%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC295-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 02:40:41 PM UTC 2026
% Result : Unsatisfiable 80.47s 10.65s
% Output : CNFRefutation 20.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 583
% Syntax : Number of formulae : 2040 ( 109 unt; 467 def)
% Number of atoms : 8112 ( 721 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 11549 (5477 ~;5605 |; 0 &)
% ( 467 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 487 ( 485 usr; 468 prp; 0-2 aty)
% Number of functors : 39 ( 39 usr; 9 con; 0-2 aty)
% Number of variables : 1628 (1628 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ singletonP(nil),
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(f15,axiom,
! [U] : ssList(skaf80(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U] : ssList(skaf73(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] : ssItem(skaf70(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] : ssItem(skaf65(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U] : ssList(skaf63(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [U] : ssItem(skaf60(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] : ssList(skaf58(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] : ssItem(skaf55(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] : ssList(skaf53(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] : ssItem(skaf50(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(f59,axiom,
! [U] :
( rearsegP(U,U)
| ~ 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(f62,axiom,
! [U] :
( leq(U,U)
| ~ ssItem(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(f79,axiom,
! [U] :
( segmentP(nil,U)
| ~ ssList(U)
| 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(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f99,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
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(f108,axiom,
! [U,V] :
( geq(V,U)
| ~ ssItem(V)
| ~ ssItem(U)
| ~ leq(U,V) ),
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(f110,axiom,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,axiom,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
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(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
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(f126,axiom,
! [U,V] :
( V = U
| ~ ssItem(V)
| ~ ssItem(U)
| ~ geq(V,U)
| ~ geq(U,V) ),
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(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(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(f145,axiom,
! [U,V] :
( app(U,V) = nil
| ~ ssList(U)
| ~ ssList(V)
| nil != V
| nil != U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,axiom,
! [U,V,W] :
( lt(U,W)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f148,axiom,
! [U,V,W] :
( geq(U,W)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ geq(V,W)
| ~ geq(U,V) ),
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(f151,axiom,
! [U,V,W] :
( U = W
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ),
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(f156,axiom,
! [U,V,W] :
( leq(U,W)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ~ leq(V,W)
| ~ leq(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [U,V,W] :
( cons(U,app(V,W)) = app(cons(U,V),W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssItem(U) ),
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(f163,axiom,
! [U] :
( app(app(skaf71(U),cons(skaf69(U),skaf72(U))),cons(skaf70(U),skaf73(U))) = U
| strictorderedP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f164,axiom,
! [U] :
( app(app(skaf66(U),cons(skaf64(U),skaf67(U))),cons(skaf65(U),skaf68(U))) = U
| totalorderedP(U)
| ~ ssList(U) ),
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(f170,axiom,
! [U,V,W,X] :
( U = W
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [U,V,W,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
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(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f189,negated_conjecture,
ssList(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,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssItem(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
( nil = sk3
| ssItem(sk9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f207,negated_conjecture,
( nil = sk3
| memberP(sk4,sk9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f208,negated_conjecture,
! [A] :
( nil = sk3
| ~ leq(sk9,A)
| ~ memberP(sk4,A)
| sk9 = A
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f216,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f219,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f220,plain,
! [X0] : ssItem(skaf83(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f221,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f223,plain,
! [X0] : ssList(skaf80(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f230,plain,
! [X0] : ssList(skaf73(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f233,plain,
! [X0] : ssItem(skaf70(X0)),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f235,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f238,plain,
! [X0] : ssItem(skaf65(X0)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f240,plain,
! [X0] : ssList(skaf63(X0)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f243,plain,
! [X0] : ssItem(skaf60(X0)),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f245,plain,
! [X0] : ssList(skaf58(X0)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f248,plain,
! [X0] : ssItem(skaf55(X0)),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f250,plain,
! [X0] : ssList(skaf53(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f253,plain,
! [X0] : ssItem(skaf50(X0)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f255,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f258,plain,
! [X0,X1] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f259,plain,
! [X0,X1] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f264,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f265,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f266,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f267,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f268,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f270,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f272,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f273,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f274,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f275,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f276,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f277,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f278,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f279,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f280,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f281,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f280]) ).
fof(f282,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f283,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f284,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f288,plain,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f294,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f295,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f305,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f306,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f307,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f308,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f309,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != V ) ),
inference(miniscoping,[status(thm)],[f99]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f312,plain,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f315,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f319,plain,
! [X0,X1] :
( geq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f320,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f321,plain,
! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f322,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f327,plain,
! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f328,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f331,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f332,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f335,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f336,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f337,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f338,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f339,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f342,plain,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f347,plain,
! [X0,X1] :
( X1 = X0
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ geq(X1,X0)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f348,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f349,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f350,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f352,plain,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f353,plain,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f354,plain,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f359,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(f360,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(f361,plain,
! [X0,X1,X2] :
( memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f363,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(f364,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(f366,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f367,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f368,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f369,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [X0,X1] :
( app(X0,X1) = nil
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X1
| nil != X0 ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f373,plain,
! [U,W] :
( lt(U,W)
| ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ~ ssItem(W)
| ~ lt(V,W)
| ~ leq(U,V) ) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f374,plain,
! [X0,X1,X2] :
( lt(X0,X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U,W] :
( geq(U,W)
| ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ~ ssItem(W)
| ~ geq(V,W)
| ~ geq(U,V) ) ),
inference(miniscoping,[status(thm)],[f148]) ).
fof(f376,plain,
! [X0,X1,X2] :
( geq(X0,X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,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(f378,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f379,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f378]) ).
fof(f380,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f381,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f380]) ).
fof(f382,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(f383,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f384,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(f385,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,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(f387,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f386]) ).
fof(f390,plain,
! [U,W] :
( leq(U,W)
| ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ~ ssItem(W)
| ~ leq(V,W)
| ~ leq(U,V) ) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f391,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f390]) ).
fof(f392,plain,
! [X0,X1,X2] :
( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f393,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(f394,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)],[f393]) ).
fof(f395,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(f396,plain,
! [X0,X1] :
( nil = X1
| totalorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ leq(X0,hd(X1)) ),
inference(cnf_transformation,[status(thm)],[f395]) ).
fof(f397,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(f398,plain,
! [X0,X1] :
( nil = X1
| strictorderedP(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ strictorderedP(X1)
| ~ lt(X0,hd(X1)) ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f399,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(f400,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)],[f399]) ).
fof(f402,plain,
! [X0] :
( app(app(skaf71(X0),cons(skaf69(X0),skaf72(X0))),cons(skaf70(X0),skaf73(X0))) = X0
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f403,plain,
! [X0] :
( app(app(skaf66(X0),cons(skaf64(X0),skaf67(X0))),cons(skaf65(X0),skaf68(X0))) = X0
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f407,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(f408,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(f409,plain,
! [U,W] :
( U = W
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f409]) ).
fof(f411,plain,
! [V,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f412,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f411]) ).
fof(f413,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(f414,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(f415,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)],[f414]) ).
fof(f416,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(f417,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)],[f416]) ).
fof(f418,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(f419,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)],[f418]) ).
fof(f420,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(f421,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)],[f420]) ).
fof(f422,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(f423,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)],[f422]) ).
fof(f424,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(f425,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(f426,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)],[f425]) ).
fof(f427,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(f428,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)],[f427]) ).
fof(f429,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(f430,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)],[f429]) ).
fof(f431,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(f432,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)],[f431]) ).
fof(f433,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(f434,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)],[f433]) ).
fof(f435,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(f436,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)],[f435]) ).
fof(f437,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(f438,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)],[f437]) ).
fof(f441,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f442,plain,
ssList(sk4),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f444,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f445,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f446,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f447,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f448,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f449,plain,
ssItem(sk8),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f450,plain,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f455,plain,
( nil = sk3
| ssItem(sk9) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f460,plain,
( nil = sk3
| cons(sk9,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f461,plain,
( nil = sk3
| memberP(sk4,sk9) ),
inference(cnf_transformation,[status(thm)],[f207]) ).
fof(f462,plain,
( nil = sk3
| ! [A] :
( ~ leq(sk9,A)
| ~ memberP(sk4,A)
| sk9 = A
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f208]) ).
fof(f463,plain,
! [X0] :
( nil = sk3
| ~ leq(sk9,X0)
| ~ memberP(sk4,X0)
| sk9 = X0
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f462]) ).
fof(f464,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f465,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f468,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f281,f464,f467]) ).
fof(f471,definition,
( sQ2_spl
<=> memberP(sk6,sk8) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ2_spl
| memberP(sk6,sk8) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,definition,
( sQ3_spl
<=> memberP(sk7,sk8) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ3_spl
| memberP(sk7,sk8) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f450,f471,f474]) ).
fof(f487,definition,
( sQ6_spl
<=> ssItem(sk9) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( ~ sQ6_spl
| ssItem(sk9) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f494,definition,
( sQ8_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ8_spl
| nil != sk3 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ8_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f455,f487,f494]) ).
fof(f498,definition,
( sQ9_spl
<=> cons(sk9,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ9_spl
| cons(sk9,nil) = sk3 ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f502,definition,
( sQ10_spl
<=> memberP(sk4,sk9) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f506,definition,
! [X0] :
( sQ11_spl
<=> ( ~ leq(sk9,X0)
| ~ memberP(sk4,X0)
| sk9 = X0
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f460,f498,f494]) ).
fof(f511,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f461,f502,f494]) ).
fof(f512,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f463,f506,f494]) ).
fof(f513,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f288]) ).
fof(f522,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f332]) ).
fof(f525,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(destructive_equality_resolution,[status(thm)],[f361]) ).
fof(f526,plain,
! [X0,X1] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f525]) ).
fof(f527,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f367]) ).
fof(f528,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f369]) ).
fof(f529,plain,
( app(nil,nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f370]) ).
fof(f530,plain,
( app(nil,nil) = nil
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f529]) ).
fof(f531,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)],[f415]) ).
fof(f532,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)],[f419]) ).
fof(f533,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)],[f424]) ).
fof(f534,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)],[f533]) ).
fof(f535,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)],[f426]) ).
fof(f536,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)],[f428]) ).
fof(f537,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)],[f430]) ).
fof(f538,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)],[f432]) ).
fof(f539,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)],[f434]) ).
fof(f540,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)],[f436]) ).
fof(f541,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)],[f438]) ).
fof(f563,definition,
( sQ12_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( sQ12_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f563]) ).
fof(f566,definition,
( sQ13_spl
<=> ssList(app(sk6,cons(sk5,sk4))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ13_spl
| ~ ssList(app(sk6,cons(sk5,sk4))) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,definition,
( sQ14_spl
<=> ssList(sk4) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( sQ14_spl
| ~ ssList(sk4) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f581,definition,
( sQ15_spl
<=> sk4 = sk4 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( sQ15_spl
| sk4 != sk4 ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f588,definition,
( sQ16_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ16_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f592,definition,
( sQ17_spl
<=> ssList(sk3) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f216]) ).
fof(f598,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f599,plain,
( sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f583]) ).
fof(f600,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f615,definition,
( sQ18_spl
<=> sk9 = sk9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( sQ13_spl
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk4)) ),
inference(resolution,[status(thm)],[f568,f294]) ).
fof(f634,definition,
( sQ19_spl
<=> ssList(cons(sk5,sk4)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ19_spl
| ~ ssList(cons(sk5,sk4)) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,definition,
( sQ20_spl
<=> ssList(sk6) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( sQ20_spl
| ~ ssList(sk6) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( sQ13_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f633,f634,f637,f566]) ).
fof(f641,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f639,f446]) ).
fof(f642,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f641]) ).
fof(f643,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f447]) ).
fof(f644,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f645,plain,
( sQ19_spl
| ~ ssList(sk4)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f636,f295]) ).
fof(f646,definition,
( sQ21_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f648,plain,
( sQ21_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f649,plain,
( sQ19_spl
| ~ sQ14_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f645,f646,f569,f634]) ).
fof(f650,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f442]) ).
fof(f651,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f648,f445]) ).
fof(f653,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f667,definition,
( sQ23_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f668,plain,
( ~ sQ23_spl
| app(nil,nil) = nil ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f670,plain,
( sQ23_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f530,f588,f667]) ).
fof(f675,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(forward_demodulation,[status(thm)],[f444,f448]) ).
fof(f677,plain,
( ssList(sk3)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f675,f294]) ).
fof(f678,definition,
( sQ24_spl
<=> ssList(app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ24_spl
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,definition,
( sQ25_spl
<=> nil = sk7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( ~ sQ25_spl
| nil = sk7 ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f683,plain,
( sQ25_spl
| nil != sk7 ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f685,plain,
( sQ17_spl
| ~ sQ24_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f677,f563,f678,f592]) ).
fof(f686,plain,
( sQ24_spl
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f680,f294]) ).
fof(f687,definition,
( sQ26_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( ~ sQ26_spl
| ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f689,plain,
( sQ26_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( sQ24_spl
| ~ sQ20_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f686,f687,f637,f678]) ).
fof(f696,definition,
( sQ27_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f702,plain,
( sQ26_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f689,f295]) ).
fof(f703,plain,
( sQ26_spl
| ~ sQ16_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f702,f646,f588,f687]) ).
fof(f714,plain,
( ~ sQ9_spl
| memberP(sk3,sk9)
| ~ ssItem(sk9)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f526]) ).
fof(f715,definition,
( sQ28_spl
<=> memberP(sk3,sk9) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ28_spl
| memberP(sk3,sk9) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,plain,
( ~ sQ9_spl
| sQ28_spl
| ~ sQ6_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f714,f588,f487,f715,f498]) ).
fof(f719,plain,
! [X0] :
( ~ sQ9_spl
| app(sk3,X0) = cons(sk9,X0)
| ~ ssList(X0)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f339]) ).
fof(f720,definition,
! [X0] :
( sQ29_spl
<=> ( app(sk3,X0) = cons(sk9,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f721,plain,
! [X0] :
( ~ sQ29_spl
| app(sk3,X0) = cons(sk9,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f723,plain,
( ~ sQ9_spl
| sQ29_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f719,f487,f720,f498]) ).
fof(f763,plain,
( ~ sQ9_spl
| ~ sQ29_spl
| app(sk3,nil) = sk3
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f721]) ).
fof(f764,definition,
( sQ30_spl
<=> app(sk3,nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ30_spl
| app(sk3,nil) = sk3 ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( ~ sQ9_spl
| ~ sQ29_spl
| sQ30_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f763,f588,f764,f720,f498]) ).
fof(f768,plain,
( ~ sQ30_spl
| sk3 = sk3
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f765,f282]) ).
fof(f771,definition,
( sQ31_spl
<=> sk3 = sk3 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ30_spl
| sQ31_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f768,f592,f771,f764]) ).
fof(f778,definition,
( sQ32_spl
<=> duplicatefreeP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f787,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| sk3 != nil ),
inference(paramodulation,[status(thm)],[f675,f336]) ).
fof(f793,definition,
( sQ33_spl
<=> nil = app(sk6,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( ~ sQ33_spl
| nil = app(sk6,cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f793]) ).
fof(f796,plain,
( sQ33_spl
| ~ sQ24_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f787,f494,f563,f678,f793]) ).
fof(f798,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f379,f283]) ).
fof(f800,plain,
! [X0] :
( ~ sQ30_spl
| nil = X0
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != app(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f379]) ).
fof(f801,plain,
! [X0] :
( ~ sQ23_spl
| nil = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| nil != app(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f379]) ).
fof(f802,plain,
! [X0] :
( sk7 = X0
| ~ ssList(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| sk3 != app(app(sk6,cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f675,f379]) ).
fof(f807,definition,
! [X0] :
( sQ34_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ16_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f798,f807,f588]) ).
fof(f812,definition,
! [X0] :
( sQ35_spl
<=> ( nil = X0
| ~ ssList(X0)
| sk3 != app(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f815,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f800,f812,f588,f592,f764]) ).
fof(f816,definition,
! [X0] :
( sQ36_spl
<=> ( nil = X0
| ~ ssList(X0)
| nil != app(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f801,f816,f588,f667]) ).
fof(f820,definition,
! [X0] :
( sQ37_spl
<=> ( sk7 = X0
| ~ ssList(X0)
| sk3 != app(app(sk6,cons(sk5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f821,plain,
! [X0] :
( ~ sQ37_spl
| sk7 = X0
| ~ ssList(X0)
| sk3 != app(app(sk6,cons(sk5,nil)),X0) ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f802,f820,f563,f678]) ).
fof(f827,definition,
! [X0] :
( sQ38_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f830,definition,
! [X1] :
( sQ39_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f831,plain,
! [X0] :
( ~ sQ39_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f847,plain,
( ~ sQ25_spl
| ~ singletonP(sk7) ),
inference(backward_demodulation,[status(thm)],[f682,f219]) ).
fof(f877,plain,
! [X0,X1] :
( ~ sQ1_spl
| ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f295,f468]) ).
fof(f915,definition,
( sQ41_spl
<=> ssList(app(sk6,cons(sk5,sk7))) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f917,plain,
( sQ41_spl
| ~ ssList(app(sk6,cons(sk5,sk7))) ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f923,definition,
! [X0] :
( sQ42_spl
<=> ( memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f944,plain,
( ~ sQ9_spl
| strictorderP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f276]) ).
fof(f945,plain,
( ~ sQ9_spl
| totalorderedP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f275]) ).
fof(f946,plain,
( ~ sQ9_spl
| strictorderedP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f274]) ).
fof(f947,definition,
( sQ43_spl
<=> strictorderP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f950,plain,
( ~ sQ9_spl
| sQ43_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f944,f487,f947,f498]) ).
fof(f951,definition,
( sQ44_spl
<=> totalorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f954,plain,
( ~ sQ9_spl
| sQ44_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f945,f487,f951,f498]) ).
fof(f955,definition,
( sQ45_spl
<=> strictorderedP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( ~ sQ9_spl
| sQ45_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f946,f487,f955,f498]) ).
fof(f959,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f675,f377]) ).
fof(f960,plain,
! [X0] :
( X0 = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ ssList(X0)
| app(X0,sk7) != sk3 ),
inference(paramodulation,[status(thm)],[f675,f381]) ).
fof(f962,plain,
! [X0] :
( app(sk3,X0) = app(app(sk6,cons(sk5,nil)),app(sk7,X0))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f675,f377]) ).
fof(f963,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f675,f364]) ).
fof(f967,definition,
( sQ46_spl
<=> sk3 = app(sk6,app(cons(sk5,nil),sk7)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( ~ sQ46_spl
| sk3 = app(sk6,app(cons(sk5,nil),sk7)) ),
inference(component_clause,[status(thm)],[f967]) ).
fof(f970,plain,
( sQ46_spl
| ~ sQ20_spl
| ~ sQ26_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f959,f563,f687,f637,f967]) ).
fof(f971,definition,
! [X0] :
( sQ47_spl
<=> ( X0 = app(sk6,cons(sk5,nil))
| ~ ssList(X0)
| app(X0,sk7) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f972,plain,
! [X0] :
( ~ sQ47_spl
| X0 = app(sk6,cons(sk5,nil))
| ~ ssList(X0)
| app(X0,sk7) != sk3 ),
inference(component_clause,[status(thm)],[f971]) ).
fof(f974,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f960,f971,f563,f678]) ).
fof(f976,definition,
! [X0] :
( sQ48_spl
<=> ( app(sk3,X0) = app(app(sk6,cons(sk5,nil)),app(sk7,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f979,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f962,f976,f563,f678]) ).
fof(f980,definition,
! [X0] :
( sQ49_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f963,f980,f563,f678]) ).
fof(f987,plain,
! [X0] :
( ~ sQ23_spl
| X0 = nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0)
| app(X0,nil) != nil ),
inference(paramodulation,[status(thm)],[f668,f381]) ).
fof(f989,plain,
! [X0] :
( ~ sQ23_spl
| app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f668,f377]) ).
fof(f990,plain,
! [X0] :
( ~ sQ23_spl
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f364]) ).
fof(f994,definition,
! [X0] :
( sQ50_spl
<=> ( X0 = nil
| ~ ssList(X0)
| app(X0,nil) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f995,plain,
! [X0] :
( ~ sQ50_spl
| X0 = nil
| ~ ssList(X0)
| app(X0,nil) != nil ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f987,f994,f588,f667]) ).
fof(f999,definition,
! [X0] :
( sQ51_spl
<=> ( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1000,plain,
! [X0] :
( ~ sQ51_spl
| app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f999]) ).
fof(f1002,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f989,f999,f588,f667]) ).
fof(f1003,definition,
! [X0] :
( sQ52_spl
<=> ( memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f990,f1003,f588,f667]) ).
fof(f1010,plain,
! [X0] :
( ~ sQ30_spl
| X0 = sk3
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(X0)
| app(X0,nil) != sk3 ),
inference(paramodulation,[status(thm)],[f765,f381]) ).
fof(f1012,plain,
! [X0] :
( ~ sQ30_spl
| app(sk3,X0) = app(sk3,app(nil,X0))
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f765,f377]) ).
fof(f1013,plain,
! [X0] :
( ~ sQ30_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f364]) ).
fof(f1017,definition,
! [X0] :
( sQ53_spl
<=> ( X0 = sk3
| ~ ssList(X0)
| app(X0,nil) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1020,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1010,f1017,f588,f592,f764]) ).
fof(f1022,definition,
! [X0] :
( sQ54_spl
<=> ( app(sk3,X0) = app(sk3,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1012,f1022,f588,f592,f764]) ).
fof(f1026,definition,
! [X0] :
( sQ55_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1029,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1013,f1026,f588,f592,f764]) ).
fof(f1039,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(X0,nil))
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f282,f381]) ).
fof(f1043,definition,
! [X0] :
( sQ56_spl
<=> ( app(X0,nil) = X0
| ~ ssList(X0)
| ~ ssList(app(X0,nil))
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( ~ sQ16_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f1039,f1043,f588]) ).
fof(f1052,plain,
( ~ sQ9_spl
| totalorderP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f277]) ).
fof(f1053,definition,
( sQ57_spl
<=> totalorderP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ9_spl
| sQ57_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1052,f487,f1053,f498]) ).
fof(f1057,plain,
( ~ sQ9_spl
| cyclefreeP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f278]) ).
fof(f1058,definition,
( sQ58_spl
<=> cyclefreeP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1061,plain,
( ~ sQ9_spl
| sQ58_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1057,f487,f1058,f498]) ).
fof(f1078,plain,
! [X0] :
( ~ sQ30_spl
| cons(X0,sk3) = app(cons(X0,sk3),nil)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f765,f392]) ).
fof(f1079,plain,
! [X0] :
( ~ sQ23_spl
| cons(X0,nil) = app(cons(X0,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f668,f392]) ).
fof(f1080,plain,
! [X0] :
( cons(X0,sk3) = app(cons(X0,app(sk6,cons(sk5,nil))),sk7)
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f675,f392]) ).
fof(f1081,definition,
! [X0] :
( sQ60_spl
<=> ( cons(X0,sk3) = app(cons(X0,sk3),nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1078,f1081,f592,f588,f764]) ).
fof(f1085,definition,
! [X0] :
( sQ61_spl
<=> ( cons(X0,nil) = app(cons(X0,nil),nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1086,plain,
! [X0] :
( ~ sQ61_spl
| cons(X0,nil) = app(cons(X0,nil),nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1085]) ).
fof(f1088,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1079,f1085,f588,f667]) ).
fof(f1089,definition,
! [X0] :
( sQ62_spl
<=> ( cons(X0,sk3) = app(cons(X0,app(sk6,cons(sk5,nil))),sk7)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1092,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1080,f1089,f678,f563]) ).
fof(f1094,plain,
! [X0] :
( ~ sQ30_spl
| memberP(sk3,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f394]) ).
fof(f1095,plain,
! [X0] :
( ~ sQ23_spl
| memberP(nil,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f394]) ).
fof(f1096,plain,
! [X0] :
( memberP(app(sk6,cons(sk5,nil)),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f675,f394]) ).
fof(f1097,definition,
! [X0] :
( sQ63_spl
<=> ( memberP(sk3,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1100,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1094,f1097,f588,f592,f764]) ).
fof(f1101,definition,
! [X0] :
( sQ64_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f1095,f1101,f588,f667]) ).
fof(f1105,definition,
! [X0] :
( sQ65_spl
<=> ( memberP(app(sk6,cons(sk5,nil)),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1106,plain,
! [X0] :
( ~ sQ65_spl
| memberP(app(sk6,cons(sk5,nil)),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f1105]) ).
fof(f1108,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1096,f1105,f563,f678]) ).
fof(f1170,plain,
! [X0] :
( ~ sQ9_spl
| X0 = sk9
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk9)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f499,f400]) ).
fof(f1171,definition,
! [X0] :
( sQ67_spl
<=> ( X0 = sk9
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1172,plain,
! [X0] :
( ~ sQ67_spl
| X0 = sk9
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f1171]) ).
fof(f1174,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1170,f1171,f588,f487,f498]) ).
fof(f1175,plain,
! [X0] :
( ~ sQ67_spl
| X0 = sk9
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1172,f279]) ).
fof(f1176,plain,
! [X0,X1] :
( ~ sQ9_spl
| sk9 = X0
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sk9)
| ~ ssItem(X0)
| sk3 != cons(X0,X1) ),
inference(paramodulation,[status(thm)],[f499,f410]) ).
fof(f1178,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[f410]) ).
fof(f1179,definition,
! [X0,X1] :
( sQ68_spl
<=> ( sk9 = X0
| ~ ssList(X1)
| ~ ssItem(X0)
| sk3 != cons(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1182,plain,
( ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ6_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1176,f1179,f487,f588,f498]) ).
fof(f1184,definition,
! [X0] :
( sQ69_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1187,definition,
! [X1] :
( sQ70_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
! [X0] :
( ~ sQ70_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1187]) ).
fof(f1190,plain,
( sQ70_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1178,f1184,f1187]) ).
fof(f1238,definition,
( sQ71_spl
<=> sk7 = sk7 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1242,definition,
( sQ72_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1243,plain,
( ~ sQ72_spl
| segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f1242]) ).
fof(f1245,plain,
( sQ72_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f513,f588,f1242]) ).
fof(f1248,plain,
! [X0,X1] :
( X1 = X1
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[f412]) ).
fof(f1249,definition,
! [X0] :
( sQ73_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1250,plain,
! [X0] :
( ~ sQ73_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1249]) ).
fof(f1252,plain,
( sQ38_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1248,f1249,f827]) ).
fof(f1336,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| memberP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f468]) ).
fof(f1337,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ1_spl
| memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f1336]) ).
fof(f1338,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ1_spl
| memberP(sk3,X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f1336]) ).
fof(f1339,plain,
! [X0] :
( ~ sQ1_spl
| memberP(sk3,X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f675,f1336]) ).
fof(f1340,definition,
! [X0] :
( sQ74_spl
<=> ( memberP(nil,X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1343,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1337,f1340,f588,f467,f667]) ).
fof(f1344,definition,
! [X0] :
( sQ75_spl
<=> ( memberP(sk3,X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1347,plain,
( ~ sQ30_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f1338,f1344,f588,f592,f467,f764]) ).
fof(f1348,definition,
! [X0] :
( sQ76_spl
<=> ( memberP(sk3,X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1351,plain,
( ~ sQ1_spl
| ~ sQ24_spl
| ~ sQ12_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1339,f1348,f563,f678,f467]) ).
fof(f1544,definition,
( sQ80_spl
<=> ssItem(skaf44(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
( sQ80_spl
| ~ ssItem(skaf44(sk7)) ),
inference(component_clause,[status(thm)],[f1544]) ).
fof(f1564,plain,
( ~ sQ9_spl
| hd(sk3) = sk9
| ~ ssList(nil)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f306]) ).
fof(f1570,definition,
( sQ81_spl
<=> hd(sk3) = sk9 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1571,plain,
( ~ sQ81_spl
| hd(sk3) = sk9 ),
inference(component_clause,[status(thm)],[f1570]) ).
fof(f1573,plain,
( ~ sQ9_spl
| sQ81_spl
| ~ sQ16_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1564,f487,f588,f1570,f498]) ).
fof(f1574,definition,
( sQ82_spl
<=> tl(sk3) = nil ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1575,plain,
( ~ sQ82_spl
| tl(sk3) = nil ),
inference(component_clause,[status(thm)],[f1574]) ).
fof(f1640,definition,
( sQ83_spl
<=> ssList(cons(sk5,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1641,plain,
( ~ sQ83_spl
| ssList(cons(sk5,sk7)) ),
inference(component_clause,[status(thm)],[f1640]) ).
fof(f1642,plain,
( sQ83_spl
| ~ ssList(cons(sk5,sk7)) ),
inference(component_clause,[status(thm)],[f1640]) ).
fof(f1669,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f522,f295]) ).
fof(f1670,definition,
! [X0] :
( sQ88_spl
<=> ( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
! [X0] :
( ~ sQ88_spl
| ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1670]) ).
fof(f1673,plain,
( ~ sQ16_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1669,f1670,f588]) ).
fof(f1674,plain,
! [X0] :
( ~ sQ88_spl
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1671]) ).
fof(f1676,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f675,f363]) ).
fof(f1684,definition,
! [X0] :
( sQ89_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1685,plain,
! [X0] :
( ~ sQ89_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(component_clause,[status(thm)],[f1684]) ).
fof(f1687,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1676,f1684,f563,f678]) ).
fof(f1710,plain,
( ~ sQ26_spl
| singletonP(cons(sk5,nil))
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f688,f522]) ).
fof(f1711,definition,
( sQ90_spl
<=> singletonP(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1712,plain,
( ~ sQ90_spl
| singletonP(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f1711]) ).
fof(f1714,plain,
( ~ sQ26_spl
| sQ90_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1710,f646,f1711,f687]) ).
fof(f1715,plain,
( ~ sQ9_spl
| singletonP(cons(sk9,nil))
| ~ ssList(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f522]) ).
fof(f1722,plain,
! [X0] :
( ~ sQ9_spl
| memberP(app(X0,sk3),sk9)
| ~ ssList(app(X0,cons(sk9,nil)))
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f532]) ).
fof(f1729,definition,
( sQ91_spl
<=> singletonP(cons(sk9,nil)) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1730,plain,
( ~ sQ91_spl
| singletonP(cons(sk9,nil)) ),
inference(component_clause,[status(thm)],[f1729]) ).
fof(f1732,plain,
( ~ sQ9_spl
| sQ91_spl
| ~ sQ17_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1715,f487,f592,f1729,f498]) ).
fof(f1737,definition,
! [X0,X1] :
( sQ92_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ sQ92_spl
| nil = X1
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != sk3 ),
inference(component_clause,[status(thm)],[f1737]) ).
fof(f1742,definition,
! [X0] :
( sQ93_spl
<=> ( memberP(app(X0,sk3),sk9)
| ~ ssList(app(X0,cons(sk9,nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ93_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1722,f588,f1742,f487,f498]) ).
fof(f1839,plain,
! [X0] :
( ~ sQ30_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f363]) ).
fof(f1848,definition,
! [X0] :
( sQ97_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1851,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1839,f1848,f588,f592,f764]) ).
fof(f1882,plain,
( ~ sQ91_spl
| ~ sQ9_spl
| singletonP(sk3) ),
inference(forward_demodulation,[status(thm)],[f499,f1730]) ).
fof(f1957,plain,
! [X0,X1] :
( skaf46(app(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf46(app(X0,X1),X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ rearsegP(app(X0,X1),X1) ),
inference(resolution,[status(thm)],[f352,f381]) ).
fof(f1959,plain,
! [X0,X1] :
( skaf46(app(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(skaf46(app(X0,X1),X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ rearsegP(app(X0,X1),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1957]) ).
fof(f1960,plain,
! [X0,X1] :
( skaf46(app(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(skaf46(app(X0,X1),X1))
| ~ ssList(X1)
| ~ rearsegP(app(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1959,f294]) ).
fof(f1963,plain,
! [X0,X1] :
( skaf45(app(X0,X1),X0) = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(skaf45(app(X0,X1),X0))
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ frontsegP(app(X0,X1),X0) ),
inference(resolution,[status(thm)],[f353,f379]) ).
fof(f1965,plain,
! [X0,X1] :
( skaf45(app(X0,X1),X0) = X1
| ~ ssList(X1)
| ~ ssList(skaf45(app(X0,X1),X0))
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ frontsegP(app(X0,X1),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1963]) ).
fof(f1966,plain,
! [X0,X1] :
( skaf45(app(X0,X1),X0) = X1
| ~ ssList(X1)
| ~ ssList(skaf45(app(X0,X1),X0))
| ~ ssList(X0)
| ~ frontsegP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1965,f294]) ).
fof(f1993,plain,
( ~ sQ9_spl
| ~ sQ88_spl
| singletonP(sk3)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f1674]) ).
fof(f1994,definition,
( sQ98_spl
<=> singletonP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1997,plain,
( ~ sQ9_spl
| ~ sQ88_spl
| sQ98_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1993,f487,f1994,f1670,f498]) ).
fof(f2027,plain,
! [X0] :
( X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f268,f350]) ).
fof(f2028,definition,
! [X0] :
( sQ99_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f2031,plain,
( ~ sQ16_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f2027,f2028,f588]) ).
fof(f2033,plain,
! [X0] :
( X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f266,f349]) ).
fof(f2034,definition,
! [X0] :
( sQ100_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f2037,plain,
( ~ sQ16_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f2033,f2034,f588]) ).
fof(f2039,plain,
! [X0] :
( X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f264,f348]) ).
fof(f2040,definition,
! [X0] :
( sQ101_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f2043,plain,
( ~ sQ16_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f2039,f2040,f588]) ).
fof(f2141,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ ssList(app(X2,X0))
| ~ ssList(X1)
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f359,f349]) ).
fof(f2142,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ ssList(app(X2,X0))
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f2141]) ).
fof(f2143,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2142,f294]) ).
fof(f2144,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)],[f360,f350]) ).
fof(f2145,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)],[f2144]) ).
fof(f2146,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)],[f2145,f294]) ).
fof(f2149,plain,
! [X0] :
( frontsegP(sk3,X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ frontsegP(app(sk6,cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f675,f360]) ).
fof(f2150,plain,
! [X0] :
( rearsegP(sk3,X0)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ rearsegP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f675,f359]) ).
fof(f2163,definition,
! [X0] :
( sQ110_spl
<=> ( frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,cons(sk5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f2164,plain,
! [X0] :
( ~ sQ110_spl
| frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,cons(sk5,nil)),X0) ),
inference(component_clause,[status(thm)],[f2163]) ).
fof(f2166,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f2149,f2163,f563,f678]) ).
fof(f2167,definition,
! [X0] :
( sQ111_spl
<=> ( rearsegP(sk3,X0)
| ~ ssList(X0)
| ~ rearsegP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f2170,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f2150,f2167,f678,f563]) ).
fof(f2182,plain,
! [X0] :
( ~ sQ23_spl
| frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f360]) ).
fof(f2183,plain,
! [X0] :
( ~ sQ23_spl
| rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f359]) ).
fof(f2195,definition,
! [X0] :
( sQ112_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f2198,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f2182,f2195,f588,f667]) ).
fof(f2199,definition,
! [X0] :
( sQ113_spl
<=> ( rearsegP(nil,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f2183,f2199,f588,f667]) ).
fof(f2217,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(skaf46(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f338,f352]) ).
fof(f2218,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = skaf45(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf45(nil,X0)) ),
inference(resolution,[status(thm)],[f338,f353]) ).
fof(f2225,definition,
( sQ115_spl
<=> ssList(skaf80(nil)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f2227,plain,
( sQ115_spl
| ~ ssList(skaf80(nil)) ),
inference(component_clause,[status(thm)],[f2225]) ).
fof(f2235,definition,
! [X0] :
( sQ118_spl
<=> ( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(skaf46(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f2238,plain,
( ~ sQ16_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f2217,f2235,f588]) ).
fof(f2239,definition,
! [X0] :
( sQ119_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = skaf45(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf45(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f2242,plain,
( ~ sQ16_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f2218,f2239,f588]) ).
fof(f2251,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = skaf46(nil,X0)
| ~ ssList(skaf46(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f336,f352]) ).
fof(f2252,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(skaf45(nil,X0)) ),
inference(resolution,[status(thm)],[f336,f353]) ).
fof(f2260,definition,
! [X0] :
( sQ121_spl
<=> ( ~ ssList(X0)
| ~ rearsegP(nil,X0)
| nil = skaf46(nil,X0)
| ~ ssList(skaf46(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f2263,plain,
( ~ sQ16_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f2251,f2260,f588]) ).
fof(f2264,definition,
! [X0] :
( sQ122_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(skaf45(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f2267,plain,
( ~ sQ16_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f2252,f2264,f588]) ).
fof(f2310,plain,
! [X0] :
( ~ sQ30_spl
| frontsegP(sk3,X0)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f360]) ).
fof(f2311,plain,
! [X0] :
( ~ sQ30_spl
| rearsegP(sk3,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f359]) ).
fof(f2325,definition,
! [X0] :
( sQ123_spl
<=> ( frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f2328,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f2310,f2325,f588,f592,f764]) ).
fof(f2329,definition,
! [X0] :
( sQ124_spl
<=> ( rearsegP(sk3,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2332,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f2311,f2329,f592,f588,f764]) ).
fof(f2367,definition,
( sQ125_spl
<=> equalelemsP(sk3) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f2379,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f294]) ).
fof(f2380,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2379,f349]) ).
fof(f2381,plain,
( ~ sQ30_spl
| rearsegP(sk3,nil)
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f765,f2379]) ).
fof(f2382,plain,
( ~ sQ23_spl
| rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f2379]) ).
fof(f2383,plain,
( rearsegP(sk3,sk7)
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(paramodulation,[status(thm)],[f675,f2379]) ).
fof(f2384,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ ssList(app(X0,X1))
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2380]) ).
fof(f2385,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2384,f294]) ).
fof(f2386,definition,
( sQ126_spl
<=> rearsegP(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f2387,plain,
( ~ sQ126_spl
| rearsegP(sk3,nil) ),
inference(component_clause,[status(thm)],[f2386]) ).
fof(f2389,plain,
( ~ sQ30_spl
| sQ126_spl
| ~ sQ16_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2381,f592,f588,f2386,f764]) ).
fof(f2390,definition,
( sQ127_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2391,plain,
( ~ sQ127_spl
| rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f2390]) ).
fof(f2393,plain,
( ~ sQ23_spl
| sQ127_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2382,f588,f2390,f667]) ).
fof(f2394,definition,
( sQ128_spl
<=> rearsegP(sk3,sk7) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f2395,plain,
( ~ sQ128_spl
| rearsegP(sk3,sk7) ),
inference(component_clause,[status(thm)],[f2394]) ).
fof(f2397,plain,
( sQ128_spl
| ~ sQ12_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f2383,f678,f563,f2394]) ).
fof(f2398,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f294]) ).
fof(f2400,plain,
( ~ sQ30_spl
| frontsegP(sk3,sk3)
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f765,f2398]) ).
fof(f2401,plain,
( ~ sQ23_spl
| frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f2398]) ).
fof(f2402,plain,
( frontsegP(sk3,app(sk6,cons(sk5,nil)))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f675,f2398]) ).
fof(f2405,definition,
( sQ129_spl
<=> frontsegP(sk3,sk3) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2406,plain,
( ~ sQ129_spl
| frontsegP(sk3,sk3) ),
inference(component_clause,[status(thm)],[f2405]) ).
fof(f2408,plain,
( ~ sQ30_spl
| sQ129_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2400,f588,f592,f2405,f764]) ).
fof(f2409,definition,
( sQ130_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2410,plain,
( ~ sQ130_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f2409]) ).
fof(f2412,plain,
( ~ sQ23_spl
| sQ130_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2401,f588,f2409,f667]) ).
fof(f2413,definition,
( sQ131_spl
<=> frontsegP(sk3,app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f2416,plain,
( sQ131_spl
| ~ sQ24_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2402,f563,f678,f2413]) ).
fof(f2421,definition,
( sQ133_spl
<=> sk3 = sk7 ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2422,plain,
( ~ sQ133_spl
| sk3 = sk7 ),
inference(component_clause,[status(thm)],[f2421]) ).
fof(f2425,plain,
( ~ sQ126_spl
| sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ rearsegP(nil,sk3) ),
inference(resolution,[status(thm)],[f2387,f349]) ).
fof(f2426,definition,
( sQ134_spl
<=> rearsegP(nil,sk3) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2429,plain,
( ~ sQ126_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ134_spl ),
inference(split_clause,[status(thm)],[f2425,f2426,f588,f592,f494,f2386]) ).
fof(f2575,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(resolution,[status(thm)],[f385,f2379]) ).
fof(f2576,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ rearsegP(X2,X3)
| rearsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(resolution,[status(thm)],[f385,f359]) ).
fof(f2578,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X2)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f2575]) ).
fof(f2579,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2578,f294]) ).
fof(f2580,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X3)
| rearsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f2576]) ).
fof(f2581,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X3)
| rearsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(X3)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2580,f294]) ).
fof(f2603,definition,
! [X0] :
( sQ149_spl
<=> ( rearsegP(X0,sk7)
| ~ ssList(X0)
| ~ rearsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2607,definition,
( sQ150_spl
<=> rearsegP(sk7,sk7) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2608,plain,
( ~ sQ150_spl
| rearsegP(sk7,sk7) ),
inference(component_clause,[status(thm)],[f2607]) ).
fof(f2609,plain,
( sQ150_spl
| ~ rearsegP(sk7,sk7) ),
inference(component_clause,[status(thm)],[f2607]) ).
fof(f2611,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(resolution,[status(thm)],[f387,f2398]) ).
fof(f2612,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ frontsegP(X1,X3)
| frontsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(resolution,[status(thm)],[f387,f360]) ).
fof(f2614,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f2611]) ).
fof(f2615,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2614,f294]) ).
fof(f2616,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X3)
| frontsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f2612]) ).
fof(f2617,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X3)
| frontsegP(X0,X3)
| ~ ssList(X0)
| ~ ssList(X3)
| ~ frontsegP(X0,app(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2616,f294]) ).
fof(f2626,definition,
! [X0] :
( sQ151_spl
<=> ( frontsegP(X0,sk7)
| ~ ssList(X0)
| ~ frontsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2630,definition,
( sQ152_spl
<=> frontsegP(sk7,sk7) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2642,definition,
! [X0] :
( sQ153_spl
<=> ( segmentP(X0,sk7)
| ~ ssList(X0)
| ~ segmentP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2646,definition,
( sQ154_spl
<=> segmentP(sk7,sk7) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2647,plain,
( ~ sQ154_spl
| segmentP(sk7,sk7) ),
inference(component_clause,[status(thm)],[f2646]) ).
fof(f2648,plain,
( sQ154_spl
| ~ segmentP(sk7,sk7) ),
inference(component_clause,[status(thm)],[f2646]) ).
fof(f2705,plain,
( sQ83_spl
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f1642,f295]) ).
fof(f2706,plain,
( sQ83_spl
| ~ sQ12_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2705,f646,f563,f1640]) ).
fof(f2726,definition,
! [X0] :
( sQ160_spl
<=> ( frontsegP(sk7,X0)
| ~ ssList(X0)
| ~ frontsegP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2839,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)],[f413,f383]) ).
fof(f2840,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)],[f413,f348]) ).
fof(f2844,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)],[f2839]) ).
fof(f2845,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)],[f2840]) ).
fof(f2912,definition,
( sQ176_spl
<=> ssList(skaf80(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2914,plain,
( sQ176_spl
| ~ ssList(skaf80(sk7)) ),
inference(component_clause,[status(thm)],[f2912]) ).
fof(f2930,definition,
( sQ181_spl
<=> ssList(cons(skaf50(sk7),skaf53(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2932,plain,
( sQ181_spl
| ~ ssList(cons(skaf50(sk7),skaf53(sk7))) ),
inference(component_clause,[status(thm)],[f2930]) ).
fof(f2943,definition,
( sQ185_spl
<=> ssList(cons(skaf55(sk7),skaf58(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2945,plain,
( sQ185_spl
| ~ ssList(cons(skaf55(sk7),skaf58(sk7))) ),
inference(component_clause,[status(thm)],[f2943]) ).
fof(f2956,definition,
( sQ189_spl
<=> ssList(cons(skaf60(sk7),skaf63(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2958,plain,
( sQ189_spl
| ~ ssList(cons(skaf60(sk7),skaf63(sk7))) ),
inference(component_clause,[status(thm)],[f2956]) ).
fof(f2969,definition,
( sQ193_spl
<=> ssList(cons(skaf65(sk7),skaf68(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2971,plain,
( sQ193_spl
| ~ ssList(cons(skaf65(sk7),skaf68(sk7))) ),
inference(component_clause,[status(thm)],[f2969]) ).
fof(f2982,definition,
( sQ197_spl
<=> ssList(cons(skaf70(sk7),skaf73(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2984,plain,
( sQ197_spl
| ~ ssList(cons(skaf70(sk7),skaf73(sk7))) ),
inference(component_clause,[status(thm)],[f2982]) ).
fof(f3032,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X2)
| ~ ssList(X3)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f531,f383]) ).
fof(f3033,plain,
! [X0,X1,X2] :
( app(app(X1,X2),X0) = X2
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ segmentP(X2,app(app(X1,X2),X0))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f531,f348]) ).
fof(f3037,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X2)
| ~ ssList(X3)
| ~ segmentP(X3,app(app(X1,X2),X0))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3032]) ).
fof(f3038,plain,
! [X0,X1,X2] :
( app(app(X1,X2),X0) = X2
| ~ segmentP(X2,app(app(X1,X2),X0))
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3033]) ).
fof(f3066,definition,
( sQ206_spl
<=> sk7 = cons(sk5,sk7) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f3067,plain,
( ~ sQ206_spl
| sk7 = cons(sk5,sk7) ),
inference(component_clause,[status(thm)],[f3066]) ).
fof(f3087,plain,
( ~ sQ133_spl
| sk1 = sk7 ),
inference(forward_demodulation,[status(thm)],[f2422,f444]) ).
fof(f3091,plain,
! [X0,X1] :
( ~ ssList(tl(X1))
| ~ ssItem(X0)
| nil = cons(X0,tl(X1))
| cons(X0,tl(X1)) = X1
| nil = X1
| ~ ssList(X1)
| ~ ssList(cons(X0,tl(X1)))
| hd(cons(X0,tl(X1))) != hd(X1) ),
inference(resolution,[status(thm)],[f423,f305]) ).
fof(f3094,plain,
! [X0,X1] :
( ~ ssList(tl(X1))
| ~ ssItem(X0)
| nil = cons(X0,tl(X1))
| cons(X0,tl(X1)) = X1
| nil = X1
| ~ ssList(X1)
| hd(cons(X0,tl(X1))) != hd(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3091,f295]) ).
fof(f3096,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)],[f534,f421]) ).
fof(f3097,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)],[f534,f417]) ).
fof(f3098,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X2,X1))
| ~ ssList(X3)
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ frontsegP(X3,cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f534,f387]) ).
fof(f3099,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)],[f534,f350]) ).
fof(f3100,definition,
! [X0,X1] :
( sQ209_spl
<=> ( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
! [X0,X1] :
( ~ sQ209_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f3100]) ).
fof(f3103,definition,
! [X2] :
( sQ210_spl
<=> ( X2 = X2
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f3106,plain,
( sQ210_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f3096,f3100,f3103]) ).
fof(f3107,definition,
! [X0,X1] :
( sQ211_spl
<=> ( frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f3110,definition,
! [X2] :
( sQ212_spl
<=> ( ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f3111,plain,
! [X0] :
( ~ sQ212_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3110]) ).
fof(f3113,plain,
( sQ212_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f3097,f3107,f3110]) ).
fof(f3114,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X2,X1))
| ~ ssList(X3)
| ~ ssList(cons(X2,X0))
| ~ frontsegP(X3,cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3098,f295]) ).
fof(f3115,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)],[f3099,f295]) ).
fof(f3116,plain,
! [X0,X1] :
( ~ sQ209_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f3101]) ).
fof(f3117,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)],[f535,f465]) ).
fof(f3129,plain,
( segmentP(sk3,cons(sk5,nil))
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f675,f531]) ).
fof(f3130,plain,
! [X0] :
( segmentP(sk3,X0)
| ~ ssList(cons(sk5,nil))
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(cons(sk5,nil),X0) ),
inference(paramodulation,[status(thm)],[f675,f413]) ).
fof(f3132,plain,
! [X0] :
( segmentP(app(sk3,X0),sk7)
| ~ ssList(app(app(app(sk6,cons(sk5,nil)),sk7),X0))
| ~ ssList(sk7)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f675,f531]) ).
fof(f3133,plain,
! [X0,X1] :
( segmentP(app(sk3,X1),X0)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f675,f413]) ).
fof(f3149,definition,
( sQ214_spl
<=> ssList(app(app(sk6,cons(sk5,nil)),sk7)) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f3151,plain,
( sQ214_spl
| ~ ssList(app(app(sk6,cons(sk5,nil)),sk7)) ),
inference(component_clause,[status(thm)],[f3149]) ).
fof(f3152,definition,
( sQ215_spl
<=> segmentP(sk3,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f3153,plain,
( ~ sQ215_spl
| segmentP(sk3,cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f3152]) ).
fof(f3155,plain,
( sQ215_spl
| ~ sQ214_spl
| ~ sQ26_spl
| ~ sQ20_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3129,f563,f637,f687,f3149,f3152]) ).
fof(f3156,definition,
! [X0] :
( sQ216_spl
<=> ( segmentP(sk3,X0)
| ~ ssList(X0)
| ~ segmentP(cons(sk5,nil),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f3159,plain,
( ~ sQ26_spl
| ~ sQ20_spl
| ~ sQ12_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f3130,f3156,f563,f637,f687]) ).
fof(f3161,definition,
! [X0] :
( sQ217_spl
<=> ( segmentP(app(sk3,X0),sk7)
| ~ ssList(app(app(app(sk6,cons(sk5,nil)),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f3162,plain,
! [X0] :
( ~ sQ217_spl
| segmentP(app(sk3,X0),sk7)
| ~ ssList(app(app(app(sk6,cons(sk5,nil)),sk7),X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3161]) ).
fof(f3164,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f3132,f3161,f678,f563]) ).
fof(f3165,definition,
! [X0,X1] :
( sQ218_spl
<=> ( segmentP(app(sk3,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f3166,plain,
! [X0,X1] :
( ~ sQ218_spl
| segmentP(app(sk3,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ),
inference(component_clause,[status(thm)],[f3165]) ).
fof(f3168,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f3133,f3165,f678,f563]) ).
fof(f3184,plain,
! [X0] :
( ~ sQ217_spl
| segmentP(app(sk3,X0),sk7)
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f675,f3162]) ).
fof(f3185,plain,
( sQ214_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f675,f3151]) ).
fof(f3187,plain,
( sQ214_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3185,f441]) ).
fof(f3188,plain,
sQ214_spl,
inference(contradiction_clause,[status(thm)],[f3187]) ).
fof(f3190,plain,
! [X0] :
( ~ sQ130_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f2410,f387]) ).
fof(f3192,definition,
! [X0] :
( sQ219_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f3195,plain,
( ~ sQ130_spl
| ~ sQ16_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f3190,f3192,f588,f2409]) ).
fof(f3197,plain,
! [X0] :
( ~ sQ129_spl
| frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ frontsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f2406,f387]) ).
fof(f3199,definition,
! [X0] :
( sQ220_spl
<=> ( frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( ~ sQ129_spl
| ~ sQ17_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f3197,f3199,f592,f2405]) ).
fof(f3204,plain,
! [X0] :
( ~ sQ127_spl
| rearsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(X0,nil) ),
inference(resolution,[status(thm)],[f2391,f385]) ).
fof(f3205,plain,
( ~ sQ127_spl
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,nil) ),
inference(resolution,[status(thm)],[f2391,f349]) ).
fof(f3206,definition,
! [X0] :
( sQ221_spl
<=> ( rearsegP(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f3209,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f3204,f3206,f588,f2390]) ).
fof(f3210,plain,
( sQ27_spl
| ~ sQ16_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f3205,f2390,f588,f696]) ).
fof(f3211,plain,
! [X0] :
( ~ sQ72_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ segmentP(X0,nil) ),
inference(resolution,[status(thm)],[f1243,f383]) ).
fof(f3213,definition,
! [X0] :
( sQ222_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3216,plain,
( ~ sQ72_spl
| ~ sQ16_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f3211,f3213,f588,f1242]) ).
fof(f3218,plain,
! [X0] :
( ~ sQ126_spl
| rearsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ rearsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f2387,f385]) ).
fof(f3220,definition,
! [X0] :
( sQ223_spl
<=> ( rearsegP(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3223,plain,
( ~ sQ126_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f3218,f3220,f588,f592,f2386]) ).
fof(f3225,plain,
! [X0] :
( ~ sQ128_spl
| rearsegP(X0,sk7)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(sk7)
| ~ rearsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f2395,f385]) ).
fof(f3227,definition,
! [X0] :
( sQ224_spl
<=> ( rearsegP(X0,sk7)
| ~ ssList(X0)
| ~ rearsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f3230,plain,
( ~ sQ128_spl
| ~ sQ17_spl
| ~ sQ12_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f3225,f3227,f563,f592,f2394]) ).
fof(f3232,plain,
! [X0] :
( ~ sQ82_spl
| nil = X0
| X0 = sk3
| nil = sk3
| ~ ssList(sk3)
| ~ ssList(X0)
| hd(X0) != hd(sk3)
| tl(X0) != nil ),
inference(paramodulation,[status(thm)],[f1575,f423]) ).
fof(f3234,definition,
! [X0] :
( sQ225_spl
<=> ( nil = X0
| X0 = sk3
| ~ ssList(X0)
| hd(X0) != hd(sk3)
| tl(X0) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3237,plain,
( ~ sQ82_spl
| sQ8_spl
| ~ sQ17_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f3232,f3234,f592,f494,f1574]) ).
fof(f3239,plain,
( ~ sQ206_spl
| ~ ssList(sk7)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f3067,f310]) ).
fof(f3267,plain,
( ~ sQ206_spl
| ~ sQ12_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3239,f646,f563,f3066]) ).
fof(f3360,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| leq(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f538]) ).
fof(f3361,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f538]) ).
fof(f3362,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f537]) ).
fof(f3363,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f537]) ).
fof(f3364,plain,
! [X0,X1] :
( ~ sQ9_spl
| X1 = sk9
| ~ ssList(app(X0,cons(X1,cons(sk9,nil))))
| ~ equalelemsP(app(X0,cons(X1,sk3)))
| ~ ssItem(X1)
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f536]) ).
fof(f3367,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ0_spl
| ~ ssList(app(app(X1,sk3),cons(sk9,X0)))
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f3117]) ).
fof(f3368,plain,
! [X0] :
( ~ sQ9_spl
| frontsegP(cons(sk9,X0),sk3)
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f499,f534]) ).
fof(f3369,plain,
! [X0] :
( ~ sQ9_spl
| frontsegP(sk3,cons(sk9,X0))
| ~ ssItem(sk9)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f499,f534]) ).
fof(f3370,plain,
! [X0,X1] :
( ~ sQ9_spl
| X0 = sk9
| ~ ssItem(X0)
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk3) ),
inference(paramodulation,[status(thm)],[f499,f421]) ).
fof(f3371,plain,
! [X0,X1] :
( ~ sQ9_spl
| sk9 = X0
| ~ ssItem(sk9)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f499,f421]) ).
fof(f3390,definition,
! [X0,X1,X2] :
( sQ246_spl
<=> ( leq(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3393,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ246_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3360,f588,f3390,f487,f498]) ).
fof(f3394,definition,
! [X0,X1,X2] :
( sQ247_spl
<=> ( leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3397,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f3361,f3394,f588,f487,f498]) ).
fof(f3398,definition,
! [X0,X1,X2] :
( sQ248_spl
<=> ( lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3399,plain,
! [X0,X1,X2] :
( ~ sQ248_spl
| lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3398]) ).
fof(f3401,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ248_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3362,f588,f3398,f487,f498]) ).
fof(f3402,definition,
! [X0,X1,X2] :
( sQ249_spl
<=> ( lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3403,plain,
! [X0,X1,X2] :
( ~ sQ249_spl
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3402]) ).
fof(f3405,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f3363,f3402,f588,f487,f498]) ).
fof(f3406,definition,
! [X0,X1] :
( sQ250_spl
<=> ( X1 = sk9
| ~ ssList(app(X0,cons(X1,cons(sk9,nil))))
| ~ equalelemsP(app(X0,cons(X1,sk3)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3409,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ250_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3364,f588,f3406,f487,f498]) ).
fof(f3415,definition,
! [X0,X1] :
( sQ252_spl
<=> ( ~ ssList(app(app(X1,sk3),cons(sk9,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3416,plain,
! [X0,X1] :
( ~ sQ252_spl
| ~ ssList(app(app(X1,sk3),cons(sk9,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3415]) ).
fof(f3418,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f3367,f3415,f588,f487,f464,f498]) ).
fof(f3419,definition,
! [X0] :
( sQ253_spl
<=> ( frontsegP(cons(sk9,X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3420,plain,
! [X0] :
( ~ sQ253_spl
| frontsegP(cons(sk9,X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f3419]) ).
fof(f3422,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f3368,f3419,f588,f487,f498]) ).
fof(f3423,definition,
! [X0] :
( sQ254_spl
<=> ( frontsegP(sk3,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
! [X0] :
( ~ sQ254_spl
| frontsegP(sk3,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f3423]) ).
fof(f3426,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f3369,f3423,f588,f487,f498]) ).
fof(f3427,definition,
! [X0,X1] :
( sQ255_spl
<=> ( X0 = sk9
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3428,plain,
! [X0,X1] :
( ~ sQ255_spl
| X0 = sk9
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk3) ),
inference(component_clause,[status(thm)],[f3427]) ).
fof(f3430,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f3370,f3427,f588,f487,f498]) ).
fof(f3431,definition,
! [X0,X1] :
( sQ256_spl
<=> ( sk9 = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3434,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f3371,f3431,f588,f487,f498]) ).
fof(f3435,definition,
! [X0,X1] :
( sQ257_spl
<=> ( frontsegP(X1,nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3439,definition,
! [X0,X1] :
( sQ258_spl
<=> ( frontsegP(nil,X1)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3458,plain,
! [X0,X1,X2] :
( ~ sQ248_spl
| ~ sQ9_spl
| lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),sk3))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f499,f3399]) ).
fof(f3459,plain,
! [X0,X1,X2] :
( ~ sQ249_spl
| ~ sQ9_spl
| lt(sk9,X2)
| ~ ssList(app(app(X1,sk3),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f499,f3403]) ).
fof(f3467,plain,
! [X0] :
( ~ sQ23_spl
| segmentP(app(nil,X0),nil)
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f668,f531]) ).
fof(f3468,plain,
! [X0,X1] :
( ~ sQ23_spl
| segmentP(app(nil,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f413]) ).
fof(f3483,definition,
! [X0] :
( sQ259_spl
<=> ( segmentP(app(nil,X0),nil)
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3486,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f3467,f3483,f588,f667]) ).
fof(f3487,definition,
! [X0,X1] :
( sQ260_spl
<=> ( segmentP(app(nil,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3490,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f3468,f3487,f588,f667]) ).
fof(f3506,plain,
! [X0] :
( ~ sQ30_spl
| segmentP(app(sk3,X0),nil)
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f765,f531]) ).
fof(f3507,plain,
! [X0,X1] :
( ~ sQ30_spl
| segmentP(app(sk3,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f413]) ).
fof(f3522,definition,
! [X0] :
( sQ261_spl
<=> ( segmentP(app(sk3,X0),nil)
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3525,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f3506,f3522,f592,f588,f764]) ).
fof(f3526,definition,
! [X0,X1] :
( sQ262_spl
<=> ( segmentP(app(sk3,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3529,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f3507,f3526,f592,f588,f764]) ).
fof(f3631,plain,
! [X0,X1] :
( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f268,f387]) ).
fof(f3633,definition,
! [X0,X1] :
( sQ263_spl
<=> ( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3636,plain,
( ~ sQ16_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f3631,f3633,f588]) ).
fof(f3639,plain,
! [X0,X1] :
( rearsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(X1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f266,f385]) ).
fof(f3641,definition,
! [X0,X1] :
( sQ264_spl
<=> ( rearsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3644,plain,
( ~ sQ16_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f3639,f3641,f588]) ).
fof(f3647,plain,
! [X0,X1] :
( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(X1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f264,f383]) ).
fof(f3649,definition,
! [X0,X1] :
( sQ265_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3652,plain,
( ~ sQ16_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f3647,f3649,f588]) ).
fof(f3658,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| lt(X4,X3)
| lt(X3,X4)
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ strictorderP(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f468]) ).
fof(f3659,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ1_spl
| lt(X2,sk9)
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f3658]) ).
fof(f3661,definition,
! [X0,X1,X2] :
( sQ266_spl
<=> ( lt(X2,sk9)
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3664,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f3659,f3661,f588,f487,f467,f498]) ).
fof(f3665,definition,
! [X0,X1,X2] :
( sQ267_spl
<=> ( lt(sk9,X2)
| lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3672,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| leq(X4,X3)
| leq(X3,X4)
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ totalorderP(app(app(X2,cons(X3,X1)),cons(X4,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f468]) ).
fof(f3673,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ1_spl
| leq(X2,sk9)
| leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f3672]) ).
fof(f3675,definition,
! [X0,X1,X2] :
( sQ268_spl
<=> ( leq(X2,sk9)
| leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3678,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3673,f3675,f588,f487,f467,f498]) ).
fof(f3679,definition,
! [X0,X1,X2] :
( sQ269_spl
<=> ( leq(sk9,X2)
| leq(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3686,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ ssList(app(app(X4,cons(X0,X3)),cons(X1,X2)))
| ~ cyclefreeP(app(app(X4,cons(X0,X3)),cons(X1,X2)))
| ~ ssItem(X0)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f468]) ).
fof(f3687,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ sQ1_spl
| ~ ssList(app(app(X2,cons(sk9,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(sk9)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ leq(X0,sk9)
| ~ leq(sk9,X0) ),
inference(paramodulation,[status(thm)],[f499,f3686]) ).
fof(f3689,definition,
! [X0,X1,X2] :
( sQ270_spl
<=> ( ~ ssList(app(app(X2,cons(sk9,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,sk9)
| ~ leq(sk9,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3692,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f3687,f3689,f588,f487,f467,f498]) ).
fof(f3693,definition,
! [X0,X1,X2] :
( sQ271_spl
<=> ( ~ ssList(app(app(X2,cons(X0,X1)),cons(sk9,nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(sk9,X0)
| ~ leq(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3700,plain,
! [X0] :
( ~ sQ215_spl
| segmentP(X0,cons(sk5,nil))
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| ~ segmentP(X0,sk3) ),
inference(resolution,[status(thm)],[f3153,f383]) ).
fof(f3702,definition,
! [X0] :
( sQ272_spl
<=> ( segmentP(X0,cons(sk5,nil))
| ~ ssList(X0)
| ~ segmentP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3705,plain,
( ~ sQ215_spl
| ~ sQ17_spl
| ~ sQ26_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f3700,f3702,f687,f592,f3152]) ).
fof(f3706,definition,
( sQ273_spl
<=> segmentP(cons(sk5,nil),sk3) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3708,plain,
( sQ273_spl
| ~ segmentP(cons(sk5,nil),sk3) ),
inference(component_clause,[status(thm)],[f3706]) ).
fof(f3709,definition,
( sQ274_spl
<=> sk3 = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f3710,plain,
( ~ sQ274_spl
| sk3 = cons(sk5,nil) ),
inference(component_clause,[status(thm)],[f3709]) ).
fof(f3711,plain,
( sQ274_spl
| sk3 != cons(sk5,nil) ),
inference(component_clause,[status(thm)],[f3709]) ).
fof(f3713,plain,
( ~ sQ215_spl
| ~ sQ274_spl
| segmentP(sk3,sk3) ),
inference(backward_demodulation,[status(thm)],[f3710,f3153]) ).
fof(f3716,plain,
( ~ sQ274_spl
| app(app(sk6,sk3),sk7) = sk3 ),
inference(backward_demodulation,[status(thm)],[f3710,f675]) ).
fof(f3719,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| ~ ssList(app(app(X2,cons(X0,X1)),cons(sk5,nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ leq(sk5,X0)
| ~ leq(X0,sk5) ),
inference(paramodulation,[status(thm)],[f3710,f3686]) ).
fof(f3720,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| ~ ssList(app(app(X2,cons(sk5,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(sk5)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ leq(X0,sk5)
| ~ leq(sk5,X0) ),
inference(paramodulation,[status(thm)],[f3710,f3686]) ).
fof(f3721,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| leq(sk5,X2)
| leq(X2,sk5)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk5,nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f3710,f3672]) ).
fof(f3722,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| leq(X2,sk5)
| leq(sk5,X2)
| ~ ssList(app(app(X1,cons(sk5,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk5)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3710,f3672]) ).
fof(f3723,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| lt(sk5,X2)
| lt(X2,sk5)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk5,nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f3710,f3658]) ).
fof(f3724,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ1_spl
| lt(X2,sk5)
| lt(sk5,X2)
| ~ ssList(app(app(X1,cons(sk5,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk5)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3710,f3658]) ).
fof(f3726,definition,
! [X0,X1,X2] :
( sQ275_spl
<=> ( ~ ssList(app(app(X2,cons(X0,X1)),cons(sk5,nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(sk5,X0)
| ~ leq(X0,sk5) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3729,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f3719,f3726,f588,f467,f3709]) ).
fof(f3730,definition,
! [X0,X1,X2] :
( sQ276_spl
<=> ( ~ ssList(app(app(X2,cons(sk5,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,sk5)
| ~ leq(sk5,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3733,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ16_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f3720,f3730,f588,f646,f467,f3709]) ).
fof(f3734,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> ( leq(sk5,X2)
| leq(X2,sk5)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk5,nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3737,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| sQ277_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3721,f588,f3734,f467,f3709]) ).
fof(f3738,definition,
! [X0,X1,X2] :
( sQ278_spl
<=> ( leq(X2,sk5)
| leq(sk5,X2)
| ~ ssList(app(app(X1,cons(sk5,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3741,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ16_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f3722,f3738,f588,f646,f467,f3709]) ).
fof(f3742,definition,
! [X0,X1,X2] :
( sQ279_spl
<=> ( lt(sk5,X2)
| lt(X2,sk5)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk5,nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3745,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| sQ279_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3723,f588,f3742,f467,f3709]) ).
fof(f3746,definition,
! [X0,X1,X2] :
( sQ280_spl
<=> ( lt(X2,sk5)
| lt(sk5,X2)
| ~ ssList(app(app(X1,cons(sk5,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3749,plain,
( ~ sQ274_spl
| ~ sQ1_spl
| ~ sQ21_spl
| ~ sQ16_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f3724,f3746,f588,f646,f467,f3709]) ).
fof(f3764,plain,
( ~ sQ39_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f441,f831]) ).
fof(f3798,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f3764]) ).
fof(f3811,plain,
( ~ sQ81_spl
| nil = sk3
| cons(sk9,tl(sk3)) = sk3
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f1571,f315]) ).
fof(f3812,plain,
( ~ sQ82_spl
| nil = sk3
| cons(hd(sk3),nil) = sk3
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f1575,f315]) ).
fof(f3813,definition,
( sQ282_spl
<=> cons(sk9,tl(sk3)) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3816,plain,
( ~ sQ81_spl
| sQ8_spl
| sQ282_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3811,f592,f3813,f494,f1570]) ).
fof(f3817,definition,
( sQ283_spl
<=> cons(hd(sk3),nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3820,plain,
( ~ sQ82_spl
| sQ8_spl
| sQ283_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3812,f592,f3817,f494,f1574]) ).
fof(f3825,definition,
( sQ284_spl
<=> ssList(app(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3826,plain,
( ~ sQ284_spl
| ssList(app(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f3825]) ).
fof(f3827,plain,
( sQ284_spl
| ~ ssList(app(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f3825]) ).
fof(f3829,definition,
( sQ285_spl
<=> nil = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3830,plain,
( ~ sQ285_spl
| nil = app(sk6,sk3) ),
inference(component_clause,[status(thm)],[f3829]) ).
fof(f3838,plain,
( ~ sQ285_spl
| nil = sk3
| ~ ssList(sk6)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f3830,f338]) ).
fof(f3843,plain,
( ~ sQ285_spl
| sQ8_spl
| ~ sQ20_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f3838,f592,f637,f494,f3829]) ).
fof(f3844,definition,
( sQ286_spl
<=> nil = sk6 ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3845,plain,
( ~ sQ286_spl
| nil = sk6 ),
inference(component_clause,[status(thm)],[f3844]) ).
fof(f3850,plain,
! [X0] :
( ~ sQ286_spl
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ),
inference(backward_demodulation,[status(thm)],[f3845,f279]) ).
fof(f3861,plain,
( ~ sQ82_spl
| ~ sQ286_spl
| tl(sk3) = sk6 ),
inference(backward_demodulation,[status(thm)],[f3845,f1575]) ).
fof(f3889,definition,
( sQ287_spl
<=> sk6 = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3890,plain,
( ~ sQ287_spl
| sk6 = app(sk6,sk3) ),
inference(component_clause,[status(thm)],[f3889]) ).
fof(f3891,plain,
( sQ287_spl
| sk6 != app(sk6,sk3) ),
inference(component_clause,[status(thm)],[f3889]) ).
fof(f3892,definition,
( sQ288_spl
<=> hd(sk3) = hd(app(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3893,plain,
( ~ sQ288_spl
| hd(sk3) = hd(app(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f3892]) ).
fof(f3896,plain,
( ~ sQ288_spl
| ~ sQ81_spl
| sk9 = hd(app(sk6,sk3)) ),
inference(forward_demodulation,[status(thm)],[f1571,f3893]) ).
fof(f3899,plain,
( ~ sQ274_spl
| ~ sQ287_spl
| app(sk6,sk7) = sk3 ),
inference(backward_demodulation,[status(thm)],[f3890,f3716]) ).
fof(f3930,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ274_spl
| sk7 = X0
| ~ ssList(X0)
| sk3 != app(app(sk6,sk3),X0) ),
inference(forward_demodulation,[status(thm)],[f3710,f821]) ).
fof(f3931,plain,
! [X0] :
( ~ sQ37_spl
| ~ sQ274_spl
| ~ sQ287_spl
| sk7 = X0
| ~ ssList(X0)
| sk3 != app(sk6,X0) ),
inference(forward_demodulation,[status(thm)],[f3890,f3930]) ).
fof(f3934,plain,
( ~ sQ287_spl
| ~ sQ37_spl
| ~ sQ274_spl
| sk7 = sk3
| ~ ssList(sk3)
| sk3 != sk6 ),
inference(paramodulation,[status(thm)],[f3890,f3931]) ).
fof(f3937,definition,
( sQ291_spl
<=> sk3 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3940,plain,
( ~ sQ287_spl
| ~ sQ37_spl
| ~ sQ274_spl
| sQ133_spl
| ~ sQ17_spl
| ~ sQ291_spl ),
inference(split_clause,[status(thm)],[f3934,f3937,f592,f2421,f3709,f820,f3889]) ).
fof(f3942,plain,
( ~ sQ133_spl
| sk3 = sk7 ),
inference(forward_demodulation,[status(thm)],[f444,f3087]) ).
fof(f3980,plain,
( ~ sQ91_spl
| ~ sQ9_spl
| ~ sQ133_spl
| singletonP(sk7) ),
inference(backward_demodulation,[status(thm)],[f2422,f1882]) ).
fof(f3983,plain,
( ~ sQ133_spl
| sk1 = sk7 ),
inference(backward_demodulation,[status(thm)],[f2422,f444]) ).
fof(f3988,plain,
( ~ sQ91_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3980,f847]) ).
fof(f3989,plain,
( ~ sQ91_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f3988]) ).
fof(f3997,plain,
! [X0] :
( ~ sQ82_spl
| tl(app(sk3,X0)) = app(nil,X0)
| nil = sk3
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1575,f354]) ).
fof(f3998,definition,
! [X0] :
( sQ292_spl
<=> ( tl(app(sk3,X0)) = app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f4001,plain,
( ~ sQ82_spl
| sQ8_spl
| ~ sQ17_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f3997,f3998,f592,f494,f1574]) ).
fof(f4011,definition,
( sQ294_spl
<=> ssItem(hd(nil)) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f4013,plain,
( sQ294_spl
| ~ ssItem(hd(nil)) ),
inference(component_clause,[status(thm)],[f4011]) ).
fof(f4021,definition,
! [X0] :
( sQ295_spl
<=> ( memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4022,plain,
! [X0] :
( ~ sQ295_spl
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(component_clause,[status(thm)],[f4021]) ).
fof(f4025,plain,
! [X0] :
( ~ sQ295_spl
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4022,f279]) ).
fof(f4038,plain,
( ~ sQ28_spl
| ~ sQ295_spl
| ~ ssItem(sk9) ),
inference(resolution,[status(thm)],[f4025,f716]) ).
fof(f4039,plain,
( ~ sQ28_spl
| ~ sQ295_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f4038,f487,f4021,f715]) ).
fof(f4079,plain,
( ~ sQ274_spl
| duplicatefreeP(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f3710,f273]) ).
fof(f4081,plain,
( ~ sQ274_spl
| sQ32_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4079,f646,f778,f3709]) ).
fof(f4087,plain,
! [X0] :
( ~ sQ81_spl
| nil = sk3
| strictorderedP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ lt(X0,sk9) ),
inference(paramodulation,[status(thm)],[f1571,f398]) ).
fof(f4088,definition,
! [X0] :
( sQ298_spl
<=> ( strictorderedP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ lt(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4091,plain,
( ~ sQ81_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ45_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f4087,f4088,f955,f592,f494,f1570]) ).
fof(f4102,plain,
( sQ273_spl
| ~ sQ274_spl
| ~ segmentP(sk3,sk3) ),
inference(forward_demodulation,[status(thm)],[f3710,f3708]) ).
fof(f4103,plain,
( sQ273_spl
| ~ sQ274_spl
| ~ sQ215_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4102,f3713]) ).
fof(f4104,plain,
( sQ273_spl
| ~ sQ274_spl
| ~ sQ215_spl ),
inference(contradiction_clause,[status(thm)],[f4103]) ).
fof(f4106,plain,
! [X0] :
( ~ sQ212_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3111]) ).
fof(f4107,plain,
( sQ176_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2914,f223]) ).
fof(f4108,plain,
sQ176_spl,
inference(contradiction_clause,[status(thm)],[f4107]) ).
fof(f4109,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1546,f255]) ).
fof(f4110,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f4109]) ).
fof(f4111,plain,
! [X0] :
( ~ sQ73_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1250]) ).
fof(f4112,plain,
! [X0] :
( ~ sQ70_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1188]) ).
fof(f4114,plain,
! [X0] :
( ~ sQ274_spl
| memberP(app(sk6,sk3),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f3716,f394]) ).
fof(f4115,plain,
! [X0] :
( ~ sQ274_spl
| cons(X0,sk3) = app(cons(X0,app(sk6,sk3)),sk7)
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f3716,f392]) ).
fof(f4117,definition,
! [X0] :
( sQ301_spl
<=> ( memberP(app(sk6,sk3),X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f4120,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f4114,f4117,f563,f3825,f3709]) ).
fof(f4121,definition,
! [X0] :
( sQ302_spl
<=> ( cons(X0,sk3) = app(cons(X0,app(sk6,sk3)),sk7)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f4124,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f4115,f4121,f3825,f563,f3709]) ).
fof(f4163,plain,
( sQ294_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4013,f468]) ).
fof(f4169,plain,
( sQ294_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f4163]) ).
fof(f4178,plain,
! [X0,X1] :
( ~ sQ1_spl
| nil = X1
| totalorderedP(cons(X0,X1))
| ~ ssList(X1)
| ~ totalorderedP(X1)
| ~ leq(X0,hd(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f468]) ).
fof(f4180,plain,
! [X0] :
( ~ sQ81_spl
| ~ sQ1_spl
| nil = sk3
| totalorderedP(cons(X0,sk3))
| ~ ssList(sk3)
| ~ totalorderedP(sk3)
| ~ leq(X0,sk9) ),
inference(paramodulation,[status(thm)],[f1571,f4178]) ).
fof(f4181,definition,
! [X0] :
( sQ303_spl
<=> ( totalorderedP(cons(X0,sk3))
| ~ leq(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f4184,plain,
( ~ sQ81_spl
| ~ sQ1_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ44_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f4180,f4181,f951,f592,f494,f467,f1570]) ).
fof(f4228,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(sk9,X0)))
| ~ duplicatefreeP(app(app(X1,sk3),cons(sk9,X0)))
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f535]) ).
fof(f4229,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ ssList(app(app(X1,cons(sk9,X0)),cons(sk9,nil)))
| ~ duplicatefreeP(app(app(X1,cons(sk9,X0)),sk3))
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f535]) ).
fof(f4230,definition,
! [X0,X1] :
( sQ305_spl
<=> ( ~ ssList(app(app(X1,cons(sk9,nil)),cons(sk9,X0)))
| ~ duplicatefreeP(app(app(X1,sk3),cons(sk9,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4233,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f4228,f4230,f588,f487,f498]) ).
fof(f4234,definition,
! [X0,X1] :
( sQ306_spl
<=> ( ~ ssList(app(app(X1,cons(sk9,X0)),cons(sk9,nil)))
| ~ duplicatefreeP(app(app(X1,cons(sk9,X0)),sk3))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f4237,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ306_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4229,f588,f4234,f487,f498]) ).
fof(f4240,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ ssList(app(app(X2,cons(sk9,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(sk9)
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ leq(X0,sk9)
| ~ leq(sk9,X0) ),
inference(paramodulation,[status(thm)],[f499,f541]) ).
fof(f4241,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| ~ ssList(app(app(X2,cons(X0,X1)),cons(sk9,nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssItem(sk9)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ leq(sk9,X0)
| ~ leq(X0,sk9) ),
inference(paramodulation,[status(thm)],[f499,f541]) ).
fof(f4242,definition,
! [X0,X1,X2] :
( sQ307_spl
<=> ( ~ ssList(app(app(X2,cons(sk9,nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,sk9)
| ~ leq(sk9,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f4245,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4240,f4242,f588,f487,f498]) ).
fof(f4246,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f4241,f3693,f588,f487,f498]) ).
fof(f4267,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,app(sk6,cons(sk5,nil))))
| app(cons(X0,app(sk6,cons(sk5,nil))),sk7) != sk3 ),
inference(resolution,[status(thm)],[f972,f310]) ).
fof(f4268,definition,
! [X0] :
( sQ311_spl
<=> ( ~ ssItem(X0)
| ~ ssList(cons(X0,app(sk6,cons(sk5,nil))))
| app(cons(X0,app(sk6,cons(sk5,nil))),sk7) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4271,plain,
( ~ sQ47_spl
| ~ sQ24_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f4267,f4268,f678,f971]) ).
fof(f4340,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| leq(X2,sk9)
| leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f540]) ).
fof(f4341,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| leq(sk9,X2)
| leq(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f540]) ).
fof(f4342,definition,
! [X0,X1,X2] :
( sQ312_spl
<=> ( leq(X2,sk9)
| leq(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4345,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f4340,f4342,f588,f487,f498]) ).
fof(f4346,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ269_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4341,f588,f3679,f487,f498]) ).
fof(f4348,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| lt(X2,sk9)
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(sk9)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f499,f539]) ).
fof(f4349,plain,
! [X0,X1,X2] :
( ~ sQ9_spl
| lt(sk9,X2)
| lt(X2,sk9)
| ~ ssList(app(app(X1,cons(X2,X0)),cons(sk9,nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(sk9)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f539]) ).
fof(f4350,definition,
! [X0,X1,X2] :
( sQ313_spl
<=> ( lt(X2,sk9)
| lt(sk9,X2)
| ~ ssList(app(app(X1,cons(sk9,nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f4353,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f4348,f4350,f588,f487,f498]) ).
fof(f4354,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ267_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4349,f588,f3665,f487,f498]) ).
fof(f4363,definition,
( sQ314_spl
<=> memberP(sk3,sk5) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f4364,plain,
( ~ sQ314_spl
| memberP(sk3,sk5) ),
inference(component_clause,[status(thm)],[f4363]) ).
fof(f4367,plain,
( ~ sQ67_spl
| ~ sQ314_spl
| sk5 = sk9
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f4364,f1175]) ).
fof(f4368,definition,
( sQ315_spl
<=> sk5 = sk9 ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f4369,plain,
( ~ sQ315_spl
| sk5 = sk9 ),
inference(component_clause,[status(thm)],[f4368]) ).
fof(f4371,plain,
( ~ sQ67_spl
| ~ sQ314_spl
| sQ315_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f4367,f646,f4368,f4363,f1171]) ).
fof(f4386,plain,
( sQ274_spl
| ~ sQ315_spl
| sk3 != cons(sk9,nil) ),
inference(backward_demodulation,[status(thm)],[f4369,f3711]) ).
fof(f4403,plain,
( sQ274_spl
| ~ sQ315_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4386,f498,f4368,f3709]) ).
fof(f4492,plain,
( ~ sQ315_spl
| app(app(sk6,cons(sk9,nil)),sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f4369,f675]) ).
fof(f4495,plain,
! [X0] :
( ~ sQ315_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk9,nil)))
| ~ ssList(sk7)
| ~ memberP(app(sk6,cons(sk9,nil)),X0) ),
inference(paramodulation,[status(thm)],[f4492,f363]) ).
fof(f4496,definition,
( sQ317_spl
<=> ssList(app(sk6,cons(sk9,nil))) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4498,plain,
( sQ317_spl
| ~ ssList(app(sk6,cons(sk9,nil))) ),
inference(component_clause,[status(thm)],[f4496]) ).
fof(f4501,definition,
! [X0] :
( sQ318_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,cons(sk9,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f4504,plain,
( ~ sQ315_spl
| ~ sQ317_spl
| ~ sQ12_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f4495,f4501,f563,f4496,f4368]) ).
fof(f4527,plain,
( ~ sQ315_spl
| frontsegP(sk3,app(sk6,cons(sk9,nil)))
| ~ ssList(app(sk6,cons(sk9,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f4492,f2398]) ).
fof(f4530,definition,
( sQ319_spl
<=> frontsegP(sk3,app(sk6,cons(sk9,nil))) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4533,plain,
( ~ sQ315_spl
| sQ319_spl
| ~ sQ317_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4527,f563,f4496,f4530,f4368]) ).
fof(f4596,plain,
( sQ284_spl
| ~ ssList(sk6)
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f3827,f294]) ).
fof(f4597,plain,
( sQ284_spl
| ~ sQ20_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f4596,f592,f637,f3825]) ).
fof(f4654,plain,
( ~ sQ70_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4112,f830,f1187]) ).
fof(f4656,plain,
( ~ sQ212_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f255,f4106]) ).
fof(f4675,plain,
~ sQ212_spl,
inference(contradiction_clause,[status(thm)],[f4656]) ).
fof(f4676,plain,
( ~ sQ6_spl
| ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f4111]) ).
fof(f4677,plain,
( ~ sQ6_spl
| ~ sQ73_spl ),
inference(contradiction_clause,[status(thm)],[f4676]) ).
fof(f4679,plain,
( ~ sQ274_spl
| frontsegP(sk3,app(sk6,sk3))
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3716,f2398]) ).
fof(f4683,definition,
( sQ320_spl
<=> frontsegP(sk3,app(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4684,plain,
( ~ sQ320_spl
| frontsegP(sk3,app(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f4683]) ).
fof(f4686,plain,
( ~ sQ274_spl
| sQ320_spl
| ~ sQ284_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4679,f563,f3825,f4683,f3709]) ).
fof(f4691,plain,
( sQ154_spl
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f2648,f265]) ).
fof(f4692,plain,
( sQ154_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4691,f563,f2646]) ).
fof(f4696,plain,
! [X0] :
( ~ sQ274_spl
| app(sk6,sk3) = X0
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| sk3 != app(X0,sk7) ),
inference(paramodulation,[status(thm)],[f3716,f381]) ).
fof(f4703,definition,
! [X0] :
( sQ321_spl
<=> ( app(sk6,sk3) = X0
| ~ ssList(X0)
| sk3 != app(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f4706,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ321_spl ),
inference(split_clause,[status(thm)],[f4696,f4703,f3825,f563,f3709]) ).
fof(f4713,plain,
( ~ sQ274_spl
| sk3 = app(sk6,app(sk3,sk7))
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3716,f377]) ).
fof(f4714,plain,
! [X0] :
( ~ sQ274_spl
| app(sk3,X0) = app(app(sk6,sk3),app(sk7,X0))
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3716,f377]) ).
fof(f4717,definition,
( sQ322_spl
<=> sk3 = app(sk6,app(sk3,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f4718,plain,
( ~ sQ322_spl
| sk3 = app(sk6,app(sk3,sk7)) ),
inference(component_clause,[status(thm)],[f4717]) ).
fof(f4720,plain,
( ~ sQ274_spl
| sQ322_spl
| ~ sQ20_spl
| ~ sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4713,f563,f592,f637,f4717,f3709]) ).
fof(f4721,definition,
! [X0] :
( sQ323_spl
<=> ( app(sk3,X0) = app(app(sk6,sk3),app(sk7,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f4724,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f4714,f4721,f563,f3825,f3709]) ).
fof(f4744,plain,
! [X0] :
( ~ sQ274_spl
| sk7 = X0
| ~ ssList(X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| sk3 != app(app(sk6,sk3),X0) ),
inference(paramodulation,[status(thm)],[f3716,f379]) ).
fof(f4751,definition,
! [X0] :
( sQ327_spl
<=> ( sk7 = X0
| ~ ssList(X0)
| sk3 != app(app(sk6,sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4754,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f4744,f4751,f563,f3825,f3709]) ).
fof(f4784,plain,
( ~ sQ130_spl
| ~ sQ209_spl
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3116,f2410]) ).
fof(f4790,plain,
( ~ sQ130_spl
| ~ sQ209_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4784,f588,f3100,f2409]) ).
fof(f4954,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| cons(X0,X1) != cons(X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f468]) ).
fof(f4955,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ1_spl
| sk9 = X0
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sk9)
| sk3 != cons(X0,X1) ),
inference(paramodulation,[status(thm)],[f499,f4954]) ).
fof(f4957,plain,
! [X0,X1] :
( ~ sQ1_spl
| X0 = X0
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[f4954]) ).
fof(f4958,definition,
! [X0,X1] :
( sQ333_spl
<=> ( sk9 = X0
| ~ ssList(X1)
| sk3 != cons(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4961,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ6_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f4955,f4958,f487,f588,f467,f498]) ).
fof(f4963,definition,
! [X0] :
( sQ334_spl
<=> ( X0 = X0
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4966,plain,
( ~ sQ1_spl
| sQ70_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f4957,f4963,f1187,f467]) ).
fof(f4986,plain,
( ~ sQ315_spl
| app(app(sk6,cons(sk9,nil)),sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f4369,f675]) ).
fof(f4987,plain,
( ~ sQ315_spl
| ~ sQ9_spl
| app(app(sk6,sk3),sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f499,f4986]) ).
fof(f4989,plain,
( ~ sQ315_spl
| ~ sQ9_spl
| segmentP(sk3,sk3)
| ~ ssList(app(app(sk6,sk3),sk7))
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f4987,f531]) ).
fof(f5003,definition,
! [X0] :
( sQ335_spl
<=> ( segmentP(sk3,X0)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f5007,definition,
( sQ336_spl
<=> ssList(app(app(sk6,sk3),sk7)) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f5009,plain,
( sQ336_spl
| ~ ssList(app(app(sk6,sk3),sk7)) ),
inference(component_clause,[status(thm)],[f5007]) ).
fof(f5010,definition,
( sQ337_spl
<=> segmentP(sk3,sk3) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f5013,plain,
( ~ sQ315_spl
| ~ sQ9_spl
| sQ337_spl
| ~ sQ336_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f4989,f563,f637,f592,f5007,f5010,f498,f4368]) ).
fof(f5016,definition,
! [X0] :
( sQ338_spl
<=> ( segmentP(app(sk3,X0),sk7)
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f5031,plain,
( sQ336_spl
| ~ sQ315_spl
| ~ sQ9_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f4987,f5009]) ).
fof(f5032,plain,
( sQ336_spl
| ~ sQ315_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5031,f441]) ).
fof(f5033,plain,
( sQ336_spl
| ~ sQ315_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f5032]) ).
fof(f5049,plain,
! [X0] :
( nil = app(skaf47(nil,X0),X0)
| ~ ssList(app(skaf47(nil,X0),X0))
| ~ ssList(skaf48(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f407,f336]) ).
fof(f5050,plain,
! [X0] :
( nil = skaf48(X0,nil)
| ~ ssList(app(skaf47(nil,X0),X0))
| ~ ssList(skaf48(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f407,f338]) ).
fof(f5051,definition,
! [X0] :
( sQ339_spl
<=> ( nil = app(skaf47(nil,X0),X0)
| ~ ssList(app(skaf47(nil,X0),X0))
| ~ ssList(skaf48(X0,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f5054,plain,
( ~ sQ16_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f5049,f5051,f588]) ).
fof(f5055,definition,
! [X0] :
( sQ340_spl
<=> ( nil = skaf48(X0,nil)
| ~ ssList(app(skaf47(nil,X0),X0))
| ~ ssList(skaf48(X0,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f5058,plain,
( ~ sQ16_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f5050,f5055,f588]) ).
fof(f5066,definition,
( sQ342_spl
<=> ssList(cons(skaf50(nil),skaf53(nil))) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f5068,plain,
( sQ342_spl
| ~ ssList(cons(skaf50(nil),skaf53(nil))) ),
inference(component_clause,[status(thm)],[f5066]) ).
fof(f5076,definition,
( sQ345_spl
<=> nil = cons(skaf50(nil),skaf53(nil)) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f5077,plain,
( ~ sQ345_spl
| nil = cons(skaf50(nil),skaf53(nil)) ),
inference(component_clause,[status(thm)],[f5076]) ).
fof(f5085,definition,
( sQ347_spl
<=> ssList(cons(skaf55(nil),skaf58(nil))) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f5087,plain,
( sQ347_spl
| ~ ssList(cons(skaf55(nil),skaf58(nil))) ),
inference(component_clause,[status(thm)],[f5085]) ).
fof(f5095,definition,
( sQ350_spl
<=> nil = cons(skaf55(nil),skaf58(nil)) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f5096,plain,
( ~ sQ350_spl
| nil = cons(skaf55(nil),skaf58(nil)) ),
inference(component_clause,[status(thm)],[f5095]) ).
fof(f5103,plain,
( ~ sQ83_spl
| ~ sQ315_spl
| ssList(cons(sk9,sk7)) ),
inference(forward_demodulation,[status(thm)],[f4369,f1641]) ).
fof(f5123,definition,
( sQ354_spl
<=> ssList(cons(skaf60(nil),skaf63(nil))) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f5125,plain,
( sQ354_spl
| ~ ssList(cons(skaf60(nil),skaf63(nil))) ),
inference(component_clause,[status(thm)],[f5123]) ).
fof(f5133,definition,
( sQ357_spl
<=> nil = cons(skaf60(nil),skaf63(nil)) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f5134,plain,
( ~ sQ357_spl
| nil = cons(skaf60(nil),skaf63(nil)) ),
inference(component_clause,[status(thm)],[f5133]) ).
fof(f5138,plain,
( nil = cons(skaf65(nil),skaf68(nil))
| ~ ssList(app(skaf66(nil),cons(skaf64(nil),skaf67(nil))))
| ~ ssList(cons(skaf65(nil),skaf68(nil)))
| totalorderedP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f403,f338]) ).
fof(f5139,definition,
( sQ358_spl
<=> totalorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f5142,definition,
( sQ359_spl
<=> ssList(cons(skaf65(nil),skaf68(nil))) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f5144,plain,
( sQ359_spl
| ~ ssList(cons(skaf65(nil),skaf68(nil))) ),
inference(component_clause,[status(thm)],[f5142]) ).
fof(f5145,definition,
( sQ360_spl
<=> ssList(app(skaf66(nil),cons(skaf64(nil),skaf67(nil)))) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f5152,definition,
( sQ362_spl
<=> nil = cons(skaf65(nil),skaf68(nil)) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f5153,plain,
( ~ sQ362_spl
| nil = cons(skaf65(nil),skaf68(nil)) ),
inference(component_clause,[status(thm)],[f5152]) ).
fof(f5155,plain,
( sQ362_spl
| ~ sQ360_spl
| ~ sQ359_spl
| sQ358_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5138,f588,f5139,f5142,f5145,f5152]) ).
fof(f5157,plain,
( nil = cons(skaf70(nil),skaf73(nil))
| ~ ssList(app(skaf71(nil),cons(skaf69(nil),skaf72(nil))))
| ~ ssList(cons(skaf70(nil),skaf73(nil)))
| strictorderedP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f402,f338]) ).
fof(f5158,definition,
( sQ363_spl
<=> strictorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f5161,definition,
( sQ364_spl
<=> ssList(cons(skaf70(nil),skaf73(nil))) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f5163,plain,
( sQ364_spl
| ~ ssList(cons(skaf70(nil),skaf73(nil))) ),
inference(component_clause,[status(thm)],[f5161]) ).
fof(f5164,definition,
( sQ365_spl
<=> ssList(app(skaf71(nil),cons(skaf69(nil),skaf72(nil)))) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f5171,definition,
( sQ367_spl
<=> nil = cons(skaf70(nil),skaf73(nil)) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f5172,plain,
( ~ sQ367_spl
| nil = cons(skaf70(nil),skaf73(nil)) ),
inference(component_clause,[status(thm)],[f5171]) ).
fof(f5174,plain,
( sQ367_spl
| ~ sQ365_spl
| ~ sQ364_spl
| sQ363_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5157,f588,f5158,f5161,f5164,f5171]) ).
fof(f5249,plain,
! [X0] :
( ~ sQ320_spl
| frontsegP(X0,app(sk6,sk3))
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| ~ frontsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f387,f4684]) ).
fof(f5256,definition,
! [X0] :
( sQ370_spl
<=> ( frontsegP(X0,app(sk6,sk3))
| ~ ssList(X0)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f5259,plain,
( ~ sQ320_spl
| ~ sQ17_spl
| ~ sQ284_spl
| sQ370_spl ),
inference(split_clause,[status(thm)],[f5249,f5256,f3825,f592,f4683]) ).
fof(f5274,plain,
! [X0] :
( ~ sQ215_spl
| ~ sQ274_spl
| segmentP(X0,sk3)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(X0,sk3) ),
inference(resolution,[status(thm)],[f383,f3713]) ).
fof(f5277,plain,
! [X0] :
( ~ sQ154_spl
| segmentP(X0,sk7)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(sk7)
| ~ segmentP(X0,sk7) ),
inference(resolution,[status(thm)],[f383,f2647]) ).
fof(f5281,definition,
! [X0] :
( sQ371_spl
<=> ( segmentP(X0,sk3)
| ~ ssList(X0)
| ~ segmentP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f5284,plain,
( ~ sQ215_spl
| ~ sQ274_spl
| ~ sQ17_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f5274,f5281,f592,f3709,f3152]) ).
fof(f5287,plain,
( ~ sQ154_spl
| ~ sQ12_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f5277,f2642,f563,f2646]) ).
fof(f5342,definition,
! [X0] :
( sQ374_spl
<=> ( frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f5364,plain,
( sQ317_spl
| ~ sQ9_spl
| ~ ssList(app(sk6,sk3)) ),
inference(forward_demodulation,[status(thm)],[f499,f4498]) ).
fof(f5365,plain,
( sQ317_spl
| ~ sQ9_spl
| ~ sQ284_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5364,f3826]) ).
fof(f5366,plain,
( sQ317_spl
| ~ sQ9_spl
| ~ sQ284_spl ),
inference(contradiction_clause,[status(thm)],[f5365]) ).
fof(f5414,plain,
! [X0] :
( ~ sQ322_spl
| rearsegP(sk3,X0)
| ~ ssList(app(sk3,sk7))
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ rearsegP(app(sk3,sk7),X0) ),
inference(paramodulation,[status(thm)],[f4718,f359]) ).
fof(f5416,plain,
! [X0] :
( ~ sQ322_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7))
| ~ memberP(app(sk3,sk7),X0) ),
inference(paramodulation,[status(thm)],[f4718,f364]) ).
fof(f5417,plain,
! [X0] :
( ~ sQ322_spl
| cons(X0,sk3) = app(cons(X0,sk6),app(sk3,sk7))
| ~ ssList(app(sk3,sk7))
| ~ ssList(sk6)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f4718,f392]) ).
fof(f5418,plain,
! [X0] :
( ~ sQ322_spl
| memberP(sk6,X0)
| memberP(app(sk3,sk7),X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7))
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f4718,f394]) ).
fof(f5419,plain,
! [X0,X1] :
( ~ sQ322_spl
| segmentP(app(sk3,X1),X0)
| ~ ssList(app(sk3,sk7))
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(X1)
| ~ segmentP(app(sk3,sk7),X0) ),
inference(paramodulation,[status(thm)],[f4718,f413]) ).
fof(f5420,plain,
! [X0] :
( ~ sQ322_spl
| segmentP(app(sk3,X0),app(sk3,sk7))
| ~ ssList(app(app(sk6,app(sk3,sk7)),X0))
| ~ ssList(app(sk3,sk7))
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4718,f531]) ).
fof(f5423,plain,
! [X0] :
( ~ sQ322_spl
| X0 = app(sk3,sk7)
| ~ ssList(app(sk3,sk7))
| ~ ssList(sk6)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(paramodulation,[status(thm)],[f4718,f379]) ).
fof(f5425,plain,
! [X0] :
( ~ sQ322_spl
| app(sk3,X0) = app(sk6,app(app(sk3,sk7),X0))
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4718,f377]) ).
fof(f5426,plain,
! [X0] :
( ~ sQ322_spl
| X0 = sk6
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7))
| ~ ssList(X0)
| app(X0,app(sk3,sk7)) != sk3 ),
inference(paramodulation,[status(thm)],[f4718,f381]) ).
fof(f5428,plain,
( ~ sQ322_spl
| rearsegP(sk3,app(sk3,sk7))
| ~ ssList(app(sk3,sk7))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f4718,f2379]) ).
fof(f5431,definition,
! [X0] :
( sQ375_spl
<=> ( rearsegP(sk3,X0)
| ~ ssList(X0)
| ~ rearsegP(app(sk3,sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f5434,definition,
( sQ376_spl
<=> ssList(app(sk3,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f5436,plain,
( sQ376_spl
| ~ ssList(app(sk3,sk7)) ),
inference(component_clause,[status(thm)],[f5434]) ).
fof(f5437,plain,
( ~ sQ322_spl
| ~ sQ376_spl
| ~ sQ20_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f5414,f5431,f637,f5434,f4717]) ).
fof(f5438,definition,
! [X0] :
( sQ377_spl
<=> ( frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f5442,definition,
! [X0] :
( sQ378_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk3,sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f5445,plain,
( ~ sQ322_spl
| ~ sQ20_spl
| ~ sQ376_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f5416,f5442,f5434,f637,f4717]) ).
fof(f5446,definition,
! [X0] :
( sQ379_spl
<=> ( cons(X0,sk3) = app(cons(X0,sk6),app(sk3,sk7))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f5449,plain,
( ~ sQ322_spl
| ~ sQ376_spl
| ~ sQ20_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f5417,f5446,f637,f5434,f4717]) ).
fof(f5450,definition,
! [X0] :
( sQ380_spl
<=> ( memberP(sk6,X0)
| memberP(app(sk3,sk7),X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f5453,plain,
( ~ sQ322_spl
| ~ sQ20_spl
| ~ sQ376_spl
| sQ380_spl ),
inference(split_clause,[status(thm)],[f5418,f5450,f5434,f637,f4717]) ).
fof(f5454,definition,
! [X0,X1] :
( sQ381_spl
<=> ( segmentP(app(sk3,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(app(sk3,sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f5457,plain,
( ~ sQ322_spl
| ~ sQ376_spl
| ~ sQ20_spl
| sQ381_spl ),
inference(split_clause,[status(thm)],[f5419,f5454,f637,f5434,f4717]) ).
fof(f5458,definition,
! [X0] :
( sQ382_spl
<=> ( segmentP(app(sk3,X0),app(sk3,sk7))
| ~ ssList(app(app(sk6,app(sk3,sk7)),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f5461,plain,
( ~ sQ322_spl
| ~ sQ376_spl
| ~ sQ20_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f5420,f5458,f637,f5434,f4717]) ).
fof(f5463,definition,
( sQ383_spl
<=> nil = app(sk3,sk7) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f5464,plain,
( ~ sQ383_spl
| nil = app(sk3,sk7) ),
inference(component_clause,[status(thm)],[f5463]) ).
fof(f5467,definition,
! [X0] :
( sQ384_spl
<=> ( X0 = app(sk3,sk7)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f5470,plain,
( ~ sQ322_spl
| ~ sQ376_spl
| ~ sQ20_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f5423,f5467,f637,f5434,f4717]) ).
fof(f5472,definition,
! [X0] :
( sQ385_spl
<=> ( app(sk3,X0) = app(sk6,app(app(sk3,sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f5475,plain,
( ~ sQ322_spl
| ~ sQ20_spl
| ~ sQ376_spl
| sQ385_spl ),
inference(split_clause,[status(thm)],[f5425,f5472,f5434,f637,f4717]) ).
fof(f5476,definition,
! [X0] :
( sQ386_spl
<=> ( X0 = sk6
| ~ ssList(X0)
| app(X0,app(sk3,sk7)) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f5479,plain,
( ~ sQ322_spl
| ~ sQ20_spl
| ~ sQ376_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f5426,f5476,f5434,f637,f4717]) ).
fof(f5481,definition,
( sQ387_spl
<=> rearsegP(sk3,app(sk3,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f5482,plain,
( ~ sQ387_spl
| rearsegP(sk3,app(sk3,sk7)) ),
inference(component_clause,[status(thm)],[f5481]) ).
fof(f5484,plain,
( ~ sQ322_spl
| sQ387_spl
| ~ sQ376_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5428,f637,f5434,f5481,f4717]) ).
fof(f5485,definition,
( sQ388_spl
<=> frontsegP(sk3,sk6) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f5486,plain,
( ~ sQ388_spl
| frontsegP(sk3,sk6) ),
inference(component_clause,[status(thm)],[f5485]) ).
fof(f5490,plain,
( ~ sQ388_spl
| sk3 = sk6
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ frontsegP(sk6,sk3) ),
inference(resolution,[status(thm)],[f5486,f350]) ).
fof(f5491,plain,
! [X0] :
( ~ sQ388_spl
| frontsegP(X0,sk6)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ frontsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f5486,f387]) ).
fof(f5492,definition,
( sQ389_spl
<=> frontsegP(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f5495,plain,
( ~ sQ388_spl
| sQ291_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ389_spl ),
inference(split_clause,[status(thm)],[f5490,f5492,f637,f592,f3937,f5485]) ).
fof(f5496,definition,
! [X0] :
( sQ390_spl
<=> ( frontsegP(X0,sk6)
| ~ ssList(X0)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f5499,plain,
( ~ sQ388_spl
| ~ sQ17_spl
| ~ sQ20_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f5491,f5496,f637,f592,f5485]) ).
fof(f5500,plain,
( sQ376_spl
| ~ ssList(sk3)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f5436,f294]) ).
fof(f5501,plain,
( sQ376_spl
| ~ sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f5500,f563,f592,f5434]) ).
fof(f5502,plain,
( ~ sQ383_spl
| nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f5464,f336]) ).
fof(f5521,plain,
( ~ sQ383_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f5502,f563,f592,f494,f5463]) ).
fof(f5531,definition,
! [X0] :
( sQ393_spl
<=> ( memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f5532,plain,
! [X0] :
( ~ sQ393_spl
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(component_clause,[status(thm)],[f5531]) ).
fof(f5567,definition,
( sQ401_spl
<=> rearsegP(nil,sk7) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f5571,definition,
( sQ402_spl
<=> frontsegP(nil,sk3) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f5572,plain,
( ~ sQ402_spl
| frontsegP(nil,sk3) ),
inference(component_clause,[status(thm)],[f5571]) ).
fof(f5573,plain,
( sQ402_spl
| ~ frontsegP(nil,sk3) ),
inference(component_clause,[status(thm)],[f5571]) ).
fof(f5576,plain,
! [X0] :
( ~ sQ393_spl
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5532,f279]) ).
fof(f5618,plain,
( ~ sQ402_spl
| nil = sk3
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ frontsegP(sk3,nil) ),
inference(resolution,[status(thm)],[f5572,f350]) ).
fof(f5621,definition,
( sQ403_spl
<=> frontsegP(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f5622,plain,
( ~ sQ403_spl
| frontsegP(sk3,nil) ),
inference(component_clause,[status(thm)],[f5621]) ).
fof(f5623,plain,
( sQ403_spl
| ~ frontsegP(sk3,nil) ),
inference(component_clause,[status(thm)],[f5621]) ).
fof(f5624,plain,
( ~ sQ402_spl
| sQ8_spl
| ~ sQ16_spl
| ~ sQ17_spl
| ~ sQ403_spl ),
inference(split_clause,[status(thm)],[f5618,f5621,f592,f588,f494,f5571]) ).
fof(f5625,definition,
! [X0] :
( sQ404_spl
<=> ( frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f5626,plain,
! [X0] :
( ~ sQ404_spl
| frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f5625]) ).
fof(f5629,plain,
! [X0] :
( ~ sQ404_spl
| frontsegP(X0,sk3)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5626,f268]) ).
fof(f5638,plain,
( sQ403_spl
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f5623,f268]) ).
fof(f5639,plain,
( sQ403_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5638,f441]) ).
fof(f5640,plain,
sQ403_spl,
inference(contradiction_clause,[status(thm)],[f5639]) ).
fof(f5642,plain,
! [X0] :
( ~ sQ403_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ frontsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f5622,f387]) ).
fof(f5644,definition,
! [X0] :
( sQ406_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f5647,plain,
( ~ sQ403_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ406_spl ),
inference(split_clause,[status(thm)],[f5642,f5644,f588,f592,f5621]) ).
fof(f5650,plain,
( sQ402_spl
| ~ sQ404_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5629,f5573]) ).
fof(f5655,plain,
( sQ402_spl
| ~ sQ404_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5650,f588,f5625,f5571]) ).
fof(f5657,definition,
! [X0] :
( sQ407_spl
<=> ( X0 = sk3
| ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f5658,plain,
! [X0] :
( ~ sQ407_spl
| X0 = sk3
| ~ ssList(X0)
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5657]) ).
fof(f5666,plain,
! [X0] :
( ~ sQ407_spl
| X0 = sk3
| ~ frontsegP(sk3,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5658]) ).
fof(f5669,plain,
( ~ sQ82_spl
| ~ sQ286_spl
| nil = sk6 ),
inference(forward_demodulation,[status(thm)],[f1575,f3861]) ).
fof(f5714,plain,
! [X0] :
( ~ sQ286_spl
| app(sk6,X0) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f3845,f283]) ).
fof(f5738,plain,
( sQ25_spl
| ~ sQ286_spl
| sk6 != sk7 ),
inference(backward_demodulation,[status(thm)],[f3845,f683]) ).
fof(f5752,plain,
( sQ115_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2227,f223]) ).
fof(f5753,plain,
sQ115_spl,
inference(contradiction_clause,[status(thm)],[f5752]) ).
fof(f5765,plain,
( ~ sQ154_spl
| sk7 = sk7
| ~ ssList(sk7)
| ~ ssList(sk7)
| ~ segmentP(sk7,sk7) ),
inference(resolution,[status(thm)],[f348,f2647]) ).
fof(f5769,plain,
( sQ71_spl
| ~ sQ12_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f5765,f2646,f563,f1238]) ).
fof(f5824,plain,
! [X0] :
( ~ sQ150_spl
| rearsegP(X0,sk7)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(sk7)
| ~ rearsegP(X0,sk7) ),
inference(resolution,[status(thm)],[f2608,f385]) ).
fof(f5826,plain,
( ~ sQ150_spl
| ~ sQ12_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f5824,f2603,f563,f2607]) ).
fof(f5832,plain,
( ~ sQ393_spl
| ~ sQ3_spl
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f475,f5576]) ).
fof(f5833,plain,
( ~ sQ393_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5832,f449]) ).
fof(f5834,plain,
( ~ sQ393_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f5833]) ).
fof(f5839,plain,
( sQ150_spl
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f2609,f267]) ).
fof(f5840,plain,
( sQ150_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f5839,f563,f2607]) ).
fof(f5960,plain,
! [X0] :
( ~ sQ387_spl
| rearsegP(X0,app(sk3,sk7))
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(app(sk3,sk7))
| ~ rearsegP(X0,sk3) ),
inference(resolution,[status(thm)],[f5482,f385]) ).
fof(f5968,definition,
! [X0] :
( sQ411_spl
<=> ( rearsegP(X0,app(sk3,sk7))
| ~ ssList(X0)
| ~ rearsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f5971,plain,
( ~ sQ387_spl
| ~ sQ17_spl
| ~ sQ376_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f5960,f5968,f5434,f592,f5481]) ).
fof(f6032,plain,
( ~ sQ320_spl
| sk3 = app(sk6,sk3)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| ~ frontsegP(app(sk6,sk3),sk3) ),
inference(resolution,[status(thm)],[f4684,f350]) ).
fof(f6034,definition,
( sQ418_spl
<=> frontsegP(app(sk6,sk3),sk3) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f6036,plain,
( sQ418_spl
| ~ frontsegP(app(sk6,sk3),sk3) ),
inference(component_clause,[status(thm)],[f6034]) ).
fof(f6037,definition,
( sQ419_spl
<=> sk3 = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f6038,plain,
( ~ sQ419_spl
| sk3 = app(sk6,sk3) ),
inference(component_clause,[status(thm)],[f6037]) ).
fof(f6039,plain,
( sQ419_spl
| sk3 != app(sk6,sk3) ),
inference(component_clause,[status(thm)],[f6037]) ).
fof(f6040,plain,
( ~ sQ320_spl
| sQ419_spl
| ~ sQ17_spl
| ~ sQ284_spl
| ~ sQ418_spl ),
inference(split_clause,[status(thm)],[f6032,f6034,f3825,f592,f6037,f4683]) ).
fof(f6044,plain,
( sQ287_spl
| ~ sQ419_spl
| sk6 != sk3 ),
inference(backward_demodulation,[status(thm)],[f6038,f3891]) ).
fof(f6071,plain,
( sQ418_spl
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ frontsegP(sk6,sk3) ),
inference(resolution,[status(thm)],[f6036,f360]) ).
fof(f6072,plain,
( sQ418_spl
| ~ sQ20_spl
| ~ sQ17_spl
| ~ sQ389_spl ),
inference(split_clause,[status(thm)],[f6071,f5492,f592,f637,f6034]) ).
fof(f6073,plain,
( ~ sQ403_spl
| ~ sQ407_spl
| nil = sk3
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5666,f5622]) ).
fof(f6077,plain,
( ~ sQ403_spl
| ~ sQ407_spl
| sQ8_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6073,f588,f494,f5657,f5621]) ).
fof(f6150,plain,
( ~ sQ30_spl
| hd(sk3) = hd(sk3)
| nil = sk3
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f765,f342]) ).
fof(f6152,plain,
( hd(sk3) = hd(app(sk6,cons(sk5,nil)))
| nil = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f675,f342]) ).
fof(f6153,definition,
( sQ420_spl
<=> hd(sk3) = hd(sk3) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f6156,plain,
( ~ sQ30_spl
| sQ420_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6150,f588,f592,f494,f6153,f764]) ).
fof(f6161,definition,
( sQ422_spl
<=> hd(sk3) = hd(app(sk6,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f6164,plain,
( sQ422_spl
| sQ33_spl
| ~ sQ24_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f6152,f563,f678,f793,f6161]) ).
fof(f6168,plain,
( ~ sQ46_spl
| hd(sk3) = hd(sk6)
| nil = sk6
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7)) ),
inference(paramodulation,[status(thm)],[f968,f342]) ).
fof(f6169,plain,
! [X0] :
( ~ sQ46_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ memberP(sk6,X0) ),
inference(paramodulation,[status(thm)],[f968,f363]) ).
fof(f6170,plain,
! [X0] :
( ~ sQ46_spl
| rearsegP(sk3,X0)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ rearsegP(app(cons(sk5,nil),sk7),X0) ),
inference(paramodulation,[status(thm)],[f968,f359]) ).
fof(f6172,plain,
! [X0] :
( ~ sQ46_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ memberP(app(cons(sk5,nil),sk7),X0) ),
inference(paramodulation,[status(thm)],[f968,f364]) ).
fof(f6173,plain,
! [X0] :
( ~ sQ46_spl
| cons(X0,sk3) = app(cons(X0,sk6),app(cons(sk5,nil),sk7))
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f968,f392]) ).
fof(f6174,plain,
! [X0] :
( ~ sQ46_spl
| memberP(sk6,X0)
| memberP(app(cons(sk5,nil),sk7),X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f968,f394]) ).
fof(f6175,plain,
! [X0,X1] :
( ~ sQ46_spl
| segmentP(app(sk3,X1),X0)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(X1)
| ~ segmentP(app(cons(sk5,nil),sk7),X0) ),
inference(paramodulation,[status(thm)],[f968,f413]) ).
fof(f6176,plain,
! [X0] :
( ~ sQ46_spl
| segmentP(app(sk3,X0),app(cons(sk5,nil),sk7))
| ~ ssList(app(app(sk6,app(cons(sk5,nil),sk7)),X0))
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f968,f531]) ).
fof(f6177,plain,
! [X0] :
( ~ sQ46_spl
| X0 = app(cons(sk5,nil),sk7)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(paramodulation,[status(thm)],[f968,f379]) ).
fof(f6179,plain,
! [X0] :
( ~ sQ46_spl
| app(sk3,X0) = app(sk6,app(app(cons(sk5,nil),sk7),X0))
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f968,f377]) ).
fof(f6180,plain,
! [X0] :
( ~ sQ46_spl
| X0 = sk6
| ~ ssList(sk6)
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(X0)
| app(X0,app(cons(sk5,nil),sk7)) != sk3 ),
inference(paramodulation,[status(thm)],[f968,f381]) ).
fof(f6182,plain,
( ~ sQ46_spl
| rearsegP(sk3,app(cons(sk5,nil),sk7))
| ~ ssList(app(cons(sk5,nil),sk7))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f968,f2379]) ).
fof(f6185,definition,
( sQ423_spl
<=> ssList(app(cons(sk5,nil),sk7)) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f6187,plain,
( sQ423_spl
| ~ ssList(app(cons(sk5,nil),sk7)) ),
inference(component_clause,[status(thm)],[f6185]) ).
fof(f6188,definition,
( sQ424_spl
<=> hd(sk3) = hd(sk6) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f6189,plain,
( ~ sQ424_spl
| hd(sk3) = hd(sk6) ),
inference(component_clause,[status(thm)],[f6188]) ).
fof(f6191,plain,
( ~ sQ46_spl
| sQ424_spl
| sQ286_spl
| ~ sQ20_spl
| ~ sQ423_spl ),
inference(split_clause,[status(thm)],[f6168,f6185,f637,f3844,f6188,f967]) ).
fof(f6192,definition,
! [X0] :
( sQ425_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk6,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f6195,plain,
( ~ sQ46_spl
| ~ sQ20_spl
| ~ sQ423_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f6169,f6192,f6185,f637,f967]) ).
fof(f6196,definition,
! [X0] :
( sQ426_spl
<=> ( rearsegP(sk3,X0)
| ~ ssList(X0)
| ~ rearsegP(app(cons(sk5,nil),sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f6199,plain,
( ~ sQ46_spl
| ~ sQ423_spl
| ~ sQ20_spl
| sQ426_spl ),
inference(split_clause,[status(thm)],[f6170,f6196,f637,f6185,f967]) ).
fof(f6201,definition,
! [X0] :
( sQ427_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(cons(sk5,nil),sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f6204,plain,
( ~ sQ46_spl
| ~ sQ20_spl
| ~ sQ423_spl
| sQ427_spl ),
inference(split_clause,[status(thm)],[f6172,f6201,f6185,f637,f967]) ).
fof(f6205,definition,
! [X0] :
( sQ428_spl
<=> ( cons(X0,sk3) = app(cons(X0,sk6),app(cons(sk5,nil),sk7))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f6208,plain,
( ~ sQ46_spl
| ~ sQ423_spl
| ~ sQ20_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f6173,f6205,f637,f6185,f967]) ).
fof(f6209,definition,
! [X0] :
( sQ429_spl
<=> ( memberP(sk6,X0)
| memberP(app(cons(sk5,nil),sk7),X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f6212,plain,
( ~ sQ46_spl
| ~ sQ20_spl
| ~ sQ423_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f6174,f6209,f6185,f637,f967]) ).
fof(f6213,definition,
! [X0,X1] :
( sQ430_spl
<=> ( segmentP(app(sk3,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(app(cons(sk5,nil),sk7),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f6216,plain,
( ~ sQ46_spl
| ~ sQ423_spl
| ~ sQ20_spl
| sQ430_spl ),
inference(split_clause,[status(thm)],[f6175,f6213,f637,f6185,f967]) ).
fof(f6217,definition,
! [X0] :
( sQ431_spl
<=> ( segmentP(app(sk3,X0),app(cons(sk5,nil),sk7))
| ~ ssList(app(app(sk6,app(cons(sk5,nil),sk7)),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f6220,plain,
( ~ sQ46_spl
| ~ sQ423_spl
| ~ sQ20_spl
| sQ431_spl ),
inference(split_clause,[status(thm)],[f6176,f6217,f637,f6185,f967]) ).
fof(f6221,definition,
! [X0] :
( sQ432_spl
<=> ( X0 = app(cons(sk5,nil),sk7)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f6224,plain,
( ~ sQ46_spl
| ~ sQ423_spl
| ~ sQ20_spl
| sQ432_spl ),
inference(split_clause,[status(thm)],[f6177,f6221,f637,f6185,f967]) ).
fof(f6226,definition,
! [X0] :
( sQ433_spl
<=> ( app(sk3,X0) = app(sk6,app(app(cons(sk5,nil),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f6229,plain,
( ~ sQ46_spl
| ~ sQ20_spl
| ~ sQ423_spl
| sQ433_spl ),
inference(split_clause,[status(thm)],[f6179,f6226,f6185,f637,f967]) ).
fof(f6230,definition,
! [X0] :
( sQ434_spl
<=> ( X0 = sk6
| ~ ssList(X0)
| app(X0,app(cons(sk5,nil),sk7)) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f6233,plain,
( ~ sQ46_spl
| ~ sQ20_spl
| ~ sQ423_spl
| sQ434_spl ),
inference(split_clause,[status(thm)],[f6180,f6230,f6185,f637,f967]) ).
fof(f6235,definition,
( sQ435_spl
<=> rearsegP(sk3,app(cons(sk5,nil),sk7)) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f6238,plain,
( ~ sQ46_spl
| sQ435_spl
| ~ sQ423_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f6182,f637,f6185,f6235,f967]) ).
fof(f6242,plain,
( ~ sQ424_spl
| ~ sQ81_spl
| sk9 = hd(sk6) ),
inference(forward_demodulation,[status(thm)],[f1571,f6189]) ).
fof(f6255,plain,
( sQ342_spl
| ~ ssList(skaf53(nil))
| ~ ssItem(skaf50(nil)) ),
inference(resolution,[status(thm)],[f5068,f295]) ).
fof(f6256,definition,
( sQ436_spl
<=> ssItem(skaf50(nil)) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f6258,plain,
( sQ436_spl
| ~ ssItem(skaf50(nil)) ),
inference(component_clause,[status(thm)],[f6256]) ).
fof(f6259,definition,
( sQ437_spl
<=> ssList(skaf53(nil)) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f6261,plain,
( sQ437_spl
| ~ ssList(skaf53(nil)) ),
inference(component_clause,[status(thm)],[f6259]) ).
fof(f6262,plain,
( sQ342_spl
| ~ sQ437_spl
| ~ sQ436_spl ),
inference(split_clause,[status(thm)],[f6255,f6256,f6259,f5066]) ).
fof(f6263,plain,
( sQ437_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6261,f250]) ).
fof(f6264,plain,
sQ437_spl,
inference(contradiction_clause,[status(thm)],[f6263]) ).
fof(f6265,plain,
( sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6258,f253]) ).
fof(f6266,plain,
sQ436_spl,
inference(contradiction_clause,[status(thm)],[f6265]) ).
fof(f6275,plain,
( ~ sQ345_spl
| memberP(nil,skaf50(nil))
| ~ ssItem(skaf50(nil))
| ~ ssList(skaf53(nil)) ),
inference(paramodulation,[status(thm)],[f5077,f526]) ).
fof(f6299,definition,
( sQ442_spl
<=> memberP(nil,skaf50(nil)) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f6300,plain,
( ~ sQ442_spl
| memberP(nil,skaf50(nil)) ),
inference(component_clause,[status(thm)],[f6299]) ).
fof(f6302,plain,
( ~ sQ345_spl
| sQ442_spl
| ~ sQ436_spl
| ~ sQ437_spl ),
inference(split_clause,[status(thm)],[f6275,f6259,f6256,f6299,f5076]) ).
fof(f6316,plain,
( ~ sQ442_spl
| ~ ssItem(skaf50(nil)) ),
inference(resolution,[status(thm)],[f6300,f279]) ).
fof(f6317,plain,
( ~ sQ442_spl
| ~ sQ436_spl ),
inference(split_clause,[status(thm)],[f6316,f6256,f6299]) ).
fof(f6318,plain,
( sQ347_spl
| ~ ssList(skaf58(nil))
| ~ ssItem(skaf55(nil)) ),
inference(resolution,[status(thm)],[f5087,f295]) ).
fof(f6319,definition,
( sQ446_spl
<=> ssItem(skaf55(nil)) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f6321,plain,
( sQ446_spl
| ~ ssItem(skaf55(nil)) ),
inference(component_clause,[status(thm)],[f6319]) ).
fof(f6322,definition,
( sQ447_spl
<=> ssList(skaf58(nil)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f6324,plain,
( sQ447_spl
| ~ ssList(skaf58(nil)) ),
inference(component_clause,[status(thm)],[f6322]) ).
fof(f6325,plain,
( sQ347_spl
| ~ sQ447_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f6318,f6319,f6322,f5085]) ).
fof(f6326,plain,
( sQ447_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6324,f245]) ).
fof(f6327,plain,
sQ447_spl,
inference(contradiction_clause,[status(thm)],[f6326]) ).
fof(f6328,plain,
( sQ446_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6321,f248]) ).
fof(f6329,plain,
sQ446_spl,
inference(contradiction_clause,[status(thm)],[f6328]) ).
fof(f6338,plain,
( ~ sQ350_spl
| ~ ssList(skaf58(nil))
| ~ ssItem(skaf55(nil))
| nil != nil ),
inference(paramodulation,[status(thm)],[f5096,f308]) ).
fof(f6355,plain,
( ~ sQ350_spl
| ~ sQ447_spl
| ~ sQ446_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6338,f696,f6319,f6322,f5095]) ).
fof(f6389,plain,
( sQ354_spl
| ~ ssList(skaf63(nil))
| ~ ssItem(skaf60(nil)) ),
inference(resolution,[status(thm)],[f5125,f295]) ).
fof(f6390,definition,
( sQ456_spl
<=> ssItem(skaf60(nil)) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f6392,plain,
( sQ456_spl
| ~ ssItem(skaf60(nil)) ),
inference(component_clause,[status(thm)],[f6390]) ).
fof(f6393,definition,
( sQ457_spl
<=> ssList(skaf63(nil)) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f6395,plain,
( sQ457_spl
| ~ ssList(skaf63(nil)) ),
inference(component_clause,[status(thm)],[f6393]) ).
fof(f6396,plain,
( sQ354_spl
| ~ sQ457_spl
| ~ sQ456_spl ),
inference(split_clause,[status(thm)],[f6389,f6390,f6393,f5123]) ).
fof(f6397,plain,
( sQ457_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6395,f240]) ).
fof(f6398,plain,
sQ457_spl,
inference(contradiction_clause,[status(thm)],[f6397]) ).
fof(f6399,plain,
( sQ456_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6392,f243]) ).
fof(f6400,plain,
sQ456_spl,
inference(contradiction_clause,[status(thm)],[f6399]) ).
fof(f6403,plain,
( ~ sQ357_spl
| ~ ssList(skaf63(nil))
| ~ ssItem(skaf60(nil))
| nil != nil ),
inference(paramodulation,[status(thm)],[f5134,f308]) ).
fof(f6420,plain,
( ~ sQ357_spl
| ~ sQ457_spl
| ~ sQ456_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6403,f696,f6390,f6393,f5133]) ).
fof(f6454,plain,
( sQ359_spl
| ~ ssList(skaf68(nil))
| ~ ssItem(skaf65(nil)) ),
inference(resolution,[status(thm)],[f5144,f295]) ).
fof(f6455,definition,
( sQ466_spl
<=> ssItem(skaf65(nil)) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f6457,plain,
( sQ466_spl
| ~ ssItem(skaf65(nil)) ),
inference(component_clause,[status(thm)],[f6455]) ).
fof(f6458,definition,
( sQ467_spl
<=> ssList(skaf68(nil)) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f6460,plain,
( sQ467_spl
| ~ ssList(skaf68(nil)) ),
inference(component_clause,[status(thm)],[f6458]) ).
fof(f6461,plain,
( sQ359_spl
| ~ sQ467_spl
| ~ sQ466_spl ),
inference(split_clause,[status(thm)],[f6454,f6455,f6458,f5142]) ).
fof(f6462,plain,
( sQ467_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6460,f235]) ).
fof(f6463,plain,
sQ467_spl,
inference(contradiction_clause,[status(thm)],[f6462]) ).
fof(f6464,plain,
( sQ466_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6457,f238]) ).
fof(f6465,plain,
sQ466_spl,
inference(contradiction_clause,[status(thm)],[f6464]) ).
fof(f6468,plain,
( ~ sQ362_spl
| ~ ssList(skaf68(nil))
| ~ ssItem(skaf65(nil))
| nil != nil ),
inference(paramodulation,[status(thm)],[f5153,f308]) ).
fof(f6485,plain,
( ~ sQ362_spl
| ~ sQ467_spl
| ~ sQ466_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6468,f696,f6455,f6458,f5152]) ).
fof(f6519,plain,
( sQ364_spl
| ~ ssList(skaf73(nil))
| ~ ssItem(skaf70(nil)) ),
inference(resolution,[status(thm)],[f5163,f295]) ).
fof(f6520,definition,
( sQ476_spl
<=> ssItem(skaf70(nil)) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f6522,plain,
( sQ476_spl
| ~ ssItem(skaf70(nil)) ),
inference(component_clause,[status(thm)],[f6520]) ).
fof(f6523,definition,
( sQ477_spl
<=> ssList(skaf73(nil)) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f6525,plain,
( sQ477_spl
| ~ ssList(skaf73(nil)) ),
inference(component_clause,[status(thm)],[f6523]) ).
fof(f6526,plain,
( sQ364_spl
| ~ sQ477_spl
| ~ sQ476_spl ),
inference(split_clause,[status(thm)],[f6519,f6520,f6523,f5161]) ).
fof(f6527,plain,
( sQ477_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6525,f230]) ).
fof(f6528,plain,
sQ477_spl,
inference(contradiction_clause,[status(thm)],[f6527]) ).
fof(f6529,plain,
( sQ476_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6522,f233]) ).
fof(f6530,plain,
sQ476_spl,
inference(contradiction_clause,[status(thm)],[f6529]) ).
fof(f6533,plain,
( ~ sQ367_spl
| ~ ssList(skaf73(nil))
| ~ ssItem(skaf70(nil))
| nil != nil ),
inference(paramodulation,[status(thm)],[f5172,f308]) ).
fof(f6550,plain,
( ~ sQ367_spl
| ~ sQ477_spl
| ~ sQ476_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6533,f696,f6520,f6523,f5171]) ).
fof(f6592,definition,
! [X0] :
( sQ486_spl
<=> ( ~ leq(X0,sk9)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f6593,plain,
! [X0] :
( ~ sQ486_spl
| ~ leq(X0,sk9)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f6592]) ).
fof(f6614,plain,
( ~ sQ486_spl
| ~ ssItem(sk9)
| ~ ssItem(sk9) ),
inference(resolution,[status(thm)],[f6593,f270]) ).
fof(f6615,plain,
( ~ sQ486_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f6614,f487,f6592]) ).
fof(f6616,plain,
( sQ41_spl
| ~ ssList(sk6)
| ~ ssList(cons(sk5,sk7)) ),
inference(resolution,[status(thm)],[f917,f294]) ).
fof(f6617,plain,
( sQ41_spl
| ~ sQ20_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f6616,f1640,f637,f915]) ).
fof(f6638,plain,
( ~ sQ33_spl
| rearsegP(nil,cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f794,f2379]) ).
fof(f6641,definition,
( sQ488_spl
<=> memberP(nil,sk5) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f6642,plain,
( ~ sQ488_spl
| memberP(nil,sk5) ),
inference(component_clause,[status(thm)],[f6641]) ).
fof(f6696,definition,
( sQ501_spl
<=> rearsegP(nil,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f6697,plain,
( ~ sQ501_spl
| rearsegP(nil,cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f6696]) ).
fof(f6699,plain,
( ~ sQ33_spl
| sQ501_spl
| ~ sQ26_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f6638,f637,f687,f6696,f793]) ).
fof(f6776,plain,
( ~ sQ488_spl
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f6642,f279]) ).
fof(f6777,plain,
( ~ sQ488_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6776,f646,f6641]) ).
fof(f6782,definition,
( sQ511_spl
<=> frontsegP(sk6,nil) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f6783,plain,
( ~ sQ511_spl
| frontsegP(sk6,nil) ),
inference(component_clause,[status(thm)],[f6782]) ).
fof(f6784,plain,
( sQ511_spl
| ~ frontsegP(sk6,nil) ),
inference(component_clause,[status(thm)],[f6782]) ).
fof(f6880,plain,
( sQ511_spl
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f6784,f268]) ).
fof(f6881,plain,
( sQ511_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f6880,f637,f6782]) ).
fof(f6883,plain,
! [X0] :
( ~ sQ511_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ frontsegP(X0,sk6) ),
inference(resolution,[status(thm)],[f6783,f387]) ).
fof(f6885,definition,
! [X0] :
( sQ515_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk6) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f6888,plain,
( ~ sQ511_spl
| ~ sQ20_spl
| ~ sQ16_spl
| sQ515_spl ),
inference(split_clause,[status(thm)],[f6883,f6885,f588,f637,f6782]) ).
fof(f6900,definition,
( sQ517_spl
<=> ssItem(hd(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f6902,plain,
( sQ517_spl
| ~ ssItem(hd(sk6)) ),
inference(component_clause,[status(thm)],[f6900]) ).
fof(f6920,plain,
( ~ ssList(nil)
| ~ ssItem(skaf44(nil))
| ~ ssList(nil)
| ~ singletonP(nil) ),
inference(resolution,[status(thm)],[f312,f308]) ).
fof(f6921,plain,
! [X0,X1] :
( skaf44(cons(X0,X1)) = X0
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(skaf44(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f312,f410]) ).
fof(f6922,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(skaf44(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f312,f412]) ).
fof(f6926,definition,
( sQ520_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f6929,definition,
( sQ521_spl
<=> ssItem(skaf44(nil)) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f6931,plain,
( sQ521_spl
| ~ ssItem(skaf44(nil)) ),
inference(component_clause,[status(thm)],[f6929]) ).
fof(f6932,plain,
( ~ sQ521_spl
| ~ sQ16_spl
| ~ sQ520_spl ),
inference(split_clause,[status(thm)],[f6920,f6926,f588,f6929]) ).
fof(f6933,definition,
! [X0,X1] :
( sQ522_spl
<=> ( skaf44(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(skaf44(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f6936,plain,
( ~ sQ16_spl
| sQ522_spl ),
inference(split_clause,[status(thm)],[f6921,f6933,f588]) ).
fof(f6937,definition,
! [X0,X1] :
( sQ523_spl
<=> ( X1 = nil
| ~ ssList(X1)
| ~ ssItem(skaf44(cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f6940,plain,
( ~ sQ16_spl
| sQ523_spl ),
inference(split_clause,[status(thm)],[f6922,f6937,f588]) ).
fof(f6946,plain,
( sQ521_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6931,f255]) ).
fof(f6947,plain,
sQ521_spl,
inference(contradiction_clause,[status(thm)],[f6946]) ).
fof(f6957,plain,
! [X0] :
( ~ sQ274_spl
| app(sk3,X0) = cons(sk5,X0)
| ~ ssList(X0)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f3710,f339]) ).
fof(f6962,plain,
( ~ sQ274_spl
| equalelemsP(sk3)
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f3710,f272]) ).
fof(f6971,plain,
! [X0,X1] :
( ~ sQ274_spl
| X0 = sk5
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sk5)
| cons(X0,X1) != sk3 ),
inference(paramodulation,[status(thm)],[f3710,f410]) ).
fof(f6973,plain,
! [X0,X1] :
( ~ sQ274_spl
| nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sk5)
| cons(X0,X1) != sk3 ),
inference(paramodulation,[status(thm)],[f3710,f412]) ).
fof(f6975,plain,
! [X0] :
( ~ sQ274_spl
| memberP(app(X0,sk3),sk5)
| ~ ssList(app(X0,cons(sk5,nil)))
| ~ ssItem(sk5)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f3710,f532]) ).
fof(f6980,plain,
! [X0] :
( ~ sQ274_spl
| X0 = sk5
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f3710,f400]) ).
fof(f6981,definition,
! [X0] :
( sQ524_spl
<=> ( app(sk3,X0) = cons(sk5,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f6984,plain,
( ~ sQ274_spl
| sQ524_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6957,f646,f6981,f3709]) ).
fof(f6989,plain,
( ~ sQ274_spl
| sQ125_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6962,f646,f2367,f3709]) ).
fof(f6998,definition,
! [X0,X1] :
( sQ525_spl
<=> ( X0 = sk5
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f7001,plain,
( ~ sQ274_spl
| ~ sQ16_spl
| ~ sQ21_spl
| sQ525_spl ),
inference(split_clause,[status(thm)],[f6971,f6998,f646,f588,f3709]) ).
fof(f7003,plain,
( ~ sQ274_spl
| ~ sQ16_spl
| ~ sQ21_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f6973,f1737,f646,f588,f3709]) ).
fof(f7005,definition,
! [X0] :
( sQ526_spl
<=> ( memberP(app(X0,sk3),sk5)
| ~ ssList(app(X0,cons(sk5,nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f7008,plain,
( ~ sQ274_spl
| ~ sQ21_spl
| sQ526_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6975,f588,f7005,f646,f3709]) ).
fof(f7013,definition,
! [X0] :
( sQ527_spl
<=> ( X0 = sk5
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f7016,plain,
( ~ sQ274_spl
| ~ sQ21_spl
| ~ sQ16_spl
| sQ527_spl ),
inference(split_clause,[status(thm)],[f6980,f7013,f588,f646,f3709]) ).
fof(f7090,plain,
( ~ sQ50_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,nil)
| skaf46(nil,nil) = nil
| ~ ssList(skaf46(nil,nil)) ),
inference(resolution,[status(thm)],[f995,f352]) ).
fof(f7096,definition,
( sQ530_spl
<=> ssList(skaf46(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f7098,plain,
( sQ530_spl
| ~ ssList(skaf46(nil,nil)) ),
inference(component_clause,[status(thm)],[f7096]) ).
fof(f7099,definition,
( sQ531_spl
<=> skaf46(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f7102,plain,
( ~ sQ50_spl
| ~ sQ16_spl
| ~ sQ127_spl
| sQ531_spl
| ~ sQ530_spl ),
inference(split_clause,[status(thm)],[f7090,f7096,f7099,f2390,f588,f994]) ).
fof(f7106,plain,
( sQ530_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7098,f258]) ).
fof(f7107,plain,
sQ530_spl,
inference(contradiction_clause,[status(thm)],[f7106]) ).
fof(f7108,plain,
! [X0] :
( ~ sQ51_spl
| X0 = app(nil,X0)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1000,f379]) ).
fof(f7110,plain,
( ~ sQ23_spl
| ~ sQ51_spl
| app(nil,nil) = app(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f1000]) ).
fof(f7111,definition,
! [X0] :
( sQ532_spl
<=> ( X0 = app(nil,X0)
| ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f7114,plain,
( ~ sQ51_spl
| ~ sQ16_spl
| sQ532_spl ),
inference(split_clause,[status(thm)],[f7108,f7111,f588,f999]) ).
fof(f7116,definition,
( sQ533_spl
<=> app(nil,nil) = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f7119,plain,
( ~ sQ23_spl
| ~ sQ51_spl
| sQ533_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f7110,f588,f7116,f999,f667]) ).
fof(f7126,plain,
( ~ sQ501_spl
| nil = cons(sk5,nil)
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil))
| ~ rearsegP(cons(sk5,nil),nil) ),
inference(resolution,[status(thm)],[f6697,f349]) ).
fof(f7128,definition,
( sQ534_spl
<=> cons(sk5,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f7129,plain,
( ~ sQ534_spl
| cons(sk5,nil) = nil ),
inference(component_clause,[status(thm)],[f7128]) ).
fof(f7132,definition,
( sQ535_spl
<=> rearsegP(cons(sk5,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f7133,plain,
( ~ sQ535_spl
| rearsegP(cons(sk5,nil),nil) ),
inference(component_clause,[status(thm)],[f7132]) ).
fof(f7134,plain,
( sQ535_spl
| ~ rearsegP(cons(sk5,nil),nil) ),
inference(component_clause,[status(thm)],[f7132]) ).
fof(f7135,plain,
( ~ sQ501_spl
| sQ534_spl
| ~ sQ16_spl
| ~ sQ26_spl
| ~ sQ535_spl ),
inference(split_clause,[status(thm)],[f7126,f7132,f687,f588,f7128,f6696]) ).
fof(f7142,plain,
( ~ sQ90_spl
| ~ sQ534_spl
| singletonP(nil) ),
inference(backward_demodulation,[status(thm)],[f7129,f1712]) ).
fof(f7172,plain,
( ~ sQ90_spl
| ~ sQ534_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7142,f219]) ).
fof(f7173,plain,
( ~ sQ90_spl
| ~ sQ534_spl ),
inference(contradiction_clause,[status(thm)],[f7172]) ).
fof(f7283,definition,
! [X0] :
( sQ538_spl
<=> ( totalorderedP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ leq(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f7287,plain,
( ~ sQ2_spl
| ~ sQ286_spl
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f3850,f472]) ).
fof(f7288,plain,
( ~ sQ2_spl
| ~ sQ286_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7287,f449]) ).
fof(f7289,plain,
( ~ sQ2_spl
| ~ sQ286_spl ),
inference(contradiction_clause,[status(thm)],[f7288]) ).
fof(f7612,plain,
( sQ535_spl
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f7134,f266]) ).
fof(f7613,plain,
( sQ535_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f7612,f687,f7132]) ).
fof(f8000,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| nil = skaf42(nil,X0)
| ~ ssList(skaf42(nil,X0))
| ~ ssList(cons(X0,skaf43(X0,nil))) ),
inference(resolution,[status(thm)],[f336,f408]) ).
fof(f8016,definition,
! [X0] :
( sQ547_spl
<=> ( ~ ssItem(X0)
| ~ memberP(nil,X0)
| nil = skaf42(nil,X0)
| ~ ssList(skaf42(nil,X0))
| ~ ssList(cons(X0,skaf43(X0,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f8019,plain,
( ~ sQ16_spl
| sQ547_spl ),
inference(split_clause,[status(thm)],[f8000,f8016,f588]) ).
fof(f8035,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| nil = cons(X0,skaf43(X0,nil))
| ~ ssList(skaf42(nil,X0))
| ~ ssList(cons(X0,skaf43(X0,nil))) ),
inference(resolution,[status(thm)],[f338,f408]) ).
fof(f8051,definition,
! [X0] :
( sQ548_spl
<=> ( ~ ssItem(X0)
| ~ memberP(nil,X0)
| nil = cons(X0,skaf43(X0,nil))
| ~ ssList(skaf42(nil,X0))
| ~ ssList(cons(X0,skaf43(X0,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f8054,plain,
( ~ sQ16_spl
| sQ548_spl ),
inference(split_clause,[status(thm)],[f8035,f8051,f588]) ).
fof(f8076,plain,
! [X0] :
( ~ sQ535_spl
| rearsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ~ rearsegP(X0,cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f7133,f385]) ).
fof(f8078,definition,
! [X0] :
( sQ549_spl
<=> ( rearsegP(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(X0,cons(sk5,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f8081,plain,
( ~ sQ535_spl
| ~ sQ26_spl
| ~ sQ16_spl
| sQ549_spl ),
inference(split_clause,[status(thm)],[f8076,f8078,f588,f687,f7132]) ).
fof(f8088,plain,
! [X0] :
( ~ sQ65_spl
| memberP(sk6,X0)
| memberP(cons(sk5,nil),X0)
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(resolution,[status(thm)],[f1106,f394]) ).
fof(f8089,definition,
! [X0] :
( sQ550_spl
<=> ( memberP(sk6,X0)
| memberP(cons(sk5,nil),X0)
| ~ ssItem(X0)
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f8092,plain,
( ~ sQ65_spl
| ~ sQ20_spl
| ~ sQ26_spl
| sQ550_spl ),
inference(split_clause,[status(thm)],[f8088,f8089,f687,f637,f1105]) ).
fof(f8127,definition,
( sQ554_spl
<=> ssItem(skaf44(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f8129,plain,
( sQ554_spl
| ~ ssItem(skaf44(sk6)) ),
inference(component_clause,[status(thm)],[f8127]) ).
fof(f8134,plain,
( sQ554_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8129,f255]) ).
fof(f8135,plain,
sQ554_spl,
inference(contradiction_clause,[status(thm)],[f8134]) ).
fof(f8163,definition,
( sQ558_spl
<=> ssList(skaf80(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f8165,plain,
( sQ558_spl
| ~ ssList(skaf80(sk6)) ),
inference(component_clause,[status(thm)],[f8163]) ).
fof(f8256,plain,
( sQ558_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8165,f223]) ).
fof(f8257,plain,
sQ558_spl,
inference(contradiction_clause,[status(thm)],[f8256]) ).
fof(f8699,plain,
! [X0] :
( ~ sQ81_spl
| nil = sk3
| totalorderedP(cons(X0,sk3))
| ~ ssItem(X0)
| ~ ssList(sk3)
| ~ totalorderedP(sk3)
| ~ leq(X0,sk9) ),
inference(paramodulation,[status(thm)],[f1571,f396]) ).
fof(f8701,plain,
( ~ sQ81_spl
| sQ8_spl
| ~ sQ17_spl
| ~ sQ44_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f8699,f7283,f951,f592,f494,f1570]) ).
fof(f8912,plain,
( sQ423_spl
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f6187,f294]) ).
fof(f8913,plain,
( sQ423_spl
| ~ sQ26_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f8912,f563,f687,f6185]) ).
fof(f8918,plain,
( ~ sQ89_spl
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ ssList(nil)
| memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f1685,f532]) ).
fof(f8919,plain,
! [X0] :
( ~ sQ89_spl
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1685,f363]) ).
fof(f8920,plain,
! [X0] :
( ~ sQ89_spl
| ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ memberP(cons(sk5,nil),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1685,f364]) ).
fof(f8921,plain,
( ~ sQ89_spl
| ~ sQ24_spl
| ~ sQ20_spl
| ~ sQ16_spl
| sQ314_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8918,f646,f4363,f588,f637,f678,f1684]) ).
fof(f8922,definition,
! [X0] :
( sQ611_spl
<=> ( ~ ssItem(X0)
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f8925,plain,
( ~ sQ89_spl
| ~ sQ20_spl
| ~ sQ26_spl
| sQ611_spl ),
inference(split_clause,[status(thm)],[f8919,f8922,f687,f637,f1684]) ).
fof(f8926,definition,
! [X0] :
( sQ612_spl
<=> ( ~ ssItem(X0)
| ~ memberP(cons(sk5,nil),X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f8929,plain,
( ~ sQ89_spl
| ~ sQ20_spl
| ~ sQ26_spl
| sQ612_spl ),
inference(split_clause,[status(thm)],[f8920,f8926,f687,f637,f1684]) ).
fof(f8970,plain,
! [X0] :
( ~ sQ274_spl
| segmentP(sk3,X0)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f3716,f413]) ).
fof(f8976,plain,
! [X0] :
( ~ sQ274_spl
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ memberP(app(sk6,sk3),X0) ),
inference(paramodulation,[status(thm)],[f3716,f363]) ).
fof(f8978,plain,
! [X0] :
( ~ sQ274_spl
| frontsegP(sk3,X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ frontsegP(app(sk6,sk3),X0) ),
inference(paramodulation,[status(thm)],[f3716,f360]) ).
fof(f8983,plain,
! [X0] :
( ~ sQ274_spl
| segmentP(app(sk3,X0),sk7)
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3716,f531]) ).
fof(f8992,plain,
( ~ sQ274_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ12_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f8970,f5003,f563,f637,f592,f3709]) ).
fof(f8998,definition,
! [X0] :
( sQ614_spl
<=> ( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(app(sk6,sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f9001,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ614_spl ),
inference(split_clause,[status(thm)],[f8976,f8998,f563,f3825,f3709]) ).
fof(f9003,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ374_spl ),
inference(split_clause,[status(thm)],[f8978,f5342,f563,f3825,f3709]) ).
fof(f9008,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f8983,f5016,f3825,f563,f3709]) ).
fof(f9067,plain,
( ~ sQ424_spl
| ~ sQ81_spl
| nil = sk6
| cons(sk9,tl(sk6)) = sk6
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f6242,f315]) ).
fof(f9071,definition,
( sQ615_spl
<=> cons(sk9,tl(sk6)) = sk6 ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f9072,plain,
( ~ sQ615_spl
| cons(sk9,tl(sk6)) = sk6 ),
inference(component_clause,[status(thm)],[f9071]) ).
fof(f9074,plain,
( ~ sQ424_spl
| ~ sQ81_spl
| sQ286_spl
| sQ615_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9067,f637,f9071,f3844,f1570,f6188]) ).
fof(f9102,plain,
( ~ sQ9_spl
| ~ sQ61_spl
| cons(sk9,nil) = app(sk3,nil)
| ~ ssItem(sk9) ),
inference(paramodulation,[status(thm)],[f499,f1086]) ).
fof(f9103,definition,
( sQ618_spl
<=> cons(sk9,nil) = app(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f9106,plain,
( ~ sQ9_spl
| ~ sQ61_spl
| sQ618_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f9102,f487,f9103,f1085,f498]) ).
fof(f9152,definition,
( sQ619_spl
<=> ssList(tl(sk6)) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f9154,plain,
( sQ619_spl
| ~ ssList(tl(sk6)) ),
inference(component_clause,[status(thm)],[f9152]) ).
fof(f9158,definition,
( sQ621_spl
<=> nil = tl(sk6) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f9159,plain,
( ~ sQ621_spl
| nil = tl(sk6) ),
inference(component_clause,[status(thm)],[f9158]) ).
fof(f9304,plain,
( ~ sQ615_spl
| ~ sQ621_spl
| cons(sk9,nil) = sk6 ),
inference(backward_demodulation,[status(thm)],[f9159,f9072]) ).
fof(f9309,plain,
( ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| sk3 = sk6 ),
inference(forward_demodulation,[status(thm)],[f499,f9304]) ).
fof(f9310,definition,
( sQ653_spl
<=> cons(hd(sk6),nil) = sk6 ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f9311,plain,
( ~ sQ653_spl
| cons(hd(sk6),nil) = sk6 ),
inference(component_clause,[status(thm)],[f9310]) ).
fof(f9312,plain,
( sQ653_spl
| cons(hd(sk6),nil) != sk6 ),
inference(component_clause,[status(thm)],[f9310]) ).
fof(f9320,plain,
( ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| cons(sk9,nil) = sk6 ),
inference(forward_demodulation,[status(thm)],[f6242,f9311]) ).
fof(f9321,plain,
( ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| sk3 = sk6 ),
inference(forward_demodulation,[status(thm)],[f499,f9320]) ).
fof(f9330,plain,
( ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| app(sk3,nil) = sk6 ),
inference(backward_demodulation,[status(thm)],[f9321,f765]) ).
fof(f9336,plain,
( ~ sQ82_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| tl(sk6) = nil ),
inference(backward_demodulation,[status(thm)],[f9321,f1575]) ).
fof(f9367,plain,
( ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| app(sk6,nil) = sk6 ),
inference(forward_demodulation,[status(thm)],[f9321,f9330]) ).
fof(f9368,plain,
( ~ sQ82_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| sQ621_spl ),
inference(split_clause,[status(thm)],[f9336,f9158,f498,f1570,f6188,f9310,f1574]) ).
fof(f9374,plain,
( sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| cons(sk9,nil) != sk6 ),
inference(forward_demodulation,[status(thm)],[f6242,f9312]) ).
fof(f9384,plain,
( ~ sQ274_spl
| hd(sk3) = hd(app(sk6,sk3))
| nil = app(sk6,sk3)
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3716,f342]) ).
fof(f9407,plain,
( ~ sQ274_spl
| sQ288_spl
| sQ285_spl
| ~ sQ284_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f9384,f563,f3825,f3829,f3892,f3709]) ).
fof(f9427,plain,
( sQ619_spl
| nil = sk6
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f9154,f284]) ).
fof(f9428,plain,
( sQ619_spl
| sQ286_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f9427,f637,f3844,f9152]) ).
fof(f9888,plain,
! [X0] :
( ~ sQ110_spl
| ~ sQ315_spl
| frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,cons(sk9,nil)),X0) ),
inference(forward_demodulation,[status(thm)],[f4369,f2164]) ).
fof(f9889,plain,
! [X0] :
( ~ sQ110_spl
| ~ sQ315_spl
| ~ sQ9_spl
| frontsegP(sk3,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,sk3),X0) ),
inference(forward_demodulation,[status(thm)],[f499,f9888]) ).
fof(f9890,plain,
! [X0] :
( ~ sQ110_spl
| ~ sQ315_spl
| ~ sQ9_spl
| ~ ssList(sk6)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ frontsegP(sk6,X0)
| frontsegP(sk3,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f9889,f360]) ).
fof(f9894,definition,
! [X0] :
( sQ677_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(sk6,X0)
| frontsegP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f9897,plain,
( ~ sQ110_spl
| ~ sQ315_spl
| ~ sQ9_spl
| ~ sQ20_spl
| ~ sQ17_spl
| sQ677_spl ),
inference(split_clause,[status(thm)],[f9890,f9894,f592,f637,f498,f4368,f2163]) ).
fof(f9995,plain,
( sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| sk3 != sk6 ),
inference(forward_demodulation,[status(thm)],[f499,f9374]) ).
fof(f10079,plain,
( ~ sQ288_spl
| ~ sQ81_spl
| nil = app(sk6,sk3)
| cons(sk9,tl(app(sk6,sk3))) = app(sk6,sk3)
| ~ ssList(app(sk6,sk3)) ),
inference(paramodulation,[status(thm)],[f3896,f315]) ).
fof(f10084,definition,
( sQ678_spl
<=> cons(sk9,tl(app(sk6,sk3))) = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f10087,plain,
( ~ sQ288_spl
| ~ sQ81_spl
| sQ285_spl
| sQ678_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f10079,f3825,f10084,f3829,f1570,f3892]) ).
fof(f10102,definition,
( sQ681_spl
<=> ssItem(hd(tl(sk6))) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f10104,plain,
( sQ681_spl
| ~ ssItem(hd(tl(sk6))) ),
inference(component_clause,[status(thm)],[f10102]) ).
fof(f10176,plain,
( ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| sk1 = sk6 ),
inference(backward_demodulation,[status(thm)],[f9309,f444]) ).
fof(f10230,definition,
( sQ692_spl
<=> ssList(app(sk6,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f10232,plain,
( sQ692_spl
| ~ ssList(app(sk6,sk6)) ),
inference(component_clause,[status(thm)],[f10230]) ).
fof(f10400,plain,
( sQ287_spl
| ~ sQ419_spl
| ~ sQ291_spl ),
inference(split_clause,[status(thm)],[f6044,f3937,f6037,f3889]) ).
fof(f10415,plain,
( ~ sQ274_spl
| ~ sQ287_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| app(sk6,sk7) = sk6 ),
inference(forward_demodulation,[status(thm)],[f9309,f3899]) ).
fof(f10420,plain,
( ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| sk6 = sk7 ),
inference(forward_demodulation,[status(thm)],[f10176,f3983]) ).
fof(f10625,definition,
! [X0] :
( sQ745_spl
<=> ( memberP(sk7,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ745_spl])],[split_symbol_definition]) ).
fof(f10648,plain,
( ~ sQ274_spl
| ~ sQ287_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| ~ sQ133_spl
| app(sk7,sk7) = sk6 ),
inference(forward_demodulation,[status(thm)],[f10420,f10415]) ).
fof(f10649,plain,
( ~ sQ274_spl
| ~ sQ287_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| ~ sQ133_spl
| app(sk7,sk7) = sk7 ),
inference(forward_demodulation,[status(thm)],[f10420,f10648]) ).
fof(f10746,definition,
! [X0] :
( sQ750_spl
<=> ( rearsegP(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ750_spl])],[split_symbol_definition]) ).
fof(f10796,plain,
! [X0,X1] :
( skaf46(app(X1,X0),X0) = X1
| ~ ssList(X1)
| ~ ssList(skaf46(app(X1,X0),X0))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1960,f2379]) ).
fof(f10799,plain,
( ~ sQ23_spl
| skaf46(app(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f10796]) ).
fof(f10800,definition,
( sQ754_spl
<=> ssList(skaf46(sk7,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ754_spl])],[split_symbol_definition]) ).
fof(f10802,plain,
( sQ754_spl
| ~ ssList(skaf46(sk7,sk7)) ),
inference(component_clause,[status(thm)],[f10800]) ).
fof(f10807,definition,
( sQ756_spl
<=> skaf46(app(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ756_spl])],[split_symbol_definition]) ).
fof(f10810,plain,
( ~ sQ23_spl
| sQ756_spl
| ~ sQ530_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10799,f588,f7096,f10807,f667]) ).
fof(f10812,plain,
( sQ754_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10802,f258]) ).
fof(f10813,plain,
sQ754_spl,
inference(contradiction_clause,[status(thm)],[f10812]) ).
fof(f10821,definition,
! [X0] :
( sQ758_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f10844,plain,
( ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| app(sk7,nil) = sk6 ),
inference(forward_demodulation,[status(thm)],[f10420,f9367]) ).
fof(f10845,plain,
( ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| app(sk7,nil) = sk7 ),
inference(forward_demodulation,[status(thm)],[f10420,f10844]) ).
fof(f10869,definition,
( sQ761_spl
<=> ssList(skaf46(sk7,nil)) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f10871,plain,
( sQ761_spl
| ~ ssList(skaf46(sk7,nil)) ),
inference(component_clause,[status(thm)],[f10869]) ).
fof(f10872,definition,
( sQ762_spl
<=> skaf46(app(sk7,nil),nil) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ762_spl])],[split_symbol_definition]) ).
fof(f10881,definition,
! [X0] :
( sQ763_spl
<=> ( rearsegP(sk7,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ763_spl])],[split_symbol_definition]) ).
fof(f10887,definition,
! [X0] :
( sQ764_spl
<=> ( cons(X0,sk7) = app(cons(X0,sk7),nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ764_spl])],[split_symbol_definition]) ).
fof(f10891,definition,
! [X0] :
( sQ765_spl
<=> ( memberP(sk7,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ765_spl])],[split_symbol_definition]) ).
fof(f10895,definition,
! [X0,X1] :
( sQ766_spl
<=> ( segmentP(app(sk7,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f10899,definition,
! [X0] :
( sQ767_spl
<=> ( segmentP(app(sk7,X0),nil)
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ767_spl])],[split_symbol_definition]) ).
fof(f10903,definition,
! [X0] :
( sQ768_spl
<=> ( X0 = nil
| ~ ssList(X0)
| app(sk7,X0) != sk7 ) ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f10908,definition,
! [X0] :
( sQ769_spl
<=> ( app(sk7,X0) = app(sk7,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ769_spl])],[split_symbol_definition]) ).
fof(f10912,definition,
! [X0] :
( sQ770_spl
<=> ( X0 = sk7
| ~ ssList(X0)
| app(X0,nil) != sk7 ) ),
introduced(definition,[new_symbols(definition,[sQ770_spl])],[split_symbol_definition]) ).
fof(f10917,definition,
( sQ771_spl
<=> rearsegP(sk7,nil) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f10924,plain,
( sQ761_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10871,f258]) ).
fof(f10925,plain,
sQ761_spl,
inference(contradiction_clause,[status(thm)],[f10924]) ).
fof(f10936,plain,
! [X0,X1] :
( skaf45(app(X0,X1),X0) = X1
| ~ ssList(X1)
| ~ ssList(skaf45(app(X0,X1),X0))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1966,f2398]) ).
fof(f10940,plain,
( ~ sQ23_spl
| skaf45(app(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(skaf45(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f10936]) ).
fof(f10941,definition,
( sQ772_spl
<=> ssList(skaf45(sk7,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ772_spl])],[split_symbol_definition]) ).
fof(f10943,plain,
( sQ772_spl
| ~ ssList(skaf45(sk7,sk7)) ),
inference(component_clause,[status(thm)],[f10941]) ).
fof(f10944,definition,
( sQ773_spl
<=> skaf45(app(sk7,nil),sk7) = nil ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f10945,plain,
( ~ sQ773_spl
| skaf45(app(sk7,nil),sk7) = nil ),
inference(component_clause,[status(thm)],[f10944]) ).
fof(f10948,definition,
( sQ774_spl
<=> skaf45(app(sk7,sk7),sk7) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ774_spl])],[split_symbol_definition]) ).
fof(f10949,plain,
( ~ sQ774_spl
| skaf45(app(sk7,sk7),sk7) = sk7 ),
inference(component_clause,[status(thm)],[f10948]) ).
fof(f10952,definition,
( sQ775_spl
<=> ssList(skaf45(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f10954,plain,
( sQ775_spl
| ~ ssList(skaf45(nil,nil)) ),
inference(component_clause,[status(thm)],[f10952]) ).
fof(f10955,definition,
( sQ776_spl
<=> skaf45(app(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f10958,plain,
( ~ sQ23_spl
| sQ776_spl
| ~ sQ775_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10940,f588,f10952,f10955,f667]) ).
fof(f10959,plain,
( sQ772_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10943,f259]) ).
fof(f10960,plain,
sQ772_spl,
inference(contradiction_clause,[status(thm)],[f10959]) ).
fof(f10961,plain,
( sQ775_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10954,f259]) ).
fof(f10962,plain,
sQ775_spl,
inference(contradiction_clause,[status(thm)],[f10961]) ).
fof(f10964,plain,
( ~ sQ774_spl
| ~ sQ274_spl
| ~ sQ287_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ9_spl
| ~ sQ133_spl
| skaf45(sk7,sk7) = sk7 ),
inference(forward_demodulation,[status(thm)],[f10649,f10949]) ).
fof(f10965,plain,
( ~ sQ773_spl
| ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| skaf45(sk7,sk7) = nil ),
inference(forward_demodulation,[status(thm)],[f10845,f10945]) ).
fof(f11021,plain,
! [X0] :
( ~ sQ23_spl
| app(nil,nil) = X0
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f2143]) ).
fof(f11024,definition,
! [X0] :
( sQ778_spl
<=> ( app(sk7,nil) = X0
| ~ rearsegP(X0,sk7)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f11032,definition,
! [X0] :
( sQ780_spl
<=> ( app(nil,nil) = X0
| ~ rearsegP(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f11035,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ780_spl ),
inference(split_clause,[status(thm)],[f11021,f11032,f588,f667]) ).
fof(f11045,plain,
! [X0] :
( ~ sQ23_spl
| app(nil,nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f2146]) ).
fof(f11048,definition,
! [X0] :
( sQ781_spl
<=> ( app(sk7,nil) = X0
| ~ frontsegP(X0,sk7)
| ~ ssList(X0)
| ~ frontsegP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f11056,definition,
! [X0] :
( sQ783_spl
<=> ( app(nil,nil) = X0
| ~ frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ783_spl])],[split_symbol_definition]) ).
fof(f11059,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ783_spl ),
inference(split_clause,[status(thm)],[f11045,f11056,f588,f667]) ).
fof(f11068,definition,
( sQ784_spl
<=> geq(sk9,sk9) ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f11069,plain,
( ~ sQ784_spl
| geq(sk9,sk9) ),
inference(component_clause,[status(thm)],[f11068]) ).
fof(f11072,definition,
( sQ785_spl
<=> leq(sk9,sk9) ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f11073,plain,
( ~ sQ785_spl
| leq(sk9,sk9) ),
inference(component_clause,[status(thm)],[f11072]) ).
fof(f11074,plain,
( sQ785_spl
| ~ leq(sk9,sk9) ),
inference(component_clause,[status(thm)],[f11072]) ).
fof(f11076,definition,
! [X0] :
( sQ786_spl
<=> ( geq(X0,sk9)
| ~ ssItem(X0)
| ~ geq(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f11083,plain,
( ~ sQ785_spl
| geq(sk9,sk9)
| ~ ssItem(sk9)
| ~ ssItem(sk9) ),
inference(resolution,[status(thm)],[f11073,f319]) ).
fof(f11086,plain,
! [X0] :
( ~ sQ785_spl
| lt(sk9,X0)
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ ssItem(X0)
| ~ lt(sk9,X0) ),
inference(resolution,[status(thm)],[f11073,f374]) ).
fof(f11087,plain,
! [X0] :
( ~ sQ785_spl
| leq(X0,sk9)
| ~ ssItem(X0)
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ leq(X0,sk9) ),
inference(resolution,[status(thm)],[f11073,f391]) ).
fof(f11089,plain,
( ~ sQ785_spl
| sQ784_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f11083,f487,f11068,f11072]) ).
fof(f11090,definition,
( sQ787_spl
<=> lt(sk9,sk9) ),
introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition]) ).
fof(f11091,plain,
( ~ sQ787_spl
| lt(sk9,sk9) ),
inference(component_clause,[status(thm)],[f11090]) ).
fof(f11092,plain,
( sQ787_spl
| ~ lt(sk9,sk9) ),
inference(component_clause,[status(thm)],[f11090]) ).
fof(f11095,definition,
! [X0] :
( sQ788_spl
<=> ( lt(sk9,X0)
| ~ ssItem(X0)
| ~ lt(sk9,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition]) ).
fof(f11098,plain,
( ~ sQ785_spl
| ~ sQ6_spl
| sQ788_spl ),
inference(split_clause,[status(thm)],[f11086,f11095,f487,f11072]) ).
fof(f11099,definition,
! [X0] :
( sQ789_spl
<=> ( leq(X0,sk9)
| ~ ssItem(X0)
| ~ leq(X0,sk9) ) ),
introduced(definition,[new_symbols(definition,[sQ789_spl])],[split_symbol_definition]) ).
fof(f11102,plain,
( ~ sQ785_spl
| ~ sQ6_spl
| sQ789_spl ),
inference(split_clause,[status(thm)],[f11087,f11099,f487,f11072]) ).
fof(f11344,plain,
( sQ785_spl
| ~ ssItem(sk9) ),
inference(resolution,[status(thm)],[f11074,f270]) ).
fof(f11345,plain,
( sQ785_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f11344,f487,f11072]) ).
fof(f11358,plain,
( ~ sQ784_spl
| sk9 = sk9
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ geq(sk9,sk9) ),
inference(resolution,[status(thm)],[f11069,f347]) ).
fof(f11360,plain,
! [X0] :
( ~ sQ784_spl
| geq(X0,sk9)
| ~ ssItem(X0)
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ geq(X0,sk9) ),
inference(resolution,[status(thm)],[f11069,f376]) ).
fof(f11361,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ784_spl ),
inference(split_clause,[status(thm)],[f11358,f11068,f487,f615]) ).
fof(f11363,plain,
( ~ sQ784_spl
| ~ sQ6_spl
| sQ786_spl ),
inference(split_clause,[status(thm)],[f11360,f11076,f487,f11068]) ).
fof(f11369,definition,
( sQ790_spl
<=> app(sk7,nil) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition]) ).
fof(f11370,plain,
( ~ sQ790_spl
| app(sk7,nil) = sk7 ),
inference(component_clause,[status(thm)],[f11369]) ).
fof(f11371,plain,
( sQ790_spl
| app(sk7,nil) != sk7 ),
inference(component_clause,[status(thm)],[f11369]) ).
fof(f11383,plain,
( ~ sQ773_spl
| ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ774_spl
| ~ sQ274_spl
| ~ sQ287_spl
| sk7 = nil ),
inference(forward_demodulation,[status(thm)],[f10964,f10965]) ).
fof(f11384,plain,
( ~ sQ773_spl
| ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ774_spl
| ~ sQ274_spl
| ~ sQ287_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11383,f683]) ).
fof(f11385,plain,
( ~ sQ773_spl
| ~ sQ30_spl
| ~ sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| ~ sQ615_spl
| ~ sQ621_spl
| ~ sQ774_spl
| ~ sQ274_spl
| ~ sQ287_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f11384]) ).
fof(f11389,plain,
( ~ sQ274_spl
| ~ sQ287_spl
| ~ sQ133_spl
| app(sk6,sk7) = sk7 ),
inference(forward_demodulation,[status(thm)],[f3942,f3899]) ).
fof(f11422,definition,
( sQ793_spl
<=> ssList(skaf45(sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ793_spl])],[split_symbol_definition]) ).
fof(f11424,plain,
( sQ793_spl
| ~ ssList(skaf45(sk7,sk6)) ),
inference(component_clause,[status(thm)],[f11422]) ).
fof(f11482,plain,
( sQ793_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11424,f259]) ).
fof(f11483,plain,
sQ793_spl,
inference(contradiction_clause,[status(thm)],[f11482]) ).
fof(f11485,plain,
( ~ sQ274_spl
| ~ sQ133_spl
| app(app(sk6,sk7),sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f3942,f3716]) ).
fof(f11486,plain,
( ~ sQ274_spl
| ~ sQ133_spl
| ~ sQ287_spl
| app(sk7,sk7) = sk3 ),
inference(forward_demodulation,[status(thm)],[f11389,f11485]) ).
fof(f11487,plain,
( ~ sQ274_spl
| ~ sQ133_spl
| ~ sQ287_spl
| app(sk7,sk7) = sk7 ),
inference(forward_demodulation,[status(thm)],[f3942,f11486]) ).
fof(f11490,plain,
( ~ sQ274_spl
| ~ sQ133_spl
| ~ sQ287_spl
| skaf45(app(sk7,sk7),sk7) = sk7
| ~ ssList(sk7)
| ~ ssList(skaf45(sk7,sk7))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f11487,f10936]) ).
fof(f11514,plain,
( ~ sQ274_spl
| ~ sQ133_spl
| ~ sQ287_spl
| sQ774_spl
| ~ sQ772_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f11490,f563,f10941,f10948,f3889,f2421,f3709]) ).
fof(f11549,plain,
( sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| ~ sQ133_spl
| sk7 != sk6 ),
inference(forward_demodulation,[status(thm)],[f3942,f9995]) ).
fof(f11747,definition,
( sQ811_spl
<=> ssItem(skaf83(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ811_spl])],[split_symbol_definition]) ).
fof(f11749,plain,
( sQ811_spl
| ~ ssItem(skaf83(sk7)) ),
inference(component_clause,[status(thm)],[f11747]) ).
fof(f11750,definition,
( sQ812_spl
<=> ssList(skaf82(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition]) ).
fof(f11752,plain,
( sQ812_spl
| ~ ssList(skaf82(sk7)) ),
inference(component_clause,[status(thm)],[f11750]) ).
fof(f11762,plain,
( sQ812_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11752,f221]) ).
fof(f11763,plain,
sQ812_spl,
inference(contradiction_clause,[status(thm)],[f11762]) ).
fof(f11764,plain,
( sQ811_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11749,f220]) ).
fof(f11765,plain,
sQ811_spl,
inference(contradiction_clause,[status(thm)],[f11764]) ).
fof(f11805,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f668,f2581]) ).
fof(f11814,definition,
! [X0,X1] :
( sQ817_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition]) ).
fof(f11817,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ817_spl ),
inference(split_clause,[status(thm)],[f11805,f11814,f588,f667]) ).
fof(f11848,plain,
! [X0] :
( ~ sQ790_spl
| ~ ssList(nil)
| frontsegP(X0,sk7)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ frontsegP(X0,sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2615]) ).
fof(f11849,plain,
! [X0,X1] :
( ~ sQ790_spl
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2581]) ).
fof(f11850,plain,
! [X0] :
( ~ sQ790_spl
| ~ ssList(sk7)
| rearsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(X0,sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2579]) ).
fof(f11852,plain,
( ~ sQ790_spl
| app(sk7,nil) = nil
| ~ rearsegP(nil,sk7)
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2385]) ).
fof(f11853,plain,
! [X0] :
( ~ sQ790_spl
| app(sk7,nil) = X0
| ~ frontsegP(X0,sk7)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f11370,f2146]) ).
fof(f11854,plain,
! [X0] :
( ~ sQ790_spl
| app(sk7,nil) = X0
| ~ rearsegP(X0,sk7)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f2143]) ).
fof(f11855,plain,
( ~ sQ790_spl
| skaf45(app(sk7,nil),sk7) = nil
| ~ ssList(nil)
| ~ ssList(skaf45(sk7,sk7))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f11370,f10936]) ).
fof(f11856,plain,
( ~ sQ790_spl
| skaf46(app(sk7,nil),nil) = sk7
| ~ ssList(sk7)
| ~ ssList(skaf46(sk7,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11370,f10796]) ).
fof(f11861,plain,
! [X0] :
( ~ sQ790_spl
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f11370,f363]) ).
fof(f11862,plain,
! [X0] :
( ~ sQ790_spl
| rearsegP(sk7,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f359]) ).
fof(f11863,plain,
! [X0] :
( ~ sQ790_spl
| frontsegP(sk7,X0)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f11370,f360]) ).
fof(f11864,plain,
! [X0] :
( ~ sQ790_spl
| memberP(sk7,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ memberP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f364]) ).
fof(f11865,plain,
! [X0] :
( ~ sQ790_spl
| cons(X0,sk7) = app(cons(X0,sk7),nil)
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f11370,f392]) ).
fof(f11866,plain,
! [X0] :
( ~ sQ790_spl
| memberP(sk7,X0)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f11370,f394]) ).
fof(f11867,plain,
! [X0,X1] :
( ~ sQ790_spl
| segmentP(app(sk7,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f413]) ).
fof(f11868,plain,
! [X0] :
( ~ sQ790_spl
| segmentP(app(sk7,X0),nil)
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11370,f531]) ).
fof(f11869,plain,
! [X0] :
( ~ sQ790_spl
| X0 = nil
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(X0)
| app(sk7,X0) != sk7 ),
inference(paramodulation,[status(thm)],[f11370,f379]) ).
fof(f11871,plain,
! [X0] :
( ~ sQ790_spl
| app(sk7,X0) = app(sk7,app(nil,X0))
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11370,f377]) ).
fof(f11872,plain,
! [X0] :
( ~ sQ790_spl
| X0 = sk7
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(X0)
| app(X0,nil) != sk7 ),
inference(paramodulation,[status(thm)],[f11370,f381]) ).
fof(f11874,plain,
( ~ sQ790_spl
| rearsegP(sk7,nil)
| ~ ssList(nil)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2379]) ).
fof(f11875,plain,
( ~ sQ790_spl
| frontsegP(sk7,sk7)
| ~ ssList(sk7)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f11370,f2398]) ).
fof(f11878,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f11848,f2626,f563,f588,f11369]) ).
fof(f11879,definition,
! [X0,X1] :
( sQ820_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ820_spl])],[split_symbol_definition]) ).
fof(f11882,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ820_spl ),
inference(split_clause,[status(thm)],[f11849,f11879,f563,f588,f11369]) ).
fof(f11883,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ750_spl ),
inference(split_clause,[status(thm)],[f11850,f10746,f588,f563,f11369]) ).
fof(f11885,definition,
( sQ821_spl
<=> app(sk7,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ821_spl])],[split_symbol_definition]) ).
fof(f11886,plain,
( ~ sQ821_spl
| app(sk7,nil) = nil ),
inference(component_clause,[status(thm)],[f11885]) ).
fof(f11888,plain,
( ~ sQ790_spl
| sQ821_spl
| ~ sQ401_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f11852,f563,f588,f5567,f11885,f11369]) ).
fof(f11889,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ781_spl ),
inference(split_clause,[status(thm)],[f11853,f11048,f588,f563,f11369]) ).
fof(f11890,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ778_spl ),
inference(split_clause,[status(thm)],[f11854,f11024,f563,f588,f11369]) ).
fof(f11891,plain,
( ~ sQ790_spl
| sQ773_spl
| ~ sQ16_spl
| ~ sQ772_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f11855,f563,f10941,f588,f10944,f11369]) ).
fof(f11892,plain,
( ~ sQ790_spl
| sQ762_spl
| ~ sQ12_spl
| ~ sQ761_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f11856,f588,f10869,f563,f10872,f11369]) ).
fof(f11897,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f11861,f923,f588,f563,f11369]) ).
fof(f11898,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ763_spl ),
inference(split_clause,[status(thm)],[f11862,f10881,f563,f588,f11369]) ).
fof(f11899,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f11863,f2726,f588,f563,f11369]) ).
fof(f11900,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ745_spl ),
inference(split_clause,[status(thm)],[f11864,f10625,f588,f563,f11369]) ).
fof(f11901,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ764_spl ),
inference(split_clause,[status(thm)],[f11865,f10887,f563,f588,f11369]) ).
fof(f11902,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ765_spl ),
inference(split_clause,[status(thm)],[f11866,f10891,f588,f563,f11369]) ).
fof(f11903,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ766_spl ),
inference(split_clause,[status(thm)],[f11867,f10895,f563,f588,f11369]) ).
fof(f11904,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ767_spl ),
inference(split_clause,[status(thm)],[f11868,f10899,f563,f588,f11369]) ).
fof(f11905,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ768_spl ),
inference(split_clause,[status(thm)],[f11869,f10903,f563,f588,f11369]) ).
fof(f11907,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ769_spl ),
inference(split_clause,[status(thm)],[f11871,f10908,f588,f563,f11369]) ).
fof(f11908,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ770_spl ),
inference(split_clause,[status(thm)],[f11872,f10912,f588,f563,f11369]) ).
fof(f11910,plain,
( ~ sQ790_spl
| sQ771_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f11874,f563,f588,f10917,f11369]) ).
fof(f11911,plain,
( ~ sQ790_spl
| sQ152_spl
| ~ sQ12_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f11875,f588,f563,f2630,f11369]) ).
fof(f11918,plain,
! [X0,X1] :
( ~ sQ23_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(nil,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f668,f2617]) ).
fof(f11922,definition,
! [X0,X1] :
( sQ822_spl
<=> ( ~ frontsegP(sk7,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk7) ) ),
introduced(definition,[new_symbols(definition,[sQ822_spl])],[split_symbol_definition]) ).
fof(f11930,definition,
! [X0,X1] :
( sQ824_spl
<=> ( ~ frontsegP(nil,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ824_spl])],[split_symbol_definition]) ).
fof(f11933,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ824_spl ),
inference(split_clause,[status(thm)],[f11918,f11930,f588,f667]) ).
fof(f11940,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f2844]) ).
fof(f11952,definition,
! [X0,X1,X2] :
( sQ827_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ827_spl])],[split_symbol_definition]) ).
fof(f11955,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ827_spl ),
inference(split_clause,[status(thm)],[f11940,f11952,f588,f667]) ).
fof(f11964,plain,
! [X0,X1] :
( ~ sQ23_spl
| app(app(nil,nil),X1) = X0
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f668,f2845]) ).
fof(f11975,definition,
! [X0,X1] :
( sQ830_spl
<=> ( app(app(nil,nil),X1) = X0
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ830_spl])],[split_symbol_definition]) ).
fof(f11978,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ830_spl ),
inference(split_clause,[status(thm)],[f11964,f11975,f588,f667]) ).
fof(f11985,plain,
( sQ692_spl
| ~ ssList(sk6)
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f10232,f294]) ).
fof(f11986,plain,
( sQ692_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f11985,f637,f10230]) ).
fof(f11987,plain,
( ~ sQ287_spl
| ~ sQ133_spl
| sk6 = app(sk6,sk7) ),
inference(forward_demodulation,[status(thm)],[f3942,f3890]) ).
fof(f11988,plain,
( ~ sQ287_spl
| ~ sQ133_spl
| ~ sQ274_spl
| sk6 = sk7 ),
inference(forward_demodulation,[status(thm)],[f11389,f11987]) ).
fof(f11989,plain,
( ~ sQ287_spl
| ~ sQ133_spl
| ~ sQ274_spl
| sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11988,f11549]) ).
fof(f11990,plain,
( ~ sQ287_spl
| ~ sQ133_spl
| ~ sQ274_spl
| sQ653_spl
| ~ sQ424_spl
| ~ sQ81_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f11989]) ).
fof(f12087,plain,
! [X0] :
( ~ sQ274_spl
| app(app(sk6,sk3),sk7) = X0
| ~ ssList(app(app(sk6,sk3),sk7))
| ~ segmentP(X0,sk3)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f3716,f2845]) ).
fof(f12088,plain,
! [X0,X1] :
( ~ sQ274_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(app(app(sk6,sk3),sk7))
| ~ segmentP(X1,sk3)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f3716,f2844]) ).
fof(f12092,plain,
! [X0,X1] :
( ~ sQ274_spl
| app(app(app(sk6,sk3),sk7),X1) = X0
| ~ ssList(app(app(app(sk6,sk3),sk7),X1))
| ~ segmentP(X0,app(sk3,X1))
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f3716,f2845]) ).
fof(f12093,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(app(sk6,sk3),sk7),X1))
| ~ segmentP(X2,app(sk3,X1))
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f3716,f2844]) ).
fof(f12094,plain,
! [X0,X1] :
( ~ sQ274_spl
| ~ ssList(app(sk6,sk3))
| ~ ssList(sk7)
| ~ frontsegP(app(sk6,sk3),X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk3) ),
inference(paramodulation,[status(thm)],[f3716,f2617]) ).
fof(f12096,plain,
! [X0,X1] :
( ~ sQ274_spl
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ rearsegP(sk7,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk3) ),
inference(paramodulation,[status(thm)],[f3716,f2581]) ).
fof(f12100,plain,
! [X0] :
( ~ sQ274_spl
| app(app(sk6,sk3),sk7) = X0
| ~ frontsegP(X0,sk3)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ frontsegP(app(sk6,sk3),X0) ),
inference(paramodulation,[status(thm)],[f3716,f2146]) ).
fof(f12101,plain,
! [X0] :
( ~ sQ274_spl
| app(app(sk6,sk3),sk7) = X0
| ~ rearsegP(X0,sk3)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(sk6,sk3))
| ~ rearsegP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f3716,f2143]) ).
fof(f12102,plain,
( ~ sQ274_spl
| skaf45(app(app(sk6,sk3),sk7),app(sk6,sk3)) = sk7
| ~ ssList(sk7)
| ~ ssList(skaf45(sk3,app(sk6,sk3)))
| ~ ssList(app(sk6,sk3)) ),
inference(paramodulation,[status(thm)],[f3716,f10936]) ).
fof(f12103,plain,
( ~ sQ274_spl
| skaf46(app(app(sk6,sk3),sk7),sk7) = app(sk6,sk3)
| ~ ssList(app(sk6,sk3))
| ~ ssList(skaf46(sk3,sk7))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3716,f10796]) ).
fof(f12124,definition,
! [X0] :
( sQ831_spl
<=> ( app(app(sk6,sk3),sk7) = X0
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ831_spl])],[split_symbol_definition]) ).
fof(f12127,plain,
( ~ sQ274_spl
| ~ sQ336_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ12_spl
| sQ831_spl ),
inference(split_clause,[status(thm)],[f12087,f12124,f563,f637,f592,f5007,f3709]) ).
fof(f12128,definition,
! [X0,X1] :
( sQ832_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,sk3)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ832_spl])],[split_symbol_definition]) ).
fof(f12131,plain,
( ~ sQ274_spl
| ~ sQ336_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ12_spl
| sQ832_spl ),
inference(split_clause,[status(thm)],[f12088,f12128,f563,f637,f592,f5007,f3709]) ).
fof(f12135,definition,
! [X0,X1] :
( sQ833_spl
<=> ( app(app(app(sk6,sk3),sk7),X1) = X0
| ~ ssList(app(app(app(sk6,sk3),sk7),X1))
| ~ segmentP(X0,app(sk3,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ833_spl])],[split_symbol_definition]) ).
fof(f12138,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ833_spl ),
inference(split_clause,[status(thm)],[f12092,f12135,f3825,f563,f3709]) ).
fof(f12139,definition,
! [X0,X1,X2] :
( sQ834_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(app(sk6,sk3),sk7),X1))
| ~ segmentP(X2,app(sk3,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ834_spl])],[split_symbol_definition]) ).
fof(f12142,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ834_spl ),
inference(split_clause,[status(thm)],[f12093,f12139,f3825,f563,f3709]) ).
fof(f12143,definition,
! [X0,X1] :
( sQ835_spl
<=> ( ~ frontsegP(app(sk6,sk3),X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ835_spl])],[split_symbol_definition]) ).
fof(f12146,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ835_spl ),
inference(split_clause,[status(thm)],[f12094,f12143,f563,f3825,f3709]) ).
fof(f12148,definition,
! [X0,X1] :
( sQ836_spl
<=> ( ~ rearsegP(sk7,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ836_spl])],[split_symbol_definition]) ).
fof(f12151,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ836_spl ),
inference(split_clause,[status(thm)],[f12096,f12148,f3825,f563,f3709]) ).
fof(f12161,definition,
! [X0] :
( sQ839_spl
<=> ( app(app(sk6,sk3),sk7) = X0
| ~ frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(app(sk6,sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ839_spl])],[split_symbol_definition]) ).
fof(f12164,plain,
( ~ sQ274_spl
| ~ sQ284_spl
| ~ sQ12_spl
| sQ839_spl ),
inference(split_clause,[status(thm)],[f12100,f12161,f563,f3825,f3709]) ).
fof(f12165,definition,
! [X0] :
( sQ840_spl
<=> ( app(app(sk6,sk3),sk7) = X0
| ~ rearsegP(X0,sk3)
| ~ ssList(X0)
| ~ rearsegP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ840_spl])],[split_symbol_definition]) ).
fof(f12168,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ840_spl ),
inference(split_clause,[status(thm)],[f12101,f12165,f3825,f563,f3709]) ).
fof(f12169,definition,
( sQ841_spl
<=> ssList(skaf45(sk3,app(sk6,sk3))) ),
introduced(definition,[new_symbols(definition,[sQ841_spl])],[split_symbol_definition]) ).
fof(f12171,plain,
( sQ841_spl
| ~ ssList(skaf45(sk3,app(sk6,sk3))) ),
inference(component_clause,[status(thm)],[f12169]) ).
fof(f12172,definition,
( sQ842_spl
<=> skaf45(app(app(sk6,sk3),sk7),app(sk6,sk3)) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ842_spl])],[split_symbol_definition]) ).
fof(f12173,plain,
( ~ sQ842_spl
| skaf45(app(app(sk6,sk3),sk7),app(sk6,sk3)) = sk7 ),
inference(component_clause,[status(thm)],[f12172]) ).
fof(f12175,plain,
( ~ sQ274_spl
| sQ842_spl
| ~ sQ12_spl
| ~ sQ841_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f12102,f3825,f12169,f563,f12172,f3709]) ).
fof(f12176,definition,
( sQ843_spl
<=> ssList(skaf46(sk3,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ843_spl])],[split_symbol_definition]) ).
fof(f12178,plain,
( sQ843_spl
| ~ ssList(skaf46(sk3,sk7)) ),
inference(component_clause,[status(thm)],[f12176]) ).
fof(f12179,definition,
( sQ844_spl
<=> skaf46(app(app(sk6,sk3),sk7),sk7) = app(sk6,sk3) ),
introduced(definition,[new_symbols(definition,[sQ844_spl])],[split_symbol_definition]) ).
fof(f12182,plain,
( ~ sQ274_spl
| sQ844_spl
| ~ sQ284_spl
| ~ sQ843_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f12103,f563,f12176,f3825,f12179,f3709]) ).
fof(f12209,plain,
( sQ841_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12171,f259]) ).
fof(f12210,plain,
sQ841_spl,
inference(contradiction_clause,[status(thm)],[f12209]) ).
fof(f12211,plain,
( sQ843_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12178,f258]) ).
fof(f12212,plain,
sQ843_spl,
inference(contradiction_clause,[status(thm)],[f12211]) ).
fof(f12214,plain,
( ~ sQ842_spl
| ~ sQ274_spl
| skaf45(sk3,app(sk6,sk3)) = sk7 ),
inference(forward_demodulation,[status(thm)],[f3716,f12173]) ).
fof(f12258,plain,
! [X0,X1] :
( ~ sQ23_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f668,f3037]) ).
fof(f12259,plain,
! [X0,X1] :
( ~ sQ274_spl
| segmentP(X1,sk7)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3716,f3037]) ).
fof(f12264,definition,
! [X0,X1] :
( sQ845_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ845_spl])],[split_symbol_definition]) ).
fof(f12267,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ845_spl ),
inference(split_clause,[status(thm)],[f12258,f12264,f588,f667]) ).
fof(f12268,definition,
! [X0,X1] :
( sQ846_spl
<=> ( segmentP(X1,sk7)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ846_spl])],[split_symbol_definition]) ).
fof(f12271,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ846_spl ),
inference(split_clause,[status(thm)],[f12259,f12268,f3825,f563,f3709]) ).
fof(f12275,plain,
( ~ sQ274_spl
| app(app(sk6,sk3),sk7) = sk3
| ~ segmentP(sk3,sk3)
| ~ ssList(app(app(sk6,sk3),sk7))
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3716,f3038]) ).
fof(f12276,plain,
! [X0] :
( ~ sQ23_spl
| app(app(nil,nil),X0) = nil
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f668,f3038]) ).
fof(f12277,plain,
! [X0] :
( ~ sQ274_spl
| app(app(app(sk6,sk3),sk7),X0) = sk7
| ~ segmentP(sk7,app(sk3,X0))
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(sk7)
| ~ ssList(app(sk6,sk3))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f3716,f3038]) ).
fof(f12279,definition,
( sQ847_spl
<=> app(app(sk6,sk3),sk7) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ847_spl])],[split_symbol_definition]) ).
fof(f12282,plain,
( ~ sQ274_spl
| sQ847_spl
| ~ sQ337_spl
| ~ sQ336_spl
| ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f12275,f563,f637,f592,f5007,f5010,f12279,f3709]) ).
fof(f12283,definition,
! [X0] :
( sQ848_spl
<=> ( app(app(nil,nil),X0) = nil
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(app(app(nil,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ848_spl])],[split_symbol_definition]) ).
fof(f12286,plain,
( ~ sQ23_spl
| ~ sQ16_spl
| sQ848_spl ),
inference(split_clause,[status(thm)],[f12276,f12283,f588,f667]) ).
fof(f12287,definition,
! [X0] :
( sQ849_spl
<=> ( app(app(app(sk6,sk3),sk7),X0) = sk7
| ~ segmentP(sk7,app(sk3,X0))
| ~ ssList(app(app(app(sk6,sk3),sk7),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ849_spl])],[split_symbol_definition]) ).
fof(f12290,plain,
( ~ sQ274_spl
| ~ sQ12_spl
| ~ sQ284_spl
| sQ849_spl ),
inference(split_clause,[status(thm)],[f12277,f12287,f3825,f563,f3709]) ).
fof(f12297,plain,
( ~ sQ92_spl
| nil = sk3
| ~ ssList(sk3)
| nil = skaf82(sk3)
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3)) ),
inference(resolution,[status(thm)],[f1738,f320]) ).
fof(f12301,definition,
( sQ850_spl
<=> ssItem(hd(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ850_spl])],[split_symbol_definition]) ).
fof(f12303,plain,
( sQ850_spl
| ~ ssItem(hd(sk3)) ),
inference(component_clause,[status(thm)],[f12301]) ).
fof(f12304,definition,
( sQ851_spl
<=> ssList(tl(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ851_spl])],[split_symbol_definition]) ).
fof(f12306,plain,
( sQ851_spl
| ~ ssList(tl(sk3)) ),
inference(component_clause,[status(thm)],[f12304]) ).
fof(f12308,definition,
( sQ852_spl
<=> ssItem(skaf83(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ852_spl])],[split_symbol_definition]) ).
fof(f12310,plain,
( sQ852_spl
| ~ ssItem(skaf83(sk3)) ),
inference(component_clause,[status(thm)],[f12308]) ).
fof(f12311,definition,
( sQ853_spl
<=> ssList(skaf82(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ853_spl])],[split_symbol_definition]) ).
fof(f12313,plain,
( sQ853_spl
| ~ ssList(skaf82(sk3)) ),
inference(component_clause,[status(thm)],[f12311]) ).
fof(f12314,definition,
( sQ854_spl
<=> nil = skaf82(sk3) ),
introduced(definition,[new_symbols(definition,[sQ854_spl])],[split_symbol_definition]) ).
fof(f12315,plain,
( ~ sQ854_spl
| nil = skaf82(sk3) ),
inference(component_clause,[status(thm)],[f12314]) ).
fof(f12317,plain,
( ~ sQ92_spl
| sQ8_spl
| ~ sQ17_spl
| sQ854_spl
| ~ sQ853_spl
| ~ sQ852_spl ),
inference(split_clause,[status(thm)],[f12297,f12308,f12311,f12314,f592,f494,f1737]) ).
fof(f12318,definition,
( sQ855_spl
<=> ssItem(skaf44(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ855_spl])],[split_symbol_definition]) ).
fof(f12320,plain,
( sQ855_spl
| ~ ssItem(skaf44(sk3)) ),
inference(component_clause,[status(thm)],[f12318]) ).
fof(f12323,plain,
( sQ855_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12320,f255]) ).
fof(f12324,plain,
sQ855_spl,
inference(contradiction_clause,[status(thm)],[f12323]) ).
fof(f12325,plain,
( sQ853_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12313,f221]) ).
fof(f12326,plain,
sQ853_spl,
inference(contradiction_clause,[status(thm)],[f12325]) ).
fof(f12327,plain,
( sQ852_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12310,f220]) ).
fof(f12328,plain,
sQ852_spl,
inference(contradiction_clause,[status(thm)],[f12327]) ).
fof(f12329,plain,
( sQ851_spl
| ~ sQ82_spl
| ~ ssList(nil) ),
inference(forward_demodulation,[status(thm)],[f1575,f12306]) ).
fof(f12330,plain,
( sQ851_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12329,f216]) ).
fof(f12331,plain,
( sQ851_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f12330]) ).
fof(f12365,plain,
( ~ sQ854_spl
| nil = sk3
| cons(skaf83(sk3),nil) = sk3
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f12315,f320]) ).
fof(f12368,definition,
( sQ857_spl
<=> cons(skaf83(sk3),nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ857_spl])],[split_symbol_definition]) ).
fof(f12369,plain,
( ~ sQ857_spl
| cons(skaf83(sk3),nil) = sk3 ),
inference(component_clause,[status(thm)],[f12368]) ).
fof(f12371,plain,
( ~ sQ854_spl
| sQ8_spl
| sQ857_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f12365,f592,f12368,f494,f12314]) ).
fof(f12372,plain,
( sQ850_spl
| ~ sQ81_spl
| ~ ssItem(sk9) ),
inference(forward_demodulation,[status(thm)],[f1571,f12303]) ).
fof(f12373,plain,
( sQ850_spl
| ~ sQ81_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12372,f488]) ).
fof(f12374,plain,
( sQ850_spl
| ~ sQ81_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f12373]) ).
fof(f12379,plain,
! [X0] :
( ~ sQ30_spl
| app(app(sk3,nil),X0) = nil
| ~ segmentP(nil,app(sk3,X0))
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f765,f3038]) ).
fof(f12380,plain,
! [X0,X1] :
( ~ sQ30_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f765,f3037]) ).
fof(f12381,plain,
! [X0,X1] :
( ~ sQ30_spl
| app(app(sk3,nil),X1) = X0
| ~ ssList(app(app(sk3,nil),X1))
| ~ segmentP(X0,app(sk3,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f2845]) ).
fof(f12382,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(sk3,nil),X1))
| ~ segmentP(X2,app(sk3,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f2844]) ).
fof(f12383,plain,
! [X0,X1] :
( ~ sQ30_spl
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ frontsegP(sk3,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk3) ),
inference(paramodulation,[status(thm)],[f765,f2617]) ).
fof(f12385,plain,
! [X0,X1] :
( ~ sQ30_spl
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk3) ),
inference(paramodulation,[status(thm)],[f765,f2581]) ).
fof(f12389,plain,
! [X0] :
( ~ sQ30_spl
| app(sk3,nil) = X0
| ~ frontsegP(X0,sk3)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f765,f2146]) ).
fof(f12390,plain,
! [X0] :
( ~ sQ30_spl
| app(sk3,nil) = X0
| ~ rearsegP(X0,sk3)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f765,f2143]) ).
fof(f12391,plain,
( ~ sQ30_spl
| skaf45(app(sk3,nil),sk3) = nil
| ~ ssList(nil)
| ~ ssList(skaf45(sk3,sk3))
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f765,f10936]) ).
fof(f12392,plain,
( ~ sQ30_spl
| skaf46(app(sk3,nil),nil) = sk3
| ~ ssList(sk3)
| ~ ssList(skaf46(sk3,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f765,f10796]) ).
fof(f12414,definition,
! [X0] :
( sQ858_spl
<=> ( app(app(sk3,nil),X0) = nil
| ~ segmentP(nil,app(sk3,X0))
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ858_spl])],[split_symbol_definition]) ).
fof(f12417,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ858_spl ),
inference(split_clause,[status(thm)],[f12379,f12414,f592,f588,f764]) ).
fof(f12418,definition,
! [X0,X1] :
( sQ859_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(app(sk3,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ859_spl])],[split_symbol_definition]) ).
fof(f12421,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ859_spl ),
inference(split_clause,[status(thm)],[f12380,f12418,f592,f588,f764]) ).
fof(f12422,definition,
! [X0,X1] :
( sQ860_spl
<=> ( app(app(sk3,nil),X1) = X0
| ~ ssList(app(app(sk3,nil),X1))
| ~ segmentP(X0,app(sk3,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ860_spl])],[split_symbol_definition]) ).
fof(f12425,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ860_spl ),
inference(split_clause,[status(thm)],[f12381,f12422,f592,f588,f764]) ).
fof(f12426,definition,
! [X0,X1,X2] :
( sQ861_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(sk3,nil),X1))
| ~ segmentP(X2,app(sk3,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ861_spl])],[split_symbol_definition]) ).
fof(f12429,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ861_spl ),
inference(split_clause,[status(thm)],[f12382,f12426,f592,f588,f764]) ).
fof(f12430,definition,
! [X0,X1] :
( sQ862_spl
<=> ( ~ frontsegP(sk3,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ862_spl])],[split_symbol_definition]) ).
fof(f12433,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ862_spl ),
inference(split_clause,[status(thm)],[f12383,f12430,f588,f592,f764]) ).
fof(f12435,definition,
! [X0,X1] :
( sQ863_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ863_spl])],[split_symbol_definition]) ).
fof(f12438,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ863_spl ),
inference(split_clause,[status(thm)],[f12385,f12435,f592,f588,f764]) ).
fof(f12441,definition,
( sQ864_spl
<=> app(sk3,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ864_spl])],[split_symbol_definition]) ).
fof(f12442,plain,
( ~ sQ864_spl
| app(sk3,nil) = nil ),
inference(component_clause,[status(thm)],[f12441]) ).
fof(f12445,definition,
! [X0] :
( sQ865_spl
<=> ( app(sk3,nil) = X0
| ~ frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ865_spl])],[split_symbol_definition]) ).
fof(f12448,plain,
( ~ sQ30_spl
| ~ sQ17_spl
| ~ sQ16_spl
| sQ865_spl ),
inference(split_clause,[status(thm)],[f12389,f12445,f588,f592,f764]) ).
fof(f12449,definition,
! [X0] :
( sQ866_spl
<=> ( app(sk3,nil) = X0
| ~ rearsegP(X0,sk3)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f12452,plain,
( ~ sQ30_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ866_spl ),
inference(split_clause,[status(thm)],[f12390,f12449,f592,f588,f764]) ).
fof(f12453,definition,
( sQ867_spl
<=> ssList(skaf45(sk3,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ867_spl])],[split_symbol_definition]) ).
fof(f12455,plain,
( sQ867_spl
| ~ ssList(skaf45(sk3,sk3)) ),
inference(component_clause,[status(thm)],[f12453]) ).
fof(f12456,definition,
( sQ868_spl
<=> skaf45(app(sk3,nil),sk3) = nil ),
introduced(definition,[new_symbols(definition,[sQ868_spl])],[split_symbol_definition]) ).
fof(f12457,plain,
( ~ sQ868_spl
| skaf45(app(sk3,nil),sk3) = nil ),
inference(component_clause,[status(thm)],[f12456]) ).
fof(f12459,plain,
( ~ sQ30_spl
| sQ868_spl
| ~ sQ16_spl
| ~ sQ867_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f12391,f592,f12453,f588,f12456,f764]) ).
fof(f12460,definition,
( sQ869_spl
<=> ssList(skaf46(sk3,nil)) ),
introduced(definition,[new_symbols(definition,[sQ869_spl])],[split_symbol_definition]) ).
fof(f12462,plain,
( sQ869_spl
| ~ ssList(skaf46(sk3,nil)) ),
inference(component_clause,[status(thm)],[f12460]) ).
fof(f12463,definition,
( sQ870_spl
<=> skaf46(app(sk3,nil),nil) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ870_spl])],[split_symbol_definition]) ).
fof(f12466,plain,
( ~ sQ30_spl
| sQ870_spl
| ~ sQ17_spl
| ~ sQ869_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f12392,f588,f12460,f592,f12463,f764]) ).
fof(f12495,plain,
( sQ867_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12455,f259]) ).
fof(f12496,plain,
sQ867_spl,
inference(contradiction_clause,[status(thm)],[f12495]) ).
fof(f12497,plain,
( sQ869_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12462,f258]) ).
fof(f12498,plain,
sQ869_spl,
inference(contradiction_clause,[status(thm)],[f12497]) ).
fof(f12500,plain,
( ~ sQ868_spl
| ~ sQ30_spl
| skaf45(sk3,sk3) = nil ),
inference(forward_demodulation,[status(thm)],[f765,f12457]) ).
fof(f12501,plain,
( ~ sQ864_spl
| ~ sQ30_spl
| sk3 = nil ),
inference(forward_demodulation,[status(thm)],[f765,f12442]) ).
fof(f12502,plain,
( ~ sQ864_spl
| ~ sQ30_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12501,f496]) ).
fof(f12503,plain,
( ~ sQ864_spl
| ~ sQ30_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f12502]) ).
fof(f12507,plain,
! [X0,X1] :
( ~ ssList(tl(X1))
| ~ ssItem(X0)
| cons(X0,tl(X1)) = X1
| nil = X1
| ~ ssList(X1)
| hd(cons(X0,tl(X1))) != hd(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3094,f308]) ).
fof(f12509,plain,
! [X0] :
( ~ sQ82_spl
| ~ ssList(tl(sk3))
| ~ ssItem(X0)
| cons(X0,tl(sk3)) = sk3
| nil = sk3
| ~ ssList(sk3)
| hd(cons(X0,nil)) != hd(sk3) ),
inference(paramodulation,[status(thm)],[f1575,f12507]) ).
fof(f12511,definition,
! [X0] :
( sQ871_spl
<=> ( ~ ssItem(X0)
| cons(X0,tl(sk3)) = sk3
| hd(cons(X0,nil)) != hd(sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ871_spl])],[split_symbol_definition]) ).
fof(f12514,plain,
( ~ sQ82_spl
| ~ sQ851_spl
| sQ8_spl
| ~ sQ17_spl
| sQ871_spl ),
inference(split_clause,[status(thm)],[f12509,f12511,f592,f494,f12304,f1574]) ).
fof(f12538,plain,
! [X0] :
( ~ sQ821_spl
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f11886,f363]) ).
fof(f12583,definition,
( sQ878_spl
<=> frontsegP(sk7,nil) ),
introduced(definition,[new_symbols(definition,[sQ878_spl])],[split_symbol_definition]) ).
fof(f12584,plain,
( ~ sQ878_spl
| frontsegP(sk7,nil) ),
inference(component_clause,[status(thm)],[f12583]) ).
fof(f12585,plain,
( sQ878_spl
| ~ frontsegP(sk7,nil) ),
inference(component_clause,[status(thm)],[f12583]) ).
fof(f12596,definition,
( sQ881_spl
<=> ssList(skaf45(nil,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ881_spl])],[split_symbol_definition]) ).
fof(f12598,plain,
( sQ881_spl
| ~ ssList(skaf45(nil,sk7)) ),
inference(component_clause,[status(thm)],[f12596]) ).
fof(f12608,plain,
( ~ sQ821_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ393_spl ),
inference(split_clause,[status(thm)],[f12538,f5531,f588,f563,f11885]) ).
fof(f12645,plain,
( sQ881_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12598,f259]) ).
fof(f12646,plain,
sQ881_spl,
inference(contradiction_clause,[status(thm)],[f12645]) ).
fof(f12651,plain,
( sQ878_spl
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f12585,f268]) ).
fof(f12652,plain,
( sQ878_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f12651,f563,f12583]) ).
fof(f12654,plain,
! [X0] :
( ~ sQ878_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(X0,sk7) ),
inference(resolution,[status(thm)],[f12584,f387]) ).
fof(f12656,plain,
( ~ sQ878_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ758_spl ),
inference(split_clause,[status(thm)],[f12654,f10821,f588,f563,f12583]) ).
fof(f12657,plain,
( sQ790_spl
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f11371,f282]) ).
fof(f12658,plain,
( sQ790_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f12657,f563,f11369]) ).
fof(f12820,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X2,X1))
| ~ ssList(X3)
| ~ frontsegP(X3,cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3114,f295]) ).
fof(f12825,plain,
! [X0,X1] :
( ~ sQ9_spl
| frontsegP(X1,cons(sk9,X0))
| ~ ssList(X1)
| ~ frontsegP(X1,sk3)
| ~ ssItem(sk9)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f499,f12820]) ).
fof(f12831,definition,
! [X0,X1] :
( sQ894_spl
<=> ( frontsegP(X1,cons(sk9,X0))
| ~ ssList(X1)
| ~ frontsegP(X1,sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ894_spl])],[split_symbol_definition]) ).
fof(f12834,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ894_spl ),
inference(split_clause,[status(thm)],[f12825,f12831,f588,f487,f498]) ).
fof(f12835,plain,
! [X0,X1,X2] :
( cons(X2,X0) = cons(X2,X1)
| ~ frontsegP(cons(X2,X1),cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f3115,f295]) ).
fof(f12838,plain,
! [X0] :
( ~ sQ9_spl
| cons(sk9,X0) = cons(sk9,nil)
| ~ frontsegP(sk3,cons(sk9,X0))
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f499,f12835]) ).
fof(f12839,plain,
! [X0] :
( ~ sQ9_spl
| cons(sk9,nil) = cons(sk9,X0)
| ~ frontsegP(cons(sk9,X0),sk3)
| ~ ssItem(sk9)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f499,f12835]) ).
fof(f12841,definition,
! [X0] :
( sQ895_spl
<=> ( cons(sk9,X0) = cons(sk9,nil)
| ~ frontsegP(sk3,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ895_spl])],[split_symbol_definition]) ).
fof(f12844,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ895_spl ),
inference(split_clause,[status(thm)],[f12838,f12841,f588,f487,f498]) ).
fof(f12845,definition,
! [X0] :
( sQ896_spl
<=> ( cons(sk9,nil) = cons(sk9,X0)
| ~ frontsegP(cons(sk9,X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ896_spl])],[split_symbol_definition]) ).
fof(f12848,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ16_spl
| sQ896_spl ),
inference(split_clause,[status(thm)],[f12839,f12845,f588,f487,f498]) ).
fof(f12863,plain,
! [X0] :
( ~ sQ217_spl
| app(sk3,X0) = sk7
| ~ ssList(app(sk3,X0))
| ~ ssList(sk7)
| ~ segmentP(sk7,app(sk3,X0))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3184,f348]) ).
fof(f12864,plain,
! [X0,X1] :
( ~ sQ217_spl
| segmentP(X1,sk7)
| ~ ssList(X1)
| ~ ssList(app(sk3,X0))
| ~ ssList(sk7)
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3184,f383]) ).
fof(f12865,plain,
( ~ sQ30_spl
| ~ sQ217_spl
| segmentP(sk3,sk7)
| ~ ssList(app(sk3,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f765,f3184]) ).
fof(f12866,definition,
! [X0] :
( sQ897_spl
<=> ( app(sk3,X0) = sk7
| ~ ssList(app(sk3,X0))
| ~ segmentP(sk7,app(sk3,X0))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ897_spl])],[split_symbol_definition]) ).
fof(f12869,plain,
( ~ sQ217_spl
| ~ sQ12_spl
| sQ897_spl ),
inference(split_clause,[status(thm)],[f12863,f12866,f563,f3161]) ).
fof(f12870,definition,
! [X0,X1] :
( sQ898_spl
<=> ( segmentP(X1,sk7)
| ~ ssList(X1)
| ~ ssList(app(sk3,X0))
| ~ segmentP(X1,app(sk3,X0))
| ~ ssList(app(sk3,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ898_spl])],[split_symbol_definition]) ).
fof(f12873,plain,
( ~ sQ217_spl
| ~ sQ12_spl
| sQ898_spl ),
inference(split_clause,[status(thm)],[f12864,f12870,f563,f3161]) ).
fof(f12874,definition,
( sQ899_spl
<=> ssList(app(sk3,nil)) ),
introduced(definition,[new_symbols(definition,[sQ899_spl])],[split_symbol_definition]) ).
fof(f12876,plain,
( sQ899_spl
| ~ ssList(app(sk3,nil)) ),
inference(component_clause,[status(thm)],[f12874]) ).
fof(f12877,definition,
( sQ900_spl
<=> segmentP(sk3,sk7) ),
introduced(definition,[new_symbols(definition,[sQ900_spl])],[split_symbol_definition]) ).
fof(f12878,plain,
( ~ sQ900_spl
| segmentP(sk3,sk7) ),
inference(component_clause,[status(thm)],[f12877]) ).
fof(f12880,plain,
( ~ sQ30_spl
| ~ sQ217_spl
| sQ900_spl
| ~ sQ899_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f12865,f588,f12874,f12877,f3161,f764]) ).
fof(f12883,plain,
( sQ899_spl
| ~ sQ30_spl
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f765,f12876]) ).
fof(f12884,plain,
( sQ899_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12883,f441]) ).
fof(f12885,plain,
( sQ899_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f12884]) ).
fof(f12888,plain,
! [X0] :
( ~ sQ900_spl
| segmentP(X0,sk7)
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(sk7)
| ~ segmentP(X0,sk3) ),
inference(resolution,[status(thm)],[f12878,f383]) ).
fof(f12893,definition,
! [X0] :
( sQ902_spl
<=> ( segmentP(X0,sk7)
| ~ ssList(X0)
| ~ segmentP(X0,sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ902_spl])],[split_symbol_definition]) ).
fof(f12896,plain,
( ~ sQ900_spl
| ~ sQ17_spl
| ~ sQ12_spl
| sQ902_spl ),
inference(split_clause,[status(thm)],[f12888,f12893,f563,f592,f12877]) ).
fof(f12931,plain,
! [X0] :
( ~ sQ790_spl
| app(app(sk7,nil),X0) = nil
| ~ segmentP(nil,app(sk7,X0))
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11370,f3038]) ).
fof(f12932,plain,
! [X0,X1] :
( ~ sQ790_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk7,X0))
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f11370,f3037]) ).
fof(f12933,plain,
! [X0,X1] :
( ~ sQ790_spl
| app(app(sk7,nil),X1) = X0
| ~ ssList(app(app(sk7,nil),X1))
| ~ segmentP(X0,app(sk7,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f2845]) ).
fof(f12934,plain,
! [X0,X1,X2] :
( ~ sQ790_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(sk7,nil),X1))
| ~ segmentP(X2,app(sk7,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk7)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f11370,f2844]) ).
fof(f12935,plain,
! [X0,X1] :
( ~ sQ790_spl
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ frontsegP(sk7,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk7) ),
inference(paramodulation,[status(thm)],[f11370,f2617]) ).
fof(f12966,definition,
! [X0] :
( sQ906_spl
<=> ( app(app(sk7,nil),X0) = nil
| ~ segmentP(nil,app(sk7,X0))
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ906_spl])],[split_symbol_definition]) ).
fof(f12969,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ906_spl ),
inference(split_clause,[status(thm)],[f12931,f12966,f563,f588,f11369]) ).
fof(f12970,definition,
! [X0,X1] :
( sQ907_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk7,X0))
| ~ ssList(app(app(sk7,nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ907_spl])],[split_symbol_definition]) ).
fof(f12973,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ907_spl ),
inference(split_clause,[status(thm)],[f12932,f12970,f563,f588,f11369]) ).
fof(f12974,definition,
! [X0,X1] :
( sQ908_spl
<=> ( app(app(sk7,nil),X1) = X0
| ~ ssList(app(app(sk7,nil),X1))
| ~ segmentP(X0,app(sk7,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ908_spl])],[split_symbol_definition]) ).
fof(f12977,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ908_spl ),
inference(split_clause,[status(thm)],[f12933,f12974,f563,f588,f11369]) ).
fof(f12978,definition,
! [X0,X1,X2] :
( sQ909_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(app(sk7,nil),X1))
| ~ segmentP(X2,app(sk7,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f12981,plain,
( ~ sQ790_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sQ909_spl ),
inference(split_clause,[status(thm)],[f12934,f12978,f563,f588,f11369]) ).
fof(f12982,plain,
( ~ sQ790_spl
| ~ sQ12_spl
| ~ sQ16_spl
| sQ822_spl ),
inference(split_clause,[status(thm)],[f12935,f11922,f588,f563,f11369]) ).
fof(f13024,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ218_spl
| segmentP(sk3,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f765,f3166]) ).
fof(f13031,definition,
! [X0] :
( sQ910_spl
<=> ( segmentP(sk3,X0)
| ~ ssList(X0)
| ~ segmentP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ910_spl])],[split_symbol_definition]) ).
fof(f13034,plain,
( ~ sQ30_spl
| ~ sQ218_spl
| ~ sQ16_spl
| sQ910_spl ),
inference(split_clause,[status(thm)],[f13024,f13031,f588,f3165,f764]) ).
fof(f13163,definition,
( sQ928_spl
<=> ssList(skaf45(sk6,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ928_spl])],[split_symbol_definition]) ).
fof(f13165,plain,
( sQ928_spl
| ~ ssList(skaf45(sk6,sk6)) ),
inference(component_clause,[status(thm)],[f13163]) ).
fof(f13170,definition,
( sQ930_spl
<=> ssList(skaf46(sk6,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ930_spl])],[split_symbol_definition]) ).
fof(f13172,plain,
( sQ930_spl
| ~ ssList(skaf46(sk6,sk6)) ),
inference(component_clause,[status(thm)],[f13170]) ).
fof(f13200,plain,
( sQ930_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13172,f258]) ).
fof(f13201,plain,
sQ930_spl,
inference(contradiction_clause,[status(thm)],[f13200]) ).
fof(f13202,plain,
( sQ928_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13165,f259]) ).
fof(f13203,plain,
sQ928_spl,
inference(contradiction_clause,[status(thm)],[f13202]) ).
fof(f13242,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ248_spl
| lt(sk9,sk9)
| ~ ssList(app(app(X0,cons(sk9,nil)),sk3))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f3458]) ).
fof(f13243,definition,
! [X0] :
( sQ940_spl
<=> ( ~ ssList(app(app(X0,cons(sk9,nil)),sk3))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ940_spl])],[split_symbol_definition]) ).
fof(f13246,plain,
( ~ sQ9_spl
| ~ sQ248_spl
| sQ787_spl
| ~ sQ6_spl
| sQ940_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f13242,f588,f13243,f487,f11090,f3398,f498]) ).
fof(f13573,plain,
( ~ sQ127_spl
| ~ sQ25_spl
| rearsegP(nil,sk7) ),
inference(backward_demodulation,[status(thm)],[f682,f2391]) ).
fof(f13607,plain,
( ~ sQ127_spl
| ~ sQ25_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f13573,f5567,f681,f2390]) ).
fof(f13654,definition,
( sQ975_spl
<=> ssList(cons(sk9,sk7)) ),
introduced(definition,[new_symbols(definition,[sQ975_spl])],[split_symbol_definition]) ).
fof(f13656,plain,
( sQ975_spl
| ~ ssList(cons(sk9,sk7)) ),
inference(component_clause,[status(thm)],[f13654]) ).
fof(f13739,definition,
( sQ997_spl
<=> ssList(skaf45(sk3,app(sk6,cons(sk9,sk7)))) ),
introduced(definition,[new_symbols(definition,[sQ997_spl])],[split_symbol_definition]) ).
fof(f13741,plain,
( sQ997_spl
| ~ ssList(skaf45(sk3,app(sk6,cons(sk9,sk7)))) ),
inference(component_clause,[status(thm)],[f13739]) ).
fof(f13794,plain,
( sQ975_spl
| ~ sQ83_spl
| ~ sQ315_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13656,f5103]) ).
fof(f13795,plain,
( sQ975_spl
| ~ sQ83_spl
| ~ sQ315_spl ),
inference(contradiction_clause,[status(thm)],[f13794]) ).
fof(f13802,plain,
( sQ997_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13741,f259]) ).
fof(f13803,plain,
sQ997_spl,
inference(contradiction_clause,[status(thm)],[f13802]) ).
fof(f14148,plain,
( ~ sQ787_spl
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ lt(sk9,sk9) ),
inference(resolution,[status(thm)],[f11091,f328]) ).
fof(f14151,definition,
( sQ1051_spl
<=> gt(sk9,sk9) ),
introduced(definition,[new_symbols(definition,[sQ1051_spl])],[split_symbol_definition]) ).
fof(f14152,plain,
( ~ sQ1051_spl
| gt(sk9,sk9) ),
inference(component_clause,[status(thm)],[f14151]) ).
fof(f14156,plain,
( ~ sQ6_spl
| ~ sQ787_spl ),
inference(split_clause,[status(thm)],[f14148,f11090,f487]) ).
fof(f14368,plain,
( ~ sQ1051_spl
| ~ ssItem(sk9)
| ~ ssItem(sk9)
| ~ gt(sk9,sk9) ),
inference(resolution,[status(thm)],[f14152,f322]) ).
fof(f14371,plain,
( ~ sQ6_spl
| ~ sQ1051_spl ),
inference(split_clause,[status(thm)],[f14368,f14151,f487]) ).
fof(f14739,definition,
( sQ1078_spl
<=> ssList(skaf46(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1078_spl])],[split_symbol_definition]) ).
fof(f14741,plain,
( sQ1078_spl
| ~ ssList(skaf46(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f14739]) ).
fof(f14801,plain,
( sQ1078_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14741,f258]) ).
fof(f14802,plain,
sQ1078_spl,
inference(contradiction_clause,[status(thm)],[f14801]) ).
fof(f14887,definition,
( sQ1096_spl
<=> ssList(skaf45(sk3,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ1096_spl])],[split_symbol_definition]) ).
fof(f14889,plain,
( sQ1096_spl
| ~ ssList(skaf45(sk3,sk6)) ),
inference(component_clause,[status(thm)],[f14887]) ).
fof(f14928,plain,
( sQ1096_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14889,f259]) ).
fof(f14929,plain,
sQ1096_spl,
inference(contradiction_clause,[status(thm)],[f14928]) ).
fof(f15006,definition,
( sQ1111_spl
<=> ssList(skaf46(sk3,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1111_spl])],[split_symbol_definition]) ).
fof(f15008,plain,
( sQ1111_spl
| ~ ssList(skaf46(sk3,sk3)) ),
inference(component_clause,[status(thm)],[f15006]) ).
fof(f15036,plain,
( sQ1111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15008,f258]) ).
fof(f15037,plain,
sQ1111_spl,
inference(contradiction_clause,[status(thm)],[f15036]) ).
fof(f15328,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ249_spl
| lt(sk9,sk9)
| ~ ssList(app(app(X0,sk3),cons(sk9,nil)))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f499,f3459]) ).
fof(f15329,definition,
! [X0] :
( sQ1120_spl
<=> ( ~ ssList(app(app(X0,sk3),cons(sk9,nil)))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1120_spl])],[split_symbol_definition]) ).
fof(f15332,plain,
( ~ sQ9_spl
| ~ sQ249_spl
| sQ787_spl
| ~ sQ6_spl
| sQ1120_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f15328,f588,f15329,f487,f11090,f3402,f498]) ).
fof(f15557,plain,
! [X0] :
( ~ sQ253_spl
| cons(sk9,X0) = sk3
| ~ ssList(cons(sk9,X0))
| ~ ssList(sk3)
| ~ frontsegP(sk3,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f3420,f350]) ).
fof(f15558,plain,
! [X0,X1] :
( ~ sQ253_spl
| frontsegP(X1,sk3)
| ~ ssList(X1)
| ~ ssList(cons(sk9,X0))
| ~ ssList(sk3)
| ~ frontsegP(X1,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f3420,f387]) ).
fof(f15560,definition,
! [X0] :
( sQ1121_spl
<=> ( cons(sk9,X0) = sk3
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(sk3,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ1121_spl])],[split_symbol_definition]) ).
fof(f15563,plain,
( ~ sQ253_spl
| ~ sQ17_spl
| sQ1121_spl ),
inference(split_clause,[status(thm)],[f15557,f15560,f592,f3419]) ).
fof(f15564,definition,
! [X0,X1] :
( sQ1122_spl
<=> ( frontsegP(X1,sk3)
| ~ ssList(X1)
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(X1,cons(sk9,X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ1122_spl])],[split_symbol_definition]) ).
fof(f15567,plain,
( ~ sQ253_spl
| ~ sQ17_spl
| sQ1122_spl ),
inference(split_clause,[status(thm)],[f15558,f15564,f592,f3419]) ).
fof(f15986,plain,
! [X0,X1] :
( ~ sQ254_spl
| frontsegP(sk3,cons(sk9,X1))
| ~ ssList(sk3)
| ~ ssItem(sk9)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f3424,f12820]) ).
fof(f15987,plain,
! [X0] :
( ~ sQ254_spl
| sk3 = cons(sk9,X0)
| ~ ssList(sk3)
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(cons(sk9,X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f3424,f350]) ).
fof(f15988,plain,
! [X0,X1] :
( ~ sQ254_spl
| frontsegP(X1,cons(sk9,X0))
| ~ ssList(X1)
| ~ ssList(sk3)
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(X1,sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f3424,f387]) ).
fof(f15990,definition,
! [X0,X1] :
( sQ1152_spl
<=> ( frontsegP(sk3,cons(sk9,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1152_spl])],[split_symbol_definition]) ).
fof(f15993,plain,
( ~ sQ254_spl
| ~ sQ17_spl
| ~ sQ6_spl
| sQ1152_spl ),
inference(split_clause,[status(thm)],[f15986,f15990,f487,f592,f3423]) ).
fof(f15994,definition,
! [X0] :
( sQ1153_spl
<=> ( sk3 = cons(sk9,X0)
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(cons(sk9,X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1153_spl])],[split_symbol_definition]) ).
fof(f15997,plain,
( ~ sQ254_spl
| ~ sQ17_spl
| sQ1153_spl ),
inference(split_clause,[status(thm)],[f15987,f15994,f592,f3423]) ).
fof(f15998,definition,
! [X0,X1] :
( sQ1154_spl
<=> ( frontsegP(X1,cons(sk9,X0))
| ~ ssList(X1)
| ~ ssList(cons(sk9,X0))
| ~ frontsegP(X1,sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1154_spl])],[split_symbol_definition]) ).
fof(f16001,plain,
( ~ sQ254_spl
| ~ sQ17_spl
| sQ1154_spl ),
inference(split_clause,[status(thm)],[f15988,f15998,f592,f3423]) ).
fof(f16005,plain,
( ~ sQ615_spl
| ~ sQ29_spl
| app(sk3,tl(sk6)) = sk6
| ~ ssList(tl(sk6)) ),
inference(paramodulation,[status(thm)],[f9072,f721]) ).
fof(f16052,definition,
( sQ1156_spl
<=> app(sk3,tl(sk6)) = sk6 ),
introduced(definition,[new_symbols(definition,[sQ1156_spl])],[split_symbol_definition]) ).
fof(f16053,plain,
( ~ sQ1156_spl
| app(sk3,tl(sk6)) = sk6 ),
inference(component_clause,[status(thm)],[f16052]) ).
fof(f16055,plain,
( ~ sQ615_spl
| ~ sQ29_spl
| sQ1156_spl
| ~ sQ619_spl ),
inference(split_clause,[status(thm)],[f16005,f9152,f16052,f720,f9071]) ).
fof(f16133,plain,
! [X0] :
( ~ sQ320_spl
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ frontsegP(sk6,X0)
| frontsegP(sk3,X0)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4684,f2617]) ).
fof(f16134,plain,
( ~ sQ320_spl
| ~ ssList(sk3)
| frontsegP(sk3,sk6)
| ~ ssList(sk3)
| ~ ssList(sk6) ),
inference(resolution,[status(thm)],[f4684,f2615]) ).
fof(f16138,plain,
( ~ sQ320_spl
| ~ sQ20_spl
| ~ sQ17_spl
| sQ377_spl ),
inference(split_clause,[status(thm)],[f16133,f5438,f592,f637,f4683]) ).
fof(f16139,plain,
( ~ sQ320_spl
| sQ388_spl
| ~ sQ17_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f16134,f637,f592,f5485,f4683]) ).
fof(f16347,definition,
! [X0] :
( sQ1199_spl
<=> ( ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1199_spl])],[split_symbol_definition]) ).
fof(f16348,plain,
! [X0] :
( ~ sQ1199_spl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f16347]) ).
fof(f16353,plain,
! [X0] :
( ~ sQ1199_spl
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f16348]) ).
fof(f16369,plain,
( ~ sQ1199_spl
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f16353,f268]) ).
fof(f16372,plain,
( ~ sQ1199_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16369,f588,f16347]) ).
fof(f16377,plain,
! [X0] :
( ~ sQ857_spl
| app(sk3,X0) = cons(skaf83(sk3),X0)
| ~ ssList(X0)
| ~ ssItem(skaf83(sk3)) ),
inference(paramodulation,[status(thm)],[f12369,f339]) ).
fof(f16379,plain,
( ~ sQ857_spl
| ~ sQ255_spl
| skaf83(sk3) = sk9
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ~ frontsegP(sk3,sk3) ),
inference(paramodulation,[status(thm)],[f12369,f3428]) ).
fof(f16383,plain,
! [X0] :
( ~ sQ857_spl
| ~ sQ249_spl
| ~ sQ9_spl
| lt(sk9,skaf83(sk3))
| ~ ssList(app(app(X0,sk3),cons(skaf83(sk3),nil)))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f3459]) ).
fof(f16384,plain,
! [X0] :
( ~ sQ857_spl
| ~ sQ248_spl
| ~ sQ9_spl
| lt(skaf83(sk3),sk9)
| ~ ssList(app(app(X0,cons(skaf83(sk3),nil)),sk3))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f3458]) ).
fof(f16387,plain,
! [X0] :
( ~ sQ857_spl
| cons(skaf83(sk3),nil) = cons(skaf83(sk3),X0)
| ~ frontsegP(cons(skaf83(sk3),X0),sk3)
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f12369,f12835]) ).
fof(f16388,plain,
! [X0] :
( ~ sQ857_spl
| cons(skaf83(sk3),X0) = cons(skaf83(sk3),nil)
| ~ frontsegP(sk3,cons(skaf83(sk3),X0))
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f12369,f12835]) ).
fof(f16389,plain,
! [X0,X1] :
( ~ sQ857_spl
| frontsegP(X1,cons(skaf83(sk3),X0))
| ~ ssList(X1)
| ~ frontsegP(X1,sk3)
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f12369,f12820]) ).
fof(f16390,plain,
( ~ sQ857_spl
| hd(sk3) = skaf83(sk3)
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3)) ),
inference(paramodulation,[status(thm)],[f12369,f306]) ).
fof(f16391,plain,
( ~ sQ857_spl
| tl(sk3) = nil
| ~ ssList(nil)
| ~ ssItem(skaf83(sk3)) ),
inference(paramodulation,[status(thm)],[f12369,f305]) ).
fof(f16394,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| ~ ssList(app(app(X2,cons(X0,X1)),cons(skaf83(sk3),nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ leq(skaf83(sk3),X0)
| ~ leq(X0,skaf83(sk3)) ),
inference(paramodulation,[status(thm)],[f12369,f541]) ).
fof(f16395,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| ~ ssList(app(app(X2,cons(skaf83(sk3),nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ leq(X0,skaf83(sk3))
| ~ leq(skaf83(sk3),X0) ),
inference(paramodulation,[status(thm)],[f12369,f541]) ).
fof(f16396,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| leq(skaf83(sk3),X2)
| leq(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f540]) ).
fof(f16397,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| leq(X2,skaf83(sk3))
| leq(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f12369,f540]) ).
fof(f16398,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| lt(skaf83(sk3),X2)
| lt(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f539]) ).
fof(f16399,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| lt(X2,skaf83(sk3))
| lt(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f12369,f539]) ).
fof(f16400,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| leq(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f538]) ).
fof(f16401,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| leq(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f12369,f538]) ).
fof(f16402,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| lt(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f537]) ).
fof(f16403,plain,
! [X0,X1,X2] :
( ~ sQ857_spl
| lt(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f12369,f537]) ).
fof(f16404,plain,
! [X0,X1] :
( ~ sQ857_spl
| X1 = skaf83(sk3)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk3),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk3)))
| ~ ssItem(X1)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f536]) ).
fof(f16405,plain,
! [X0] :
( ~ sQ857_spl
| frontsegP(cons(skaf83(sk3),X0),sk3)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f12369,f534]) ).
fof(f16406,plain,
! [X0] :
( ~ sQ857_spl
| frontsegP(sk3,cons(skaf83(sk3),X0))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f12369,f534]) ).
fof(f16407,plain,
! [X0,X1] :
( ~ sQ857_spl
| X0 = skaf83(sk3)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk3) ),
inference(paramodulation,[status(thm)],[f12369,f421]) ).
fof(f16408,plain,
! [X0,X1] :
( ~ sQ857_spl
| skaf83(sk3) = X0
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f12369,f421]) ).
fof(f16409,plain,
! [X0,X1] :
( ~ sQ857_spl
| frontsegP(X1,nil)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk3))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(cons(X0,X1),sk3) ),
inference(paramodulation,[status(thm)],[f12369,f417]) ).
fof(f16410,plain,
! [X0,X1] :
( ~ sQ857_spl
| frontsegP(nil,X1)
| ~ ssItem(skaf83(sk3))
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ),
inference(paramodulation,[status(thm)],[f12369,f417]) ).
fof(f16412,plain,
! [X0,X1] :
( ~ sQ857_spl
| X0 = skaf83(sk3)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk3))
| cons(X0,X1) != sk3 ),
inference(paramodulation,[status(thm)],[f12369,f410]) ).
fof(f16416,plain,
! [X0] :
( ~ sQ857_spl
| memberP(app(X0,sk3),skaf83(sk3))
| ~ ssList(app(X0,cons(skaf83(sk3),nil)))
| ~ ssItem(skaf83(sk3))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f532]) ).
fof(f16418,plain,
( ~ sQ857_spl
| memberP(sk3,skaf83(sk3))
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f12369,f526]) ).
fof(f16421,plain,
! [X0] :
( ~ sQ857_spl
| X0 = skaf83(sk3)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(skaf83(sk3))
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f12369,f400]) ).
fof(f16423,definition,
! [X0] :
( sQ1201_spl
<=> ( app(sk3,X0) = cons(skaf83(sk3),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1201_spl])],[split_symbol_definition]) ).
fof(f16426,plain,
( ~ sQ857_spl
| sQ1201_spl
| ~ sQ852_spl ),
inference(split_clause,[status(thm)],[f16377,f12308,f16423,f12368]) ).
fof(f16427,definition,
( sQ1202_spl
<=> sk9 = skaf83(sk3) ),
introduced(definition,[new_symbols(definition,[sQ1202_spl])],[split_symbol_definition]) ).
fof(f16428,plain,
( ~ sQ1202_spl
| sk9 = skaf83(sk3) ),
inference(component_clause,[status(thm)],[f16427]) ).
fof(f16431,plain,
( ~ sQ857_spl
| ~ sQ255_spl
| sQ1202_spl
| ~ sQ852_spl
| ~ sQ16_spl
| ~ sQ129_spl ),
inference(split_clause,[status(thm)],[f16379,f2405,f588,f12308,f16427,f3427,f12368]) ).
fof(f16435,definition,
! [X0] :
( sQ1203_spl
<=> ( ~ ssList(app(app(X0,sk3),cons(skaf83(sk3),nil)))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1203_spl])],[split_symbol_definition]) ).
fof(f16438,definition,
( sQ1204_spl
<=> lt(sk9,skaf83(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1204_spl])],[split_symbol_definition]) ).
fof(f16439,plain,
( ~ sQ1204_spl
| lt(sk9,skaf83(sk3)) ),
inference(component_clause,[status(thm)],[f16438]) ).
fof(f16441,plain,
( ~ sQ857_spl
| ~ sQ249_spl
| ~ sQ9_spl
| sQ1204_spl
| ~ sQ852_spl
| sQ1203_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16383,f588,f16435,f12308,f16438,f498,f3402,f12368]) ).
fof(f16442,definition,
! [X0] :
( sQ1205_spl
<=> ( ~ ssList(app(app(X0,cons(skaf83(sk3),nil)),sk3))
| ~ strictorderedP(app(app(X0,sk3),sk3))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1205_spl])],[split_symbol_definition]) ).
fof(f16445,definition,
( sQ1206_spl
<=> lt(skaf83(sk3),sk9) ),
introduced(definition,[new_symbols(definition,[sQ1206_spl])],[split_symbol_definition]) ).
fof(f16446,plain,
( ~ sQ1206_spl
| lt(skaf83(sk3),sk9) ),
inference(component_clause,[status(thm)],[f16445]) ).
fof(f16448,plain,
( ~ sQ857_spl
| ~ sQ248_spl
| ~ sQ9_spl
| sQ1206_spl
| ~ sQ852_spl
| sQ1205_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16384,f588,f16442,f12308,f16445,f498,f3398,f12368]) ).
fof(f16463,definition,
! [X0] :
( sQ1211_spl
<=> ( cons(skaf83(sk3),nil) = cons(skaf83(sk3),X0)
| ~ frontsegP(cons(skaf83(sk3),X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1211_spl])],[split_symbol_definition]) ).
fof(f16466,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1211_spl ),
inference(split_clause,[status(thm)],[f16387,f16463,f588,f12308,f12368]) ).
fof(f16467,definition,
! [X0] :
( sQ1212_spl
<=> ( cons(skaf83(sk3),X0) = cons(skaf83(sk3),nil)
| ~ frontsegP(sk3,cons(skaf83(sk3),X0))
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ1212_spl])],[split_symbol_definition]) ).
fof(f16470,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1212_spl ),
inference(split_clause,[status(thm)],[f16388,f16467,f588,f12308,f12368]) ).
fof(f16471,definition,
! [X0,X1] :
( sQ1213_spl
<=> ( frontsegP(X1,cons(skaf83(sk3),X0))
| ~ ssList(X1)
| ~ frontsegP(X1,sk3)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1213_spl])],[split_symbol_definition]) ).
fof(f16474,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1213_spl ),
inference(split_clause,[status(thm)],[f16389,f16471,f588,f12308,f12368]) ).
fof(f16475,definition,
( sQ1214_spl
<=> hd(sk3) = skaf83(sk3) ),
introduced(definition,[new_symbols(definition,[sQ1214_spl])],[split_symbol_definition]) ).
fof(f16478,plain,
( ~ sQ857_spl
| sQ1214_spl
| ~ sQ16_spl
| ~ sQ852_spl ),
inference(split_clause,[status(thm)],[f16390,f12308,f588,f16475,f12368]) ).
fof(f16479,plain,
( ~ sQ857_spl
| sQ82_spl
| ~ sQ16_spl
| ~ sQ852_spl ),
inference(split_clause,[status(thm)],[f16391,f12308,f588,f1574,f12368]) ).
fof(f16488,definition,
! [X0,X1,X2] :
( sQ1217_spl
<=> ( ~ ssList(app(app(X2,cons(X0,X1)),cons(skaf83(sk3),nil)))
| ~ cyclefreeP(app(app(X2,cons(X0,X1)),sk3))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(skaf83(sk3),X0)
| ~ leq(X0,skaf83(sk3)) ) ),
introduced(definition,[new_symbols(definition,[sQ1217_spl])],[split_symbol_definition]) ).
fof(f16491,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1217_spl ),
inference(split_clause,[status(thm)],[f16394,f16488,f588,f12308,f12368]) ).
fof(f16492,definition,
! [X0,X1,X2] :
( sQ1218_spl
<=> ( ~ ssList(app(app(X2,cons(skaf83(sk3),nil)),cons(X0,X1)))
| ~ cyclefreeP(app(app(X2,sk3),cons(X0,X1)))
| ~ ssItem(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ leq(X0,skaf83(sk3))
| ~ leq(skaf83(sk3),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1218_spl])],[split_symbol_definition]) ).
fof(f16495,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1218_spl ),
inference(split_clause,[status(thm)],[f16395,f16492,f588,f12308,f12368]) ).
fof(f16496,definition,
! [X0,X1,X2] :
( sQ1219_spl
<=> ( leq(skaf83(sk3),X2)
| leq(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ totalorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1219_spl])],[split_symbol_definition]) ).
fof(f16499,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1219_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16396,f588,f16496,f12308,f12368]) ).
fof(f16500,definition,
! [X0,X1,X2] :
( sQ1220_spl
<=> ( leq(X2,skaf83(sk3))
| leq(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ totalorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1220_spl])],[split_symbol_definition]) ).
fof(f16503,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1220_spl ),
inference(split_clause,[status(thm)],[f16397,f16500,f588,f12308,f12368]) ).
fof(f16504,definition,
! [X0,X1,X2] :
( sQ1221_spl
<=> ( lt(skaf83(sk3),X2)
| lt(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ strictorderP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1221_spl])],[split_symbol_definition]) ).
fof(f16507,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1221_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16398,f588,f16504,f12308,f12368]) ).
fof(f16508,definition,
! [X0,X1,X2] :
( sQ1222_spl
<=> ( lt(X2,skaf83(sk3))
| lt(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ strictorderP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1222_spl])],[split_symbol_definition]) ).
fof(f16511,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1222_spl ),
inference(split_clause,[status(thm)],[f16399,f16508,f588,f12308,f12368]) ).
fof(f16512,definition,
! [X0,X1,X2] :
( sQ1223_spl
<=> ( leq(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ totalorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1223_spl])],[split_symbol_definition]) ).
fof(f16515,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1223_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16400,f588,f16512,f12308,f12368]) ).
fof(f16516,definition,
! [X0,X1,X2] :
( sQ1224_spl
<=> ( leq(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ totalorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1224_spl])],[split_symbol_definition]) ).
fof(f16519,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1224_spl ),
inference(split_clause,[status(thm)],[f16401,f16516,f588,f12308,f12368]) ).
fof(f16520,definition,
! [X0,X1,X2] :
( sQ1225_spl
<=> ( lt(X2,skaf83(sk3))
| ~ ssList(app(app(X1,cons(X2,X0)),cons(skaf83(sk3),nil)))
| ~ strictorderedP(app(app(X1,cons(X2,X0)),sk3))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1225_spl])],[split_symbol_definition]) ).
fof(f16523,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1225_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16402,f588,f16520,f12308,f12368]) ).
fof(f16524,definition,
! [X0,X1,X2] :
( sQ1226_spl
<=> ( lt(skaf83(sk3),X2)
| ~ ssList(app(app(X1,cons(skaf83(sk3),nil)),cons(X2,X0)))
| ~ strictorderedP(app(app(X1,sk3),cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1226_spl])],[split_symbol_definition]) ).
fof(f16527,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1226_spl ),
inference(split_clause,[status(thm)],[f16403,f16524,f588,f12308,f12368]) ).
fof(f16528,definition,
! [X0,X1] :
( sQ1227_spl
<=> ( X1 = skaf83(sk3)
| ~ ssList(app(X0,cons(X1,cons(skaf83(sk3),nil))))
| ~ equalelemsP(app(X0,cons(X1,sk3)))
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1227_spl])],[split_symbol_definition]) ).
fof(f16531,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1227_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16404,f588,f16528,f12308,f12368]) ).
fof(f16532,definition,
! [X0] :
( sQ1228_spl
<=> ( frontsegP(cons(skaf83(sk3),X0),sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ1228_spl])],[split_symbol_definition]) ).
fof(f16535,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1228_spl ),
inference(split_clause,[status(thm)],[f16405,f16532,f588,f12308,f12368]) ).
fof(f16536,definition,
! [X0] :
( sQ1229_spl
<=> ( frontsegP(sk3,cons(skaf83(sk3),X0))
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1229_spl])],[split_symbol_definition]) ).
fof(f16539,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1229_spl ),
inference(split_clause,[status(thm)],[f16406,f16536,f588,f12308,f12368]) ).
fof(f16540,definition,
! [X0,X1] :
( sQ1230_spl
<=> ( X0 = skaf83(sk3)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),sk3) ) ),
introduced(definition,[new_symbols(definition,[sQ1230_spl])],[split_symbol_definition]) ).
fof(f16543,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1230_spl ),
inference(split_clause,[status(thm)],[f16407,f16540,f588,f12308,f12368]) ).
fof(f16544,definition,
! [X0,X1] :
( sQ1231_spl
<=> ( skaf83(sk3) = X0
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(sk3,cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ1231_spl])],[split_symbol_definition]) ).
fof(f16547,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1231_spl ),
inference(split_clause,[status(thm)],[f16408,f16544,f588,f12308,f12368]) ).
fof(f16548,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f16409,f3435,f588,f12308,f12368]) ).
fof(f16549,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f16410,f3439,f588,f12308,f12368]) ).
fof(f16551,definition,
! [X0,X1] :
( sQ1232_spl
<=> ( X0 = skaf83(sk3)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != sk3 ) ),
introduced(definition,[new_symbols(definition,[sQ1232_spl])],[split_symbol_definition]) ).
fof(f16554,plain,
( ~ sQ857_spl
| ~ sQ16_spl
| ~ sQ852_spl
| sQ1232_spl ),
inference(split_clause,[status(thm)],[f16412,f16551,f12308,f588,f12368]) ).
fof(f16558,definition,
! [X0] :
( sQ1233_spl
<=> ( memberP(app(X0,sk3),skaf83(sk3))
| ~ ssList(app(X0,cons(skaf83(sk3),nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f16561,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| sQ1233_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16416,f588,f16558,f12308,f12368]) ).
fof(f16563,definition,
( sQ1234_spl
<=> memberP(sk3,skaf83(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1234_spl])],[split_symbol_definition]) ).
fof(f16566,plain,
( ~ sQ857_spl
| sQ1234_spl
| ~ sQ852_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f16418,f588,f12308,f16563,f12368]) ).
fof(f16569,definition,
! [X0] :
( sQ1235_spl
<=> ( X0 = skaf83(sk3)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1235_spl])],[split_symbol_definition]) ).
fof(f16572,plain,
( ~ sQ857_spl
| ~ sQ852_spl
| ~ sQ16_spl
| sQ1235_spl ),
inference(split_clause,[status(thm)],[f16421,f16569,f588,f12308,f12368]) ).
fof(f16596,plain,
( ~ sQ1202_spl
| nil = sk3
| cons(sk9,skaf82(sk3)) = sk3
| ~ ssList(sk3) ),
inference(paramodulation,[status(thm)],[f16428,f320]) ).
fof(f16598,definition,
( sQ1236_spl
<=> cons(sk9,skaf82(sk3)) = sk3 ),
introduced(definition,[new_symbols(definition,[sQ1236_spl])],[split_symbol_definition]) ).
fof(f16601,plain,
( ~ sQ1202_spl
| sQ8_spl
| sQ1236_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f16596,f592,f16598,f494,f16427]) ).
fof(f16624,plain,
( ~ sQ1206_spl
| ~ sQ1202_spl
| lt(sk9,sk9) ),
inference(forward_demodulation,[status(thm)],[f16428,f16446]) ).
fof(f16625,plain,
( ~ sQ1206_spl
| ~ sQ1202_spl
| sQ787_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16624,f11092]) ).
fof(f16626,plain,
( ~ sQ1206_spl
| ~ sQ1202_spl
| sQ787_spl ),
inference(contradiction_clause,[status(thm)],[f16625]) ).
fof(f16628,plain,
( ~ sQ1204_spl
| ~ sQ1202_spl
| lt(sk9,sk9) ),
inference(forward_demodulation,[status(thm)],[f16428,f16439]) ).
fof(f16629,plain,
( ~ sQ1204_spl
| ~ sQ1202_spl
| sQ787_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16628,f11092]) ).
fof(f16630,plain,
( ~ sQ1204_spl
| ~ sQ1202_spl
| sQ787_spl ),
inference(contradiction_clause,[status(thm)],[f16629]) ).
fof(f16887,plain,
! [X0,X1] :
( ~ sQ252_spl
| ~ ssList(app(X1,sk3))
| ~ ssList(cons(sk9,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3416,f294]) ).
fof(f16890,definition,
! [X0] :
( sQ1248_spl
<=> ( ~ ssList(cons(sk9,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1248_spl])],[split_symbol_definition]) ).
fof(f16891,plain,
! [X0] :
( ~ sQ1248_spl
| ~ ssList(cons(sk9,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f16890]) ).
fof(f16893,definition,
! [X1] :
( sQ1249_spl
<=> ( ~ ssList(app(X1,sk3))
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1249_spl])],[split_symbol_definition]) ).
fof(f16894,plain,
! [X0] :
( ~ sQ1249_spl
| ~ ssList(app(X0,sk3))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f16893]) ).
fof(f16896,plain,
( ~ sQ252_spl
| sQ1249_spl
| sQ1248_spl ),
inference(split_clause,[status(thm)],[f16887,f16890,f16893,f3415]) ).
fof(f16971,plain,
( ~ sQ868_spl
| ~ sQ30_spl
| ~ sQ82_spl
| ~ sQ286_spl
| skaf45(sk3,sk3) = sk6 ),
inference(backward_demodulation,[status(thm)],[f5669,f12500]) ).
fof(f17405,definition,
( sQ1293_spl
<=> ssList(skaf46(sk3,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ1293_spl])],[split_symbol_definition]) ).
fof(f17407,plain,
( sQ1293_spl
| ~ ssList(skaf46(sk3,sk6)) ),
inference(component_clause,[status(thm)],[f17405]) ).
fof(f17460,plain,
( sQ1293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17407,f258]) ).
fof(f17461,plain,
sQ1293_spl,
inference(contradiction_clause,[status(thm)],[f17460]) ).
fof(f17909,definition,
( sQ1319_spl
<=> ssList(skaf46(sk7,sk6)) ),
introduced(definition,[new_symbols(definition,[sQ1319_spl])],[split_symbol_definition]) ).
fof(f17911,plain,
( sQ1319_spl
| ~ ssList(skaf46(sk7,sk6)) ),
inference(component_clause,[status(thm)],[f17909]) ).
fof(f17964,plain,
( sQ1319_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17911,f258]) ).
fof(f17965,plain,
sQ1319_spl,
inference(contradiction_clause,[status(thm)],[f17964]) ).
fof(f18042,plain,
( ~ sQ286_spl
| sQ419_spl
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f6039,f5714]) ).
fof(f18043,plain,
( ~ sQ286_spl
| sQ419_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18042,f441]) ).
fof(f18044,plain,
( ~ sQ286_spl
| sQ419_spl ),
inference(contradiction_clause,[status(thm)],[f18043]) ).
fof(f18501,definition,
( sQ1379_spl
<=> ssList(skaf45(sk7,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1379_spl])],[split_symbol_definition]) ).
fof(f18503,plain,
( sQ1379_spl
| ~ ssList(skaf45(sk7,sk3)) ),
inference(component_clause,[status(thm)],[f18501]) ).
fof(f18508,definition,
( sQ1381_spl
<=> ssList(skaf46(sk7,tl(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ1381_spl])],[split_symbol_definition]) ).
fof(f18510,plain,
( sQ1381_spl
| ~ ssList(skaf46(sk7,tl(sk7))) ),
inference(component_clause,[status(thm)],[f18508]) ).
fof(f18565,plain,
( sQ1381_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18510,f258]) ).
fof(f18566,plain,
sQ1381_spl,
inference(contradiction_clause,[status(thm)],[f18565]) ).
fof(f18567,plain,
( sQ1379_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18503,f259]) ).
fof(f18568,plain,
sQ1379_spl,
inference(contradiction_clause,[status(thm)],[f18567]) ).
fof(f18658,plain,
( ~ sQ1156_spl
| frontsegP(sk6,sk3)
| ~ ssList(sk3)
| ~ ssList(tl(sk6)) ),
inference(paramodulation,[status(thm)],[f16053,f2398]) ).
fof(f18720,definition,
( sQ1414_spl
<=> ssList(skaf45(sk6,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1414_spl])],[split_symbol_definition]) ).
fof(f18722,plain,
( sQ1414_spl
| ~ ssList(skaf45(sk6,sk3)) ),
inference(component_clause,[status(thm)],[f18720]) ).
fof(f18727,definition,
( sQ1416_spl
<=> ssList(skaf46(sk6,tl(sk6))) ),
introduced(definition,[new_symbols(definition,[sQ1416_spl])],[split_symbol_definition]) ).
fof(f18729,plain,
( sQ1416_spl
| ~ ssList(skaf46(sk6,tl(sk6))) ),
inference(component_clause,[status(thm)],[f18727]) ).
fof(f18779,plain,
( ~ sQ1156_spl
| sQ389_spl
| ~ sQ17_spl
| ~ sQ619_spl ),
inference(split_clause,[status(thm)],[f18658,f9152,f592,f5492,f16052]) ).
fof(f18787,plain,
( sQ1416_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18729,f258]) ).
fof(f18788,plain,
sQ1416_spl,
inference(contradiction_clause,[status(thm)],[f18787]) ).
fof(f18789,plain,
( sQ1414_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18722,f259]) ).
fof(f18790,plain,
sQ1414_spl,
inference(contradiction_clause,[status(thm)],[f18789]) ).
fof(f18895,definition,
( sQ1441_spl
<=> ssList(skaf46(sk7,skaf82(sk7))) ),
introduced(definition,[new_symbols(definition,[sQ1441_spl])],[split_symbol_definition]) ).
fof(f18897,plain,
( sQ1441_spl
| ~ ssList(skaf46(sk7,skaf82(sk7))) ),
inference(component_clause,[status(thm)],[f18895]) ).
fof(f18946,plain,
( sQ1441_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18897,f258]) ).
fof(f18947,plain,
sQ1441_spl,
inference(contradiction_clause,[status(thm)],[f18946]) ).
fof(f19302,plain,
( ~ sQ83_spl
| ~ sQ315_spl
| ~ sQ1248_spl
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f16891,f5103]) ).
fof(f19306,plain,
( ~ sQ83_spl
| ~ sQ315_spl
| ~ sQ1248_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f19302,f563,f16890,f4368,f1640]) ).
fof(f19310,plain,
! [X0] :
( ~ sQ1249_spl
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f16894,f294]) ).
fof(f19312,plain,
( ~ sQ1249_spl
| ~ sQ17_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f19310,f1187,f592,f16893]) ).
fof(f19435,plain,
( sQ681_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10104,f468]) ).
fof(f19464,plain,
( sQ681_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f19435]) ).
fof(f19473,plain,
( sQ517_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6902,f468]) ).
fof(f19474,plain,
( sQ517_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f19473]) ).
fof(f19781,plain,
( ~ sQ1_spl
| sQ181_spl
| ~ ssList(skaf53(sk7)) ),
inference(resolution,[status(thm)],[f2932,f877]) ).
fof(f19782,plain,
( ~ sQ1_spl
| sQ181_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19781,f250]) ).
fof(f19783,plain,
( ~ sQ1_spl
| sQ181_spl ),
inference(contradiction_clause,[status(thm)],[f19782]) ).
fof(f19784,plain,
( ~ sQ1_spl
| sQ185_spl
| ~ ssList(skaf58(sk7)) ),
inference(resolution,[status(thm)],[f2945,f877]) ).
fof(f19785,plain,
( ~ sQ1_spl
| sQ185_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19784,f245]) ).
fof(f19786,plain,
( ~ sQ1_spl
| sQ185_spl ),
inference(contradiction_clause,[status(thm)],[f19785]) ).
fof(f19787,plain,
( ~ sQ1_spl
| sQ189_spl
| ~ ssList(skaf63(sk7)) ),
inference(resolution,[status(thm)],[f2958,f877]) ).
fof(f19788,plain,
( ~ sQ1_spl
| sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19787,f240]) ).
fof(f19789,plain,
( ~ sQ1_spl
| sQ189_spl ),
inference(contradiction_clause,[status(thm)],[f19788]) ).
fof(f19790,plain,
( ~ sQ1_spl
| sQ193_spl
| ~ ssList(skaf68(sk7)) ),
inference(resolution,[status(thm)],[f2971,f877]) ).
fof(f19791,plain,
( ~ sQ1_spl
| sQ193_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19790,f235]) ).
fof(f19792,plain,
( ~ sQ1_spl
| sQ193_spl ),
inference(contradiction_clause,[status(thm)],[f19791]) ).
fof(f19793,plain,
( ~ sQ1_spl
| sQ197_spl
| ~ ssList(skaf73(sk7)) ),
inference(resolution,[status(thm)],[f2984,f877]) ).
fof(f19794,plain,
( ~ sQ1_spl
| sQ197_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19793,f230]) ).
fof(f19795,plain,
( ~ sQ1_spl
| sQ197_spl ),
inference(contradiction_clause,[status(thm)],[f19794]) ).
fof(f19830,plain,
( ~ sQ842_spl
| ~ sQ274_spl
| ~ sQ419_spl
| skaf45(sk3,sk3) = sk7 ),
inference(forward_demodulation,[status(thm)],[f6038,f12214]) ).
fof(f19831,plain,
( ~ sQ842_spl
| ~ sQ274_spl
| ~ sQ419_spl
| ~ sQ868_spl
| ~ sQ30_spl
| ~ sQ82_spl
| ~ sQ286_spl
| sk6 = sk7 ),
inference(forward_demodulation,[status(thm)],[f16971,f19830]) ).
fof(f19832,plain,
( ~ sQ842_spl
| ~ sQ274_spl
| ~ sQ419_spl
| ~ sQ868_spl
| ~ sQ30_spl
| ~ sQ82_spl
| ~ sQ286_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19831,f5738]) ).
fof(f19833,plain,
( ~ sQ842_spl
| ~ sQ274_spl
| ~ sQ419_spl
| ~ sQ868_spl
| ~ sQ30_spl
| ~ sQ82_spl
| ~ sQ286_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f19832]) ).
fof(f19834,plain,
$false,
inference(sat_refutation,[status(thm)],[f470,f477,f497,f510,f511,f512,f598,f600,f640,f642,f644,f649,f651,f653,f670,f685,f690,f703,f718,f723,f767,f774,f796,f810,f815,f819,f823,f950,f954,f958,f970,f974,f979,f983,f997,f1002,f1006,f1020,f1025,f1029,f1046,f1056,f1061,f1084,f1088,f1092,f1100,f1104,f1108,f1174,f1182,f1190,f1245,f1252,f1343,f1347,f1351,f1573,f1673,f1687,f1714,f1732,f1745,f1851,f1997,f2031,f2037,f2043,f2166,f2170,f2198,f2202,f2238,f2242,f2263,f2267,f2328,f2332,f2389,f2393,f2397,f2408,f2412,f2416,f2429,f2706,f3106,f3113,f3155,f3159,f3164,f3168,f3188,f3195,f3202,f3209,f3210,f3216,f3223,f3230,f3237,f3267,f3393,f3397,f3401,f3405,f3409,f3418,f3422,f3426,f3430,f3434,f3486,f3490,f3525,f3529,f3636,f3644,f3652,f3664,f3678,f3692,f3705,f3729,f3733,f3737,f3741,f3745,f3749,f3798,f3816,f3820,f3843,f3940,f3989,f4001,f4039,f4081,f4091,f4104,f4108,f4110,f4120,f4124,f4169,f4184,f4233,f4237,f4245,f4246,f4271,f4345,f4346,f4353,f4354,f4371,f4403,f4504,f4533,f4597,f4654,f4675,f4677,f4686,f4692,f4706,f4720,f4724,f4754,f4790,f4961,f4966,f5013,f5033,f5054,f5058,f5155,f5174,f5259,f5284,f5287,f5366,f5437,f5445,f5449,f5453,f5457,f5461,f5470,f5475,f5479,f5484,f5495,f5499,f5501,f5521,f5624,f5640,f5647,f5655,f5753,f5769,f5826,f5834,f5840,f5971,f6040,f6072,f6077,f6156,f6164,f6191,f6195,f6199,f6204,f6208,f6212,f6216,f6220,f6224,f6229,f6233,f6238,f6262,f6264,f6266,f6302,f6317,f6325,f6327,f6329,f6355,f6396,f6398,f6400,f6420,f6461,f6463,f6465,f6485,f6526,f6528,f6530,f6550,f6615,f6617,f6699,f6777,f6881,f6888,f6932,f6936,f6940,f6947,f6984,f6989,f7001,f7003,f7008,f7016,f7102,f7107,f7114,f7119,f7135,f7173,f7289,f7613,f8019,f8054,f8081,f8092,f8135,f8257,f8701,f8913,f8921,f8925,f8929,f8992,f9001,f9003,f9008,f9074,f9106,f9368,f9407,f9428,f9897,f10087,f10400,f10810,f10813,f10925,f10958,f10960,f10962,f11035,f11059,f11089,f11098,f11102,f11345,f11361,f11363,f11385,f11483,f11514,f11763,f11765,f11817,f11878,f11882,f11883,f11888,f11889,f11890,f11891,f11892,f11897,f11898,f11899,f11900,f11901,f11902,f11903,f11904,f11905,f11907,f11908,f11910,f11911,f11933,f11955,f11978,f11986,f11990,f12127,f12131,f12138,f12142,f12146,f12151,f12164,f12168,f12175,f12182,f12210,f12212,f12267,f12271,f12282,f12286,f12290,f12317,f12324,f12326,f12328,f12331,f12371,f12374,f12417,f12421,f12425,f12429,f12433,f12438,f12448,f12452,f12459,f12466,f12496,f12498,f12503,f12514,f12608,f12646,f12652,f12656,f12658,f12834,f12844,f12848,f12869,f12873,f12880,f12885,f12896,f12969,f12973,f12977,f12981,f12982,f13034,f13201,f13203,f13246,f13607,f13795,f13803,f14156,f14371,f14802,f14929,f15037,f15332,f15563,f15567,f15993,f15997,f16001,f16055,f16138,f16139,f16372,f16426,f16431,f16441,f16448,f16466,f16470,f16474,f16478,f16479,f16491,f16495,f16499,f16503,f16507,f16511,f16515,f16519,f16523,f16527,f16531,f16535,f16539,f16543,f16547,f16548,f16549,f16554,f16561,f16566,f16572,f16601,f16626,f16630,f16896,f17461,f17965,f18044,f18566,f18568,f18779,f18788,f18790,f18947,f19306,f19312,f19464,f19474,f19783,f19786,f19789,f19792,f19795,f19833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC295-1 : 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 : n001.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:18:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 80.47/10.65 % Refutation found
% 80.47/10.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 80.47/10.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 20.12/10.75 % Elapsed time: 10.375547 seconds
% 20.12/10.75 % CPU time: 81.185766 seconds
% 20.12/10.75 % Total memory used: 394.589 MB
% 20.12/10.75 % Net memory used: 370.625 MB
%------------------------------------------------------------------------------