,f534,f6405]) ).
fof(f6409,definition,
! [X0] :
( sQ678_spl
<=> ( hd(skaf52(X0)) = hd(skaf52(X0))
| nil = skaf52(X0)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f6412,plain,
( sQ678_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6383,f534,f6409]) ).
fof(f6413,definition,
! [X0,X1] :
( sQ679_spl
<=> ( app(skaf52(X0),nil) = X1
| ~ frontsegP(X1,skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f6416,plain,
( ~ sQ13_spl
| sQ679_spl ),
inference(split_clause,[status(thm)],[f6384,f6413,f534]) ).
fof(f6417,definition,
! [X0] :
( sQ680_spl
<=> ( frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f6420,plain,
( sQ680_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6385,f534,f6417]) ).
fof(f6421,definition,
! [X0,X1] :
( sQ681_spl
<=> ( frontsegP(skaf52(X0),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f6424,plain,
( ~ sQ13_spl
| sQ681_spl ),
inference(split_clause,[status(thm)],[f6386,f6421,f534]) ).
fof(f6568,plain,
! [X0] :
( app(nil,skaf53(X0)) = nil
| ~ frontsegP(nil,skaf53(X0))
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1043,f1192]) ).
fof(f6570,plain,
! [X0,X1] :
( segmentP(app(skaf53(X1),X0),skaf53(X1))
| ~ ssList(skaf53(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1043,f1086]) ).
fof(f6571,plain,
! [X0,X1] :
( app(app(X1,nil),skaf53(X0)) = app(X1,skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1043,f369]) ).
fof(f6572,plain,
! [X0,X1] :
( app(skaf53(X1),X0) = app(nil,app(skaf53(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1043,f369]) ).
fof(f6573,plain,
! [X0] :
( rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1043,f3479]) ).
fof(f6576,plain,
! [X0,X1] :
( app(nil,skaf53(X1)) = X0
| ~ frontsegP(X0,skaf53(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1043,f1279]) ).
fof(f6577,plain,
! [X0] :
( frontsegP(skaf53(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1043,f982]) ).
fof(f6578,plain,
! [X0,X1] :
( frontsegP(skaf53(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1043,f352]) ).
fof(f6579,definition,
! [X0] :
( sQ683_spl
<=> ( app(nil,skaf53(X0)) = nil
| ~ frontsegP(nil,skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f6582,plain,
( ~ sQ13_spl
| sQ683_spl ),
inference(split_clause,[status(thm)],[f6568,f6579,f534]) ).
fof(f6583,definition,
! [X0,X1] :
( sQ684_spl
<=> ( segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f6587,definition,
! [X0,X1] :
( sQ685_spl
<=> ( segmentP(app(skaf53(X1),X0),skaf53(X1))
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f6590,plain,
( ~ sQ13_spl
| sQ685_spl ),
inference(split_clause,[status(thm)],[f6570,f6587,f534]) ).
fof(f6591,definition,
! [X0,X1] :
( sQ686_spl
<=> ( app(app(X1,nil),skaf53(X0)) = app(X1,skaf53(X0))
| ~ ssList(X1)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f6594,plain,
( ~ sQ13_spl
| sQ686_spl ),
inference(split_clause,[status(thm)],[f6571,f6591,f534]) ).
fof(f6595,definition,
! [X0,X1] :
( sQ687_spl
<=> ( app(skaf53(X1),X0) = app(nil,app(skaf53(X1),X0))
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ687_spl])],[split_symbol_definition]) ).
fof(f6598,plain,
( ~ sQ13_spl
| sQ687_spl ),
inference(split_clause,[status(thm)],[f6572,f6595,f534]) ).
fof(f6599,definition,
! [X0] :
( sQ688_spl
<=> ( rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ688_spl])],[split_symbol_definition]) ).
fof(f6602,plain,
( sQ688_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6573,f534,f6599]) ).
fof(f6611,definition,
! [X0,X1] :
( sQ691_spl
<=> ( app(nil,skaf53(X1)) = X0
| ~ frontsegP(X0,skaf53(X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ691_spl])],[split_symbol_definition]) ).
fof(f6614,plain,
( ~ sQ13_spl
| sQ691_spl ),
inference(split_clause,[status(thm)],[f6576,f6611,f534]) ).
fof(f6615,definition,
! [X0] :
( sQ692_spl
<=> ( frontsegP(skaf53(X0),nil)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f6618,plain,
( ~ sQ13_spl
| sQ692_spl ),
inference(split_clause,[status(thm)],[f6577,f6615,f534]) ).
fof(f6619,definition,
! [X0,X1] :
( sQ693_spl
<=> ( frontsegP(skaf53(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ693_spl])],[split_symbol_definition]) ).
fof(f6622,plain,
( ~ sQ13_spl
| sQ693_spl ),
inference(split_clause,[status(thm)],[f6578,f6619,f534]) ).
fof(f6631,plain,
! [X0] :
( ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f1042]) ).
fof(f6633,plain,
! [X0] :
( app(skaf53(X0),nil) = skaf53(X0)
| ~ frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f1192]) ).
fof(f6635,plain,
! [X0,X1] :
( segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1044,f1086]) ).
fof(f6636,plain,
! [X0,X1] :
( app(app(X1,skaf53(X0)),nil) = app(X1,skaf53(X0))
| ~ ssList(X1)
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f369]) ).
fof(f6637,plain,
! [X0] :
( rearsegP(skaf53(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1044,f3479]) ).
fof(f6638,plain,
! [X0] :
( tl(skaf53(X0)) = app(tl(skaf53(X0)),nil)
| nil = skaf53(X0)
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f346]) ).
fof(f6639,plain,
! [X0] :
( hd(skaf53(X0)) = hd(skaf53(X0))
| nil = skaf53(X0)
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f334]) ).
fof(f6640,plain,
! [X0,X1] :
( app(skaf53(X0),nil) = X1
| ~ frontsegP(X1,skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1044,f1279]) ).
fof(f6641,plain,
! [X0] :
( frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1044,f982]) ).
fof(f6642,plain,
! [X0,X1] :
( frontsegP(skaf53(X0),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1044,f352]) ).
fof(f6643,definition,
! [X0] :
( sQ694_spl
<=> ssList(skaf53(X0)) ),
introduced(definition,[new_symbols(definition,[sQ694_spl])],[split_symbol_definition]) ).
fof(f6646,plain,
( sQ694_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6631,f534,f6643]) ).
fof(f6647,definition,
! [X0] :
( sQ695_spl
<=> ( app(skaf53(X0),nil) = skaf53(X0)
| ~ frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ695_spl])],[split_symbol_definition]) ).
fof(f6650,plain,
( sQ695_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6633,f534,f6647]) ).
fof(f6652,plain,
( ~ sQ13_spl
| sQ684_spl ),
inference(split_clause,[status(thm)],[f6635,f6583,f534]) ).
fof(f6653,definition,
! [X0,X1] :
( sQ696_spl
<=> ( app(app(X1,skaf53(X0)),nil) = app(X1,skaf53(X0))
| ~ ssList(X1)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ696_spl])],[split_symbol_definition]) ).
fof(f6656,plain,
( sQ696_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6636,f534,f6653]) ).
fof(f6657,definition,
! [X0] :
( sQ697_spl
<=> ( rearsegP(skaf53(X0),nil)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ697_spl])],[split_symbol_definition]) ).
fof(f6660,plain,
( ~ sQ13_spl
| sQ697_spl ),
inference(split_clause,[status(thm)],[f6637,f6657,f534]) ).
fof(f6661,definition,
! [X0] :
( sQ698_spl
<=> ( tl(skaf53(X0)) = app(tl(skaf53(X0)),nil)
| nil = skaf53(X0)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ698_spl])],[split_symbol_definition]) ).
fof(f6664,plain,
( sQ698_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6638,f534,f6661]) ).
fof(f6665,definition,
! [X0] :
( sQ699_spl
<=> ( hd(skaf53(X0)) = hd(skaf53(X0))
| nil = skaf53(X0)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ699_spl])],[split_symbol_definition]) ).
fof(f6668,plain,
( sQ699_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6639,f534,f6665]) ).
fof(f6669,definition,
! [X0,X1] :
( sQ700_spl
<=> ( app(skaf53(X0),nil) = X1
| ~ frontsegP(X1,skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ700_spl])],[split_symbol_definition]) ).
fof(f6672,plain,
( ~ sQ13_spl
| sQ700_spl ),
inference(split_clause,[status(thm)],[f6640,f6669,f534]) ).
fof(f6673,definition,
! [X0] :
( sQ701_spl
<=> ( frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f6676,plain,
( sQ701_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6641,f534,f6673]) ).
fof(f6677,definition,
! [X0,X1] :
( sQ702_spl
<=> ( frontsegP(skaf53(X0),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ702_spl])],[split_symbol_definition]) ).
fof(f6680,plain,
( ~ sQ13_spl
| sQ702_spl ),
inference(split_clause,[status(thm)],[f6642,f6677,f534]) ).
fof(f6742,plain,
( ~ sQ52_spl
| sk1 = sk1
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ frontsegP(sk1,sk1) ),
inference(resolution,[status(thm)],[f930,f682]) ).
fof(f6751,plain,
( ~ sQ52_spl
| sQ55_spl
| ~ sQ26_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f6742,f935,f634,f938,f922]) ).
fof(f6756,plain,
( ~ sQ435_spl
| app(skaf42(sk2,hd(sk2)),cons(hd(sk2),skaf43(hd(sk2),sk2))) = sk2
| ~ ssList(sk2)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[f4100,f400]) ).
fof(f6760,definition,
( sQ703_spl
<=> app(skaf42(sk2,hd(sk2)),cons(hd(sk2),skaf43(hd(sk2),sk2))) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ703_spl])],[split_symbol_definition]) ).
fof(f6763,plain,
( ~ sQ435_spl
| sQ703_spl
| ~ sQ15_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f6756,f1799,f560,f6760,f4099]) ).
fof(f6852,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| app(skaf42(sk5,hd(sk2)),cons(hd(sk2),skaf43(hd(sk2),sk5))) = sk5
| ~ ssList(sk5)
| ~ ssItem(hd(sk2)) ),
inference(resolution,[status(thm)],[f4907,f400]) ).
fof(f6856,definition,
( sQ704_spl
<=> app(skaf42(sk5,hd(sk2)),cons(hd(sk2),skaf43(hd(sk2),sk5))) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ704_spl])],[split_symbol_definition]) ).
fof(f6859,plain,
( ~ sQ356_spl
| ~ sQ526_spl
| sQ704_spl
| ~ sQ4_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f6852,f1799,f460,f6856,f4686,f3381]) ).
fof(f6873,plain,
( ~ sQ359_spl
| app(skaf42(sk5,skaf83(sk5)),cons(skaf83(sk5),skaf43(skaf83(sk5),sk5))) = sk5
| ~ ssList(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(resolution,[status(thm)],[f3394,f400]) ).
fof(f6877,definition,
( sQ705_spl
<=> app(skaf42(sk5,skaf83(sk5)),cons(skaf83(sk5),skaf43(skaf83(sk5),sk5))) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ705_spl])],[split_symbol_definition]) ).
fof(f6880,plain,
( ~ sQ359_spl
| sQ705_spl
| ~ sQ4_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f6873,f2166,f460,f6877,f3393]) ).
fof(f6989,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ ssList(app(app(X2,cons(X0,X1)),sk5))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),cons(hd(sk2),nil)))
| ~ ssItem(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ leq(hd(sk2),X0)
| ~ leq(X0,hd(sk2)) ),
inference(paramodulation,[status(thm)],[f4908,f523]) ).
fof(f6990,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ ssList(app(app(X2,sk5),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,cons(hd(sk2),nil)),cons(X0,X1)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ leq(X0,hd(sk2))
| ~ leq(hd(sk2),X0) ),
inference(paramodulation,[status(thm)],[f4908,f523]) ).
fof(f6991,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| leq(hd(sk2),X2)
| leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f522]) ).
fof(f6992,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| leq(X2,hd(sk2))
| leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f522]) ).
fof(f6993,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| lt(hd(sk2),X2)
| lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f521]) ).
fof(f6994,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| lt(X2,hd(sk2))
| lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f521]) ).
fof(f6995,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f520]) ).
fof(f6996,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f520]) ).
fof(f6997,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f519]) ).
fof(f6998,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f519]) ).
fof(f6999,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| X1 = hd(sk2)
| ~ ssList(app(X0,cons(X1,cons(hd(sk2),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f518]) ).
fof(f7000,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,cons(hd(sk2),X0)),sk5))
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f5619]) ).
fof(f7001,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,sk5),cons(hd(sk2),X0)))
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f5619]) ).
fof(f7002,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| memberP(app(X0,cons(hd(sk2),nil)),hd(sk2))
| ~ ssList(app(X0,sk5))
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f514]) ).
fof(f7003,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf59(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f828]) ).
fof(f7004,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| memberP(sk5,hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f508]) ).
fof(f7006,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf55(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f826]) ).
fof(f7008,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf54(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f824]) ).
fof(f7010,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf50(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f808]) ).
fof(f7012,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf49(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f806]) ).
fof(f7014,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf44(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f804]) ).
fof(f7020,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| cons(hd(sk2),nil) = cons(hd(sk2),X0)
| ~ ssList(sk5)
| ~ frontsegP(cons(hd(sk2),X0),cons(hd(sk2),nil))
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f4908,f1711]) ).
fof(f7021,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk2),nil),X2)
| hd(sk2) = X1
| ~ ssItem(hd(sk2))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f1703]) ).
fof(f7022,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(cons(hd(sk2),nil),X2)
| frontsegP(nil,X0)
| ~ ssItem(hd(sk2))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f1638]) ).
fof(f7024,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| X0 = hd(sk2)
| ~ ssItem(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f4908,f413]) ).
fof(f7025,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = X0
| ~ ssItem(hd(sk2))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4908,f413]) ).
fof(f7026,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| frontsegP(cons(hd(sk2),X0),sk5)
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f4908,f516]) ).
fof(f7027,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| frontsegP(sk5,cons(hd(sk2),X0))
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f4908,f516]) ).
fof(f7038,definition,
! [X0,X1,X2] :
( sQ706_spl
<=> ( ~ ssList(app(app(X2,cons(X0,X1)),sk5))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),cons(hd(sk2),nil)))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(hd(sk2),X0)
| ~ leq(X0,hd(sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ706_spl])],[split_symbol_definition]) ).
fof(f7041,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ706_spl ),
inference(split_clause,[status(thm)],[f6989,f7038,f534,f1799,f4686,f1848,f1617]) ).
fof(f7042,definition,
! [X0,X1,X2] :
( sQ707_spl
<=> ( ~ ssList(app(app(X2,sk5),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,cons(hd(sk2),nil)),cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,hd(sk2))
| ~ leq(hd(sk2),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ707_spl])],[split_symbol_definition]) ).
fof(f7045,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ707_spl ),
inference(split_clause,[status(thm)],[f6990,f7042,f534,f1799,f4686,f1848,f1617]) ).
fof(f7046,definition,
! [X0,X1,X2] :
( sQ708_spl
<=> ( leq(hd(sk2),X2)
| leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ708_spl])],[split_symbol_definition]) ).
fof(f7049,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ708_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6991,f534,f7046,f1799,f4686,f1848,f1617]) ).
fof(f7050,definition,
! [X0,X1,X2] :
( sQ709_spl
<=> ( leq(X2,hd(sk2))
| leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ709_spl])],[split_symbol_definition]) ).
fof(f7053,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ709_spl ),
inference(split_clause,[status(thm)],[f6992,f7050,f534,f1799,f4686,f1848,f1617]) ).
fof(f7054,definition,
! [X0,X1,X2] :
( sQ710_spl
<=> ( lt(hd(sk2),X2)
| lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ710_spl])],[split_symbol_definition]) ).
fof(f7057,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ710_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6993,f534,f7054,f1799,f4686,f1848,f1617]) ).
fof(f7058,definition,
! [X0,X1,X2] :
( sQ711_spl
<=> ( lt(X2,hd(sk2))
| lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ711_spl])],[split_symbol_definition]) ).
fof(f7061,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ711_spl ),
inference(split_clause,[status(thm)],[f6994,f7058,f534,f1799,f4686,f1848,f1617]) ).
fof(f7062,definition,
! [X0,X1,X2] :
( sQ712_spl
<=> ( leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ712_spl])],[split_symbol_definition]) ).
fof(f7065,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ712_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6995,f534,f7062,f1799,f4686,f1848,f1617]) ).
fof(f7066,definition,
! [X0,X1,X2] :
( sQ713_spl
<=> ( leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ713_spl])],[split_symbol_definition]) ).
fof(f7069,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ713_spl ),
inference(split_clause,[status(thm)],[f6996,f7066,f534,f1799,f4686,f1848,f1617]) ).
fof(f7070,definition,
! [X0,X1,X2] :
( sQ714_spl
<=> ( lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),cons(hd(sk2),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ714_spl])],[split_symbol_definition]) ).
fof(f7073,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ714_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6997,f534,f7070,f1799,f4686,f1848,f1617]) ).
fof(f7074,definition,
! [X0,X1,X2] :
( sQ715_spl
<=> ( lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,cons(hd(sk2),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ715_spl])],[split_symbol_definition]) ).
fof(f7077,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ715_spl ),
inference(split_clause,[status(thm)],[f6998,f7074,f534,f1799,f4686,f1848,f1617]) ).
fof(f7078,definition,
! [X0,X1] :
( sQ716_spl
<=> ( X1 = hd(sk2)
| ~ ssList(app(X0,cons(X1,cons(hd(sk2),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ716_spl])],[split_symbol_definition]) ).
fof(f7081,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ716_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6999,f534,f7078,f1799,f4686,f1848,f1617]) ).
fof(f7082,definition,
! [X0,X1] :
( sQ717_spl
<=> ( ~ ssList(app(app(X1,cons(hd(sk2),X0)),sk5))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f7085,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ0_spl
| ~ sQ136_spl
| sQ717_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7000,f534,f7082,f1799,f446,f4686,f1848,f1617]) ).
fof(f7086,definition,
! [X0,X1] :
( sQ718_spl
<=> ( ~ ssList(app(app(X1,sk5),cons(hd(sk2),X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f7089,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ0_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ718_spl ),
inference(split_clause,[status(thm)],[f7001,f7086,f534,f1799,f446,f4686,f1848,f1617]) ).
fof(f7090,definition,
! [X0] :
( sQ719_spl
<=> ( memberP(app(X0,cons(hd(sk2),nil)),hd(sk2))
| ~ ssList(app(X0,sk5))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ719_spl])],[split_symbol_definition]) ).
fof(f7093,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ719_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7002,f534,f7090,f1799,f4686,f1848,f1617]) ).
fof(f7094,definition,
! [X0,X1] :
( sQ720_spl
<=> ( hd(sk2) = skaf59(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ720_spl])],[split_symbol_definition]) ).
fof(f7097,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ720_spl ),
inference(split_clause,[status(thm)],[f7003,f7094,f534,f1799,f4686,f1848,f1617]) ).
fof(f7098,definition,
( sQ721_spl
<=> memberP(sk5,hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ721_spl])],[split_symbol_definition]) ).
fof(f7101,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| sQ721_spl
| ~ sQ136_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7004,f534,f1799,f7098,f4686,f1848,f1617]) ).
fof(f7103,definition,
! [X0,X1] :
( sQ722_spl
<=> ( hd(sk2) = skaf55(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ722_spl])],[split_symbol_definition]) ).
fof(f7106,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ722_spl ),
inference(split_clause,[status(thm)],[f7006,f7103,f534,f1799,f4686,f1848,f1617]) ).
fof(f7108,definition,
! [X0,X1] :
( sQ723_spl
<=> ( hd(sk2) = skaf54(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ723_spl])],[split_symbol_definition]) ).
fof(f7111,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ723_spl ),
inference(split_clause,[status(thm)],[f7008,f7108,f534,f1799,f4686,f1848,f1617]) ).
fof(f7113,definition,
! [X0,X1] :
( sQ724_spl
<=> ( hd(sk2) = skaf50(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition]) ).
fof(f7116,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ724_spl ),
inference(split_clause,[status(thm)],[f7010,f7113,f534,f1799,f4686,f1848,f1617]) ).
fof(f7118,definition,
! [X0,X1] :
( sQ725_spl
<=> ( hd(sk2) = skaf49(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ725_spl])],[split_symbol_definition]) ).
fof(f7121,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ725_spl ),
inference(split_clause,[status(thm)],[f7012,f7118,f534,f1799,f4686,f1848,f1617]) ).
fof(f7123,definition,
! [X0,X1] :
( sQ726_spl
<=> ( hd(sk2) = skaf44(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f7126,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ726_spl ),
inference(split_clause,[status(thm)],[f7014,f7123,f534,f1799,f4686,f1848,f1617]) ).
fof(f7132,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ4_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ449_spl ),
inference(split_clause,[status(thm)],[f7020,f4157,f534,f1799,f460,f4686,f1848,f1617]) ).
fof(f7133,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ4_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f7021,f4161,f534,f1799,f460,f4686,f1848,f1617]) ).
fof(f7134,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ4_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f7022,f4165,f534,f1799,f460,f4686,f1848,f1617]) ).
fof(f7136,definition,
! [X0,X1] :
( sQ727_spl
<=> ( X0 = hd(sk2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f7139,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ727_spl ),
inference(split_clause,[status(thm)],[f7024,f7136,f534,f1799,f4686,f1848,f1617]) ).
fof(f7140,definition,
! [X0,X1] :
( sQ728_spl
<=> ( hd(sk2) = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f7143,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ728_spl ),
inference(split_clause,[status(thm)],[f7025,f7140,f534,f1799,f4686,f1848,f1617]) ).
fof(f7144,definition,
! [X0] :
( sQ729_spl
<=> ( frontsegP(cons(hd(sk2),X0),sk5)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ729_spl])],[split_symbol_definition]) ).
fof(f7147,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ729_spl ),
inference(split_clause,[status(thm)],[f7026,f7144,f534,f1799,f4686,f1848,f1617]) ).
fof(f7148,definition,
! [X0] :
( sQ730_spl
<=> ( frontsegP(sk5,cons(hd(sk2),X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ730_spl])],[split_symbol_definition]) ).
fof(f7151,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ730_spl ),
inference(split_clause,[status(thm)],[f7027,f7148,f534,f1799,f4686,f1848,f1617]) ).
fof(f7184,plain,
( ~ sQ114_spl
| memberP(sk2,hd(sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(tl(sk2)) ),
inference(paramodulation,[status(thm)],[f1610,f508]) ).
fof(f7259,plain,
( ~ sQ114_spl
| sQ435_spl
| ~ sQ136_spl
| ~ sQ135_spl ),
inference(split_clause,[status(thm)],[f7184,f1796,f1799,f4099,f1609]) ).
fof(f7326,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| memberP(X0,X2)
| memberP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ memberP(app(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f450]) ).
fof(f7335,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| memberP(cons(X2,X0),X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f354,f450]) ).
fof(f7371,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f413,f450]) ).
fof(f7372,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f516,f450]) ).
fof(f7373,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| frontsegP(X1,X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f409,f450]) ).
fof(f7374,plain,
! [X0] :
( ~ sQ1_spl
| ~ memberP(nil,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f271,f450]) ).
fof(f7410,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| memberP(cons(X2,X0),X1)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f7335,f450]) ).
fof(f7423,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f7371,f450]) ).
fof(f7424,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| frontsegP(X1,X3)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f7373,f450]) ).
fof(f7427,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f450]) ).
fof(f7429,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ ssList(app(app(X1,cons(hd(sk2),nil)),cons(hd(sk2),X0)))
| ~ duplicatefreeP(app(app(X1,sk5),cons(hd(sk2),X0)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f7427]) ).
fof(f7432,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ ssList(app(app(X1,cons(hd(sk2),X0)),cons(hd(sk2),nil)))
| ~ duplicatefreeP(app(app(X1,cons(hd(sk2),X0)),sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f7427]) ).
fof(f7438,definition,
! [X0,X1] :
( sQ749_spl
<=> ( ~ ssList(app(app(X1,cons(hd(sk2),nil)),cons(hd(sk2),X0)))
| ~ duplicatefreeP(app(app(X1,sk5),cons(hd(sk2),X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f7441,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sQ749_spl ),
inference(split_clause,[status(thm)],[f7429,f7438,f534,f449,f4686,f1848,f1617]) ).
fof(f7450,definition,
! [X0,X1] :
( sQ752_spl
<=> ( ~ ssList(app(app(X1,cons(hd(sk2),X0)),cons(hd(sk2),nil)))
| ~ duplicatefreeP(app(app(X1,cons(hd(sk2),X0)),sk5))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ752_spl])],[split_symbol_definition]) ).
fof(f7453,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| sQ752_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7432,f534,f7450,f449,f4686,f1848,f1617]) ).
fof(f7507,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| hd(sk2) = X0
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4908,f7423]) ).
fof(f7510,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| X0 = hd(sk2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f4908,f7423]) ).
fof(f7516,definition,
! [X0,X1] :
( sQ761_spl
<=> ( hd(sk2) = X0
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f7519,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sQ761_spl ),
inference(split_clause,[status(thm)],[f7507,f7516,f534,f449,f4686,f1848,f1617]) ).
fof(f7528,definition,
! [X0,X1] :
( sQ764_spl
<=> ( X0 = hd(sk2)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ764_spl])],[split_symbol_definition]) ).
fof(f7531,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sQ764_spl ),
inference(split_clause,[status(thm)],[f7510,f7528,f534,f449,f4686,f1848,f1617]) ).
fof(f7536,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| X2 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f7372,f7423]) ).
fof(f7551,definition,
! [X2] :
( sQ766_spl
<=> X2 = X2 ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f7554,plain,
( ~ sQ1_spl
| sQ766_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f7536,f745,f7551,f449]) ).
fof(f7584,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| frontsegP(nil,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4908,f7424]) ).
fof(f7587,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f4908,f7424]) ).
fof(f7594,definition,
! [X0,X1] :
( sQ768_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f7597,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sQ768_spl ),
inference(split_clause,[status(thm)],[f7584,f7594,f534,f449,f4686,f1848,f1617]) ).
fof(f7606,definition,
! [X0,X1] :
( sQ771_spl
<=> ( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f7609,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ1_spl
| ~ sQ13_spl
| sQ771_spl ),
inference(split_clause,[status(thm)],[f7587,f7606,f534,f449,f4686,f1848,f1617]) ).
fof(f7686,definition,
! [X0] :
( sQ776_spl
<=> ( memberP(app(X0,sk2),skaf83(sk2))
| ~ ssList(app(X0,cons(skaf83(sk2),skaf82(sk2))))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f7705,definition,
( sQ777_spl
<=> ssList(skaf45(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f7707,plain,
( sQ777_spl
| ~ ssList(skaf45(sk1,sk2)) ),
inference(component_clause,[status(thm)],[f7705]) ).
fof(f7743,plain,
( sQ777_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7707,f251]) ).
fof(f7744,plain,
sQ777_spl,
inference(contradiction_clause,[status(thm)],[f7743]) ).
fof(f7760,definition,
( sQ786_spl
<=> ssList(skaf45(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f7762,plain,
( sQ786_spl
| ~ ssList(skaf45(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f7760]) ).
fof(f7789,plain,
( sQ786_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7762,f251]) ).
fof(f7790,plain,
sQ786_spl,
inference(contradiction_clause,[status(thm)],[f7789]) ).
fof(f7915,plain,
! [X0,X1] :
( ~ sQ1_spl
| memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ memberP(app(X0,nil),X1) ),
inference(resolution,[status(thm)],[f7326,f7374]) ).
fof(f7917,definition,
! [X0,X1] :
( sQ802_spl
<=> ( memberP(X0,X1)
| ~ ssList(X0)
| ~ memberP(app(X0,nil),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ802_spl])],[split_symbol_definition]) ).
fof(f7920,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| sQ802_spl ),
inference(split_clause,[status(thm)],[f7915,f7917,f534,f449]) ).
fof(f8217,plain,
( ~ sQ340_spl
| rearsegP(sk1,nil)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f899,f3220]) ).
fof(f8228,plain,
( ~ sQ340_spl
| sQ378_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f8217,f634,f3513,f3219]) ).
fof(f8325,plain,
( sQ19_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f450]) ).
fof(f8326,plain,
( sQ19_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f8325]) ).
fof(f8595,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ435_spl
| memberP(cons(X0,sk2),hd(sk2))
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f4100,f7410]) ).
fof(f8599,definition,
! [X0] :
( sQ845_spl
<=> memberP(cons(X0,sk2),hd(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ845_spl])],[split_symbol_definition]) ).
fof(f8602,plain,
( ~ sQ1_spl
| ~ sQ435_spl
| sQ845_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8595,f560,f8599,f4099,f449]) ).
fof(f8620,plain,
! [X0,X1] :
( frontsegP(cons(skac3,X0),cons(skac3,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f209,f516]) ).
fof(f8623,plain,
! [X0,X1] :
( frontsegP(cons(skac2,X0),cons(skac2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f210,f516]) ).
fof(f8626,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf83(X2),X0),cons(skaf83(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f212,f516]) ).
fof(f8627,plain,
! [X0,X1,X2,X3] :
( X0 = skaf83(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf83(X2),X3)) ),
inference(resolution,[status(thm)],[f212,f413]) ).
fof(f8629,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf79(X2),X0),cons(skaf79(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f216,f516]) ).
fof(f8630,plain,
! [X0,X1,X2,X3] :
( X0 = skaf79(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf79(X2),X3)) ),
inference(resolution,[status(thm)],[f216,f413]) ).
fof(f8632,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf78(X2),X0),cons(skaf78(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f217,f516]) ).
fof(f8633,plain,
! [X0,X1,X2,X3] :
( X0 = skaf78(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf78(X2),X3)) ),
inference(resolution,[status(thm)],[f217,f413]) ).
fof(f8635,plain,
! [X0,X1,X2] :
( frontsegP(cons(hd(X0),X1),cons(hd(X0),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f277,f516]) ).
fof(f8636,plain,
! [X0,X1,X2,X3] :
( X1 = hd(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ frontsegP(cons(X1,X2),cons(hd(X0),X3))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f277,f413]) ).
fof(f8686,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf74(X2),X0),cons(skaf74(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f221,f516]) ).
fof(f8687,plain,
! [X0,X1,X2,X3] :
( X0 = skaf74(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf74(X2),X3)) ),
inference(resolution,[status(thm)],[f221,f413]) ).
fof(f8689,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf70(X2),X0),cons(skaf70(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f225,f516]) ).
fof(f8690,plain,
! [X0,X1,X2,X3] :
( X0 = skaf70(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf70(X2),X3)) ),
inference(resolution,[status(thm)],[f225,f413]) ).
fof(f8692,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf69(X2),X0),cons(skaf69(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f226,f516]) ).
fof(f8693,plain,
! [X0,X1,X2,X3] :
( X0 = skaf69(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf69(X2),X3)) ),
inference(resolution,[status(thm)],[f226,f413]) ).
fof(f8695,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf65(X2),X0),cons(skaf65(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f230,f516]) ).
fof(f8696,plain,
! [X0,X1,X2,X3] :
( X0 = skaf65(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf65(X2),X3)) ),
inference(resolution,[status(thm)],[f230,f413]) ).
fof(f8698,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf64(X2),X0),cons(skaf64(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f231,f516]) ).
fof(f8699,plain,
! [X0,X1,X2,X3] :
( X0 = skaf64(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf64(X2),X3)) ),
inference(resolution,[status(thm)],[f231,f413]) ).
fof(f8701,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf60(X2),X0),cons(skaf60(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f235,f516]) ).
fof(f8702,plain,
! [X0,X1,X2,X3] :
( X0 = skaf60(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(skaf60(X2),X3)) ),
inference(resolution,[status(thm)],[f235,f413]) ).
fof(f8708,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf59(X2),X0),cons(skaf59(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f236,f516]) ).
fof(f8711,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf55(X2),X0),cons(skaf55(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f240,f516]) ).
fof(f8714,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf54(X2),X0),cons(skaf54(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f241,f516]) ).
fof(f8717,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf50(X2),X0),cons(skaf50(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f245,f516]) ).
fof(f8720,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf49(X2),X0),cons(skaf49(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f246,f516]) ).
fof(f8723,plain,
! [X0,X1,X2] :
( frontsegP(cons(skaf44(X2),X0),cons(skaf44(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f247,f516]) ).
fof(f8919,plain,
! [X0] :
( ~ sQ131_spl
| memberP(app(X0,sk2),skaf83(sk2))
| ~ ssList(app(X0,cons(skaf83(sk2),skaf82(sk2))))
| ~ ssItem(skaf83(sk2))
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f514]) ).
fof(f8923,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| sQ776_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f8919,f2380,f7686,f2383,f1765]) ).
fof(f8970,plain,
( ~ sQ61_spl
| ~ ssList(nil)
| frontsegP(sk1,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f995,f260]) ).
fof(f8971,plain,
! [X0,X1] :
( ~ sQ61_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| frontsegP(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f995,f379]) ).
fof(f8974,plain,
( ~ sQ61_spl
| sQ79_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f8970,f534,f1201,f994]) ).
fof(f8975,definition,
! [X0,X1] :
( sQ865_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| frontsegP(sk1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ865_spl])],[split_symbol_definition]) ).
fof(f8978,plain,
( ~ sQ61_spl
| ~ sQ13_spl
| sQ865_spl ),
inference(split_clause,[status(thm)],[f8971,f8975,f534,f994]) ).
fof(f9039,plain,
! [X0] :
( ~ sQ62_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1031,f986]) ).
fof(f9040,plain,
! [X0] :
( ~ sQ62_spl
| app(app(skaf47(app(sk1,X0),sk1),sk1),skaf48(sk1,app(sk1,X0))) = app(sk1,X0)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f399]) ).
fof(f9041,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| app(app(X2,app(sk1,X0)),X1) = sk1
| ~ ssList(app(app(X2,app(sk1,X0)),X1))
| ~ segmentP(sk1,app(app(X2,app(sk1,X0)),X1))
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f708]) ).
fof(f9042,plain,
! [X0,X1,X2,X3] :
( ~ sQ62_spl
| segmentP(X3,sk1)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk1,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk1,X0)),X1))
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f707]) ).
fof(f9043,plain,
! [X0] :
( ~ sQ62_spl
| app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ segmentP(sk1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f340]) ).
fof(f9044,plain,
! [X0,X1] :
( ~ sQ62_spl
| segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f375]) ).
fof(f9045,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| segmentP(app(app(X2,app(sk1,X0)),X1),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9039,f405]) ).
fof(f9046,plain,
( ~ sQ62_spl
| segmentP(sk1,sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f899,f9039]) ).
fof(f9047,definition,
! [X0] :
( sQ871_spl
<=> ( app(app(skaf47(app(sk1,X0),sk1),sk1),skaf48(sk1,app(sk1,X0))) = app(sk1,X0)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ871_spl])],[split_symbol_definition]) ).
fof(f9050,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ871_spl ),
inference(split_clause,[status(thm)],[f9040,f9047,f634,f1011]) ).
fof(f9051,definition,
! [X0,X1,X2] :
( sQ872_spl
<=> ( app(app(X2,app(sk1,X0)),X1) = sk1
| ~ ssList(app(app(X2,app(sk1,X0)),X1))
| ~ segmentP(sk1,app(app(X2,app(sk1,X0)),X1))
| ~ ssList(app(sk1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ872_spl])],[split_symbol_definition]) ).
fof(f9054,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ872_spl ),
inference(split_clause,[status(thm)],[f9041,f9051,f634,f1011]) ).
fof(f9055,definition,
! [X0,X1,X2,X3] :
( sQ873_spl
<=> ( segmentP(X3,sk1)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk1,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk1,X0)),X1))
| ~ ssList(app(sk1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ873_spl])],[split_symbol_definition]) ).
fof(f9058,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ873_spl ),
inference(split_clause,[status(thm)],[f9042,f9055,f634,f1011]) ).
fof(f9059,definition,
! [X0] :
( sQ874_spl
<=> ( app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ segmentP(sk1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ874_spl])],[split_symbol_definition]) ).
fof(f9062,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ874_spl ),
inference(split_clause,[status(thm)],[f9043,f9059,f634,f1011]) ).
fof(f9063,definition,
! [X0,X1] :
( sQ875_spl
<=> ( segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ875_spl])],[split_symbol_definition]) ).
fof(f9066,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ875_spl ),
inference(split_clause,[status(thm)],[f9044,f9063,f634,f1011]) ).
fof(f9067,definition,
! [X0,X1,X2] :
( sQ876_spl
<=> ( segmentP(app(app(X2,app(sk1,X0)),X1),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ876_spl])],[split_symbol_definition]) ).
fof(f9070,plain,
( ~ sQ62_spl
| ~ sQ26_spl
| sQ876_spl ),
inference(split_clause,[status(thm)],[f9045,f9067,f634,f1011]) ).
fof(f9071,definition,
( sQ877_spl
<=> segmentP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ877_spl])],[split_symbol_definition]) ).
fof(f9072,plain,
( ~ sQ877_spl
| segmentP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f9071]) ).
fof(f9074,plain,
( ~ sQ62_spl
| sQ877_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f9046,f534,f9071,f1011]) ).
fof(f9082,plain,
( ~ sQ877_spl
| app(app(skaf47(sk1,sk1),sk1),skaf48(sk1,sk1)) = sk1
| ~ ssList(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f9072,f399]) ).
fof(f9083,plain,
! [X0,X1] :
( ~ sQ877_spl
| app(app(X1,sk1),X0) = sk1
| ~ ssList(app(app(X1,sk1),X0))
| ~ segmentP(sk1,app(app(X1,sk1),X0))
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9072,f708]) ).
fof(f9084,plain,
! [X0,X1,X2] :
( ~ sQ877_spl
| segmentP(X2,sk1)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk1),X0))
| ~ segmentP(X2,app(app(X1,sk1),X0))
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9072,f707]) ).
fof(f9086,plain,
! [X0] :
( ~ sQ877_spl
| segmentP(X0,sk1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ segmentP(X0,sk1) ),
inference(resolution,[status(thm)],[f9072,f375]) ).
fof(f9087,plain,
! [X0,X1] :
( ~ sQ877_spl
| segmentP(app(app(X1,sk1),X0),sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9072,f405]) ).
fof(f9089,definition,
( sQ878_spl
<=> app(app(skaf47(sk1,sk1),sk1),skaf48(sk1,sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ878_spl])],[split_symbol_definition]) ).
fof(f9092,plain,
( ~ sQ877_spl
| sQ878_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f9082,f634,f9089,f9071]) ).
fof(f9093,definition,
! [X0,X1] :
( sQ879_spl
<=> ( app(app(X1,sk1),X0) = sk1
| ~ ssList(app(app(X1,sk1),X0))
| ~ segmentP(sk1,app(app(X1,sk1),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ879_spl])],[split_symbol_definition]) ).
fof(f9096,plain,
( ~ sQ877_spl
| ~ sQ26_spl
| sQ879_spl ),
inference(split_clause,[status(thm)],[f9083,f9093,f634,f9071]) ).
fof(f9097,definition,
! [X0,X1,X2] :
( sQ880_spl
<=> ( segmentP(X2,sk1)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk1),X0))
| ~ segmentP(X2,app(app(X1,sk1),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ880_spl])],[split_symbol_definition]) ).
fof(f9100,plain,
( ~ sQ877_spl
| ~ sQ26_spl
| sQ880_spl ),
inference(split_clause,[status(thm)],[f9084,f9097,f634,f9071]) ).
fof(f9102,definition,
! [X0] :
( sQ881_spl
<=> ( segmentP(X0,sk1)
| ~ ssList(X0)
| ~ segmentP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ881_spl])],[split_symbol_definition]) ).
fof(f9105,plain,
( ~ sQ877_spl
| ~ sQ26_spl
| sQ881_spl ),
inference(split_clause,[status(thm)],[f9086,f9102,f634,f9071]) ).
fof(f9106,definition,
! [X0,X1] :
( sQ882_spl
<=> ( segmentP(app(app(X1,sk1),X0),sk1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ882_spl])],[split_symbol_definition]) ).
fof(f9109,plain,
( ~ sQ877_spl
| ~ sQ26_spl
| sQ882_spl ),
inference(split_clause,[status(thm)],[f9087,f9106,f634,f9071]) ).
fof(f9172,plain,
! [X0] :
( ~ sQ63_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1032,f985]) ).
fof(f9173,plain,
! [X0] :
( ~ sQ63_spl
| app(app(skaf47(app(sk2,X0),sk2),sk2),skaf48(sk2,app(sk2,X0))) = app(sk2,X0)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f399]) ).
fof(f9174,plain,
! [X0,X1,X2] :
( ~ sQ63_spl
| app(app(X2,app(sk2,X0)),X1) = sk2
| ~ ssList(app(app(X2,app(sk2,X0)),X1))
| ~ segmentP(sk2,app(app(X2,app(sk2,X0)),X1))
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f708]) ).
fof(f9175,plain,
! [X0,X1,X2,X3] :
( ~ sQ63_spl
| segmentP(X3,sk2)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk2,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk2,X0)),X1))
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f707]) ).
fof(f9176,plain,
! [X0] :
( ~ sQ63_spl
| app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ segmentP(sk2,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f340]) ).
fof(f9177,plain,
! [X0,X1] :
( ~ sQ63_spl
| segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f375]) ).
fof(f9178,plain,
! [X0,X1,X2] :
( ~ sQ63_spl
| segmentP(app(app(X2,app(sk2,X0)),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9172,f405]) ).
fof(f9181,plain,
( ~ sQ63_spl
| segmentP(sk2,sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f898,f9172]) ).
fof(f9182,definition,
! [X0] :
( sQ887_spl
<=> ( app(app(skaf47(app(sk2,X0),sk2),sk2),skaf48(sk2,app(sk2,X0))) = app(sk2,X0)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ887_spl])],[split_symbol_definition]) ).
fof(f9185,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ887_spl ),
inference(split_clause,[status(thm)],[f9173,f9182,f560,f1015]) ).
fof(f9186,definition,
! [X0,X1,X2] :
( sQ888_spl
<=> ( app(app(X2,app(sk2,X0)),X1) = sk2
| ~ ssList(app(app(X2,app(sk2,X0)),X1))
| ~ segmentP(sk2,app(app(X2,app(sk2,X0)),X1))
| ~ ssList(app(sk2,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ888_spl])],[split_symbol_definition]) ).
fof(f9189,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ888_spl ),
inference(split_clause,[status(thm)],[f9174,f9186,f560,f1015]) ).
fof(f9190,definition,
! [X0,X1,X2,X3] :
( sQ889_spl
<=> ( segmentP(X3,sk2)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk2,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk2,X0)),X1))
| ~ ssList(app(sk2,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ889_spl])],[split_symbol_definition]) ).
fof(f9193,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ889_spl ),
inference(split_clause,[status(thm)],[f9175,f9190,f560,f1015]) ).
fof(f9194,definition,
! [X0] :
( sQ890_spl
<=> ( app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ segmentP(sk2,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ890_spl])],[split_symbol_definition]) ).
fof(f9197,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ890_spl ),
inference(split_clause,[status(thm)],[f9176,f9194,f560,f1015]) ).
fof(f9198,definition,
! [X0,X1] :
( sQ891_spl
<=> ( segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ891_spl])],[split_symbol_definition]) ).
fof(f9201,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ891_spl ),
inference(split_clause,[status(thm)],[f9177,f9198,f560,f1015]) ).
fof(f9202,definition,
! [X0,X1,X2] :
( sQ892_spl
<=> ( segmentP(app(app(X2,app(sk2,X0)),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ892_spl])],[split_symbol_definition]) ).
fof(f9205,plain,
( ~ sQ63_spl
| ~ sQ15_spl
| sQ892_spl ),
inference(split_clause,[status(thm)],[f9178,f9202,f560,f1015]) ).
fof(f9211,plain,
( ~ sQ63_spl
| sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f9181,f534,f563,f1015]) ).
fof(f9305,plain,
! [X0] :
( ~ sQ277_spl
| nil = sk5
| strictorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ lt(X0,hd(sk5)) ),
inference(resolution,[status(thm)],[f2818,f390]) ).
fof(f9306,definition,
! [X0] :
( sQ899_spl
<=> ( strictorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ lt(X0,hd(sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ899_spl])],[split_symbol_definition]) ).
fof(f9309,plain,
( ~ sQ277_spl
| sQ21_spl
| ~ sQ4_spl
| sQ899_spl ),
inference(split_clause,[status(thm)],[f9305,f9306,f460,f591,f2817]) ).
fof(f9324,plain,
! [X0] :
( ~ sQ276_spl
| nil = sk5
| totalorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ ssList(sk5)
| ~ leq(X0,hd(sk5)) ),
inference(resolution,[status(thm)],[f2814,f388]) ).
fof(f9325,definition,
! [X0] :
( sQ900_spl
<=> ( totalorderedP(cons(X0,sk5))
| ~ ssItem(X0)
| ~ leq(X0,hd(sk5)) ) ),
introduced(definition,[new_symbols(definition,[sQ900_spl])],[split_symbol_definition]) ).
fof(f9328,plain,
( ~ sQ276_spl
| sQ21_spl
| ~ sQ4_spl
| sQ900_spl ),
inference(split_clause,[status(thm)],[f9324,f9325,f460,f591,f2813]) ).
fof(f9373,plain,
( ~ sQ16_spl
| app(app(skaf47(sk2,sk2),sk2),skaf48(sk2,sk2)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f564,f399]) ).
fof(f9374,plain,
! [X0,X1] :
( ~ sQ16_spl
| app(app(X1,sk2),X0) = sk2
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(sk2,app(app(X1,sk2),X0))
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f564,f708]) ).
fof(f9375,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| segmentP(X2,sk2)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(X2,app(app(X1,sk2),X0))
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f564,f707]) ).
fof(f9376,plain,
( ~ sQ16_spl
| sk2 = sk2
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ segmentP(sk2,sk2) ),
inference(resolution,[status(thm)],[f564,f340]) ).
fof(f9377,plain,
! [X0] :
( ~ sQ16_spl
| segmentP(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ segmentP(X0,sk2) ),
inference(resolution,[status(thm)],[f564,f375]) ).
fof(f9378,plain,
! [X0,X1] :
( ~ sQ16_spl
| segmentP(app(app(X1,sk2),X0),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f564,f405]) ).
fof(f9379,definition,
( sQ902_spl
<=> app(app(skaf47(sk2,sk2),sk2),skaf48(sk2,sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ902_spl])],[split_symbol_definition]) ).
fof(f9382,plain,
( ~ sQ16_spl
| sQ902_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9373,f560,f9379,f563]) ).
fof(f9383,definition,
! [X0,X1] :
( sQ903_spl
<=> ( app(app(X1,sk2),X0) = sk2
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(sk2,app(app(X1,sk2),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ903_spl])],[split_symbol_definition]) ).
fof(f9386,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ903_spl ),
inference(split_clause,[status(thm)],[f9374,f9383,f560,f563]) ).
fof(f9387,definition,
! [X0,X1,X2] :
( sQ904_spl
<=> ( segmentP(X2,sk2)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk2),X0))
| ~ segmentP(X2,app(app(X1,sk2),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ904_spl])],[split_symbol_definition]) ).
fof(f9390,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ904_spl ),
inference(split_clause,[status(thm)],[f9375,f9387,f560,f563]) ).
fof(f9391,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9376,f563,f560,f788]) ).
fof(f9392,definition,
! [X0] :
( sQ905_spl
<=> ( segmentP(X0,sk2)
| ~ ssList(X0)
| ~ segmentP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ905_spl])],[split_symbol_definition]) ).
fof(f9395,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ905_spl ),
inference(split_clause,[status(thm)],[f9377,f9392,f560,f563]) ).
fof(f9396,definition,
! [X0,X1] :
( sQ906_spl
<=> ( segmentP(app(app(X1,sk2),X0),sk2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ906_spl])],[split_symbol_definition]) ).
fof(f9399,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| sQ906_spl ),
inference(split_clause,[status(thm)],[f9378,f9396,f560,f563]) ).
fof(f9467,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| sk5 = sk5
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ frontsegP(sk5,sk5) ),
inference(resolution,[status(thm)],[f954,f682]) ).
fof(f9476,plain,
( ~ sQ56_spl
| sQ59_spl
| ~ sQ4_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f9467,f960,f460,f963,f946]) ).
fof(f9498,plain,
! [X0] :
( ~ sQ131_spl
| memberP(sk2,X0)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ memberP(skaf82(sk2),X0) ),
inference(paramodulation,[status(thm)],[f1766,f354]) ).
fof(f9504,definition,
! [X0] :
( sQ909_spl
<=> ( memberP(sk2,X0)
| ~ ssItem(X0)
| ~ memberP(skaf82(sk2),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f9507,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ909_spl ),
inference(split_clause,[status(thm)],[f9498,f9504,f2380,f2383,f1765]) ).
fof(f9726,plain,
( ~ sQ4_spl
| nil = sk5
| app(sk5,sk5) != nil ),
inference(resolution,[status(thm)],[f5681,f461]) ).
fof(f9768,definition,
( sQ923_spl
<=> app(sk5,sk5) = nil ),
introduced(definition,[new_symbols(definition,[sQ923_spl])],[split_symbol_definition]) ).
fof(f9771,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ923_spl ),
inference(split_clause,[status(thm)],[f9726,f9768,f591,f460]) ).
fof(f10045,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ frontsegP(X4,cons(X2,X0))
| ~ frontsegP(cons(X3,X1),X4)
| frontsegP(X1,X0)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1638,f287]) ).
fof(f10046,plain,
! [X0,X1,X2,X3] :
( ~ ssList(cons(X3,X1))
| ~ ssList(nil)
| ~ frontsegP(nil,cons(X2,X0))
| frontsegP(X1,X0)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f10045,f260]) ).
fof(f10051,definition,
! [X0,X1,X2,X3] :
( sQ932_spl
<=> ( ~ ssList(cons(X3,X1))
| ~ frontsegP(nil,cons(X2,X0))
| frontsegP(X1,X0)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ932_spl])],[split_symbol_definition]) ).
fof(f10054,plain,
( ~ sQ13_spl
| sQ932_spl ),
inference(split_clause,[status(thm)],[f10046,f10051,f534]) ).
fof(f10070,plain,
! [X0,X1,X2,X3] :
( ~ ssList(cons(skac3,X1))
| ~ frontsegP(cons(skac3,X1),cons(X3,X2))
| frontsegP(X0,X2)
| ~ ssItem(skac3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8620,f10045]) ).
fof(f10083,definition,
! [X0,X1,X2,X3] :
( sQ935_spl
<=> ( ~ ssList(cons(skac3,X1))
| ~ frontsegP(cons(skac3,X1),cons(X3,X2))
| frontsegP(X0,X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ935_spl])],[split_symbol_definition]) ).
fof(f10086,plain,
( ~ sQ148_spl
| sQ935_spl ),
inference(split_clause,[status(thm)],[f10070,f10083,f1861]) ).
fof(f10158,plain,
! [X0,X1,X2,X3] :
( ~ ssList(cons(skac2,X1))
| ~ frontsegP(cons(skac2,X1),cons(X3,X2))
| frontsegP(X0,X2)
| ~ ssItem(skac2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8623,f10045]) ).
fof(f10171,definition,
! [X0,X1,X2,X3] :
( sQ936_spl
<=> ( ~ ssList(cons(skac2,X1))
| ~ frontsegP(cons(skac2,X1),cons(X3,X2))
| frontsegP(X0,X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ936_spl])],[split_symbol_definition]) ).
fof(f10174,plain,
( ~ sQ168_spl
| sQ936_spl ),
inference(split_clause,[status(thm)],[f10158,f10171,f1982]) ).
fof(f10291,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf83(X2) = skaf83(X2)
| ~ ssItem(skaf83(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8627,f8626]) ).
fof(f10294,definition,
! [X2] :
( sQ940_spl
<=> ( skaf83(X2) = skaf83(X2)
| ~ ssItem(skaf83(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ940_spl])],[split_symbol_definition]) ).
fof(f10297,plain,
( sQ940_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f10291,f745,f10294]) ).
fof(f10373,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf79(X2) = skaf79(X2)
| ~ ssItem(skaf79(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8630,f8629]) ).
fof(f10376,definition,
! [X2] :
( sQ942_spl
<=> ( skaf79(X2) = skaf79(X2)
| ~ ssItem(skaf79(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ942_spl])],[split_symbol_definition]) ).
fof(f10379,plain,
( sQ942_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f10373,f745,f10376]) ).
fof(f10431,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf78(X2) = skaf78(X2)
| ~ ssItem(skaf78(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8633,f8632]) ).
fof(f10434,definition,
! [X2] :
( sQ944_spl
<=> ( skaf78(X2) = skaf78(X2)
| ~ ssItem(skaf78(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ944_spl])],[split_symbol_definition]) ).
fof(f10437,plain,
( sQ944_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f10431,f745,f10434]) ).
fof(f10450,plain,
! [X0,X1] :
( ~ sQ526_spl
| frontsegP(cons(hd(sk2),X0),cons(hd(sk5),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| nil = sk5
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f4687,f8635]) ).
fof(f10451,plain,
! [X0,X1] :
( ~ sQ526_spl
| frontsegP(cons(hd(sk5),X0),cons(hd(sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| nil = sk5
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f4687,f8635]) ).
fof(f10458,definition,
! [X0,X1] :
( sQ946_spl
<=> ( frontsegP(cons(hd(sk2),X0),cons(hd(sk5),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ946_spl])],[split_symbol_definition]) ).
fof(f10461,plain,
( ~ sQ526_spl
| sQ946_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f10450,f460,f591,f10458,f4686]) ).
fof(f10462,definition,
! [X0,X1] :
( sQ947_spl
<=> ( frontsegP(cons(hd(sk5),X0),cons(hd(sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ947_spl])],[split_symbol_definition]) ).
fof(f10465,plain,
( ~ sQ526_spl
| sQ947_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f10451,f460,f591,f10462,f4686]) ).
fof(f10504,plain,
! [X0] :
( app(nil,skaf56(X0)) = nil
| ~ frontsegP(nil,skaf56(X0))
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1094,f1192]) ).
fof(f10506,plain,
! [X0,X1] :
( segmentP(app(skaf56(X1),X0),skaf56(X1))
| ~ ssList(skaf56(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1094,f1086]) ).
fof(f10507,plain,
! [X0,X1] :
( app(app(X1,nil),skaf56(X0)) = app(X1,skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1094,f369]) ).
fof(f10508,plain,
! [X0,X1] :
( app(skaf56(X1),X0) = app(nil,app(skaf56(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1094,f369]) ).
fof(f10509,plain,
! [X0] :
( rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1094,f3479]) ).
fof(f10512,plain,
! [X0,X1] :
( app(nil,skaf56(X1)) = X0
| ~ frontsegP(X0,skaf56(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1094,f1279]) ).
fof(f10513,plain,
! [X0] :
( frontsegP(skaf56(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1094,f982]) ).
fof(f10514,plain,
! [X0,X1] :
( frontsegP(skaf56(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1094,f352]) ).
fof(f10515,definition,
! [X0] :
( sQ948_spl
<=> ( app(nil,skaf56(X0)) = nil
| ~ frontsegP(nil,skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ948_spl])],[split_symbol_definition]) ).
fof(f10518,plain,
( ~ sQ13_spl
| sQ948_spl ),
inference(split_clause,[status(thm)],[f10504,f10515,f534]) ).
fof(f10519,definition,
! [X0,X1] :
( sQ949_spl
<=> ( segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ949_spl])],[split_symbol_definition]) ).
fof(f10523,definition,
! [X0,X1] :
( sQ950_spl
<=> ( segmentP(app(skaf56(X1),X0),skaf56(X1))
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ950_spl])],[split_symbol_definition]) ).
fof(f10526,plain,
( ~ sQ13_spl
| sQ950_spl ),
inference(split_clause,[status(thm)],[f10506,f10523,f534]) ).
fof(f10527,definition,
! [X0,X1] :
( sQ951_spl
<=> ( app(app(X1,nil),skaf56(X0)) = app(X1,skaf56(X0))
| ~ ssList(X1)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ951_spl])],[split_symbol_definition]) ).
fof(f10530,plain,
( ~ sQ13_spl
| sQ951_spl ),
inference(split_clause,[status(thm)],[f10507,f10527,f534]) ).
fof(f10531,definition,
! [X0,X1] :
( sQ952_spl
<=> ( app(skaf56(X1),X0) = app(nil,app(skaf56(X1),X0))
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ952_spl])],[split_symbol_definition]) ).
fof(f10534,plain,
( ~ sQ13_spl
| sQ952_spl ),
inference(split_clause,[status(thm)],[f10508,f10531,f534]) ).
fof(f10535,definition,
! [X0] :
( sQ953_spl
<=> ( rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ953_spl])],[split_symbol_definition]) ).
fof(f10538,plain,
( sQ953_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10509,f534,f10535]) ).
fof(f10547,definition,
! [X0,X1] :
( sQ956_spl
<=> ( app(nil,skaf56(X1)) = X0
| ~ frontsegP(X0,skaf56(X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ956_spl])],[split_symbol_definition]) ).
fof(f10550,plain,
( ~ sQ13_spl
| sQ956_spl ),
inference(split_clause,[status(thm)],[f10512,f10547,f534]) ).
fof(f10551,definition,
! [X0] :
( sQ957_spl
<=> ( frontsegP(skaf56(X0),nil)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ957_spl])],[split_symbol_definition]) ).
fof(f10554,plain,
( ~ sQ13_spl
| sQ957_spl ),
inference(split_clause,[status(thm)],[f10513,f10551,f534]) ).
fof(f10555,definition,
! [X0,X1] :
( sQ958_spl
<=> ( frontsegP(skaf56(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ958_spl])],[split_symbol_definition]) ).
fof(f10558,plain,
( ~ sQ13_spl
| sQ958_spl ),
inference(split_clause,[status(thm)],[f10514,f10555,f534]) ).
fof(f10567,plain,
! [X0] :
( ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f1093]) ).
fof(f10569,plain,
! [X0] :
( app(skaf56(X0),nil) = skaf56(X0)
| ~ frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f1192]) ).
fof(f10571,plain,
! [X0,X1] :
( segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1095,f1086]) ).
fof(f10572,plain,
! [X0,X1] :
( app(app(X1,skaf56(X0)),nil) = app(X1,skaf56(X0))
| ~ ssList(X1)
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f369]) ).
fof(f10573,plain,
! [X0] :
( rearsegP(skaf56(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1095,f3479]) ).
fof(f10574,plain,
! [X0] :
( tl(skaf56(X0)) = app(tl(skaf56(X0)),nil)
| nil = skaf56(X0)
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f346]) ).
fof(f10575,plain,
! [X0] :
( hd(skaf56(X0)) = hd(skaf56(X0))
| nil = skaf56(X0)
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f334]) ).
fof(f10576,plain,
! [X0,X1] :
( app(skaf56(X0),nil) = X1
| ~ frontsegP(X1,skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1095,f1279]) ).
fof(f10577,plain,
! [X0] :
( frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1095,f982]) ).
fof(f10578,plain,
! [X0,X1] :
( frontsegP(skaf56(X0),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1095,f352]) ).
fof(f10579,definition,
! [X0] :
( sQ959_spl
<=> ssList(skaf56(X0)) ),
introduced(definition,[new_symbols(definition,[sQ959_spl])],[split_symbol_definition]) ).
fof(f10582,plain,
( sQ959_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10567,f534,f10579]) ).
fof(f10583,definition,
! [X0] :
( sQ960_spl
<=> ( app(skaf56(X0),nil) = skaf56(X0)
| ~ frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ960_spl])],[split_symbol_definition]) ).
fof(f10586,plain,
( sQ960_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10569,f534,f10583]) ).
fof(f10588,plain,
( ~ sQ13_spl
| sQ949_spl ),
inference(split_clause,[status(thm)],[f10571,f10519,f534]) ).
fof(f10589,definition,
! [X0,X1] :
( sQ961_spl
<=> ( app(app(X1,skaf56(X0)),nil) = app(X1,skaf56(X0))
| ~ ssList(X1)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ961_spl])],[split_symbol_definition]) ).
fof(f10592,plain,
( sQ961_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10572,f534,f10589]) ).
fof(f10593,definition,
! [X0] :
( sQ962_spl
<=> ( rearsegP(skaf56(X0),nil)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ962_spl])],[split_symbol_definition]) ).
fof(f10596,plain,
( ~ sQ13_spl
| sQ962_spl ),
inference(split_clause,[status(thm)],[f10573,f10593,f534]) ).
fof(f10597,definition,
! [X0] :
( sQ963_spl
<=> ( tl(skaf56(X0)) = app(tl(skaf56(X0)),nil)
| nil = skaf56(X0)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ963_spl])],[split_symbol_definition]) ).
fof(f10600,plain,
( sQ963_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10574,f534,f10597]) ).
fof(f10601,definition,
! [X0] :
( sQ964_spl
<=> ( hd(skaf56(X0)) = hd(skaf56(X0))
| nil = skaf56(X0)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ964_spl])],[split_symbol_definition]) ).
fof(f10604,plain,
( sQ964_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10575,f534,f10601]) ).
fof(f10605,definition,
! [X0,X1] :
( sQ965_spl
<=> ( app(skaf56(X0),nil) = X1
| ~ frontsegP(X1,skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ965_spl])],[split_symbol_definition]) ).
fof(f10608,plain,
( ~ sQ13_spl
| sQ965_spl ),
inference(split_clause,[status(thm)],[f10576,f10605,f534]) ).
fof(f10609,definition,
! [X0] :
( sQ966_spl
<=> ( frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ966_spl])],[split_symbol_definition]) ).
fof(f10612,plain,
( sQ966_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10577,f534,f10609]) ).
fof(f10613,definition,
! [X0,X1] :
( sQ967_spl
<=> ( frontsegP(skaf56(X0),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ967_spl])],[split_symbol_definition]) ).
fof(f10616,plain,
( ~ sQ13_spl
| sQ967_spl ),
inference(split_clause,[status(thm)],[f10578,f10613,f534]) ).
fof(f10619,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| nil = X0
| ~ ssList(X0)
| hd(X0) = hd(X0)
| ~ ssItem(hd(X0))
| ~ ssList(X2)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8636,f8635]) ).
fof(f10622,plain,
! [X0,X1,X2] :
( ~ sQ526_spl
| X0 = hd(sk5)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(hd(sk2),X2))
| nil = sk5
| ~ ssList(sk5) ),
inference(paramodulation,[status(thm)],[f4687,f8636]) ).
fof(f10623,definition,
! [X0] :
( sQ968_spl
<=> ( nil = X0
| ~ ssList(X0)
| hd(X0) = hd(X0)
| ~ ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ968_spl])],[split_symbol_definition]) ).
fof(f10626,plain,
( sQ41_spl
| sQ968_spl ),
inference(split_clause,[status(thm)],[f10619,f10623,f745]) ).
fof(f10628,definition,
! [X0,X1,X2] :
( sQ969_spl
<=> ( X0 = hd(sk5)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(cons(X0,X1),cons(hd(sk2),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ969_spl])],[split_symbol_definition]) ).
fof(f10631,plain,
( ~ sQ526_spl
| sQ969_spl
| sQ21_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f10622,f460,f591,f10628,f4686]) ).
fof(f10669,plain,
! [X0] :
( app(nil,skaf57(X0)) = nil
| ~ frontsegP(nil,skaf57(X0))
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1097,f1192]) ).
fof(f10671,plain,
! [X0,X1] :
( segmentP(app(skaf57(X1),X0),skaf57(X1))
| ~ ssList(skaf57(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1097,f1086]) ).
fof(f10672,plain,
! [X0,X1] :
( app(app(X1,nil),skaf57(X0)) = app(X1,skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1097,f369]) ).
fof(f10673,plain,
! [X0,X1] :
( app(skaf57(X1),X0) = app(nil,app(skaf57(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1097,f369]) ).
fof(f10674,plain,
! [X0] :
( rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1097,f3479]) ).
fof(f10677,plain,
! [X0,X1] :
( app(nil,skaf57(X1)) = X0
| ~ frontsegP(X0,skaf57(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1097,f1279]) ).
fof(f10678,plain,
! [X0] :
( frontsegP(skaf57(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1097,f982]) ).
fof(f10679,plain,
! [X0,X1] :
( frontsegP(skaf57(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1097,f352]) ).
fof(f10680,definition,
! [X0] :
( sQ970_spl
<=> ( app(nil,skaf57(X0)) = nil
| ~ frontsegP(nil,skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ970_spl])],[split_symbol_definition]) ).
fof(f10683,plain,
( ~ sQ13_spl
| sQ970_spl ),
inference(split_clause,[status(thm)],[f10669,f10680,f534]) ).
fof(f10684,definition,
! [X0,X1] :
( sQ971_spl
<=> ( segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ971_spl])],[split_symbol_definition]) ).
fof(f10688,definition,
! [X0,X1] :
( sQ972_spl
<=> ( segmentP(app(skaf57(X1),X0),skaf57(X1))
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ972_spl])],[split_symbol_definition]) ).
fof(f10691,plain,
( ~ sQ13_spl
| sQ972_spl ),
inference(split_clause,[status(thm)],[f10671,f10688,f534]) ).
fof(f10692,definition,
! [X0,X1] :
( sQ973_spl
<=> ( app(app(X1,nil),skaf57(X0)) = app(X1,skaf57(X0))
| ~ ssList(X1)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ973_spl])],[split_symbol_definition]) ).
fof(f10695,plain,
( ~ sQ13_spl
| sQ973_spl ),
inference(split_clause,[status(thm)],[f10672,f10692,f534]) ).
fof(f10696,definition,
! [X0,X1] :
( sQ974_spl
<=> ( app(skaf57(X1),X0) = app(nil,app(skaf57(X1),X0))
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ974_spl])],[split_symbol_definition]) ).
fof(f10699,plain,
( ~ sQ13_spl
| sQ974_spl ),
inference(split_clause,[status(thm)],[f10673,f10696,f534]) ).
fof(f10700,definition,
! [X0] :
( sQ975_spl
<=> ( rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ975_spl])],[split_symbol_definition]) ).
fof(f10703,plain,
( sQ975_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10674,f534,f10700]) ).
fof(f10712,definition,
! [X0,X1] :
( sQ978_spl
<=> ( app(nil,skaf57(X1)) = X0
| ~ frontsegP(X0,skaf57(X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ978_spl])],[split_symbol_definition]) ).
fof(f10715,plain,
( ~ sQ13_spl
| sQ978_spl ),
inference(split_clause,[status(thm)],[f10677,f10712,f534]) ).
fof(f10716,definition,
! [X0] :
( sQ979_spl
<=> ( frontsegP(skaf57(X0),nil)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ979_spl])],[split_symbol_definition]) ).
fof(f10719,plain,
( ~ sQ13_spl
| sQ979_spl ),
inference(split_clause,[status(thm)],[f10678,f10716,f534]) ).
fof(f10720,definition,
! [X0,X1] :
( sQ980_spl
<=> ( frontsegP(skaf57(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ980_spl])],[split_symbol_definition]) ).
fof(f10723,plain,
( ~ sQ13_spl
| sQ980_spl ),
inference(split_clause,[status(thm)],[f10679,f10720,f534]) ).
fof(f10732,plain,
! [X0] :
( ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f1096]) ).
fof(f10734,plain,
! [X0] :
( app(skaf57(X0),nil) = skaf57(X0)
| ~ frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f1192]) ).
fof(f10736,plain,
! [X0,X1] :
( segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1098,f1086]) ).
fof(f10737,plain,
! [X0,X1] :
( app(app(X1,skaf57(X0)),nil) = app(X1,skaf57(X0))
| ~ ssList(X1)
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f369]) ).
fof(f10738,plain,
! [X0] :
( rearsegP(skaf57(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1098,f3479]) ).
fof(f10739,plain,
! [X0] :
( tl(skaf57(X0)) = app(tl(skaf57(X0)),nil)
| nil = skaf57(X0)
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f346]) ).
fof(f10740,plain,
! [X0] :
( hd(skaf57(X0)) = hd(skaf57(X0))
| nil = skaf57(X0)
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f334]) ).
fof(f10741,plain,
! [X0,X1] :
( app(skaf57(X0),nil) = X1
| ~ frontsegP(X1,skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1098,f1279]) ).
fof(f10742,plain,
! [X0] :
( frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1098,f982]) ).
fof(f10743,plain,
! [X0,X1] :
( frontsegP(skaf57(X0),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1098,f352]) ).
fof(f10744,definition,
! [X0] :
( sQ981_spl
<=> ssList(skaf57(X0)) ),
introduced(definition,[new_symbols(definition,[sQ981_spl])],[split_symbol_definition]) ).
fof(f10747,plain,
( sQ981_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10732,f534,f10744]) ).
fof(f10748,definition,
! [X0] :
( sQ982_spl
<=> ( app(skaf57(X0),nil) = skaf57(X0)
| ~ frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ982_spl])],[split_symbol_definition]) ).
fof(f10751,plain,
( sQ982_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10734,f534,f10748]) ).
fof(f10753,plain,
( ~ sQ13_spl
| sQ971_spl ),
inference(split_clause,[status(thm)],[f10736,f10684,f534]) ).
fof(f10754,definition,
! [X0,X1] :
( sQ983_spl
<=> ( app(app(X1,skaf57(X0)),nil) = app(X1,skaf57(X0))
| ~ ssList(X1)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ983_spl])],[split_symbol_definition]) ).
fof(f10757,plain,
( sQ983_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10737,f534,f10754]) ).
fof(f10758,definition,
! [X0] :
( sQ984_spl
<=> ( rearsegP(skaf57(X0),nil)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ984_spl])],[split_symbol_definition]) ).
fof(f10761,plain,
( ~ sQ13_spl
| sQ984_spl ),
inference(split_clause,[status(thm)],[f10738,f10758,f534]) ).
fof(f10762,definition,
! [X0] :
( sQ985_spl
<=> ( tl(skaf57(X0)) = app(tl(skaf57(X0)),nil)
| nil = skaf57(X0)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ985_spl])],[split_symbol_definition]) ).
fof(f10765,plain,
( sQ985_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10739,f534,f10762]) ).
fof(f10766,definition,
! [X0] :
( sQ986_spl
<=> ( hd(skaf57(X0)) = hd(skaf57(X0))
| nil = skaf57(X0)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ986_spl])],[split_symbol_definition]) ).
fof(f10769,plain,
( sQ986_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10740,f534,f10766]) ).
fof(f10770,definition,
! [X0,X1] :
( sQ987_spl
<=> ( app(skaf57(X0),nil) = X1
| ~ frontsegP(X1,skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ987_spl])],[split_symbol_definition]) ).
fof(f10773,plain,
( ~ sQ13_spl
| sQ987_spl ),
inference(split_clause,[status(thm)],[f10741,f10770,f534]) ).
fof(f10774,definition,
! [X0] :
( sQ988_spl
<=> ( frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ988_spl])],[split_symbol_definition]) ).
fof(f10777,plain,
( sQ988_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10742,f534,f10774]) ).
fof(f10778,definition,
! [X0,X1] :
( sQ989_spl
<=> ( frontsegP(skaf57(X0),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ989_spl])],[split_symbol_definition]) ).
fof(f10781,plain,
( ~ sQ13_spl
| sQ989_spl ),
inference(split_clause,[status(thm)],[f10743,f10778,f534]) ).
fof(f10833,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf74(X2) = skaf74(X2)
| ~ ssItem(skaf74(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8687,f8686]) ).
fof(f10836,definition,
! [X2] :
( sQ994_spl
<=> ( skaf74(X2) = skaf74(X2)
| ~ ssItem(skaf74(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ994_spl])],[split_symbol_definition]) ).
fof(f10839,plain,
( sQ994_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f10833,f745,f10836]) ).
fof(f10877,plain,
! [X0] :
( app(nil,skaf58(X0)) = nil
| ~ frontsegP(nil,skaf58(X0))
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1100,f1192]) ).
fof(f10879,plain,
! [X0,X1] :
( segmentP(app(skaf58(X1),X0),skaf58(X1))
| ~ ssList(skaf58(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1100,f1086]) ).
fof(f10880,plain,
! [X0,X1] :
( app(app(X1,nil),skaf58(X0)) = app(X1,skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1100,f369]) ).
fof(f10881,plain,
! [X0,X1] :
( app(skaf58(X1),X0) = app(nil,app(skaf58(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1100,f369]) ).
fof(f10882,plain,
! [X0] :
( rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1100,f3479]) ).
fof(f10885,plain,
! [X0,X1] :
( app(nil,skaf58(X1)) = X0
| ~ frontsegP(X0,skaf58(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1100,f1279]) ).
fof(f10886,plain,
! [X0] :
( frontsegP(skaf58(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1100,f982]) ).
fof(f10887,plain,
! [X0,X1] :
( frontsegP(skaf58(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1100,f352]) ).
fof(f10888,definition,
! [X0] :
( sQ995_spl
<=> ( app(nil,skaf58(X0)) = nil
| ~ frontsegP(nil,skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ995_spl])],[split_symbol_definition]) ).
fof(f10891,plain,
( ~ sQ13_spl
| sQ995_spl ),
inference(split_clause,[status(thm)],[f10877,f10888,f534]) ).
fof(f10892,definition,
! [X0,X1] :
( sQ996_spl
<=> ( segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ996_spl])],[split_symbol_definition]) ).
fof(f10896,definition,
! [X0,X1] :
( sQ997_spl
<=> ( segmentP(app(skaf58(X1),X0),skaf58(X1))
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ997_spl])],[split_symbol_definition]) ).
fof(f10899,plain,
( ~ sQ13_spl
| sQ997_spl ),
inference(split_clause,[status(thm)],[f10879,f10896,f534]) ).
fof(f10900,definition,
! [X0,X1] :
( sQ998_spl
<=> ( app(app(X1,nil),skaf58(X0)) = app(X1,skaf58(X0))
| ~ ssList(X1)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ998_spl])],[split_symbol_definition]) ).
fof(f10903,plain,
( ~ sQ13_spl
| sQ998_spl ),
inference(split_clause,[status(thm)],[f10880,f10900,f534]) ).
fof(f10904,definition,
! [X0,X1] :
( sQ999_spl
<=> ( app(skaf58(X1),X0) = app(nil,app(skaf58(X1),X0))
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ999_spl])],[split_symbol_definition]) ).
fof(f10907,plain,
( ~ sQ13_spl
| sQ999_spl ),
inference(split_clause,[status(thm)],[f10881,f10904,f534]) ).
fof(f10908,definition,
! [X0] :
( sQ1000_spl
<=> ( rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1000_spl])],[split_symbol_definition]) ).
fof(f10911,plain,
( sQ1000_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10882,f534,f10908]) ).
fof(f10920,definition,
! [X0,X1] :
( sQ1003_spl
<=> ( app(nil,skaf58(X1)) = X0
| ~ frontsegP(X0,skaf58(X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1003_spl])],[split_symbol_definition]) ).
fof(f10923,plain,
( ~ sQ13_spl
| sQ1003_spl ),
inference(split_clause,[status(thm)],[f10885,f10920,f534]) ).
fof(f10924,definition,
! [X0] :
( sQ1004_spl
<=> ( frontsegP(skaf58(X0),nil)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1004_spl])],[split_symbol_definition]) ).
fof(f10927,plain,
( ~ sQ13_spl
| sQ1004_spl ),
inference(split_clause,[status(thm)],[f10886,f10924,f534]) ).
fof(f10928,definition,
! [X0,X1] :
( sQ1005_spl
<=> ( frontsegP(skaf58(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1005_spl])],[split_symbol_definition]) ).
fof(f10931,plain,
( ~ sQ13_spl
| sQ1005_spl ),
inference(split_clause,[status(thm)],[f10887,f10928,f534]) ).
fof(f10940,plain,
! [X0] :
( ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f1099]) ).
fof(f10942,plain,
! [X0] :
( app(skaf58(X0),nil) = skaf58(X0)
| ~ frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f1192]) ).
fof(f10944,plain,
! [X0,X1] :
( segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1101,f1086]) ).
fof(f10945,plain,
! [X0,X1] :
( app(app(X1,skaf58(X0)),nil) = app(X1,skaf58(X0))
| ~ ssList(X1)
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f369]) ).
fof(f10946,plain,
! [X0] :
( rearsegP(skaf58(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1101,f3479]) ).
fof(f10947,plain,
! [X0] :
( tl(skaf58(X0)) = app(tl(skaf58(X0)),nil)
| nil = skaf58(X0)
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f346]) ).
fof(f10948,plain,
! [X0] :
( hd(skaf58(X0)) = hd(skaf58(X0))
| nil = skaf58(X0)
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f334]) ).
fof(f10949,plain,
! [X0,X1] :
( app(skaf58(X0),nil) = X1
| ~ frontsegP(X1,skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1101,f1279]) ).
fof(f10950,plain,
! [X0] :
( frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1101,f982]) ).
fof(f10951,plain,
! [X0,X1] :
( frontsegP(skaf58(X0),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1101,f352]) ).
fof(f10952,definition,
! [X0] :
( sQ1006_spl
<=> ssList(skaf58(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1006_spl])],[split_symbol_definition]) ).
fof(f10955,plain,
( sQ1006_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10940,f534,f10952]) ).
fof(f10956,definition,
! [X0] :
( sQ1007_spl
<=> ( app(skaf58(X0),nil) = skaf58(X0)
| ~ frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1007_spl])],[split_symbol_definition]) ).
fof(f10959,plain,
( sQ1007_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10942,f534,f10956]) ).
fof(f10961,plain,
( ~ sQ13_spl
| sQ996_spl ),
inference(split_clause,[status(thm)],[f10944,f10892,f534]) ).
fof(f10962,definition,
! [X0,X1] :
( sQ1008_spl
<=> ( app(app(X1,skaf58(X0)),nil) = app(X1,skaf58(X0))
| ~ ssList(X1)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1008_spl])],[split_symbol_definition]) ).
fof(f10965,plain,
( sQ1008_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10945,f534,f10962]) ).
fof(f10966,definition,
! [X0] :
( sQ1009_spl
<=> ( rearsegP(skaf58(X0),nil)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1009_spl])],[split_symbol_definition]) ).
fof(f10969,plain,
( ~ sQ13_spl
| sQ1009_spl ),
inference(split_clause,[status(thm)],[f10946,f10966,f534]) ).
fof(f10970,definition,
! [X0] :
( sQ1010_spl
<=> ( tl(skaf58(X0)) = app(tl(skaf58(X0)),nil)
| nil = skaf58(X0)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1010_spl])],[split_symbol_definition]) ).
fof(f10973,plain,
( sQ1010_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10947,f534,f10970]) ).
fof(f10974,definition,
! [X0] :
( sQ1011_spl
<=> ( hd(skaf58(X0)) = hd(skaf58(X0))
| nil = skaf58(X0)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1011_spl])],[split_symbol_definition]) ).
fof(f10977,plain,
( sQ1011_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10948,f534,f10974]) ).
fof(f10978,definition,
! [X0,X1] :
( sQ1012_spl
<=> ( app(skaf58(X0),nil) = X1
| ~ frontsegP(X1,skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1012_spl])],[split_symbol_definition]) ).
fof(f10981,plain,
( ~ sQ13_spl
| sQ1012_spl ),
inference(split_clause,[status(thm)],[f10949,f10978,f534]) ).
fof(f10982,definition,
! [X0] :
( sQ1013_spl
<=> ( frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1013_spl])],[split_symbol_definition]) ).
fof(f10985,plain,
( sQ1013_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f10950,f534,f10982]) ).
fof(f10986,definition,
! [X0,X1] :
( sQ1014_spl
<=> ( frontsegP(skaf58(X0),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1014_spl])],[split_symbol_definition]) ).
fof(f10989,plain,
( ~ sQ13_spl
| sQ1014_spl ),
inference(split_clause,[status(thm)],[f10951,f10986,f534]) ).
fof(f11009,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf70(X2) = skaf70(X2)
| ~ ssItem(skaf70(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8690,f8689]) ).
fof(f11012,definition,
! [X2] :
( sQ1016_spl
<=> ( skaf70(X2) = skaf70(X2)
| ~ ssItem(skaf70(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1016_spl])],[split_symbol_definition]) ).
fof(f11015,plain,
( sQ1016_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f11009,f745,f11012]) ).
fof(f11053,plain,
! [X0] :
( app(nil,skaf61(X0)) = nil
| ~ frontsegP(nil,skaf61(X0))
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1139,f1192]) ).
fof(f11055,plain,
! [X0,X1] :
( segmentP(app(skaf61(X1),X0),skaf61(X1))
| ~ ssList(skaf61(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1139,f1086]) ).
fof(f11056,plain,
! [X0,X1] :
( app(app(X1,nil),skaf61(X0)) = app(X1,skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1139,f369]) ).
fof(f11057,plain,
! [X0,X1] :
( app(skaf61(X1),X0) = app(nil,app(skaf61(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1139,f369]) ).
fof(f11058,plain,
! [X0] :
( rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1139,f3479]) ).
fof(f11061,plain,
! [X0,X1] :
( app(nil,skaf61(X1)) = X0
| ~ frontsegP(X0,skaf61(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1139,f1279]) ).
fof(f11062,plain,
! [X0] :
( frontsegP(skaf61(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1139,f982]) ).
fof(f11063,plain,
! [X0,X1] :
( frontsegP(skaf61(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1139,f352]) ).
fof(f11064,definition,
! [X0] :
( sQ1017_spl
<=> ( app(nil,skaf61(X0)) = nil
| ~ frontsegP(nil,skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1017_spl])],[split_symbol_definition]) ).
fof(f11067,plain,
( ~ sQ13_spl
| sQ1017_spl ),
inference(split_clause,[status(thm)],[f11053,f11064,f534]) ).
fof(f11068,definition,
! [X0,X1] :
( sQ1018_spl
<=> ( segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1018_spl])],[split_symbol_definition]) ).
fof(f11072,definition,
! [X0,X1] :
( sQ1019_spl
<=> ( segmentP(app(skaf61(X1),X0),skaf61(X1))
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1019_spl])],[split_symbol_definition]) ).
fof(f11075,plain,
( ~ sQ13_spl
| sQ1019_spl ),
inference(split_clause,[status(thm)],[f11055,f11072,f534]) ).
fof(f11076,definition,
! [X0,X1] :
( sQ1020_spl
<=> ( app(app(X1,nil),skaf61(X0)) = app(X1,skaf61(X0))
| ~ ssList(X1)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1020_spl])],[split_symbol_definition]) ).
fof(f11079,plain,
( ~ sQ13_spl
| sQ1020_spl ),
inference(split_clause,[status(thm)],[f11056,f11076,f534]) ).
fof(f11080,definition,
! [X0,X1] :
( sQ1021_spl
<=> ( app(skaf61(X1),X0) = app(nil,app(skaf61(X1),X0))
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1021_spl])],[split_symbol_definition]) ).
fof(f11083,plain,
( ~ sQ13_spl
| sQ1021_spl ),
inference(split_clause,[status(thm)],[f11057,f11080,f534]) ).
fof(f11084,definition,
! [X0] :
( sQ1022_spl
<=> ( rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1022_spl])],[split_symbol_definition]) ).
fof(f11087,plain,
( sQ1022_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11058,f534,f11084]) ).
fof(f11096,definition,
! [X0,X1] :
( sQ1025_spl
<=> ( app(nil,skaf61(X1)) = X0
| ~ frontsegP(X0,skaf61(X1))
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1025_spl])],[split_symbol_definition]) ).
fof(f11099,plain,
( ~ sQ13_spl
| sQ1025_spl ),
inference(split_clause,[status(thm)],[f11061,f11096,f534]) ).
fof(f11100,definition,
! [X0] :
( sQ1026_spl
<=> ( frontsegP(skaf61(X0),nil)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1026_spl])],[split_symbol_definition]) ).
fof(f11103,plain,
( ~ sQ13_spl
| sQ1026_spl ),
inference(split_clause,[status(thm)],[f11062,f11100,f534]) ).
fof(f11104,definition,
! [X0,X1] :
( sQ1027_spl
<=> ( frontsegP(skaf61(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1027_spl])],[split_symbol_definition]) ).
fof(f11107,plain,
( ~ sQ13_spl
| sQ1027_spl ),
inference(split_clause,[status(thm)],[f11063,f11104,f534]) ).
fof(f11116,plain,
! [X0] :
( ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f1138]) ).
fof(f11118,plain,
! [X0] :
( app(skaf61(X0),nil) = skaf61(X0)
| ~ frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f1192]) ).
fof(f11120,plain,
! [X0,X1] :
( segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1140,f1086]) ).
fof(f11121,plain,
! [X0,X1] :
( app(app(X1,skaf61(X0)),nil) = app(X1,skaf61(X0))
| ~ ssList(X1)
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f369]) ).
fof(f11122,plain,
! [X0] :
( rearsegP(skaf61(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1140,f3479]) ).
fof(f11123,plain,
! [X0] :
( tl(skaf61(X0)) = app(tl(skaf61(X0)),nil)
| nil = skaf61(X0)
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f346]) ).
fof(f11124,plain,
! [X0] :
( hd(skaf61(X0)) = hd(skaf61(X0))
| nil = skaf61(X0)
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f334]) ).
fof(f11125,plain,
! [X0,X1] :
( app(skaf61(X0),nil) = X1
| ~ frontsegP(X1,skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1140,f1279]) ).
fof(f11126,plain,
! [X0] :
( frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1140,f982]) ).
fof(f11127,plain,
! [X0,X1] :
( frontsegP(skaf61(X0),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1140,f352]) ).
fof(f11128,definition,
! [X0] :
( sQ1028_spl
<=> ssList(skaf61(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1028_spl])],[split_symbol_definition]) ).
fof(f11131,plain,
( sQ1028_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11116,f534,f11128]) ).
fof(f11132,definition,
! [X0] :
( sQ1029_spl
<=> ( app(skaf61(X0),nil) = skaf61(X0)
| ~ frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1029_spl])],[split_symbol_definition]) ).
fof(f11135,plain,
( sQ1029_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11118,f534,f11132]) ).
fof(f11137,plain,
( ~ sQ13_spl
| sQ1018_spl ),
inference(split_clause,[status(thm)],[f11120,f11068,f534]) ).
fof(f11138,definition,
! [X0,X1] :
( sQ1030_spl
<=> ( app(app(X1,skaf61(X0)),nil) = app(X1,skaf61(X0))
| ~ ssList(X1)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1030_spl])],[split_symbol_definition]) ).
fof(f11141,plain,
( sQ1030_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11121,f534,f11138]) ).
fof(f11142,definition,
! [X0] :
( sQ1031_spl
<=> ( rearsegP(skaf61(X0),nil)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1031_spl])],[split_symbol_definition]) ).
fof(f11145,plain,
( ~ sQ13_spl
| sQ1031_spl ),
inference(split_clause,[status(thm)],[f11122,f11142,f534]) ).
fof(f11146,definition,
! [X0] :
( sQ1032_spl
<=> ( tl(skaf61(X0)) = app(tl(skaf61(X0)),nil)
| nil = skaf61(X0)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1032_spl])],[split_symbol_definition]) ).
fof(f11149,plain,
( sQ1032_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11123,f534,f11146]) ).
fof(f11150,definition,
! [X0] :
( sQ1033_spl
<=> ( hd(skaf61(X0)) = hd(skaf61(X0))
| nil = skaf61(X0)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1033_spl])],[split_symbol_definition]) ).
fof(f11153,plain,
( sQ1033_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11124,f534,f11150]) ).
fof(f11154,definition,
! [X0,X1] :
( sQ1034_spl
<=> ( app(skaf61(X0),nil) = X1
| ~ frontsegP(X1,skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1034_spl])],[split_symbol_definition]) ).
fof(f11157,plain,
( ~ sQ13_spl
| sQ1034_spl ),
inference(split_clause,[status(thm)],[f11125,f11154,f534]) ).
fof(f11158,definition,
! [X0] :
( sQ1035_spl
<=> ( frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1035_spl])],[split_symbol_definition]) ).
fof(f11161,plain,
( sQ1035_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11126,f534,f11158]) ).
fof(f11162,definition,
! [X0,X1] :
( sQ1036_spl
<=> ( frontsegP(skaf61(X0),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1036_spl])],[split_symbol_definition]) ).
fof(f11165,plain,
( ~ sQ13_spl
| sQ1036_spl ),
inference(split_clause,[status(thm)],[f11127,f11162,f534]) ).
fof(f11189,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf69(X2) = skaf69(X2)
| ~ ssItem(skaf69(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8693,f8692]) ).
fof(f11192,definition,
! [X2] :
( sQ1038_spl
<=> ( skaf69(X2) = skaf69(X2)
| ~ ssItem(skaf69(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1038_spl])],[split_symbol_definition]) ).
fof(f11195,plain,
( sQ1038_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f11189,f745,f11192]) ).
fof(f11233,plain,
! [X0] :
( app(nil,skaf62(X0)) = nil
| ~ frontsegP(nil,skaf62(X0))
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1142,f1192]) ).
fof(f11235,plain,
! [X0,X1] :
( segmentP(app(skaf62(X1),X0),skaf62(X1))
| ~ ssList(skaf62(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1142,f1086]) ).
fof(f11236,plain,
! [X0,X1] :
( app(app(X1,nil),skaf62(X0)) = app(X1,skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1142,f369]) ).
fof(f11237,plain,
! [X0,X1] :
( app(skaf62(X1),X0) = app(nil,app(skaf62(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1142,f369]) ).
fof(f11238,plain,
! [X0] :
( rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1142,f3479]) ).
fof(f11241,plain,
! [X0,X1] :
( app(nil,skaf62(X1)) = X0
| ~ frontsegP(X0,skaf62(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1142,f1279]) ).
fof(f11242,plain,
! [X0] :
( frontsegP(skaf62(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1142,f982]) ).
fof(f11243,plain,
! [X0,X1] :
( frontsegP(skaf62(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1142,f352]) ).
fof(f11244,definition,
! [X0] :
( sQ1039_spl
<=> ( app(nil,skaf62(X0)) = nil
| ~ frontsegP(nil,skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1039_spl])],[split_symbol_definition]) ).
fof(f11247,plain,
( ~ sQ13_spl
| sQ1039_spl ),
inference(split_clause,[status(thm)],[f11233,f11244,f534]) ).
fof(f11248,definition,
! [X0,X1] :
( sQ1040_spl
<=> ( segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1040_spl])],[split_symbol_definition]) ).
fof(f11252,definition,
! [X0,X1] :
( sQ1041_spl
<=> ( segmentP(app(skaf62(X1),X0),skaf62(X1))
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1041_spl])],[split_symbol_definition]) ).
fof(f11255,plain,
( ~ sQ13_spl
| sQ1041_spl ),
inference(split_clause,[status(thm)],[f11235,f11252,f534]) ).
fof(f11256,definition,
! [X0,X1] :
( sQ1042_spl
<=> ( app(app(X1,nil),skaf62(X0)) = app(X1,skaf62(X0))
| ~ ssList(X1)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1042_spl])],[split_symbol_definition]) ).
fof(f11259,plain,
( ~ sQ13_spl
| sQ1042_spl ),
inference(split_clause,[status(thm)],[f11236,f11256,f534]) ).
fof(f11260,definition,
! [X0,X1] :
( sQ1043_spl
<=> ( app(skaf62(X1),X0) = app(nil,app(skaf62(X1),X0))
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1043_spl])],[split_symbol_definition]) ).
fof(f11263,plain,
( ~ sQ13_spl
| sQ1043_spl ),
inference(split_clause,[status(thm)],[f11237,f11260,f534]) ).
fof(f11264,definition,
! [X0] :
( sQ1044_spl
<=> ( rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1044_spl])],[split_symbol_definition]) ).
fof(f11267,plain,
( sQ1044_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11238,f534,f11264]) ).
fof(f11276,definition,
! [X0,X1] :
( sQ1047_spl
<=> ( app(nil,skaf62(X1)) = X0
| ~ frontsegP(X0,skaf62(X1))
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1047_spl])],[split_symbol_definition]) ).
fof(f11279,plain,
( ~ sQ13_spl
| sQ1047_spl ),
inference(split_clause,[status(thm)],[f11241,f11276,f534]) ).
fof(f11280,definition,
! [X0] :
( sQ1048_spl
<=> ( frontsegP(skaf62(X0),nil)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1048_spl])],[split_symbol_definition]) ).
fof(f11283,plain,
( ~ sQ13_spl
| sQ1048_spl ),
inference(split_clause,[status(thm)],[f11242,f11280,f534]) ).
fof(f11284,definition,
! [X0,X1] :
( sQ1049_spl
<=> ( frontsegP(skaf62(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1049_spl])],[split_symbol_definition]) ).
fof(f11287,plain,
( ~ sQ13_spl
| sQ1049_spl ),
inference(split_clause,[status(thm)],[f11243,f11284,f534]) ).
fof(f11296,plain,
! [X0] :
( ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f1141]) ).
fof(f11298,plain,
! [X0] :
( app(skaf62(X0),nil) = skaf62(X0)
| ~ frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f1192]) ).
fof(f11300,plain,
! [X0,X1] :
( segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1143,f1086]) ).
fof(f11301,plain,
! [X0,X1] :
( app(app(X1,skaf62(X0)),nil) = app(X1,skaf62(X0))
| ~ ssList(X1)
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f369]) ).
fof(f11302,plain,
! [X0] :
( rearsegP(skaf62(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1143,f3479]) ).
fof(f11303,plain,
! [X0] :
( tl(skaf62(X0)) = app(tl(skaf62(X0)),nil)
| nil = skaf62(X0)
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f346]) ).
fof(f11304,plain,
! [X0] :
( hd(skaf62(X0)) = hd(skaf62(X0))
| nil = skaf62(X0)
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f334]) ).
fof(f11305,plain,
! [X0,X1] :
( app(skaf62(X0),nil) = X1
| ~ frontsegP(X1,skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1143,f1279]) ).
fof(f11306,plain,
! [X0] :
( frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1143,f982]) ).
fof(f11307,plain,
! [X0,X1] :
( frontsegP(skaf62(X0),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1143,f352]) ).
fof(f11308,definition,
! [X0] :
( sQ1050_spl
<=> ssList(skaf62(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1050_spl])],[split_symbol_definition]) ).
fof(f11311,plain,
( sQ1050_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11296,f534,f11308]) ).
fof(f11312,definition,
! [X0] :
( sQ1051_spl
<=> ( app(skaf62(X0),nil) = skaf62(X0)
| ~ frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1051_spl])],[split_symbol_definition]) ).
fof(f11315,plain,
( sQ1051_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11298,f534,f11312]) ).
fof(f11317,plain,
( ~ sQ13_spl
| sQ1040_spl ),
inference(split_clause,[status(thm)],[f11300,f11248,f534]) ).
fof(f11318,definition,
! [X0,X1] :
( sQ1052_spl
<=> ( app(app(X1,skaf62(X0)),nil) = app(X1,skaf62(X0))
| ~ ssList(X1)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1052_spl])],[split_symbol_definition]) ).
fof(f11321,plain,
( sQ1052_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11301,f534,f11318]) ).
fof(f11322,definition,
! [X0] :
( sQ1053_spl
<=> ( rearsegP(skaf62(X0),nil)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1053_spl])],[split_symbol_definition]) ).
fof(f11325,plain,
( ~ sQ13_spl
| sQ1053_spl ),
inference(split_clause,[status(thm)],[f11302,f11322,f534]) ).
fof(f11326,definition,
! [X0] :
( sQ1054_spl
<=> ( tl(skaf62(X0)) = app(tl(skaf62(X0)),nil)
| nil = skaf62(X0)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1054_spl])],[split_symbol_definition]) ).
fof(f11329,plain,
( sQ1054_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11303,f534,f11326]) ).
fof(f11330,definition,
! [X0] :
( sQ1055_spl
<=> ( hd(skaf62(X0)) = hd(skaf62(X0))
| nil = skaf62(X0)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1055_spl])],[split_symbol_definition]) ).
fof(f11333,plain,
( sQ1055_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11304,f534,f11330]) ).
fof(f11334,definition,
! [X0,X1] :
( sQ1056_spl
<=> ( app(skaf62(X0),nil) = X1
| ~ frontsegP(X1,skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1056_spl])],[split_symbol_definition]) ).
fof(f11337,plain,
( ~ sQ13_spl
| sQ1056_spl ),
inference(split_clause,[status(thm)],[f11305,f11334,f534]) ).
fof(f11338,definition,
! [X0] :
( sQ1057_spl
<=> ( frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1057_spl])],[split_symbol_definition]) ).
fof(f11341,plain,
( sQ1057_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11306,f534,f11338]) ).
fof(f11342,definition,
! [X0,X1] :
( sQ1058_spl
<=> ( frontsegP(skaf62(X0),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1058_spl])],[split_symbol_definition]) ).
fof(f11345,plain,
( ~ sQ13_spl
| sQ1058_spl ),
inference(split_clause,[status(thm)],[f11307,f11342,f534]) ).
fof(f11365,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf65(X2) = skaf65(X2)
| ~ ssItem(skaf65(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8696,f8695]) ).
fof(f11368,definition,
! [X2] :
( sQ1060_spl
<=> ( skaf65(X2) = skaf65(X2)
| ~ ssItem(skaf65(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1060_spl])],[split_symbol_definition]) ).
fof(f11371,plain,
( sQ1060_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f11365,f745,f11368]) ).
fof(f11409,plain,
! [X0] :
( app(nil,skaf63(X0)) = nil
| ~ frontsegP(nil,skaf63(X0))
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1145,f1192]) ).
fof(f11411,plain,
! [X0,X1] :
( segmentP(app(skaf63(X1),X0),skaf63(X1))
| ~ ssList(skaf63(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1145,f1086]) ).
fof(f11412,plain,
! [X0,X1] :
( app(app(X1,nil),skaf63(X0)) = app(X1,skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1145,f369]) ).
fof(f11413,plain,
! [X0,X1] :
( app(skaf63(X1),X0) = app(nil,app(skaf63(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1145,f369]) ).
fof(f11414,plain,
! [X0] :
( rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1145,f3479]) ).
fof(f11417,plain,
! [X0,X1] :
( app(nil,skaf63(X1)) = X0
| ~ frontsegP(X0,skaf63(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1145,f1279]) ).
fof(f11418,plain,
! [X0] :
( frontsegP(skaf63(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1145,f982]) ).
fof(f11419,plain,
! [X0,X1] :
( frontsegP(skaf63(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1145,f352]) ).
fof(f11420,definition,
! [X0] :
( sQ1061_spl
<=> ( app(nil,skaf63(X0)) = nil
| ~ frontsegP(nil,skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1061_spl])],[split_symbol_definition]) ).
fof(f11423,plain,
( ~ sQ13_spl
| sQ1061_spl ),
inference(split_clause,[status(thm)],[f11409,f11420,f534]) ).
fof(f11424,definition,
! [X0,X1] :
( sQ1062_spl
<=> ( segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1062_spl])],[split_symbol_definition]) ).
fof(f11428,definition,
! [X0,X1] :
( sQ1063_spl
<=> ( segmentP(app(skaf63(X1),X0),skaf63(X1))
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1063_spl])],[split_symbol_definition]) ).
fof(f11431,plain,
( ~ sQ13_spl
| sQ1063_spl ),
inference(split_clause,[status(thm)],[f11411,f11428,f534]) ).
fof(f11432,definition,
! [X0,X1] :
( sQ1064_spl
<=> ( app(app(X1,nil),skaf63(X0)) = app(X1,skaf63(X0))
| ~ ssList(X1)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1064_spl])],[split_symbol_definition]) ).
fof(f11435,plain,
( ~ sQ13_spl
| sQ1064_spl ),
inference(split_clause,[status(thm)],[f11412,f11432,f534]) ).
fof(f11436,definition,
! [X0,X1] :
( sQ1065_spl
<=> ( app(skaf63(X1),X0) = app(nil,app(skaf63(X1),X0))
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1065_spl])],[split_symbol_definition]) ).
fof(f11439,plain,
( ~ sQ13_spl
| sQ1065_spl ),
inference(split_clause,[status(thm)],[f11413,f11436,f534]) ).
fof(f11440,definition,
! [X0] :
( sQ1066_spl
<=> ( rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1066_spl])],[split_symbol_definition]) ).
fof(f11443,plain,
( sQ1066_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11414,f534,f11440]) ).
fof(f11452,definition,
! [X0,X1] :
( sQ1069_spl
<=> ( app(nil,skaf63(X1)) = X0
| ~ frontsegP(X0,skaf63(X1))
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1069_spl])],[split_symbol_definition]) ).
fof(f11455,plain,
( ~ sQ13_spl
| sQ1069_spl ),
inference(split_clause,[status(thm)],[f11417,f11452,f534]) ).
fof(f11456,definition,
! [X0] :
( sQ1070_spl
<=> ( frontsegP(skaf63(X0),nil)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1070_spl])],[split_symbol_definition]) ).
fof(f11459,plain,
( ~ sQ13_spl
| sQ1070_spl ),
inference(split_clause,[status(thm)],[f11418,f11456,f534]) ).
fof(f11460,definition,
! [X0,X1] :
( sQ1071_spl
<=> ( frontsegP(skaf63(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1071_spl])],[split_symbol_definition]) ).
fof(f11463,plain,
( ~ sQ13_spl
| sQ1071_spl ),
inference(split_clause,[status(thm)],[f11419,f11460,f534]) ).
fof(f11472,plain,
! [X0] :
( ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f1144]) ).
fof(f11474,plain,
! [X0] :
( app(skaf63(X0),nil) = skaf63(X0)
| ~ frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f1192]) ).
fof(f11476,plain,
! [X0,X1] :
( segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1146,f1086]) ).
fof(f11477,plain,
! [X0,X1] :
( app(app(X1,skaf63(X0)),nil) = app(X1,skaf63(X0))
| ~ ssList(X1)
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f369]) ).
fof(f11478,plain,
! [X0] :
( rearsegP(skaf63(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1146,f3479]) ).
fof(f11479,plain,
! [X0] :
( tl(skaf63(X0)) = app(tl(skaf63(X0)),nil)
| nil = skaf63(X0)
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f346]) ).
fof(f11480,plain,
! [X0] :
( hd(skaf63(X0)) = hd(skaf63(X0))
| nil = skaf63(X0)
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f334]) ).
fof(f11481,plain,
! [X0,X1] :
( app(skaf63(X0),nil) = X1
| ~ frontsegP(X1,skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1146,f1279]) ).
fof(f11482,plain,
! [X0] :
( frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1146,f982]) ).
fof(f11483,plain,
! [X0,X1] :
( frontsegP(skaf63(X0),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1146,f352]) ).
fof(f11484,definition,
! [X0] :
( sQ1072_spl
<=> ssList(skaf63(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1072_spl])],[split_symbol_definition]) ).
fof(f11487,plain,
( sQ1072_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11472,f534,f11484]) ).
fof(f11488,definition,
! [X0] :
( sQ1073_spl
<=> ( app(skaf63(X0),nil) = skaf63(X0)
| ~ frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1073_spl])],[split_symbol_definition]) ).
fof(f11491,plain,
( sQ1073_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11474,f534,f11488]) ).
fof(f11493,plain,
( ~ sQ13_spl
| sQ1062_spl ),
inference(split_clause,[status(thm)],[f11476,f11424,f534]) ).
fof(f11494,definition,
! [X0,X1] :
( sQ1074_spl
<=> ( app(app(X1,skaf63(X0)),nil) = app(X1,skaf63(X0))
| ~ ssList(X1)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1074_spl])],[split_symbol_definition]) ).
fof(f11497,plain,
( sQ1074_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11477,f534,f11494]) ).
fof(f11498,definition,
! [X0] :
( sQ1075_spl
<=> ( rearsegP(skaf63(X0),nil)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1075_spl])],[split_symbol_definition]) ).
fof(f11501,plain,
( ~ sQ13_spl
| sQ1075_spl ),
inference(split_clause,[status(thm)],[f11478,f11498,f534]) ).
fof(f11502,definition,
! [X0] :
( sQ1076_spl
<=> ( tl(skaf63(X0)) = app(tl(skaf63(X0)),nil)
| nil = skaf63(X0)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1076_spl])],[split_symbol_definition]) ).
fof(f11505,plain,
( sQ1076_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11479,f534,f11502]) ).
fof(f11506,definition,
! [X0] :
( sQ1077_spl
<=> ( hd(skaf63(X0)) = hd(skaf63(X0))
| nil = skaf63(X0)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1077_spl])],[split_symbol_definition]) ).
fof(f11509,plain,
( sQ1077_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11480,f534,f11506]) ).
fof(f11510,definition,
! [X0,X1] :
( sQ1078_spl
<=> ( app(skaf63(X0),nil) = X1
| ~ frontsegP(X1,skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1078_spl])],[split_symbol_definition]) ).
fof(f11513,plain,
( ~ sQ13_spl
| sQ1078_spl ),
inference(split_clause,[status(thm)],[f11481,f11510,f534]) ).
fof(f11514,definition,
! [X0] :
( sQ1079_spl
<=> ( frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1079_spl])],[split_symbol_definition]) ).
fof(f11517,plain,
( sQ1079_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11482,f534,f11514]) ).
fof(f11518,definition,
! [X0,X1] :
( sQ1080_spl
<=> ( frontsegP(skaf63(X0),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1080_spl])],[split_symbol_definition]) ).
fof(f11521,plain,
( ~ sQ13_spl
| sQ1080_spl ),
inference(split_clause,[status(thm)],[f11483,f11518,f534]) ).
fof(f11541,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf64(X2) = skaf64(X2)
| ~ ssItem(skaf64(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8699,f8698]) ).
fof(f11544,definition,
! [X2] :
( sQ1082_spl
<=> ( skaf64(X2) = skaf64(X2)
| ~ ssItem(skaf64(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1082_spl])],[split_symbol_definition]) ).
fof(f11547,plain,
( sQ1082_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f11541,f745,f11544]) ).
fof(f11585,plain,
! [X0] :
( app(nil,skaf66(X0)) = nil
| ~ frontsegP(nil,skaf66(X0))
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1213,f1192]) ).
fof(f11587,plain,
! [X0,X1] :
( segmentP(app(skaf66(X1),X0),skaf66(X1))
| ~ ssList(skaf66(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1213,f1086]) ).
fof(f11588,plain,
! [X0,X1] :
( app(app(X1,nil),skaf66(X0)) = app(X1,skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1213,f369]) ).
fof(f11589,plain,
! [X0,X1] :
( app(skaf66(X1),X0) = app(nil,app(skaf66(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1213,f369]) ).
fof(f11590,plain,
! [X0] :
( rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1213,f3479]) ).
fof(f11593,plain,
! [X0,X1] :
( app(nil,skaf66(X1)) = X0
| ~ frontsegP(X0,skaf66(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1213,f1279]) ).
fof(f11594,plain,
! [X0] :
( frontsegP(skaf66(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1213,f982]) ).
fof(f11595,plain,
! [X0,X1] :
( frontsegP(skaf66(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1213,f352]) ).
fof(f11596,definition,
! [X0] :
( sQ1083_spl
<=> ( app(nil,skaf66(X0)) = nil
| ~ frontsegP(nil,skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1083_spl])],[split_symbol_definition]) ).
fof(f11599,plain,
( ~ sQ13_spl
| sQ1083_spl ),
inference(split_clause,[status(thm)],[f11585,f11596,f534]) ).
fof(f11600,definition,
! [X0,X1] :
( sQ1084_spl
<=> ( segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1084_spl])],[split_symbol_definition]) ).
fof(f11604,definition,
! [X0,X1] :
( sQ1085_spl
<=> ( segmentP(app(skaf66(X1),X0),skaf66(X1))
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1085_spl])],[split_symbol_definition]) ).
fof(f11607,plain,
( ~ sQ13_spl
| sQ1085_spl ),
inference(split_clause,[status(thm)],[f11587,f11604,f534]) ).
fof(f11608,definition,
! [X0,X1] :
( sQ1086_spl
<=> ( app(app(X1,nil),skaf66(X0)) = app(X1,skaf66(X0))
| ~ ssList(X1)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1086_spl])],[split_symbol_definition]) ).
fof(f11611,plain,
( ~ sQ13_spl
| sQ1086_spl ),
inference(split_clause,[status(thm)],[f11588,f11608,f534]) ).
fof(f11612,definition,
! [X0,X1] :
( sQ1087_spl
<=> ( app(skaf66(X1),X0) = app(nil,app(skaf66(X1),X0))
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1087_spl])],[split_symbol_definition]) ).
fof(f11615,plain,
( ~ sQ13_spl
| sQ1087_spl ),
inference(split_clause,[status(thm)],[f11589,f11612,f534]) ).
fof(f11616,definition,
! [X0] :
( sQ1088_spl
<=> ( rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1088_spl])],[split_symbol_definition]) ).
fof(f11619,plain,
( sQ1088_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11590,f534,f11616]) ).
fof(f11628,definition,
! [X0,X1] :
( sQ1091_spl
<=> ( app(nil,skaf66(X1)) = X0
| ~ frontsegP(X0,skaf66(X1))
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1091_spl])],[split_symbol_definition]) ).
fof(f11631,plain,
( ~ sQ13_spl
| sQ1091_spl ),
inference(split_clause,[status(thm)],[f11593,f11628,f534]) ).
fof(f11632,definition,
! [X0] :
( sQ1092_spl
<=> ( frontsegP(skaf66(X0),nil)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1092_spl])],[split_symbol_definition]) ).
fof(f11635,plain,
( ~ sQ13_spl
| sQ1092_spl ),
inference(split_clause,[status(thm)],[f11594,f11632,f534]) ).
fof(f11636,definition,
! [X0,X1] :
( sQ1093_spl
<=> ( frontsegP(skaf66(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1093_spl])],[split_symbol_definition]) ).
fof(f11639,plain,
( ~ sQ13_spl
| sQ1093_spl ),
inference(split_clause,[status(thm)],[f11595,f11636,f534]) ).
fof(f11648,plain,
! [X0] :
( ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f1212]) ).
fof(f11650,plain,
! [X0] :
( app(skaf66(X0),nil) = skaf66(X0)
| ~ frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f1192]) ).
fof(f11652,plain,
! [X0,X1] :
( segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1214,f1086]) ).
fof(f11653,plain,
! [X0,X1] :
( app(app(X1,skaf66(X0)),nil) = app(X1,skaf66(X0))
| ~ ssList(X1)
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f369]) ).
fof(f11654,plain,
! [X0] :
( rearsegP(skaf66(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1214,f3479]) ).
fof(f11655,plain,
! [X0] :
( tl(skaf66(X0)) = app(tl(skaf66(X0)),nil)
| nil = skaf66(X0)
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f346]) ).
fof(f11656,plain,
! [X0] :
( hd(skaf66(X0)) = hd(skaf66(X0))
| nil = skaf66(X0)
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f334]) ).
fof(f11657,plain,
! [X0,X1] :
( app(skaf66(X0),nil) = X1
| ~ frontsegP(X1,skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1214,f1279]) ).
fof(f11658,plain,
! [X0] :
( frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1214,f982]) ).
fof(f11659,plain,
! [X0,X1] :
( frontsegP(skaf66(X0),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1214,f352]) ).
fof(f11660,definition,
! [X0] :
( sQ1094_spl
<=> ssList(skaf66(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1094_spl])],[split_symbol_definition]) ).
fof(f11663,plain,
( sQ1094_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11648,f534,f11660]) ).
fof(f11664,definition,
! [X0] :
( sQ1095_spl
<=> ( app(skaf66(X0),nil) = skaf66(X0)
| ~ frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1095_spl])],[split_symbol_definition]) ).
fof(f11667,plain,
( sQ1095_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11650,f534,f11664]) ).
fof(f11669,plain,
( ~ sQ13_spl
| sQ1084_spl ),
inference(split_clause,[status(thm)],[f11652,f11600,f534]) ).
fof(f11670,definition,
! [X0,X1] :
( sQ1096_spl
<=> ( app(app(X1,skaf66(X0)),nil) = app(X1,skaf66(X0))
| ~ ssList(X1)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1096_spl])],[split_symbol_definition]) ).
fof(f11673,plain,
( sQ1096_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11653,f534,f11670]) ).
fof(f11674,definition,
! [X0] :
( sQ1097_spl
<=> ( rearsegP(skaf66(X0),nil)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1097_spl])],[split_symbol_definition]) ).
fof(f11677,plain,
( ~ sQ13_spl
| sQ1097_spl ),
inference(split_clause,[status(thm)],[f11654,f11674,f534]) ).
fof(f11678,definition,
! [X0] :
( sQ1098_spl
<=> ( tl(skaf66(X0)) = app(tl(skaf66(X0)),nil)
| nil = skaf66(X0)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1098_spl])],[split_symbol_definition]) ).
fof(f11681,plain,
( sQ1098_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11655,f534,f11678]) ).
fof(f11682,definition,
! [X0] :
( sQ1099_spl
<=> ( hd(skaf66(X0)) = hd(skaf66(X0))
| nil = skaf66(X0)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1099_spl])],[split_symbol_definition]) ).
fof(f11685,plain,
( sQ1099_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11656,f534,f11682]) ).
fof(f11686,definition,
! [X0,X1] :
( sQ1100_spl
<=> ( app(skaf66(X0),nil) = X1
| ~ frontsegP(X1,skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1100_spl])],[split_symbol_definition]) ).
fof(f11689,plain,
( ~ sQ13_spl
| sQ1100_spl ),
inference(split_clause,[status(thm)],[f11657,f11686,f534]) ).
fof(f11690,definition,
! [X0] :
( sQ1101_spl
<=> ( frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1101_spl])],[split_symbol_definition]) ).
fof(f11693,plain,
( sQ1101_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11658,f534,f11690]) ).
fof(f11694,definition,
! [X0,X1] :
( sQ1102_spl
<=> ( frontsegP(skaf66(X0),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1102_spl])],[split_symbol_definition]) ).
fof(f11697,plain,
( ~ sQ13_spl
| sQ1102_spl ),
inference(split_clause,[status(thm)],[f11659,f11694,f534]) ).
fof(f11700,plain,
! [X0,X1] :
( ~ sQ133_spl
| X0 = skaf83(sk5)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(skaf82(sk5))
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f1774,f8627]) ).
fof(f11701,plain,
! [X0] :
( ~ sQ133_spl
| frontsegP(cons(skaf83(sk5),X0),sk5)
| ~ ssList(X0)
| ~ ssList(skaf82(sk5))
| ~ frontsegP(X0,skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f8626]) ).
fof(f11702,plain,
! [X0] :
( ~ sQ133_spl
| frontsegP(sk5,cons(skaf83(sk5),X0))
| ~ ssList(skaf82(sk5))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk5),X0) ),
inference(paramodulation,[status(thm)],[f1774,f8626]) ).
fof(f11703,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf64(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf64(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8699]) ).
fof(f11704,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf65(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf65(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8696]) ).
fof(f11705,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf69(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf69(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8693]) ).
fof(f11706,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf70(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf70(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8690]) ).
fof(f11707,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf74(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf74(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8687]) ).
fof(f11708,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = hd(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f8636]) ).
fof(f11709,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf78(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf78(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8633]) ).
fof(f11710,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,cons(skaf83(sk5),X0)),sk5))
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f5619]) ).
fof(f11711,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,sk5),cons(skaf83(sk5),X0)))
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f5619]) ).
fof(f11712,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf79(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf79(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8630]) ).
fof(f11713,plain,
! [X0,X1] :
( ~ sQ133_spl
| skaf83(sk5) = skaf83(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf83(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1774,f8627]) ).
fof(f11714,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk5,X2)
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f10045]) ).
fof(f11721,plain,
( ~ sQ133_spl
| nil = skaf82(sk5)
| lt(skaf83(sk5),hd(skaf82(sk5)))
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ strictorderedP(sk5) ),
inference(paramodulation,[status(thm)],[f1774,f348]) ).
fof(f11724,plain,
( ~ sQ133_spl
| nil = skaf82(sk5)
| leq(skaf83(sk5),hd(skaf82(sk5)))
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ totalorderedP(sk5) ),
inference(paramodulation,[status(thm)],[f1774,f350]) ).
fof(f11726,plain,
! [X0] :
( ~ sQ133_spl
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(skaf82(sk5))
| ~ memberP(skaf82(sk5),X0) ),
inference(paramodulation,[status(thm)],[f1774,f354]) ).
fof(f11734,plain,
! [X0] :
( ~ sQ133_spl
| memberP(app(X0,sk5),skaf83(sk5))
| ~ ssList(app(X0,cons(skaf83(sk5),skaf82(sk5))))
| ~ ssItem(skaf83(sk5))
| ~ ssList(X0)
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f514]) ).
fof(f11736,plain,
! [X0,X1] :
( ~ sQ133_spl
| X1 = skaf83(sk5)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk5),skaf82(sk5)))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X0)
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f518]) ).
fof(f11737,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| lt(skaf83(sk5),X2)
| lt(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),skaf82(sk5))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f521]) ).
fof(f11738,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| lt(X2,skaf83(sk5))
| lt(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk5),skaf82(sk5))),cons(X2,X0)))
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f521]) ).
fof(f11739,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| leq(skaf83(sk5),X2)
| leq(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),skaf82(sk5))))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk5)) ),
inference(paramodulation,[status(thm)],[f1774,f522]) ).
fof(f11740,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| leq(X2,skaf83(sk5))
| leq(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk5),skaf82(sk5))),cons(X2,X0)))
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk5))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1774,f522]) ).
fof(f11743,plain,
( ~ sQ133_spl
| ~ sQ184_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f11700,f2194,f2163,f1773]) ).
fof(f11744,plain,
( ~ sQ133_spl
| ~ sQ184_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f11701,f2202,f2163,f1773]) ).
fof(f11745,plain,
( ~ sQ133_spl
| ~ sQ184_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f11702,f2206,f2163,f1773]) ).
fof(f11746,definition,
! [X0,X1] :
( sQ1103_spl
<=> ( skaf83(sk5) = skaf64(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf64(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1103_spl])],[split_symbol_definition]) ).
fof(f11749,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1103_spl ),
inference(split_clause,[status(thm)],[f11703,f11746,f2163,f2166,f1773]) ).
fof(f11750,definition,
! [X0,X1] :
( sQ1104_spl
<=> ( skaf83(sk5) = skaf65(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf65(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1104_spl])],[split_symbol_definition]) ).
fof(f11753,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1104_spl ),
inference(split_clause,[status(thm)],[f11704,f11750,f2163,f2166,f1773]) ).
fof(f11754,definition,
! [X0,X1] :
( sQ1105_spl
<=> ( skaf83(sk5) = skaf69(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf69(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1105_spl])],[split_symbol_definition]) ).
fof(f11757,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1105_spl ),
inference(split_clause,[status(thm)],[f11705,f11754,f2163,f2166,f1773]) ).
fof(f11758,definition,
! [X0,X1] :
( sQ1106_spl
<=> ( skaf83(sk5) = skaf70(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf70(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1106_spl])],[split_symbol_definition]) ).
fof(f11761,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1106_spl ),
inference(split_clause,[status(thm)],[f11706,f11758,f2163,f2166,f1773]) ).
fof(f11762,definition,
! [X0,X1] :
( sQ1107_spl
<=> ( skaf83(sk5) = skaf74(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf74(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1107_spl])],[split_symbol_definition]) ).
fof(f11765,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1107_spl ),
inference(split_clause,[status(thm)],[f11707,f11762,f2163,f2166,f1773]) ).
fof(f11766,definition,
! [X0,X1] :
( sQ1108_spl
<=> ( skaf83(sk5) = hd(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1108_spl])],[split_symbol_definition]) ).
fof(f11769,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1108_spl ),
inference(split_clause,[status(thm)],[f11708,f11766,f2163,f2166,f1773]) ).
fof(f11770,definition,
! [X0,X1] :
( sQ1109_spl
<=> ( skaf83(sk5) = skaf78(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf78(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1109_spl])],[split_symbol_definition]) ).
fof(f11773,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1109_spl ),
inference(split_clause,[status(thm)],[f11709,f11770,f2163,f2166,f1773]) ).
fof(f11774,definition,
! [X0,X1] :
( sQ1110_spl
<=> ( ~ ssList(app(app(X1,cons(skaf83(sk5),X0)),sk5))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1110_spl])],[split_symbol_definition]) ).
fof(f11777,plain,
( ~ sQ133_spl
| ~ sQ0_spl
| ~ sQ185_spl
| sQ1110_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f11710,f2163,f11774,f2166,f446,f1773]) ).
fof(f11778,definition,
! [X0,X1] :
( sQ1111_spl
<=> ( ~ ssList(app(app(X1,sk5),cons(skaf83(sk5),X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1111_spl])],[split_symbol_definition]) ).
fof(f11781,plain,
( ~ sQ133_spl
| ~ sQ0_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1111_spl ),
inference(split_clause,[status(thm)],[f11711,f11778,f2163,f2166,f446,f1773]) ).
fof(f11782,definition,
! [X0,X1] :
( sQ1112_spl
<=> ( skaf83(sk5) = skaf79(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf79(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1112_spl])],[split_symbol_definition]) ).
fof(f11785,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1112_spl ),
inference(split_clause,[status(thm)],[f11712,f11782,f2163,f2166,f1773]) ).
fof(f11786,definition,
! [X0,X1] :
( sQ1113_spl
<=> ( skaf83(sk5) = skaf83(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf83(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1113_spl])],[split_symbol_definition]) ).
fof(f11789,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1113_spl ),
inference(split_clause,[status(thm)],[f11713,f11786,f2163,f2166,f1773]) ).
fof(f11790,definition,
! [X0,X1,X2] :
( sQ1114_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk5,X2)
| frontsegP(skaf82(sk5),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1114_spl])],[split_symbol_definition]) ).
fof(f11793,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1114_spl ),
inference(split_clause,[status(thm)],[f11714,f11790,f2163,f2166,f1773]) ).
fof(f11800,definition,
( sQ1115_spl
<=> lt(skaf83(sk5),hd(skaf82(sk5))) ),
introduced(definition,[new_symbols(definition,[sQ1115_spl])],[split_symbol_definition]) ).
fof(f11803,definition,
( sQ1116_spl
<=> nil = skaf82(sk5) ),
introduced(definition,[new_symbols(definition,[sQ1116_spl])],[split_symbol_definition]) ).
fof(f11804,plain,
( ~ sQ1116_spl
| nil = skaf82(sk5) ),
inference(component_clause,[status(thm)],[f11803]) ).
fof(f11806,plain,
( ~ sQ133_spl
| sQ1116_spl
| sQ1115_spl
| ~ sQ185_spl
| ~ sQ184_spl
| ~ sQ277_spl ),
inference(split_clause,[status(thm)],[f11721,f2817,f2163,f2166,f11800,f11803,f1773]) ).
fof(f11809,definition,
( sQ1117_spl
<=> leq(skaf83(sk5),hd(skaf82(sk5))) ),
introduced(definition,[new_symbols(definition,[sQ1117_spl])],[split_symbol_definition]) ).
fof(f11812,plain,
( ~ sQ133_spl
| sQ1116_spl
| sQ1117_spl
| ~ sQ185_spl
| ~ sQ184_spl
| ~ sQ276_spl ),
inference(split_clause,[status(thm)],[f11724,f2813,f2163,f2166,f11809,f11803,f1773]) ).
fof(f11814,definition,
! [X0] :
( sQ1118_spl
<=> ( memberP(sk5,X0)
| ~ ssItem(X0)
| ~ memberP(skaf82(sk5),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1118_spl])],[split_symbol_definition]) ).
fof(f11817,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1118_spl ),
inference(split_clause,[status(thm)],[f11726,f11814,f2163,f2166,f1773]) ).
fof(f11825,definition,
! [X0] :
( sQ1119_spl
<=> ( memberP(app(X0,sk5),skaf83(sk5))
| ~ ssList(app(X0,cons(skaf83(sk5),skaf82(sk5))))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1119_spl])],[split_symbol_definition]) ).
fof(f11828,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| sQ1119_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f11734,f2163,f11825,f2166,f1773]) ).
fof(f11830,definition,
! [X0,X1] :
( sQ1120_spl
<=> ( X1 = skaf83(sk5)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk5),skaf82(sk5)))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1120_spl])],[split_symbol_definition]) ).
fof(f11833,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| sQ1120_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f11736,f2163,f11830,f2166,f1773]) ).
fof(f11834,definition,
! [X0,X1,X2] :
( sQ1121_spl
<=> ( lt(skaf83(sk5),X2)
| lt(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),skaf82(sk5))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1121_spl])],[split_symbol_definition]) ).
fof(f11837,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| sQ1121_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f11737,f2163,f11834,f2166,f1773]) ).
fof(f11838,definition,
! [X0,X1,X2] :
( sQ1122_spl
<=> ( lt(X2,skaf83(sk5))
| lt(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk5),skaf82(sk5))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1122_spl])],[split_symbol_definition]) ).
fof(f11841,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1122_spl ),
inference(split_clause,[status(thm)],[f11738,f11838,f2163,f2166,f1773]) ).
fof(f11842,definition,
! [X0,X1,X2] :
( sQ1123_spl
<=> ( leq(skaf83(sk5),X2)
| leq(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),skaf82(sk5))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1123_spl])],[split_symbol_definition]) ).
fof(f11845,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| sQ1123_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f11739,f2163,f11842,f2166,f1773]) ).
fof(f11846,definition,
! [X0,X1,X2] :
( sQ1124_spl
<=> ( leq(X2,skaf83(sk5))
| leq(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk5),skaf82(sk5))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1124_spl])],[split_symbol_definition]) ).
fof(f11849,plain,
( ~ sQ133_spl
| ~ sQ185_spl
| ~ sQ184_spl
| sQ1124_spl ),
inference(split_clause,[status(thm)],[f11740,f11846,f2163,f2166,f1773]) ).
fof(f11858,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| cons(skaf83(sk5),nil) = sk5 ),
inference(backward_demodulation,[status(thm)],[f11804,f1774]) ).
fof(f11881,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| skaf60(X2) = skaf60(X2)
| ~ ssItem(skaf60(X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8702,f8701]) ).
fof(f11884,definition,
! [X2] :
( sQ1126_spl
<=> ( skaf60(X2) = skaf60(X2)
| ~ ssItem(skaf60(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1126_spl])],[split_symbol_definition]) ).
fof(f11887,plain,
( sQ1126_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f11881,f745,f11884]) ).
fof(f11925,plain,
! [X0] :
( app(nil,skaf67(X0)) = nil
| ~ frontsegP(nil,skaf67(X0))
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1216,f1192]) ).
fof(f11927,plain,
! [X0,X1] :
( segmentP(app(skaf67(X1),X0),skaf67(X1))
| ~ ssList(skaf67(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1216,f1086]) ).
fof(f11928,plain,
! [X0,X1] :
( app(app(X1,nil),skaf67(X0)) = app(X1,skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1216,f369]) ).
fof(f11929,plain,
! [X0,X1] :
( app(skaf67(X1),X0) = app(nil,app(skaf67(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1216,f369]) ).
fof(f11930,plain,
! [X0] :
( rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1216,f3479]) ).
fof(f11933,plain,
! [X0,X1] :
( app(nil,skaf67(X1)) = X0
| ~ frontsegP(X0,skaf67(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1216,f1279]) ).
fof(f11934,plain,
! [X0] :
( frontsegP(skaf67(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1216,f982]) ).
fof(f11935,plain,
! [X0,X1] :
( frontsegP(skaf67(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1216,f352]) ).
fof(f11936,definition,
! [X0] :
( sQ1127_spl
<=> ( app(nil,skaf67(X0)) = nil
| ~ frontsegP(nil,skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1127_spl])],[split_symbol_definition]) ).
fof(f11939,plain,
( ~ sQ13_spl
| sQ1127_spl ),
inference(split_clause,[status(thm)],[f11925,f11936,f534]) ).
fof(f11940,definition,
! [X0,X1] :
( sQ1128_spl
<=> ( segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1128_spl])],[split_symbol_definition]) ).
fof(f11944,definition,
! [X0,X1] :
( sQ1129_spl
<=> ( segmentP(app(skaf67(X1),X0),skaf67(X1))
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1129_spl])],[split_symbol_definition]) ).
fof(f11947,plain,
( ~ sQ13_spl
| sQ1129_spl ),
inference(split_clause,[status(thm)],[f11927,f11944,f534]) ).
fof(f11948,definition,
! [X0,X1] :
( sQ1130_spl
<=> ( app(app(X1,nil),skaf67(X0)) = app(X1,skaf67(X0))
| ~ ssList(X1)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1130_spl])],[split_symbol_definition]) ).
fof(f11951,plain,
( ~ sQ13_spl
| sQ1130_spl ),
inference(split_clause,[status(thm)],[f11928,f11948,f534]) ).
fof(f11952,definition,
! [X0,X1] :
( sQ1131_spl
<=> ( app(skaf67(X1),X0) = app(nil,app(skaf67(X1),X0))
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1131_spl])],[split_symbol_definition]) ).
fof(f11955,plain,
( ~ sQ13_spl
| sQ1131_spl ),
inference(split_clause,[status(thm)],[f11929,f11952,f534]) ).
fof(f11956,definition,
! [X0] :
( sQ1132_spl
<=> ( rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1132_spl])],[split_symbol_definition]) ).
fof(f11959,plain,
( sQ1132_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11930,f534,f11956]) ).
fof(f11968,definition,
! [X0,X1] :
( sQ1135_spl
<=> ( app(nil,skaf67(X1)) = X0
| ~ frontsegP(X0,skaf67(X1))
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1135_spl])],[split_symbol_definition]) ).
fof(f11971,plain,
( ~ sQ13_spl
| sQ1135_spl ),
inference(split_clause,[status(thm)],[f11933,f11968,f534]) ).
fof(f11972,definition,
! [X0] :
( sQ1136_spl
<=> ( frontsegP(skaf67(X0),nil)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1136_spl])],[split_symbol_definition]) ).
fof(f11975,plain,
( ~ sQ13_spl
| sQ1136_spl ),
inference(split_clause,[status(thm)],[f11934,f11972,f534]) ).
fof(f11976,definition,
! [X0,X1] :
( sQ1137_spl
<=> ( frontsegP(skaf67(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1137_spl])],[split_symbol_definition]) ).
fof(f11979,plain,
( ~ sQ13_spl
| sQ1137_spl ),
inference(split_clause,[status(thm)],[f11935,f11976,f534]) ).
fof(f11988,plain,
! [X0] :
( ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f1215]) ).
fof(f11990,plain,
! [X0] :
( app(skaf67(X0),nil) = skaf67(X0)
| ~ frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f1192]) ).
fof(f11992,plain,
! [X0,X1] :
( segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1217,f1086]) ).
fof(f11993,plain,
! [X0,X1] :
( app(app(X1,skaf67(X0)),nil) = app(X1,skaf67(X0))
| ~ ssList(X1)
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f369]) ).
fof(f11994,plain,
! [X0] :
( rearsegP(skaf67(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1217,f3479]) ).
fof(f11995,plain,
! [X0] :
( tl(skaf67(X0)) = app(tl(skaf67(X0)),nil)
| nil = skaf67(X0)
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f346]) ).
fof(f11996,plain,
! [X0] :
( hd(skaf67(X0)) = hd(skaf67(X0))
| nil = skaf67(X0)
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f334]) ).
fof(f11997,plain,
! [X0,X1] :
( app(skaf67(X0),nil) = X1
| ~ frontsegP(X1,skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1217,f1279]) ).
fof(f11998,plain,
! [X0] :
( frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1217,f982]) ).
fof(f11999,plain,
! [X0,X1] :
( frontsegP(skaf67(X0),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1217,f352]) ).
fof(f12000,definition,
! [X0] :
( sQ1138_spl
<=> ssList(skaf67(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1138_spl])],[split_symbol_definition]) ).
fof(f12003,plain,
( sQ1138_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11988,f534,f12000]) ).
fof(f12004,definition,
! [X0] :
( sQ1139_spl
<=> ( app(skaf67(X0),nil) = skaf67(X0)
| ~ frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1139_spl])],[split_symbol_definition]) ).
fof(f12007,plain,
( sQ1139_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11990,f534,f12004]) ).
fof(f12009,plain,
( ~ sQ13_spl
| sQ1128_spl ),
inference(split_clause,[status(thm)],[f11992,f11940,f534]) ).
fof(f12010,definition,
! [X0,X1] :
( sQ1140_spl
<=> ( app(app(X1,skaf67(X0)),nil) = app(X1,skaf67(X0))
| ~ ssList(X1)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1140_spl])],[split_symbol_definition]) ).
fof(f12013,plain,
( sQ1140_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11993,f534,f12010]) ).
fof(f12014,definition,
! [X0] :
( sQ1141_spl
<=> ( rearsegP(skaf67(X0),nil)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1141_spl])],[split_symbol_definition]) ).
fof(f12017,plain,
( ~ sQ13_spl
| sQ1141_spl ),
inference(split_clause,[status(thm)],[f11994,f12014,f534]) ).
fof(f12018,definition,
! [X0] :
( sQ1142_spl
<=> ( tl(skaf67(X0)) = app(tl(skaf67(X0)),nil)
| nil = skaf67(X0)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1142_spl])],[split_symbol_definition]) ).
fof(f12021,plain,
( sQ1142_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11995,f534,f12018]) ).
fof(f12022,definition,
! [X0] :
( sQ1143_spl
<=> ( hd(skaf67(X0)) = hd(skaf67(X0))
| nil = skaf67(X0)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1143_spl])],[split_symbol_definition]) ).
fof(f12025,plain,
( sQ1143_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11996,f534,f12022]) ).
fof(f12026,definition,
! [X0,X1] :
( sQ1144_spl
<=> ( app(skaf67(X0),nil) = X1
| ~ frontsegP(X1,skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1144_spl])],[split_symbol_definition]) ).
fof(f12029,plain,
( ~ sQ13_spl
| sQ1144_spl ),
inference(split_clause,[status(thm)],[f11997,f12026,f534]) ).
fof(f12030,definition,
! [X0] :
( sQ1145_spl
<=> ( frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1145_spl])],[split_symbol_definition]) ).
fof(f12033,plain,
( sQ1145_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f11998,f534,f12030]) ).
fof(f12034,definition,
! [X0,X1] :
( sQ1146_spl
<=> ( frontsegP(skaf67(X0),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1146_spl])],[split_symbol_definition]) ).
fof(f12037,plain,
( ~ sQ13_spl
| sQ1146_spl ),
inference(split_clause,[status(thm)],[f11999,f12034,f534]) ).
fof(f12091,plain,
! [X0,X1,X2] :
( skaf59(X2) = skaf59(X2)
| ~ ssItem(skaf59(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8708,f828]) ).
fof(f12107,definition,
! [X2] :
( sQ1148_spl
<=> ( skaf59(X2) = skaf59(X2)
| ~ ssItem(skaf59(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1148_spl])],[split_symbol_definition]) ).
fof(f12110,plain,
( sQ1148_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f12091,f745,f12107]) ).
fof(f12150,plain,
! [X0] :
( app(nil,skaf68(X0)) = nil
| ~ frontsegP(nil,skaf68(X0))
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1219,f1192]) ).
fof(f12152,plain,
! [X0,X1] :
( segmentP(app(skaf68(X1),X0),skaf68(X1))
| ~ ssList(skaf68(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1219,f1086]) ).
fof(f12153,plain,
! [X0,X1] :
( app(app(X1,nil),skaf68(X0)) = app(X1,skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1219,f369]) ).
fof(f12154,plain,
! [X0,X1] :
( app(skaf68(X1),X0) = app(nil,app(skaf68(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1219,f369]) ).
fof(f12155,plain,
! [X0] :
( rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1219,f3479]) ).
fof(f12158,plain,
! [X0,X1] :
( app(nil,skaf68(X1)) = X0
| ~ frontsegP(X0,skaf68(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1219,f1279]) ).
fof(f12159,plain,
! [X0] :
( frontsegP(skaf68(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1219,f982]) ).
fof(f12160,plain,
! [X0,X1] :
( frontsegP(skaf68(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1219,f352]) ).
fof(f12161,definition,
! [X0] :
( sQ1149_spl
<=> ( app(nil,skaf68(X0)) = nil
| ~ frontsegP(nil,skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1149_spl])],[split_symbol_definition]) ).
fof(f12164,plain,
( ~ sQ13_spl
| sQ1149_spl ),
inference(split_clause,[status(thm)],[f12150,f12161,f534]) ).
fof(f12165,definition,
! [X0,X1] :
( sQ1150_spl
<=> ( segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1150_spl])],[split_symbol_definition]) ).
fof(f12169,definition,
! [X0,X1] :
( sQ1151_spl
<=> ( segmentP(app(skaf68(X1),X0),skaf68(X1))
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1151_spl])],[split_symbol_definition]) ).
fof(f12172,plain,
( ~ sQ13_spl
| sQ1151_spl ),
inference(split_clause,[status(thm)],[f12152,f12169,f534]) ).
fof(f12173,definition,
! [X0,X1] :
( sQ1152_spl
<=> ( app(app(X1,nil),skaf68(X0)) = app(X1,skaf68(X0))
| ~ ssList(X1)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1152_spl])],[split_symbol_definition]) ).
fof(f12176,plain,
( ~ sQ13_spl
| sQ1152_spl ),
inference(split_clause,[status(thm)],[f12153,f12173,f534]) ).
fof(f12177,definition,
! [X0,X1] :
( sQ1153_spl
<=> ( app(skaf68(X1),X0) = app(nil,app(skaf68(X1),X0))
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1153_spl])],[split_symbol_definition]) ).
fof(f12180,plain,
( ~ sQ13_spl
| sQ1153_spl ),
inference(split_clause,[status(thm)],[f12154,f12177,f534]) ).
fof(f12181,definition,
! [X0] :
( sQ1154_spl
<=> ( rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1154_spl])],[split_symbol_definition]) ).
fof(f12184,plain,
( sQ1154_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12155,f534,f12181]) ).
fof(f12193,definition,
! [X0,X1] :
( sQ1157_spl
<=> ( app(nil,skaf68(X1)) = X0
| ~ frontsegP(X0,skaf68(X1))
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1157_spl])],[split_symbol_definition]) ).
fof(f12196,plain,
( ~ sQ13_spl
| sQ1157_spl ),
inference(split_clause,[status(thm)],[f12158,f12193,f534]) ).
fof(f12197,definition,
! [X0] :
( sQ1158_spl
<=> ( frontsegP(skaf68(X0),nil)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1158_spl])],[split_symbol_definition]) ).
fof(f12200,plain,
( ~ sQ13_spl
| sQ1158_spl ),
inference(split_clause,[status(thm)],[f12159,f12197,f534]) ).
fof(f12201,definition,
! [X0,X1] :
( sQ1159_spl
<=> ( frontsegP(skaf68(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1159_spl])],[split_symbol_definition]) ).
fof(f12204,plain,
( ~ sQ13_spl
| sQ1159_spl ),
inference(split_clause,[status(thm)],[f12160,f12201,f534]) ).
fof(f12213,plain,
! [X0] :
( ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f1218]) ).
fof(f12215,plain,
! [X0] :
( app(skaf68(X0),nil) = skaf68(X0)
| ~ frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f1192]) ).
fof(f12217,plain,
! [X0,X1] :
( segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1220,f1086]) ).
fof(f12218,plain,
! [X0,X1] :
( app(app(X1,skaf68(X0)),nil) = app(X1,skaf68(X0))
| ~ ssList(X1)
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f369]) ).
fof(f12219,plain,
! [X0] :
( rearsegP(skaf68(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1220,f3479]) ).
fof(f12220,plain,
! [X0] :
( tl(skaf68(X0)) = app(tl(skaf68(X0)),nil)
| nil = skaf68(X0)
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f346]) ).
fof(f12221,plain,
! [X0] :
( hd(skaf68(X0)) = hd(skaf68(X0))
| nil = skaf68(X0)
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f334]) ).
fof(f12222,plain,
! [X0,X1] :
( app(skaf68(X0),nil) = X1
| ~ frontsegP(X1,skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1220,f1279]) ).
fof(f12223,plain,
! [X0] :
( frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1220,f982]) ).
fof(f12224,plain,
! [X0,X1] :
( frontsegP(skaf68(X0),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1220,f352]) ).
fof(f12225,definition,
! [X0] :
( sQ1160_spl
<=> ssList(skaf68(X0)) ),
introduced(definition,[new_symbols(definition,[sQ1160_spl])],[split_symbol_definition]) ).
fof(f12228,plain,
( sQ1160_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12213,f534,f12225]) ).
fof(f12229,definition,
! [X0] :
( sQ1161_spl
<=> ( app(skaf68(X0),nil) = skaf68(X0)
| ~ frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1161_spl])],[split_symbol_definition]) ).
fof(f12232,plain,
( sQ1161_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12215,f534,f12229]) ).
fof(f12234,plain,
( ~ sQ13_spl
| sQ1150_spl ),
inference(split_clause,[status(thm)],[f12217,f12165,f534]) ).
fof(f12235,definition,
! [X0,X1] :
( sQ1162_spl
<=> ( app(app(X1,skaf68(X0)),nil) = app(X1,skaf68(X0))
| ~ ssList(X1)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1162_spl])],[split_symbol_definition]) ).
fof(f12238,plain,
( sQ1162_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12218,f534,f12235]) ).
fof(f12239,definition,
! [X0] :
( sQ1163_spl
<=> ( rearsegP(skaf68(X0),nil)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1163_spl])],[split_symbol_definition]) ).
fof(f12242,plain,
( ~ sQ13_spl
| sQ1163_spl ),
inference(split_clause,[status(thm)],[f12219,f12239,f534]) ).
fof(f12243,definition,
! [X0] :
( sQ1164_spl
<=> ( tl(skaf68(X0)) = app(tl(skaf68(X0)),nil)
| nil = skaf68(X0)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1164_spl])],[split_symbol_definition]) ).
fof(f12246,plain,
( sQ1164_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12220,f534,f12243]) ).
fof(f12247,definition,
! [X0] :
( sQ1165_spl
<=> ( hd(skaf68(X0)) = hd(skaf68(X0))
| nil = skaf68(X0)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1165_spl])],[split_symbol_definition]) ).
fof(f12250,plain,
( sQ1165_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12221,f534,f12247]) ).
fof(f12251,definition,
! [X0,X1] :
( sQ1166_spl
<=> ( app(skaf68(X0),nil) = X1
| ~ frontsegP(X1,skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1166_spl])],[split_symbol_definition]) ).
fof(f12254,plain,
( ~ sQ13_spl
| sQ1166_spl ),
inference(split_clause,[status(thm)],[f12222,f12251,f534]) ).
fof(f12255,definition,
! [X0] :
( sQ1167_spl
<=> ( frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1167_spl])],[split_symbol_definition]) ).
fof(f12258,plain,
( sQ1167_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12223,f534,f12255]) ).
fof(f12259,definition,
! [X0,X1] :
( sQ1168_spl
<=> ( frontsegP(skaf68(X0),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1168_spl])],[split_symbol_definition]) ).
fof(f12262,plain,
( ~ sQ13_spl
| sQ1168_spl ),
inference(split_clause,[status(thm)],[f12224,f12259,f534]) ).
fof(f12294,plain,
! [X0,X1,X2] :
( skaf55(X2) = skaf55(X2)
| ~ ssItem(skaf55(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8711,f826]) ).
fof(f12310,definition,
! [X2] :
( sQ1170_spl
<=> ( skaf55(X2) = skaf55(X2)
| ~ ssItem(skaf55(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1170_spl])],[split_symbol_definition]) ).
fof(f12313,plain,
( sQ1170_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f12294,f745,f12310]) ).
fof(f12490,plain,
! [X0,X1,X2] :
( skaf54(X2) = skaf54(X2)
| ~ ssItem(skaf54(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8714,f824]) ).
fof(f12506,definition,
! [X2] :
( sQ1172_spl
<=> ( skaf54(X2) = skaf54(X2)
| ~ ssItem(skaf54(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1172_spl])],[split_symbol_definition]) ).
fof(f12509,plain,
( sQ1172_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f12490,f745,f12506]) ).
fof(f12513,plain,
! [X0] :
( ~ sQ4_spl
| nil = sk5
| tl(cons(hd(sk5),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1224,f461]) ).
fof(f12563,definition,
! [X0] :
( sQ1173_spl
<=> ( tl(cons(hd(sk5),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1173_spl])],[split_symbol_definition]) ).
fof(f12566,plain,
( ~ sQ4_spl
| sQ21_spl
| sQ1173_spl ),
inference(split_clause,[status(thm)],[f12513,f12563,f591,f460]) ).
fof(f12695,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| singletonP(cons(hd(sk2),nil))
| ~ ssList(sk5)
| ~ ssItem(hd(sk2)) ),
inference(paramodulation,[status(thm)],[f4908,f504]) ).
fof(f12696,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf60(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf60(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8702]) ).
fof(f12697,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf64(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf64(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8699]) ).
fof(f12698,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf65(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf65(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8696]) ).
fof(f12699,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf69(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf69(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8693]) ).
fof(f12700,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf70(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf70(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8690]) ).
fof(f12701,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf74(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf74(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8687]) ).
fof(f12702,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = hd(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f8636]) ).
fof(f12703,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf78(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf78(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8633]) ).
fof(f12706,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf79(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf79(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8630]) ).
fof(f12707,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| hd(sk2) = skaf83(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf83(X0),X1)) ),
inference(paramodulation,[status(thm)],[f4908,f8627]) ).
fof(f12708,plain,
! [X0,X1,X2] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk5,X2)
| frontsegP(nil,X0)
| ~ ssItem(hd(sk2))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4908,f10045]) ).
fof(f12720,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f4908,f354]) ).
fof(f12728,plain,
! [X0] :
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| memberP(app(X0,sk5),hd(sk2))
| ~ ssList(app(X0,cons(hd(sk2),nil)))
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f4908,f514]) ).
fof(f12747,definition,
( sQ1178_spl
<=> singletonP(cons(hd(sk2),nil)) ),
introduced(definition,[new_symbols(definition,[sQ1178_spl])],[split_symbol_definition]) ).
fof(f12750,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| sQ1178_spl
| ~ sQ4_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f12695,f1799,f460,f12747,f4686,f1848,f1617]) ).
fof(f12751,definition,
! [X0,X1] :
( sQ1179_spl
<=> ( hd(sk2) = skaf60(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf60(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1179_spl])],[split_symbol_definition]) ).
fof(f12754,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1179_spl ),
inference(split_clause,[status(thm)],[f12696,f12751,f534,f1799,f4686,f1848,f1617]) ).
fof(f12755,definition,
! [X0,X1] :
( sQ1180_spl
<=> ( hd(sk2) = skaf64(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf64(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1180_spl])],[split_symbol_definition]) ).
fof(f12758,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1180_spl ),
inference(split_clause,[status(thm)],[f12697,f12755,f534,f1799,f4686,f1848,f1617]) ).
fof(f12759,definition,
! [X0,X1] :
( sQ1181_spl
<=> ( hd(sk2) = skaf65(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf65(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1181_spl])],[split_symbol_definition]) ).
fof(f12762,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1181_spl ),
inference(split_clause,[status(thm)],[f12698,f12759,f534,f1799,f4686,f1848,f1617]) ).
fof(f12763,definition,
! [X0,X1] :
( sQ1182_spl
<=> ( hd(sk2) = skaf69(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf69(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1182_spl])],[split_symbol_definition]) ).
fof(f12766,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1182_spl ),
inference(split_clause,[status(thm)],[f12699,f12763,f534,f1799,f4686,f1848,f1617]) ).
fof(f12767,definition,
! [X0,X1] :
( sQ1183_spl
<=> ( hd(sk2) = skaf70(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf70(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1183_spl])],[split_symbol_definition]) ).
fof(f12770,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1183_spl ),
inference(split_clause,[status(thm)],[f12700,f12767,f534,f1799,f4686,f1848,f1617]) ).
fof(f12771,definition,
! [X0,X1] :
( sQ1184_spl
<=> ( hd(sk2) = skaf74(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf74(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1184_spl])],[split_symbol_definition]) ).
fof(f12774,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1184_spl ),
inference(split_clause,[status(thm)],[f12701,f12771,f534,f1799,f4686,f1848,f1617]) ).
fof(f12775,definition,
! [X0,X1] :
( sQ1185_spl
<=> ( hd(sk2) = hd(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1185_spl])],[split_symbol_definition]) ).
fof(f12778,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1185_spl ),
inference(split_clause,[status(thm)],[f12702,f12775,f534,f1799,f4686,f1848,f1617]) ).
fof(f12779,definition,
! [X0,X1] :
( sQ1186_spl
<=> ( hd(sk2) = skaf78(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf78(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1186_spl])],[split_symbol_definition]) ).
fof(f12782,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1186_spl ),
inference(split_clause,[status(thm)],[f12703,f12779,f534,f1799,f4686,f1848,f1617]) ).
fof(f12785,definition,
! [X0,X1] :
( sQ1187_spl
<=> ( hd(sk2) = skaf79(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf79(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1187_spl])],[split_symbol_definition]) ).
fof(f12788,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1187_spl ),
inference(split_clause,[status(thm)],[f12706,f12785,f534,f1799,f4686,f1848,f1617]) ).
fof(f12789,definition,
! [X0,X1] :
( sQ1188_spl
<=> ( hd(sk2) = skaf83(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf83(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1188_spl])],[split_symbol_definition]) ).
fof(f12792,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1188_spl ),
inference(split_clause,[status(thm)],[f12707,f12789,f534,f1799,f4686,f1848,f1617]) ).
fof(f12793,definition,
! [X0,X1,X2] :
( sQ1189_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk5,X2)
| frontsegP(nil,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1189_spl])],[split_symbol_definition]) ).
fof(f12796,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1189_spl ),
inference(split_clause,[status(thm)],[f12708,f12793,f534,f1799,f4686,f1848,f1617]) ).
fof(f12814,definition,
! [X0] :
( sQ1192_spl
<=> ( memberP(sk5,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1192_spl])],[split_symbol_definition]) ).
fof(f12817,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| ~ sQ13_spl
| sQ1192_spl ),
inference(split_clause,[status(thm)],[f12720,f12814,f534,f1799,f4686,f1848,f1617]) ).
fof(f12825,definition,
! [X0] :
( sQ1193_spl
<=> ( memberP(app(X0,sk5),hd(sk2))
| ~ ssList(app(X0,cons(hd(sk2),nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1193_spl])],[split_symbol_definition]) ).
fof(f12828,plain,
( ~ sQ116_spl
| ~ sQ146_spl
| ~ sQ526_spl
| ~ sQ136_spl
| sQ1193_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f12728,f534,f12825,f1799,f4686,f1848,f1617]) ).
fof(f12840,plain,
! [X0,X1,X2] :
( skaf50(X2) = skaf50(X2)
| ~ ssItem(skaf50(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8717,f808]) ).
fof(f12856,definition,
! [X2] :
( sQ1195_spl
<=> ( skaf50(X2) = skaf50(X2)
| ~ ssItem(skaf50(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1195_spl])],[split_symbol_definition]) ).
fof(f12859,plain,
( sQ1195_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f12840,f745,f12856]) ).
fof(f13014,plain,
! [X0,X1,X2] :
( skaf49(X2) = skaf49(X2)
| ~ ssItem(skaf49(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8720,f806]) ).
fof(f13030,definition,
! [X2] :
( sQ1197_spl
<=> ( skaf49(X2) = skaf49(X2)
| ~ ssItem(skaf49(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1197_spl])],[split_symbol_definition]) ).
fof(f13033,plain,
( sQ1197_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f13014,f745,f13030]) ).
fof(f13188,plain,
! [X0,X1,X2] :
( skaf44(X2) = skaf44(X2)
| ~ ssItem(skaf44(X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f8723,f804]) ).
fof(f13204,definition,
! [X2] :
( sQ1199_spl
<=> ( skaf44(X2) = skaf44(X2)
| ~ ssItem(skaf44(X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ1199_spl])],[split_symbol_definition]) ).
fof(f13207,plain,
( sQ1199_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f13188,f745,f13204]) ).
fof(f13513,plain,
! [X0] :
( ~ sQ526_spl
| nil = sk5
| ~ ssList(sk5)
| hd(cons(hd(sk2),X0)) = hd(sk5)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4687,f1242]) ).
fof(f13519,definition,
! [X0] :
( sQ1201_spl
<=> ( hd(cons(hd(sk2),X0)) = hd(sk5)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1201_spl])],[split_symbol_definition]) ).
fof(f13522,plain,
( ~ sQ526_spl
| sQ21_spl
| ~ sQ4_spl
| sQ1201_spl ),
inference(split_clause,[status(thm)],[f13513,f13519,f460,f591,f4686]) ).
fof(f13782,definition,
( sQ1228_spl
<=> hd(sk2) = skaf83(sk2) ),
introduced(definition,[new_symbols(definition,[sQ1228_spl])],[split_symbol_definition]) ).
fof(f13783,plain,
( ~ sQ1228_spl
| hd(sk2) = skaf83(sk2) ),
inference(component_clause,[status(thm)],[f13782]) ).
fof(f13806,definition,
! [X0,X1] :
( sQ1232_spl
<=> ( skaf83(sk2) = skaf60(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf60(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1232_spl])],[split_symbol_definition]) ).
fof(f13810,definition,
! [X0,X1] :
( sQ1233_spl
<=> ( skaf83(sk2) = skaf64(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf64(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f13814,definition,
! [X0,X1] :
( sQ1234_spl
<=> ( skaf83(sk2) = skaf65(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf65(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1234_spl])],[split_symbol_definition]) ).
fof(f13818,definition,
! [X0,X1] :
( sQ1235_spl
<=> ( skaf83(sk2) = skaf69(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf69(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1235_spl])],[split_symbol_definition]) ).
fof(f13822,definition,
! [X0,X1] :
( sQ1236_spl
<=> ( skaf83(sk2) = skaf70(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf70(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1236_spl])],[split_symbol_definition]) ).
fof(f13826,definition,
! [X0,X1] :
( sQ1237_spl
<=> ( skaf83(sk2) = skaf74(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf74(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1237_spl])],[split_symbol_definition]) ).
fof(f13830,definition,
! [X0,X1] :
( sQ1238_spl
<=> ( skaf83(sk2) = hd(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1238_spl])],[split_symbol_definition]) ).
fof(f13834,definition,
! [X0,X1] :
( sQ1239_spl
<=> ( skaf83(sk2) = skaf78(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf78(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1239_spl])],[split_symbol_definition]) ).
fof(f13840,definition,
! [X0,X1] :
( sQ1240_spl
<=> ( skaf83(sk2) = skaf79(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf79(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1240_spl])],[split_symbol_definition]) ).
fof(f13844,definition,
! [X0,X1] :
( sQ1241_spl
<=> ( skaf83(sk2) = skaf83(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf83(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1241_spl])],[split_symbol_definition]) ).
fof(f14145,definition,
! [X0,X1] :
( sQ1275_spl
<=> ( hd(sk2) = skaf60(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf60(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1275_spl])],[split_symbol_definition]) ).
fof(f14149,definition,
! [X0,X1] :
( sQ1276_spl
<=> ( hd(sk2) = skaf64(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf64(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1276_spl])],[split_symbol_definition]) ).
fof(f14153,definition,
! [X0,X1] :
( sQ1277_spl
<=> ( hd(sk2) = skaf65(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf65(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1277_spl])],[split_symbol_definition]) ).
fof(f14157,definition,
! [X0,X1] :
( sQ1278_spl
<=> ( hd(sk2) = skaf69(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf69(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1278_spl])],[split_symbol_definition]) ).
fof(f14161,definition,
! [X0,X1] :
( sQ1279_spl
<=> ( hd(sk2) = skaf70(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf70(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1279_spl])],[split_symbol_definition]) ).
fof(f14165,definition,
! [X0,X1] :
( sQ1280_spl
<=> ( hd(sk2) = skaf74(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf74(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1280_spl])],[split_symbol_definition]) ).
fof(f14169,definition,
! [X0,X1] :
( sQ1281_spl
<=> ( hd(sk2) = hd(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1281_spl])],[split_symbol_definition]) ).
fof(f14173,definition,
! [X0,X1] :
( sQ1282_spl
<=> ( hd(sk2) = skaf78(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf78(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1282_spl])],[split_symbol_definition]) ).
fof(f14177,definition,
! [X0,X1] :
( sQ1283_spl
<=> ( ~ ssList(app(app(X1,cons(hd(sk2),X0)),sk2))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1283_spl])],[split_symbol_definition]) ).
fof(f14181,definition,
! [X0,X1] :
( sQ1284_spl
<=> ( ~ ssList(app(app(X1,sk2),cons(hd(sk2),X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1284_spl])],[split_symbol_definition]) ).
fof(f14185,definition,
! [X0,X1] :
( sQ1285_spl
<=> ( hd(sk2) = skaf79(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf79(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1285_spl])],[split_symbol_definition]) ).
fof(f14189,definition,
! [X0,X1] :
( sQ1286_spl
<=> ( hd(sk2) = skaf83(X0)
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf83(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1286_spl])],[split_symbol_definition]) ).
fof(f14387,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| hd(sk5) = skaf83(sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11858,f1239]) ).
fof(f14389,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(cons(skaf83(sk5),X0),sk5)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f11858,f8626]) ).
fof(f14390,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(sk5,cons(skaf83(sk5),X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11858,f8626]) ).
fof(f14391,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| equalelemsP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f264]) ).
fof(f14392,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| duplicatefreeP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f265]) ).
fof(f14393,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| strictorderedP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f266]) ).
fof(f14394,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| totalorderedP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f267]) ).
fof(f14395,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| strictorderP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f268]) ).
fof(f14396,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| totalorderP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f269]) ).
fof(f14397,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| cyclefreeP(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f270]) ).
fof(f14398,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| singletonP(cons(skaf83(sk5),nil))
| ~ ssList(sk5)
| ~ ssItem(skaf83(sk5)) ),
inference(paramodulation,[status(thm)],[f11858,f504]) ).
fof(f14399,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| skaf83(sk5) = skaf60(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf60(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f8702]) ).
fof(f14411,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk5,X2)
| frontsegP(nil,X0)
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11858,f10045]) ).
fof(f14414,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac3,X0)) ),
inference(paramodulation,[status(thm)],[f11858,f801]) ).
fof(f14415,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sk5,cons(skac2,X0)) ),
inference(paramodulation,[status(thm)],[f11858,f802]) ).
fof(f14416,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f803]) ).
fof(f14419,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f805]) ).
fof(f14423,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| memberP(sk5,X0)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11858,f354]) ).
fof(f14424,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f807]) ).
fof(f14426,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f823]) ).
fof(f14428,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f825]) ).
fof(f14430,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f11858,f827]) ).
fof(f14431,plain,
! [X0] :
( ~ sQ133_spl
| ~ sQ1116_spl
| memberP(app(X0,sk5),skaf83(sk5))
| ~ ssList(app(X0,cons(skaf83(sk5),nil)))
| ~ ssItem(skaf83(sk5))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11858,f514]) ).
fof(f14433,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| X1 = skaf83(sk5)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk5),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11858,f518]) ).
fof(f14434,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ sQ1116_spl
| lt(skaf83(sk5),X2)
| lt(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),nil)))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11858,f521]) ).
fof(f14435,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ sQ1116_spl
| lt(X2,skaf83(sk5))
| lt(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk5),nil)),cons(X2,X0)))
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11858,f521]) ).
fof(f14436,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ sQ1116_spl
| leq(skaf83(sk5),X2)
| leq(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),nil)))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11858,f522]) ).
fof(f14437,plain,
! [X0,X1,X2] :
( ~ sQ133_spl
| ~ sQ1116_spl
| leq(X2,skaf83(sk5))
| leq(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk5),nil)),cons(X2,X0)))
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11858,f522]) ).
fof(f14438,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(X1,nil)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk5))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk5) ),
inference(paramodulation,[status(thm)],[f11858,f409]) ).
fof(f14439,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ sQ1116_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk5))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f11858,f409]) ).
fof(f14440,definition,
( sQ1296_spl
<=> hd(sk5) = skaf83(sk5) ),
introduced(definition,[new_symbols(definition,[sQ1296_spl])],[split_symbol_definition]) ).
fof(f14443,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ1296_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f14387,f534,f14440,f11803,f1773]) ).
fof(f14445,definition,
! [X0] :
( sQ1297_spl
<=> ( frontsegP(cons(skaf83(sk5),X0),sk5)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ1297_spl])],[split_symbol_definition]) ).
fof(f14448,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ13_spl
| sQ1297_spl ),
inference(split_clause,[status(thm)],[f14389,f14445,f534,f11803,f1773]) ).
fof(f14449,definition,
! [X0] :
( sQ1298_spl
<=> ( frontsegP(sk5,cons(skaf83(sk5),X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1298_spl])],[split_symbol_definition]) ).
fof(f14452,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ13_spl
| sQ1298_spl ),
inference(split_clause,[status(thm)],[f14390,f14449,f534,f11803,f1773]) ).
fof(f14453,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ279_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14391,f2166,f2825,f11803,f1773]) ).
fof(f14454,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ278_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14392,f2166,f2821,f11803,f1773]) ).
fof(f14455,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ277_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14393,f2166,f2817,f11803,f1773]) ).
fof(f14456,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ276_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14394,f2166,f2813,f11803,f1773]) ).
fof(f14457,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ275_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14395,f2166,f2809,f11803,f1773]) ).
fof(f14458,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ274_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14396,f2166,f2805,f11803,f1773]) ).
fof(f14459,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ273_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14397,f2166,f2801,f11803,f1773]) ).
fof(f14460,definition,
( sQ1299_spl
<=> singletonP(cons(skaf83(sk5),nil)) ),
introduced(definition,[new_symbols(definition,[sQ1299_spl])],[split_symbol_definition]) ).
fof(f14463,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| sQ1299_spl
| ~ sQ4_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f14398,f2166,f460,f14460,f11803,f1773]) ).
fof(f14464,definition,
! [X0,X1] :
( sQ1300_spl
<=> ( skaf83(sk5) = skaf60(X0)
| ~ ssList(X1)
| ~ frontsegP(sk5,cons(skaf60(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1300_spl])],[split_symbol_definition]) ).
fof(f14467,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ1300_spl ),
inference(split_clause,[status(thm)],[f14399,f14464,f534,f2166,f11803,f1773]) ).
fof(f14479,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ1189_spl ),
inference(split_clause,[status(thm)],[f14411,f12793,f534,f2166,f11803,f1773]) ).
fof(f14482,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f14414,f2853,f534,f2166,f11803,f1773]) ).
fof(f14483,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f14415,f2849,f534,f2166,f11803,f1773]) ).
fof(f14484,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f14416,f2845,f534,f2166,f11803,f1773]) ).
fof(f14490,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f14419,f2837,f534,f2166,f11803,f1773]) ).
fof(f14497,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ1192_spl ),
inference(split_clause,[status(thm)],[f14423,f12814,f534,f2166,f11803,f1773]) ).
fof(f14498,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f14424,f2829,f534,f2166,f11803,f1773]) ).
fof(f14500,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f14426,f2943,f534,f2166,f11803,f1773]) ).
fof(f14502,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f14428,f3182,f534,f2166,f11803,f1773]) ).
fof(f14504,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f14430,f3324,f534,f2166,f11803,f1773]) ).
fof(f14505,definition,
! [X0] :
( sQ1303_spl
<=> ( memberP(app(X0,sk5),skaf83(sk5))
| ~ ssList(app(X0,cons(skaf83(sk5),nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1303_spl])],[split_symbol_definition]) ).
fof(f14508,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| sQ1303_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f14431,f534,f14505,f2166,f11803,f1773]) ).
fof(f14510,definition,
! [X0,X1] :
( sQ1304_spl
<=> ( X1 = skaf83(sk5)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk5),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk5)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1304_spl])],[split_symbol_definition]) ).
fof(f14513,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| sQ1304_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f14433,f534,f14510,f2166,f11803,f1773]) ).
fof(f14514,definition,
! [X0,X1,X2] :
( sQ1305_spl
<=> ( lt(skaf83(sk5),X2)
| lt(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1305_spl])],[split_symbol_definition]) ).
fof(f14517,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| sQ1305_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f14434,f534,f14514,f2166,f11803,f1773]) ).
fof(f14518,definition,
! [X0,X1,X2] :
( sQ1306_spl
<=> ( lt(X2,skaf83(sk5))
| lt(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(skaf83(sk5),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1306_spl])],[split_symbol_definition]) ).
fof(f14521,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ1306_spl ),
inference(split_clause,[status(thm)],[f14435,f14518,f534,f2166,f11803,f1773]) ).
fof(f14522,definition,
! [X0,X1,X2] :
( sQ1307_spl
<=> ( leq(skaf83(sk5),X2)
| leq(X2,skaf83(sk5))
| ~ ssList(app(app(X1,cons(X2,X0)),sk5))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(skaf83(sk5),nil)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1307_spl])],[split_symbol_definition]) ).
fof(f14525,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| sQ1307_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f14436,f534,f14522,f2166,f11803,f1773]) ).
fof(f14526,definition,
! [X0,X1,X2] :
( sQ1308_spl
<=> ( leq(X2,skaf83(sk5))
| leq(skaf83(sk5),X2)
| ~ ssList(app(app(X1,sk5),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(skaf83(sk5),nil)),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1308_spl])],[split_symbol_definition]) ).
fof(f14529,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ1308_spl ),
inference(split_clause,[status(thm)],[f14437,f14526,f534,f2166,f11803,f1773]) ).
fof(f14530,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f14438,f2885,f534,f2166,f11803,f1773]) ).
fof(f14531,plain,
( ~ sQ133_spl
| ~ sQ1116_spl
| ~ sQ185_spl
| ~ sQ13_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f14439,f2889,f534,f2166,f11803,f1773]) ).
fof(f14556,plain,
( ~ sQ131_spl
| hd(sk2) = skaf83(sk2)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f1239]) ).
fof(f14557,plain,
! [X0,X1] :
( ~ sQ131_spl
| X0 = skaf83(sk2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ frontsegP(cons(X0,X1),sk2) ),
inference(paramodulation,[status(thm)],[f1766,f8627]) ).
fof(f14558,plain,
! [X0] :
( ~ sQ131_spl
| frontsegP(cons(skaf83(sk2),X0),sk2)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2))
| ~ frontsegP(X0,skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f1766,f8626]) ).
fof(f14559,plain,
! [X0] :
( ~ sQ131_spl
| frontsegP(sk2,cons(skaf83(sk2),X0))
| ~ ssList(skaf82(sk2))
| ~ ssList(X0)
| ~ frontsegP(skaf82(sk2),X0) ),
inference(paramodulation,[status(thm)],[f1766,f8626]) ).
fof(f14560,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf60(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf60(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8702]) ).
fof(f14561,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf64(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf64(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8699]) ).
fof(f14562,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf65(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf65(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8696]) ).
fof(f14563,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf69(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf69(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8693]) ).
fof(f14564,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf70(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf70(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8690]) ).
fof(f14565,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf74(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf74(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8687]) ).
fof(f14566,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = hd(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1766,f8636]) ).
fof(f14567,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf78(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf78(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8633]) ).
fof(f14570,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf79(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf79(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8630]) ).
fof(f14571,plain,
! [X0,X1] :
( ~ sQ131_spl
| skaf83(sk2) = skaf83(X0)
| ~ ssItem(skaf83(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf83(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1766,f8627]) ).
fof(f14601,plain,
( ~ sQ131_spl
| sQ1228_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f14556,f2380,f13782,f1765]) ).
fof(f14602,plain,
( ~ sQ131_spl
| ~ sQ215_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f14557,f2416,f2380,f1765]) ).
fof(f14603,plain,
( ~ sQ131_spl
| ~ sQ215_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f14558,f2424,f2380,f1765]) ).
fof(f14604,plain,
( ~ sQ131_spl
| ~ sQ215_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f14559,f2428,f2380,f1765]) ).
fof(f14605,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1232_spl ),
inference(split_clause,[status(thm)],[f14560,f13806,f2380,f2383,f1765]) ).
fof(f14606,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1233_spl ),
inference(split_clause,[status(thm)],[f14561,f13810,f2380,f2383,f1765]) ).
fof(f14607,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1234_spl ),
inference(split_clause,[status(thm)],[f14562,f13814,f2380,f2383,f1765]) ).
fof(f14608,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1235_spl ),
inference(split_clause,[status(thm)],[f14563,f13818,f2380,f2383,f1765]) ).
fof(f14609,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1236_spl ),
inference(split_clause,[status(thm)],[f14564,f13822,f2380,f2383,f1765]) ).
fof(f14610,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1237_spl ),
inference(split_clause,[status(thm)],[f14565,f13826,f2380,f2383,f1765]) ).
fof(f14611,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1238_spl ),
inference(split_clause,[status(thm)],[f14566,f13830,f2380,f2383,f1765]) ).
fof(f14612,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1239_spl ),
inference(split_clause,[status(thm)],[f14567,f13834,f2380,f2383,f1765]) ).
fof(f14615,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1240_spl ),
inference(split_clause,[status(thm)],[f14570,f13840,f2380,f2383,f1765]) ).
fof(f14616,plain,
( ~ sQ131_spl
| ~ sQ216_spl
| ~ sQ215_spl
| sQ1241_spl ),
inference(split_clause,[status(thm)],[f14571,f13844,f2380,f2383,f1765]) ).
fof(f14617,definition,
! [X0,X1,X2] :
( sQ1309_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk2,X2)
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1309_spl])],[split_symbol_definition]) ).
fof(f14885,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| cons(hd(sk2),skaf82(sk2)) = sk2 ),
inference(backward_demodulation,[status(thm)],[f13783,f1766]) ).
fof(f15094,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf60(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf60(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8702]) ).
fof(f15095,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf64(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf64(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8699]) ).
fof(f15096,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf65(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf65(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8696]) ).
fof(f15097,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf69(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf69(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8693]) ).
fof(f15098,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf70(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf70(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8690]) ).
fof(f15099,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf74(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf74(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8687]) ).
fof(f15100,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = hd(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(hd(X0),X1))
| nil = X0
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f14885,f8636]) ).
fof(f15101,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf78(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf78(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8633]) ).
fof(f15102,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,cons(hd(sk2),X0)),sk2))
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f14885,f5619]) ).
fof(f15103,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,sk2),cons(hd(sk2),X0)))
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f14885,f5619]) ).
fof(f15104,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf79(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf79(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8630]) ).
fof(f15105,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf83(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf83(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f8627]) ).
fof(f15106,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ ssList(X2)
| ~ frontsegP(X2,cons(X1,X0))
| ~ frontsegP(sk2,X2)
| frontsegP(skaf82(sk2),X0)
| ~ ssItem(hd(sk2))
| ~ ssItem(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f14885,f10045]) ).
fof(f15112,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf44(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf44(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f804]) ).
fof(f15115,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf49(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf49(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f806]) ).
fof(f15120,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf50(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf50(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f808]) ).
fof(f15122,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf54(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf54(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f824]) ).
fof(f15124,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf55(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf55(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f826]) ).
fof(f15126,plain,
! [X0] :
( ~ sQ131_spl
| ~ sQ1228_spl
| memberP(app(X0,sk2),hd(sk2))
| ~ ssList(app(X0,cons(hd(sk2),skaf82(sk2))))
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f14885,f514]) ).
fof(f15127,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| hd(sk2) = skaf59(X0)
| ~ ssItem(hd(sk2))
| ~ ssList(skaf82(sk2))
| ~ ssList(X1)
| ~ frontsegP(sk2,cons(skaf59(X0),X1)) ),
inference(paramodulation,[status(thm)],[f14885,f828]) ).
fof(f15128,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ sQ1228_spl
| X1 = hd(sk2)
| ~ ssList(app(X0,cons(X1,cons(hd(sk2),skaf82(sk2)))))
| ~ equalelemsP(app(X0,cons(X1,sk2)))
| ~ ssItem(X1)
| ~ ssItem(hd(sk2))
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f14885,f518]) ).
fof(f15129,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ sQ1228_spl
| lt(hd(sk2),X2)
| lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f14885,f521]) ).
fof(f15130,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ sQ1228_spl
| lt(X2,hd(sk2))
| lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(hd(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f14885,f521]) ).
fof(f15131,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ sQ1228_spl
| leq(hd(sk2),X2)
| leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssItem(hd(sk2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf82(sk2)) ),
inference(paramodulation,[status(thm)],[f14885,f522]) ).
fof(f15132,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ sQ1228_spl
| leq(X2,hd(sk2))
| leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(hd(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(hd(sk2))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(skaf82(sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f14885,f522]) ).
fof(f15145,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1275_spl ),
inference(split_clause,[status(thm)],[f15094,f14145,f2380,f1799,f13782,f1765]) ).
fof(f15146,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1276_spl ),
inference(split_clause,[status(thm)],[f15095,f14149,f2380,f1799,f13782,f1765]) ).
fof(f15147,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1277_spl ),
inference(split_clause,[status(thm)],[f15096,f14153,f2380,f1799,f13782,f1765]) ).
fof(f15148,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1278_spl ),
inference(split_clause,[status(thm)],[f15097,f14157,f2380,f1799,f13782,f1765]) ).
fof(f15149,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1279_spl ),
inference(split_clause,[status(thm)],[f15098,f14161,f2380,f1799,f13782,f1765]) ).
fof(f15150,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1280_spl ),
inference(split_clause,[status(thm)],[f15099,f14165,f2380,f1799,f13782,f1765]) ).
fof(f15151,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1281_spl ),
inference(split_clause,[status(thm)],[f15100,f14169,f2380,f1799,f13782,f1765]) ).
fof(f15152,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1282_spl ),
inference(split_clause,[status(thm)],[f15101,f14173,f2380,f1799,f13782,f1765]) ).
fof(f15153,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ0_spl
| ~ sQ136_spl
| sQ1283_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f15102,f2380,f14177,f1799,f446,f13782,f1765]) ).
fof(f15154,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ0_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1284_spl ),
inference(split_clause,[status(thm)],[f15103,f14181,f2380,f1799,f446,f13782,f1765]) ).
fof(f15155,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1285_spl ),
inference(split_clause,[status(thm)],[f15104,f14185,f2380,f1799,f13782,f1765]) ).
fof(f15156,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1286_spl ),
inference(split_clause,[status(thm)],[f15105,f14189,f2380,f1799,f13782,f1765]) ).
fof(f15157,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1309_spl ),
inference(split_clause,[status(thm)],[f15106,f14617,f2380,f1799,f13782,f1765]) ).
fof(f15163,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f15112,f4139,f2380,f1799,f13782,f1765]) ).
fof(f15169,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ443_spl ),
inference(split_clause,[status(thm)],[f15115,f4131,f2380,f1799,f13782,f1765]) ).
fof(f15177,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f15120,f4123,f2380,f1799,f13782,f1765]) ).
fof(f15179,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f15122,f4115,f2380,f1799,f13782,f1765]) ).
fof(f15181,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f15124,f4107,f2380,f1799,f13782,f1765]) ).
fof(f15183,definition,
! [X0] :
( sQ1315_spl
<=> ( memberP(app(X0,sk2),hd(sk2))
| ~ ssList(app(X0,cons(hd(sk2),skaf82(sk2))))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1315_spl])],[split_symbol_definition]) ).
fof(f15186,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| sQ1315_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f15126,f2380,f15183,f1799,f13782,f1765]) ).
fof(f15187,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ434_spl ),
inference(split_clause,[status(thm)],[f15127,f4095,f2380,f1799,f13782,f1765]) ).
fof(f15188,definition,
! [X0,X1] :
( sQ1316_spl
<=> ( X1 = hd(sk2)
| ~ ssList(app(X0,cons(X1,cons(hd(sk2),skaf82(sk2)))))
| ~ equalelemsP(app(X0,cons(X1,sk2)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1316_spl])],[split_symbol_definition]) ).
fof(f15191,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| sQ1316_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f15128,f2380,f15188,f1799,f13782,f1765]) ).
fof(f15192,definition,
! [X0,X1,X2] :
( sQ1317_spl
<=> ( lt(hd(sk2),X2)
| lt(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ strictorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1317_spl])],[split_symbol_definition]) ).
fof(f15195,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| sQ1317_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f15129,f2380,f15192,f1799,f13782,f1765]) ).
fof(f15196,definition,
! [X0,X1,X2] :
( sQ1318_spl
<=> ( lt(X2,hd(sk2))
| lt(hd(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ strictorderP(app(app(X1,cons(hd(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1318_spl])],[split_symbol_definition]) ).
fof(f15199,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1318_spl ),
inference(split_clause,[status(thm)],[f15130,f15196,f2380,f1799,f13782,f1765]) ).
fof(f15200,definition,
! [X0,X1,X2] :
( sQ1319_spl
<=> ( leq(hd(sk2),X2)
| leq(X2,hd(sk2))
| ~ ssList(app(app(X1,cons(X2,X0)),sk2))
| ~ totalorderP(app(app(X1,cons(X2,X0)),cons(hd(sk2),skaf82(sk2))))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1319_spl])],[split_symbol_definition]) ).
fof(f15203,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| sQ1319_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f15131,f2380,f15200,f1799,f13782,f1765]) ).
fof(f15204,definition,
! [X0,X1,X2] :
( sQ1320_spl
<=> ( leq(X2,hd(sk2))
| leq(hd(sk2),X2)
| ~ ssList(app(app(X1,sk2),cons(X2,X0)))
| ~ totalorderP(app(app(X1,cons(hd(sk2),skaf82(sk2))),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1320_spl])],[split_symbol_definition]) ).
fof(f15207,plain,
( ~ sQ131_spl
| ~ sQ1228_spl
| ~ sQ136_spl
| ~ sQ215_spl
| sQ1320_spl ),
inference(split_clause,[status(thm)],[f15132,f15204,f2380,f1799,f13782,f1765]) ).
fof(f15346,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ4_spl
| segmentP(app(sk5,X0),sk5)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1058,f5684]) ).
fof(f15347,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ4_spl
| app(app(skaf47(app(sk5,X0),sk5),sk5),skaf48(sk5,app(sk5,X0))) = app(sk5,X0)
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f399]) ).
fof(f15348,plain,
! [X0,X1,X2] :
( ~ sQ67_spl
| ~ sQ4_spl
| app(app(X2,app(sk5,X0)),X1) = sk5
| ~ ssList(app(app(X2,app(sk5,X0)),X1))
| ~ segmentP(sk5,app(app(X2,app(sk5,X0)),X1))
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f708]) ).
fof(f15349,plain,
! [X0,X1,X2,X3] :
( ~ sQ67_spl
| ~ sQ4_spl
| segmentP(X3,sk5)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk5,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk5,X0)),X1))
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f707]) ).
fof(f15350,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ4_spl
| app(sk5,X0) = sk5
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ segmentP(sk5,app(sk5,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f340]) ).
fof(f15351,plain,
! [X0,X1] :
( ~ sQ67_spl
| ~ sQ4_spl
| segmentP(X1,sk5)
| ~ ssList(X1)
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ segmentP(X1,app(sk5,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f375]) ).
fof(f15352,plain,
! [X0,X1,X2] :
( ~ sQ67_spl
| ~ sQ4_spl
| segmentP(app(app(X2,app(sk5,X0)),X1),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(sk5)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15346,f405]) ).
fof(f15353,plain,
( ~ sQ312_spl
| ~ sQ67_spl
| ~ sQ4_spl
| segmentP(sk1,sk5)
| ~ ssList(skaf45(sk1,sk5)) ),
inference(paramodulation,[status(thm)],[f3014,f15346]) ).
fof(f15354,plain,
( ~ sQ315_spl
| ~ sQ67_spl
| ~ sQ4_spl
| segmentP(sk2,sk5)
| ~ ssList(skaf45(sk2,sk5)) ),
inference(paramodulation,[status(thm)],[f3026,f15346]) ).
fof(f15355,plain,
( ~ sQ4_spl
| ~ sQ67_spl
| segmentP(sk5,sk5)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5686,f15346]) ).
fof(f15356,definition,
! [X0] :
( sQ1331_spl
<=> ( app(app(skaf47(app(sk5,X0),sk5),sk5),skaf48(sk5,app(sk5,X0))) = app(sk5,X0)
| ~ ssList(app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1331_spl])],[split_symbol_definition]) ).
fof(f15359,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1331_spl ),
inference(split_clause,[status(thm)],[f15347,f15356,f460,f1050]) ).
fof(f15360,definition,
! [X0,X1,X2] :
( sQ1332_spl
<=> ( app(app(X2,app(sk5,X0)),X1) = sk5
| ~ ssList(app(app(X2,app(sk5,X0)),X1))
| ~ segmentP(sk5,app(app(X2,app(sk5,X0)),X1))
| ~ ssList(app(sk5,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1332_spl])],[split_symbol_definition]) ).
fof(f15363,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1332_spl ),
inference(split_clause,[status(thm)],[f15348,f15360,f460,f1050]) ).
fof(f15364,definition,
! [X0,X1,X2,X3] :
( sQ1333_spl
<=> ( segmentP(X3,sk5)
| ~ ssList(X3)
| ~ ssList(app(app(X2,app(sk5,X0)),X1))
| ~ segmentP(X3,app(app(X2,app(sk5,X0)),X1))
| ~ ssList(app(sk5,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1333_spl])],[split_symbol_definition]) ).
fof(f15367,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1333_spl ),
inference(split_clause,[status(thm)],[f15349,f15364,f460,f1050]) ).
fof(f15368,definition,
! [X0] :
( sQ1334_spl
<=> ( app(sk5,X0) = sk5
| ~ ssList(app(sk5,X0))
| ~ segmentP(sk5,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1334_spl])],[split_symbol_definition]) ).
fof(f15371,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1334_spl ),
inference(split_clause,[status(thm)],[f15350,f15368,f460,f1050]) ).
fof(f15372,definition,
! [X0,X1] :
( sQ1335_spl
<=> ( segmentP(X1,sk5)
| ~ ssList(X1)
| ~ ssList(app(sk5,X0))
| ~ segmentP(X1,app(sk5,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1335_spl])],[split_symbol_definition]) ).
fof(f15375,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1335_spl ),
inference(split_clause,[status(thm)],[f15351,f15372,f460,f1050]) ).
fof(f15376,definition,
! [X0,X1,X2] :
( sQ1336_spl
<=> ( segmentP(app(app(X2,app(sk5,X0)),X1),sk5)
| ~ ssList(app(sk5,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1336_spl])],[split_symbol_definition]) ).
fof(f15379,plain,
( ~ sQ67_spl
| ~ sQ4_spl
| sQ1336_spl ),
inference(split_clause,[status(thm)],[f15352,f15376,f460,f1050]) ).
fof(f15380,definition,
( sQ1337_spl
<=> segmentP(sk1,sk5) ),
introduced(definition,[new_symbols(definition,[sQ1337_spl])],[split_symbol_definition]) ).
fof(f15381,plain,
( ~ sQ1337_spl
| segmentP(sk1,sk5) ),
inference(component_clause,[status(thm)],[f15380]) ).
fof(f15383,plain,
( ~ sQ312_spl
| ~ sQ67_spl
| ~ sQ4_spl
| sQ1337_spl
| ~ sQ548_spl ),
inference(split_clause,[status(thm)],[f15353,f4859,f15380,f460,f1050,f3013]) ).
fof(f15384,definition,
( sQ1338_spl
<=> segmentP(sk2,sk5) ),
introduced(definition,[new_symbols(definition,[sQ1338_spl])],[split_symbol_definition]) ).
fof(f15387,plain,
( ~ sQ315_spl
| ~ sQ67_spl
| ~ sQ4_spl
| sQ1338_spl
| ~ sQ520_spl ),
inference(split_clause,[status(thm)],[f15354,f4661,f15384,f460,f1050,f3025]) ).
fof(f15388,definition,
( sQ1339_spl
<=> segmentP(sk5,sk5) ),
introduced(definition,[new_symbols(definition,[sQ1339_spl])],[split_symbol_definition]) ).
fof(f15389,plain,
( ~ sQ1339_spl
| segmentP(sk5,sk5) ),
inference(component_clause,[status(thm)],[f15388]) ).
fof(f15391,plain,
( ~ sQ4_spl
| ~ sQ67_spl
| sQ1339_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15355,f534,f15388,f1050,f460]) ).
fof(f15398,plain,
( ~ sQ1339_spl
| app(app(skaf47(sk5,sk5),sk5),skaf48(sk5,sk5)) = sk5
| ~ ssList(sk5)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f15389,f399]) ).
fof(f15399,plain,
! [X0,X1] :
( ~ sQ1339_spl
| app(app(X1,sk5),X0) = sk5
| ~ ssList(app(app(X1,sk5),X0))
| ~ segmentP(sk5,app(app(X1,sk5),X0))
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15389,f708]) ).
fof(f15400,plain,
! [X0,X1,X2] :
( ~ sQ1339_spl
| segmentP(X2,sk5)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk5),X0))
| ~ segmentP(X2,app(app(X1,sk5),X0))
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15389,f707]) ).
fof(f15402,plain,
! [X0] :
( ~ sQ1339_spl
| segmentP(X0,sk5)
| ~ ssList(X0)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ segmentP(X0,sk5) ),
inference(resolution,[status(thm)],[f15389,f375]) ).
fof(f15403,plain,
! [X0,X1] :
( ~ sQ1339_spl
| segmentP(app(app(X1,sk5),X0),sk5)
| ~ ssList(sk5)
| ~ ssList(sk5)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f15389,f405]) ).
fof(f15404,definition,
( sQ1340_spl
<=> app(app(skaf47(sk5,sk5),sk5),skaf48(sk5,sk5)) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ1340_spl])],[split_symbol_definition]) ).
fof(f15407,plain,
( ~ sQ1339_spl
| sQ1340_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f15398,f460,f15404,f15388]) ).
fof(f15408,definition,
! [X0,X1] :
( sQ1341_spl
<=> ( app(app(X1,sk5),X0) = sk5
| ~ ssList(app(app(X1,sk5),X0))
| ~ segmentP(sk5,app(app(X1,sk5),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1341_spl])],[split_symbol_definition]) ).
fof(f15411,plain,
( ~ sQ1339_spl
| ~ sQ4_spl
| sQ1341_spl ),
inference(split_clause,[status(thm)],[f15399,f15408,f460,f15388]) ).
fof(f15412,definition,
! [X0,X1,X2] :
( sQ1342_spl
<=> ( segmentP(X2,sk5)
| ~ ssList(X2)
| ~ ssList(app(app(X1,sk5),X0))
| ~ segmentP(X2,app(app(X1,sk5),X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1342_spl])],[split_symbol_definition]) ).
fof(f15415,plain,
( ~ sQ1339_spl
| ~ sQ4_spl
| sQ1342_spl ),
inference(split_clause,[status(thm)],[f15400,f15412,f460,f15388]) ).
fof(f15417,definition,
! [X0] :
( sQ1343_spl
<=> ( segmentP(X0,sk5)
| ~ ssList(X0)
| ~ segmentP(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ1343_spl])],[split_symbol_definition]) ).
fof(f15420,plain,
( ~ sQ1339_spl
| ~ sQ4_spl
| sQ1343_spl ),
inference(split_clause,[status(thm)],[f15402,f15417,f460,f15388]) ).
fof(f15421,definition,
! [X0,X1] :
( sQ1344_spl
<=> ( segmentP(app(app(X1,sk5),X0),sk5)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1344_spl])],[split_symbol_definition]) ).
fof(f15424,plain,
( ~ sQ1339_spl
| ~ sQ4_spl
| sQ1344_spl ),
inference(split_clause,[status(thm)],[f15403,f15421,f460,f15388]) ).
fof(f15477,plain,
! [X0] :
( app(nil,skaf71(X0)) = nil
| ~ frontsegP(nil,skaf71(X0))
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1444,f1192]) ).
fof(f15479,plain,
! [X0,X1] :
( segmentP(app(skaf71(X1),X0),skaf71(X1))
| ~ ssList(skaf71(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1444,f1086]) ).
fof(f15480,plain,
! [X0,X1] :
( app(app(X1,nil),skaf71(X0)) = app(X1,skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1444,f369]) ).
fof(f15481,plain,
! [X0,X1] :
( app(skaf71(X1),X0) = app(nil,app(skaf71(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1444,f369]) ).
fof(f15482,plain,
! [X0] :
( rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1444,f3479]) ).
fof(f15485,plain,
! [X0,X1] :
( app(nil,skaf71(X1)) = X0
| ~ frontsegP(X0,skaf71(X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1444,f1279]) ).
fof(f15486,plain,
! [X0] :
( frontsegP(skaf71(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1444,f982]) ).
fof(f15487,plain,
! [X0,X1] :
( frontsegP(skaf71(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1444,f352]) ).
fof(f15488,definition,
! [X0] :
( sQ1345_spl
<=> ( app(nil,skaf71(X0)) = nil
| ~ frontsegP(nil,skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1345_spl])],[split_symbol_definition]) ).
fof(f15491,plain,
( ~ sQ13_spl
| sQ1345_spl ),
inference(split_clause,[status(thm)],[f15477,f15488,f534]) ).
fof(f15492,definition,
! [X0,X1] :
( sQ1346_spl
<=> ( segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1346_spl])],[split_symbol_definition]) ).
fof(f15496,definition,
! [X0,X1] :
( sQ1347_spl
<=> ( segmentP(app(skaf71(X1),X0),skaf71(X1))
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1347_spl])],[split_symbol_definition]) ).
fof(f15499,plain,
( ~ sQ13_spl
| sQ1347_spl ),
inference(split_clause,[status(thm)],[f15479,f15496,f534]) ).
fof(f15500,definition,
! [X0,X1] :
( sQ1348_spl
<=> ( app(app(X1,nil),skaf71(X0)) = app(X1,skaf71(X0))
| ~ ssList(X1)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1348_spl])],[split_symbol_definition]) ).
fof(f15503,plain,
( ~ sQ13_spl
| sQ1348_spl ),
inference(split_clause,[status(thm)],[f15480,f15500,f534]) ).
fof(f15504,definition,
! [X0,X1] :
( sQ1349_spl
<=> ( app(skaf71(X1),X0) = app(nil,app(skaf71(X1),X0))
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1349_spl])],[split_symbol_definition]) ).
fof(f15507,plain,
( ~ sQ13_spl
| sQ1349_spl ),
inference(split_clause,[status(thm)],[f15481,f15504,f534]) ).
fof(f15508,definition,
! [X0] :
( sQ1350_spl
<=> ( rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1350_spl])],[split_symbol_definition]) ).
fof(f15511,plain,
( sQ1350_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15482,f534,f15508]) ).
fof(f15520,definition,
! [X0,X1] :
( sQ1353_spl
<=> ( app(nil,skaf71(X1)) = X0
| ~ frontsegP(X0,skaf71(X1))
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1353_spl])],[split_symbol_definition]) ).
fof(f15523,plain,
( ~ sQ13_spl
| sQ1353_spl ),
inference(split_clause,[status(thm)],[f15485,f15520,f534]) ).
fof(f15524,definition,
! [X0] :
( sQ1354_spl
<=> ( frontsegP(skaf71(X0),nil)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1354_spl])],[split_symbol_definition]) ).
fof(f15527,plain,
( ~ sQ13_spl
| sQ1354_spl ),
inference(split_clause,[status(thm)],[f15486,f15524,f534]) ).
fof(f15528,definition,
! [X0,X1] :
( sQ1355_spl
<=> ( frontsegP(skaf71(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1355_spl])],[split_symbol_definition]) ).
fof(f15531,plain,
( ~ sQ13_spl
| sQ1355_spl ),
inference(split_clause,[status(thm)],[f15487,f15528,f534]) ).
fof(f15541,plain,
! [X0] :
( app(skaf71(X0),nil) = skaf71(X0)
| ~ frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1445,f1192]) ).
fof(f15543,plain,
! [X0,X1] :
( segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1445,f1086]) ).
fof(f15544,plain,
! [X0,X1] :
( app(app(X1,skaf71(X0)),nil) = app(X1,skaf71(X0))
| ~ ssList(X1)
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1445,f369]) ).
fof(f15545,plain,
! [X0] :
( rearsegP(skaf71(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1445,f3479]) ).
fof(f15546,plain,
! [X0] :
( tl(skaf71(X0)) = app(tl(skaf71(X0)),nil)
| nil = skaf71(X0)
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1445,f346]) ).
fof(f15547,plain,
! [X0] :
( hd(skaf71(X0)) = hd(skaf71(X0))
| nil = skaf71(X0)
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1445,f334]) ).
fof(f15548,plain,
! [X0,X1] :
( app(skaf71(X0),nil) = X1
| ~ frontsegP(X1,skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1445,f1279]) ).
fof(f15549,plain,
! [X0] :
( frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1445,f982]) ).
fof(f15550,plain,
! [X0,X1] :
( frontsegP(skaf71(X0),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1445,f352]) ).
fof(f15551,definition,
! [X0] :
( sQ1356_spl
<=> ( app(skaf71(X0),nil) = skaf71(X0)
| ~ frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1356_spl])],[split_symbol_definition]) ).
fof(f15554,plain,
( sQ1356_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15541,f534,f15551]) ).
fof(f15556,plain,
( ~ sQ13_spl
| sQ1346_spl ),
inference(split_clause,[status(thm)],[f15543,f15492,f534]) ).
fof(f15557,definition,
! [X0,X1] :
( sQ1357_spl
<=> ( app(app(X1,skaf71(X0)),nil) = app(X1,skaf71(X0))
| ~ ssList(X1)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1357_spl])],[split_symbol_definition]) ).
fof(f15560,plain,
( sQ1357_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15544,f534,f15557]) ).
fof(f15561,definition,
! [X0] :
( sQ1358_spl
<=> ( rearsegP(skaf71(X0),nil)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1358_spl])],[split_symbol_definition]) ).
fof(f15564,plain,
( ~ sQ13_spl
| sQ1358_spl ),
inference(split_clause,[status(thm)],[f15545,f15561,f534]) ).
fof(f15565,definition,
! [X0] :
( sQ1359_spl
<=> ( tl(skaf71(X0)) = app(tl(skaf71(X0)),nil)
| nil = skaf71(X0)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1359_spl])],[split_symbol_definition]) ).
fof(f15568,plain,
( sQ1359_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15546,f534,f15565]) ).
fof(f15569,definition,
! [X0] :
( sQ1360_spl
<=> ( hd(skaf71(X0)) = hd(skaf71(X0))
| nil = skaf71(X0)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1360_spl])],[split_symbol_definition]) ).
fof(f15572,plain,
( sQ1360_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15547,f534,f15569]) ).
fof(f15573,definition,
! [X0,X1] :
( sQ1361_spl
<=> ( app(skaf71(X0),nil) = X1
| ~ frontsegP(X1,skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1361_spl])],[split_symbol_definition]) ).
fof(f15576,plain,
( ~ sQ13_spl
| sQ1361_spl ),
inference(split_clause,[status(thm)],[f15548,f15573,f534]) ).
fof(f15577,definition,
! [X0] :
( sQ1362_spl
<=> ( frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1362_spl])],[split_symbol_definition]) ).
fof(f15580,plain,
( sQ1362_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15549,f534,f15577]) ).
fof(f15581,definition,
! [X0,X1] :
( sQ1363_spl
<=> ( frontsegP(skaf71(X0),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ frontsegP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1363_spl])],[split_symbol_definition]) ).
fof(f15584,plain,
( ~ sQ13_spl
| sQ1363_spl ),
inference(split_clause,[status(thm)],[f15550,f15581,f534]) ).
fof(f15618,plain,
( ~ sQ68_spl
| ~ ssList(nil)
| frontsegP(sk5,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1055,f260]) ).
fof(f15619,plain,
! [X0,X1] :
( ~ sQ68_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| frontsegP(sk5,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1055,f379]) ).
fof(f15622,plain,
( ~ sQ68_spl
| sQ78_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f15618,f534,f1197,f1054]) ).
fof(f15623,definition,
! [X0,X1] :
( sQ1370_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| frontsegP(sk5,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1370_spl])],[split_symbol_definition]) ).
fof(f15626,plain,
( ~ sQ68_spl
| ~ sQ13_spl
| sQ1370_spl ),
inference(split_clause,[status(thm)],[f15619,f15623,f534,f1054]) ).
fof(f15629,plain,
( ~ sQ11_spl
| ~ sQ1337_spl
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ ssList(sk5) ),
inference(resolution,[status(thm)],[f15381,f487]) ).
fof(f15636,plain,
( ~ sQ11_spl
| ~ sQ1337_spl
| ~ sQ1338_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f15629,f460,f467,f15384,f15380,f486]) ).
fof(f15661,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f459,f466,f470,f474,f478,f485,f489,f493,f494,f530,f540,f543,f548,f554,f594,f617,f624,f649,f658,f668,f674,f681,f751,f758,f778,f780,f816,f849,f889,f911,f916,f925,f929,f943,f949,f953,f958,f968,f992,f997,f1014,f1018,f1022,f1026,f1030,f1053,f1057,f1069,f1073,f1081,f1085,f1196,f1208,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1371,f1377,f1385,f1390,f1398,f1403,f1412,f1498,f1502,f1506,f1508,f1520,f1525,f1530,f1534,f1547,f1551,f1560,f1564,f1612,f1620,f1631,f1635,f1675,f1680,f1684,f1688,f1692,f1696,f1700,f1702,f1710,f1718,f1768,f1776,f1778,f1851,f1855,f1867,f1888,f1972,f1988,f2009,f2020,f2133,f2144,f2169,f2184,f2188,f2192,f2201,f2213,f2217,f2219,f2221,f2265,f2269,f2294,f2386,f2390,f2394,f2406,f2410,f2414,f2423,f2435,f2439,f2441,f2443,f2498,f2503,f2507,f2522,f2526,f2557,f2655,f2657,f2671,f2680,f2684,f2704,f2708,f2759,f2800,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2840,f2844,f2848,f2852,f2856,f2865,f2869,f2873,f2880,f2884,f2888,f2892,f2900,f2912,f2917,f2925,f2929,f2946,f2954,f2958,f2965,f2969,f2991,f2996,f3000,f3008,f3012,f3016,f3020,f3024,f3028,f3032,f3036,f3067,f3135,f3140,f3151,f3156,f3164,f3168,f3185,f3193,f3197,f3222,f3226,f3282,f3293,f3298,f3306,f3310,f3327,f3335,f3339,f3384,f3392,f3396,f3413,f3418,f3426,f3430,f3436,f3440,f3446,f3450,f3456,f3460,f3468,f3472,f3476,f3500,f3504,f3508,f3512,f3527,f3531,f3577,f3581,f3589,f3593,f3604,f3608,f3619,f3623,f3631,f3635,f3639,f3721,f3725,f3729,f3733,f3737,f3741,f3745,f3749,f3753,f3757,f3761,f3819,f3823,f3827,f3831,f3835,f3839,f3843,f3859,f3863,f3867,f3871,f3875,f4005,f4017,f4211,f4217,f4227,f4231,f4235,f4287,f4327,f4534,f4535,f4550,f4554,f4558,f4560,f4583,f4588,f4592,f4600,f4604,f4612,f4616,f4624,f4628,f4645,f4689,f4703,f4763,f4768,f4772,f4780,f4784,f4792,f4796,f4804,f4808,f4824,f4828,f4832,f4901,f4919,f4923,f4927,f4931,f4932,f4953,f4958,f4962,f4970,f4974,f4982,f4986,f4994,f4998,f5100,f5104,f5108,f5172,f5223,f5288,f5293,f5297,f5312,f5414,f5418,f5422,f5430,f5625,f5629,f5638,f5645,f5649,f5697,f5701,f5709,f5713,f5721,f5725,f5757,f5761,f5801,f5805,f5809,f5811,f5852,f5958,f5962,f5967,f6068,f6076,f6080,f6084,f6088,f6100,f6104,f6108,f6132,f6136,f6138,f6142,f6146,f6150,f6154,f6158,f6162,f6166,f6326,f6334,f6338,f6342,f6346,f6358,f6362,f6366,f6390,f6394,f6396,f6400,f6404,f6408,f6412,f6416,f6420,f6424,f6582,f6590,f6594,f6598,f6602,f6614,f6618,f6622,f6646,f6650,f6652,f6656,f6660,f6664,f6668,f6672,f6676,f6680,f6751,f6763,f6859,f6880,f7041,f7045,f7049,f7053,f7057,f7061,f7065,f7069,f7073,f7077,f7081,f7085,f7089,f7093,f7097,f7101,f7106,f7111,f7116,f7121,f7126,f7132,f7133,f7134,f7139,f7143,f7147,f7151,f7259,f7441,f7453,f7519,f7531,f7554,f7597,f7609,f7744,f7790,f7920,f8228,f8326,f8602,f8923,f8974,f8978,f9050,f9054,f9058,f9062,f9066,f9070,f9074,f9092,f9096,f9100,f9105,f9109,f9185,f9189,f9193,f9197,f9201,f9205,f9211,f9309,f9328,f9382,f9386,f9390,f9391,f9395,f9399,f9476,f9507,f9771,f10054,f10086,f10174,f10297,f10379,f10437,f10461,f10465,f10518,f10526,f10530,f10534,f10538,f10550,f10554,f10558,f10582,f10586,f10588,f10592,f10596,f10600,f10604,f10608,f10612,f10616,f10626,f10631,f10683,f10691,f10695,f10699,f10703,f10715,f10719,f10723,f10747,f10751,f10753,f10757,f10761,f10765,f10769,f10773,f10777,f10781,f10839,f10891,f10899,f10903,f10907,f10911,f10923,f10927,f10931,f10955,f10959,f10961,f10965,f10969,f10973,f10977,f10981,f10985,f10989,f11015,f11067,f11075,f11079,f11083,f11087,f11099,f11103,f11107,f11131,f11135,f11137,f11141,f11145,f11149,f11153,f11157,f11161,f11165,f11195,f11247,f11255,f11259,f11263,f11267,f11279,f11283,f11287,f11311,f11315,f11317,f11321,f11325,f11329,f11333,f11337,f11341,f11345,f11371,f11423,f11431,f11435,f11439,f11443,f11455,f11459,f11463,f11487,f11491,f11493,f11497,f11501,f11505,f11509,f11513,f11517,f11521,f11547,f11599,f11607,f11611,f11615,f11619,f11631,f11635,f11639,f11663,f11667,f11669,f11673,f11677,f11681,f11685,f11689,f11693,f11697,f11743,f11744,f11745,f11749,f11753,f11757,f11761,f11765,f11769,f11773,f11777,f11781,f11785,f11789,f11793,f11806,f11812,f11817,f11828,f11833,f11837,f11841,f11845,f11849,f11887,f11939,f11947,f11951,f11955,f11959,f11971,f11975,f11979,f12003,f12007,f12009,f12013,f12017,f12021,f12025,f12029,f12033,f12037,f12110,f12164,f12172,f12176,f12180,f12184,f12196,f12200,f12204,f12228,f12232,f12234,f12238,f12242,f12246,f12250,f12254,f12258,f12262,f12313,f12509,f12566,f12750,f12754,f12758,f12762,f12766,f12770,f12774,f12778,f12782,f12788,f12792,f12796,f12817,f12828,f12859,f13033,f13207,f13522,f14443,f14448,f14452,f14453,f14454,f14455,f14456,f14457,f14458,f14459,f14463,f14467,f14479,f14482,f14483,f14484,f14490,f14497,f14498,f14500,f14502,f14504,f14508,f14513,f14517,f14521,f14525,f14529,f14530,f14531,f14601,f14602,f14603,f14604,f14605,f14606,f14607,f14608,f14609,f14610,f14611,f14612,f14615,f14616,f15145,f15146,f15147,f15148,f15149,f15150,f15151,f15152,f15153,f15154,f15155,f15156,f15157,f15163,f15169,f15177,f15179,f15181,f15186,f15187,f15191,f15195,f15199,f15203,f15207,f15359,f15363,f15367,f15371,f15375,f15379,f15383,f15387,f15391,f15407,f15411,f15415,f15420,f15424,f15491,f15499,f15503,f15507,f15511,f15523,f15527,f15531,f15554,f15556,f15560,f15564,f15568,f15572,f15576,f15580,f15584,f15622,f15626,f15636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC052-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 07:51:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 14.92/2.39 % Refutation found
% 14.92/2.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 14.92/2.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.92/2.43 % Elapsed time: 2.043875 seconds
% 14.92/2.43 % CPU time: 15.717538 seconds
% 14.92/2.43 % Total memory used: 246.628 MB
% 14.92/2.43 % Net memory used: 232.714 MB
%------------------------------------------------------------------------------