%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC165+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:40:13 PM UTC 2026
% Result : Theorem 71.60s 9.85s
% Output : CNFRefutation 72.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 378
% Syntax : Number of formulae : 1419 ( 22 unt; 314 def)
% Number of atoms : 6615 ( 657 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 9420 (4224 ~;4372 |; 278 &)
% ( 355 <=>; 191 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 333 ( 331 usr; 313 prp; 0-3 aty)
% Number of functors : 63 ( 63 usr; 12 con; 0-5 aty)
% Number of variables : 1592 (1495 !; 97 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U] :
( ssList(U)
=> ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(W,V)
| leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U] :
( ssList(U)
=> ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(W,V)
| lt(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U] :
( ssList(U)
=> ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( ssItem(U)
=> totalorderP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( tl(V) = tl(U)
& hd(V) = hd(U)
& nil != U
& nil != V )
=> V = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] :
( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| app(app(X4,W),X5) != X
| cons(X3,nil) != W ) ) ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(Y,Z)
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) ) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] :
( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| app(app(X4,W),X5) != X
| cons(X3,nil) != W ) ) ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( neq(Y,Z)
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) ) ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [U] :
( ( cyclefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f139,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [U] :
( ( ( ( leq(sK10_skl(U),sK9_skl(U))
& leq(sK9_skl(U),sK10_skl(U))
& app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U))) = U
& ssList(sK13_skl(U))
& ssList(sK12_skl(U))
& ssList(sK11_skl(U))
& ssItem(sK10_skl(U))
& ssItem(sK9_skl(U)) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
! [U] :
( ( totalorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f151,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(W,V)
& ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [U] :
( ( ( ( ~ leq(sK15_skl(U),sK14_skl(U))
& ~ leq(sK14_skl(U),sK15_skl(U))
& app(app(sK16_skl(U),cons(sK14_skl(U),sK17_skl(U))),cons(sK15_skl(U),sK18_skl(U))) = U
& ssList(sK18_skl(U))
& ssList(sK17_skl(U))
& ssList(sK16_skl(U))
& ssItem(sK15_skl(U))
& ssItem(sK14_skl(U)) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(V,sK14_skl(U)),skolemize(W,sK15_skl(U)),skolemize(X,sK16_skl(U)),skolemize(Y,sK17_skl(U)),skolemize(Z,sK18_skl(U))],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f162,plain,
! [U] :
( ( strictorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f163,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(W,V)
& ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [U] :
( ( ( ( ~ lt(sK20_skl(U),sK19_skl(U))
& ~ lt(sK19_skl(U),sK20_skl(U))
& app(app(sK21_skl(U),cons(sK19_skl(U),sK22_skl(U))),cons(sK20_skl(U),sK23_skl(U))) = U
& ssList(sK23_skl(U))
& ssList(sK22_skl(U))
& ssList(sK21_skl(U))
& ssItem(sK20_skl(U))
& ssItem(sK19_skl(U)) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(V,sK19_skl(U)),skolemize(W,sK20_skl(U)),skolemize(X,sK21_skl(U)),skolemize(Y,sK22_skl(U)),skolemize(Z,sK23_skl(U))],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f174,plain,
! [U] :
( ( totalorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f175,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [U] :
( ( ( ( ~ leq(sK24_skl(U),sK25_skl(U))
& app(app(sK26_skl(U),cons(sK24_skl(U),sK27_skl(U))),cons(sK25_skl(U),sK28_skl(U))) = U
& ssList(sK28_skl(U))
& ssList(sK27_skl(U))
& ssList(sK26_skl(U))
& ssItem(sK25_skl(U))
& ssItem(sK24_skl(U)) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(V,sK24_skl(U)),skolemize(W,sK25_skl(U)),skolemize(X,sK26_skl(U)),skolemize(Y,sK27_skl(U)),skolemize(Z,sK28_skl(U))],[f175]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f185,plain,
! [U] :
( ( strictorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f186,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [U] :
( ( ( ( ~ lt(sK29_skl(U),sK30_skl(U))
& app(app(sK31_skl(U),cons(sK29_skl(U),sK32_skl(U))),cons(sK30_skl(U),sK33_skl(U))) = U
& ssList(sK33_skl(U))
& ssList(sK32_skl(U))
& ssList(sK31_skl(U))
& ssItem(sK30_skl(U))
& ssItem(sK29_skl(U)) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(V,sK29_skl(U)),skolemize(W,sK30_skl(U)),skolemize(X,sK31_skl(U)),skolemize(Y,sK32_skl(U)),skolemize(Z,sK33_skl(U))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f196,plain,
! [U] :
( ( duplicatefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f197,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U] :
( ( ( ( sK34_skl(U) = sK35_skl(U)
& app(app(sK36_skl(U),cons(sK34_skl(U),sK37_skl(U))),cons(sK35_skl(U),sK38_skl(U))) = U
& ssList(sK38_skl(U))
& ssList(sK37_skl(U))
& ssList(sK36_skl(U))
& ssItem(sK35_skl(U))
& ssItem(sK34_skl(U)) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl]),skolemize(V,sK34_skl(U)),skolemize(W,sK35_skl(U)),skolemize(X,sK36_skl(U)),skolemize(Y,sK37_skl(U)),skolemize(Z,sK38_skl(U))],[f197]) ).
fof(f199,plain,
! [X0,X1,X2,X3,X4,X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f207,plain,
! [U] :
( ( equalelemsP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f208,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( V != W
& app(X,cons(V,cons(W,Y))) = U
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
! [U] :
( ( ( ( sK39_skl(U) != sK40_skl(U)
& app(sK41_skl(U),cons(sK39_skl(U),cons(sK40_skl(U),sK42_skl(U)))) = U
& ssList(sK42_skl(U))
& ssList(sK41_skl(U))
& ssItem(sK40_skl(U))
& ssItem(sK39_skl(U)) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl]),skolemize(V,sK39_skl(U)),skolemize(W,sK40_skl(U)),skolemize(X,sK41_skl(U)),skolemize(Y,sK42_skl(U))],[f208]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f229,plain,
! [U] :
( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f230,plain,
! [U] :
( ( cons(sK44_skl(U),sK43_skl(U)) = U
& ssItem(sK44_skl(U))
& ssList(sK43_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(V,sK43_skl(U)),skolemize(W,sK44_skl(U))],[f229]) ).
fof(f231,plain,
! [X0] :
( ssList(sK43_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [X0] :
( ssItem(sK44_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f233,plain,
! [X0] :
( cons(sK44_skl(X0),sK43_skl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [U] :
( ! [V] :
( hd(cons(V,U)) = V
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f239,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f242,plain,
! [U] :
( ! [V] :
( tl(cons(V,U)) = U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f243,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [U] :
( ! [V] :
( ! [W] :
( cons(W,app(V,U)) = app(cons(W,V),U)
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f247,plain,
! [X0,X1,X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0,X1,X2] :
( X0 != X1
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
! [X0,X1,X2,X3] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f300,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(U,W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f301,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
! [U] :
( ! [V] :
( U = V
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f303,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f306,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(app(W,U),V)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f307,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f328,plain,
! [U] :
( cyclefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f329,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f331,plain,
! [U] :
( totalorderP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f332,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f334,plain,
! [U] :
( strictorderP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f335,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f337,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f338,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f347,plain,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f348,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f357,plain,
! [U] :
( duplicatefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f358,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f360,plain,
! [U] :
( equalelemsP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f361,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f371,plain,
! [U] :
( ! [V] :
( V = U
| tl(V) != tl(U)
| hd(V) != hd(U)
| nil = U
| nil = V
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f372,plain,
! [X0,X1] :
( X1 = X0
| tl(X1) != tl(X0)
| hd(X1) != hd(X0)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
! [U] :
( cons(hd(U),tl(U)) = U
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f374,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
! [U] :
( ! [V] :
( ! [W] :
( app(app(U,V),W) = app(U,app(V,W))
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f382,plain,
! [X0,X1,X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f390,plain,
! [U] :
( ! [V] :
( hd(app(U,V)) = hd(U)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f391,plain,
! [X0,X1] :
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f390]) ).
fof(f392,plain,
! [U] :
( ! [V] :
( tl(app(U,V)) = app(tl(U),V)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f393,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] :
( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ~ neq(Y,Z)
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] :
( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ~ neq(Y,Z)
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) )
& ~ neq(sK51_skl,sK52_skl)
& app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
~ neq(sK51_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,definition,
! [X3,X4,X6] :
( sP1_prd(X6,X4,X3)
<=> ( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f434,plain,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) ),
inference(formula_renaming,[status(thm)],[f416,f433]) ).
fof(f435,plain,
! [W,X,X3] :
( ( ! [X4] :
( ! [X5] :
( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] : ~ sP1_prd(X6,X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
( ! [W,X,X3] :
( ! [X4] :
( ! [X5] :
( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] : ~ sP1_prd(X6,X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
( ! [W,X,X3] :
( ! [X4] :
( ! [X5] :
( ( lt(sK59_skl(X5,X4,X3,X,W),X3)
& memberP(X5,sK59_skl(X5,X4,X3,X,W))
& ssItem(sK59_skl(X5,X4,X3,X,W)) )
| ~ sP1_prd(sK58_skl(X5,X4,X3,X,W),X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(sK57_skl(X3,X,W),X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,sK56_skl(X3,X,W),X3)
& app(app(sK56_skl(X3,X,W),W),sK57_skl(X3,X,W)) = X
& cons(X3,nil) = W
& ssList(sK57_skl(X3,X,W))
& ssList(sK56_skl(X3,X,W))
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl,sK57_skl,sK58_skl,sK59_skl]),skolemize(X4,sK56_skl(X3,X,W)),skolemize(X5,sK57_skl(X3,X,W)),skolemize(X6,sK58_skl(X5,X4,X3,X,W)),skolemize(X7,sK59_skl(X5,X4,X3,X,W))],[f436]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f441,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK59_skl(X4,X3,X0,X1,X2))
| ~ sP1_prd(sK58_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f446,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X4,sK59_skl(X4,X3,X0,X1,X2))
| ~ sP1_prd(sK58_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f447,plain,
! [X0,X1,X2,X3,X4] :
( lt(sK59_skl(X4,X3,X0,X1,X2),X0)
| ~ sP1_prd(sK58_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f448,plain,
! [X3,X4,X6] :
( ( ( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| sP1_prd(X6,X4,X3) )
& ( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6)
| ~ sP1_prd(X6,X4,X3) ) ),
inference(NNF_transformation,[status(thm)],[f433]) ).
fof(f449,plain,
( ! [X3,X4,X6] :
( ( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| sP1_prd(X6,X4,X3) )
& ! [X3,X4,X6] :
( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6)
| ~ sP1_prd(X6,X4,X3) ) ),
inference(miniscoping,[status(thm)],[f448]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ssItem(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f452,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f453,plain,
! [X0,X1,X2] :
( lt(X2,X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f449]) ).
fof(f454,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f461,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f454,f461]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f468,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f469,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f470,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f472,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X3,X1)
| ~ leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f473,plain,
! [X0,X1,X2,X3,X4] :
( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f153]) ).
fof(f474,plain,
! [X0,X1,X2,X3,X4] :
( lt(X3,X1)
| lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f165]) ).
fof(f475,plain,
! [X0,X1,X2,X3,X4] :
( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f177]) ).
fof(f476,plain,
! [X0,X1,X2,X3,X4] :
( lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f477,plain,
! [X3,X2,X4,X5] :
( ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ duplicatefreeP(app(app(X3,cons(X2,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X2,X5))) ),
inference(destructive_equality_resolution,[status(thm)],[f199]) ).
fof(f478,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(duplicate_literals_removal,[status(thm)],[f477]) ).
fof(f479,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(app(X0,cons(X1,cons(X2,X3)))) ),
inference(destructive_equality_resolution,[status(thm)],[f210]) ).
fof(f482,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f483,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f482]) ).
fof(f484,plain,
! [X1,X2,X3] :
( ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ~ frontsegP(X1,X2)
| frontsegP(cons(X0,X1),cons(X0,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f484]) ).
fof(f495,plain,
! [X0,X1,X2] :
( ssItem(sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ~ sP1_prd(sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)),X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f445]) ).
fof(f496,plain,
! [X0,X1,X2] :
( memberP(X2,sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ~ sP1_prd(sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)),X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f446]) ).
fof(f497,plain,
! [X0,X1,X2] :
( lt(sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)),X0)
| ~ sP1_prd(sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)),X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f447]) ).
fof(f500,plain,
( sK51_skl = sK52_skl
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f101,f430]) ).
fof(f503,definition,
( sQ3_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ3_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ5_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ5_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f500,f503,f506,f509]) ).
fof(f513,plain,
( ~ sQ5_spl
| ~ neq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f510,f430]) ).
fof(f515,plain,
( ~ sQ5_spl
| sK51_skl = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f513,f101]) ).
fof(f516,definition,
( sQ6_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ5_spl
| sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f515,f503,f516,f509]) ).
fof(f520,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f425]) ).
fof(f521,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f527,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f426]) ).
fof(f528,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f531,plain,
( ~ sQ5_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f510,f429]) ).
fof(f541,plain,
( ~ sQ5_spl
| ssList(sK47_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f245]) ).
fof(f542,definition,
( sQ8_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( ~ sQ8_spl
| ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ8_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ9_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( sQ9_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
( sQ10_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( ~ sQ5_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f541,f542,f545,f548,f509]) ).
fof(f552,plain,
! [X0] :
( ~ sQ5_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f531,f271]) ).
fof(f553,definition,
! [X0] :
( sQ11_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f554,plain,
! [X0] :
( ~ sQ11_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f553]) ).
fof(f556,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f552,f553,f542,f545,f509]) ).
fof(f557,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f428]) ).
fof(f558,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
! [X0] :
( ~ sQ5_spl
| ~ memberP(sK54_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f531,f272]) ).
fof(f560,definition,
! [X0] :
( sQ12_spl
<=> ( ~ memberP(sK54_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f561,plain,
! [X0] :
( ~ sQ12_spl
| ~ memberP(sK54_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f559,f560,f542,f545,f509]) ).
fof(f564,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f565,definition,
! [X0] :
( sQ13_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f566,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,definition,
! [X1] :
( sQ14_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f564,f565,f568]) ).
fof(f572,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f566]) ).
fof(f574,definition,
! [X0] :
( sQ15_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f577,definition,
! [X1] :
( sQ16_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f578,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f583,plain,
( ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f428,f572]) ).
fof(f588,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f590,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f455]) ).
fof(f591,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f590]) ).
fof(f592,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f591,f438]) ).
fof(f593,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f441,f591]) ).
fof(f594,plain,
( ~ sQ0_spl
| ~ ssItem(sK55_skl)
| singletonP(sK47_skl)
| ~ ssList(cons(sK55_skl,nil)) ),
inference(paramodulation,[status(thm)],[f593,f468]) ).
fof(f595,definition,
( sQ17_spl
<=> ssList(cons(sK55_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ17_spl
| ~ ssList(cons(sK55_skl,nil)) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,definition,
( sQ18_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f601,definition,
( sQ19_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f603,plain,
( sQ19_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f594,f595,f598,f601,f454]) ).
fof(f605,plain,
( sQ19_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f592]) ).
fof(f606,plain,
( sQ19_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f611,definition,
( sQ20_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ20_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f651,plain,
! [X0] :
( ~ sQ5_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f531,f270]) ).
fof(f652,definition,
! [X0] :
( sQ23_spl
<=> ( memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f653,plain,
! [X0] :
( ~ sQ23_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f652]) ).
fof(f655,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f651,f652,f542,f545,f509]) ).
fof(f656,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f245]) ).
fof(f657,plain,
( ~ sQ5_spl
| ~ ssList(sK54_skl)
| frontsegP(sK47_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f656]) ).
fof(f658,definition,
( sQ24_spl
<=> frontsegP(sK47_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( ~ sQ24_spl
| frontsegP(sK47_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ24_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f657,f542,f658,f545,f509]) ).
fof(f662,plain,
! [X0] :
( ~ sQ23_spl
| memberP(cons(sK51_skl,nil),X0)
| memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f653,f270]) ).
fof(f663,definition,
! [X0] :
( sQ25_spl
<=> ( memberP(cons(sK51_skl,nil),X0)
| memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f666,definition,
( sQ26_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( ~ sQ26_spl
| ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f668,plain,
( sQ26_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,definition,
( sQ27_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( sQ27_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f669]) ).
fof(f672,plain,
( ~ sQ23_spl
| ~ sQ27_spl
| ~ sQ26_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f662,f663,f666,f669,f652]) ).
fof(f674,plain,
( sQ27_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f671,f222]) ).
fof(f675,plain,
( sQ27_spl
| ~ sQ3_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f674,f611,f503,f669]) ).
fof(f676,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f223]) ).
fof(f677,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f679,plain,
( ~ sQ2_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f462,f424]) ).
fof(f738,plain,
( sQ26_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f668,f245]) ).
fof(f739,definition,
( sQ28_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ28_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f738,f739,f669,f666]) ).
fof(f743,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f741,f427]) ).
fof(f744,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f743]) ).
fof(f748,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f389]) ).
fof(f750,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f376]) ).
fof(f751,definition,
! [X0] :
( sQ29_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ20_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f748,f751,f611]) ).
fof(f756,definition,
! [X1] :
( sQ30_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f757,plain,
! [X0] :
( ~ sQ30_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f759,plain,
( sQ30_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f750,f574,f756]) ).
fof(f763,plain,
! [X0,X1] :
( sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(sK6_skl(X1,app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f129,f376]) ).
fof(f765,plain,
! [X0,X1] :
( sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(sK6_skl(X1,app(X0,X1)))
| ~ ssList(X0)
| ~ rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f763]) ).
fof(f766,plain,
! [X0,X1] :
( sK6_skl(X0,app(X1,X0)) = X1
| ~ ssList(sK6_skl(X0,app(X1,X0)))
| ~ ssList(X1)
| ~ rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f765,f245]) ).
fof(f769,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f245]) ).
fof(f770,plain,
( sQ8_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f544,f245]) ).
fof(f771,plain,
( sQ8_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f770,f666,f669,f542]) ).
fof(f774,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ memberP(sK54_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f679,f561]) ).
fof(f775,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ memberP(sK54_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f774,f279]) ).
fof(f786,definition,
( sQ31_spl
<=> rearsegP(nil,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f787,plain,
( ~ sQ31_spl
| rearsegP(nil,sK54_skl) ),
inference(component_clause,[status(thm)],[f786]) ).
fof(f788,plain,
( sQ31_spl
| ~ rearsegP(nil,sK54_skl) ),
inference(component_clause,[status(thm)],[f786]) ).
fof(f813,plain,
! [X0,X1,X2] :
( lt(X0,sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ssItem(sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f495,f453]) ).
fof(f814,plain,
! [X0,X1,X2] :
( memberP(X1,sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ssItem(sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f495,f452]) ).
fof(f815,plain,
! [X0,X1,X2] :
( ssItem(sK58_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ssItem(sK59_skl(X2,X1,X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(X1,cons(X0,nil)),X2),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f495,f451]) ).
fof(f817,plain,
( sQ17_spl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f597,f222]) ).
fof(f818,plain,
( sQ17_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f817,f611,f601,f595]) ).
fof(f819,plain,
! [X0,X1] :
( ~ sQ0_spl
| ssItem(sK59_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),sK47_skl),X0,sK55_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| sP0_prd(sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)) ),
inference(paramodulation,[status(thm)],[f593,f495]) ).
fof(f820,plain,
! [X0,X1] :
( ~ sQ0_spl
| ssItem(sK59_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK55_skl,app(app(X0,sK47_skl),X1),cons(sK55_skl,nil)),X0,sK55_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| sP0_prd(sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)) ),
inference(paramodulation,[status(thm)],[f593,f495]) ).
fof(f822,plain,
( ~ sQ0_spl
| tl(sK47_skl) = nil
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f593,f243]) ).
fof(f823,plain,
( ~ sQ0_spl
| hd(sK47_skl) = sK55_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f593,f239]) ).
fof(f824,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f593,f275]) ).
fof(f825,plain,
! [X0] :
( ~ sQ0_spl
| cons(sK55_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f593,f247]) ).
fof(f827,plain,
( ~ sQ0_spl
| memberP(sK47_skl,sK55_skl)
| ~ ssList(nil)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f593,f483]) ).
fof(f829,plain,
( ~ sQ0_spl
| nil != sK47_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f593,f235]) ).
fof(f831,definition,
! [X0,X1] :
( sQ37_spl
<=> ( ssItem(sK59_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),sK47_skl),X0,sK55_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f819,f831,f601,f454]) ).
fof(f835,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ssItem(sK59_skl(X1,X0,sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK55_skl,app(app(X0,sK47_skl),X1),cons(sK55_skl,nil)),X0,sK55_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK55_skl,app(app(X0,cons(sK55_skl,nil)),X1),cons(sK55_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f838,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f820,f835,f601,f454]) ).
fof(f840,definition,
( sQ39_spl
<=> tl(sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f841,plain,
( ~ sQ39_spl
| tl(sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f840]) ).
fof(f843,plain,
( ~ sQ0_spl
| sQ39_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f822,f611,f601,f840,f454]) ).
fof(f844,definition,
( sQ40_spl
<=> hd(sK47_skl) = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f847,plain,
( ~ sQ0_spl
| sQ40_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f823,f611,f601,f844,f454]) ).
fof(f848,definition,
! [X0] :
( sQ41_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f849,plain,
! [X0] :
( ~ sQ41_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f848]) ).
fof(f851,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f824,f848,f601,f611,f454]) ).
fof(f852,definition,
! [X0] :
( sQ42_spl
<=> ( cons(sK55_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ20_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f825,f852,f611,f601,f454]) ).
fof(f856,definition,
! [X0] :
( sQ43_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f860,definition,
( sQ44_spl
<=> memberP(sK47_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f861,plain,
( ~ sQ44_spl
| memberP(sK47_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( ~ sQ0_spl
| sQ44_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f827,f601,f611,f860,f454]) ).
fof(f865,definition,
( sQ45_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f868,plain,
( ~ sQ0_spl
| ~ sQ45_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f829,f611,f601,f865,f454]) ).
fof(f880,plain,
! [X0] :
( ~ sQ41_spl
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f279]) ).
fof(f881,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| sK55_skl = sK55_skl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f880,f861]) ).
fof(f882,definition,
( sQ46_spl
<=> sK55_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f885,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| sQ46_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f881,f601,f882,f848,f860]) ).
fof(f886,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f249]) ).
fof(f887,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f123]) ).
fof(f891,definition,
! [X0] :
( sQ47_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f894,plain,
( ~ sQ20_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f886,f891,f611]) ).
fof(f895,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f887]) ).
fof(f896,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f895,f122]) ).
fof(f902,plain,
! [X0] :
( ~ sQ0_spl
| cons(sK55_skl,X0) = app(sK47_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f593,f380]) ).
fof(f903,definition,
! [X0] :
( sQ48_spl
<=> ( cons(sK55_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f904,plain,
! [X0] :
( ~ sQ48_spl
| cons(sK55_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f906,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f902,f903,f601,f454]) ).
fof(f917,definition,
( sQ49_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f997,plain,
! [X0] :
( ~ sQ11_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f554,f271]) ).
fof(f999,definition,
! [X0] :
( sQ52_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1000,plain,
! [X0] :
( ~ sQ52_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f999]) ).
fof(f1002,plain,
( ~ sQ11_spl
| ~ sQ27_spl
| ~ sQ26_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f997,f999,f666,f669,f553]) ).
fof(f1003,definition,
! [X0] :
( sQ53_spl
<=> ( ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1004,plain,
! [X0] :
( ~ sQ53_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1003]) ).
fof(f1007,plain,
! [X0] :
( ~ sQ52_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1000]) ).
fof(f1008,plain,
! [X0] :
( ~ sQ53_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1004]) ).
fof(f1009,plain,
! [X0] :
( ~ sQ53_spl
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1008,f277]) ).
fof(f1010,plain,
( ~ sQ53_spl
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| memberP(sK47_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1008,f483]) ).
fof(f1011,definition,
! [X0] :
( sQ54_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
( ~ sQ53_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1009,f1011,f503,f611,f1003]) ).
fof(f1015,definition,
( sQ55_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1016,plain,
( ~ sQ55_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,plain,
( ~ sQ53_spl
| ~ sQ20_spl
| sQ55_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1010,f503,f1015,f611,f1003]) ).
fof(f1020,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f593,f472]) ).
fof(f1021,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f593,f472]) ).
fof(f1022,definition,
! [X0,X1,X2] :
( sQ56_spl
<=> ( ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f1020,f1022,f601,f611,f454]) ).
fof(f1026,definition,
! [X0,X1,X2] :
( sQ57_spl
<=> ( ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1029,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ19_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f1021,f1026,f601,f611,f454]) ).
fof(f1032,plain,
( ~ sQ41_spl
| ~ sQ55_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1016,f880]) ).
fof(f1033,definition,
( sQ58_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1034,plain,
( ~ sQ58_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1033]) ).
fof(f1036,plain,
( ~ sQ41_spl
| ~ sQ55_spl
| sQ58_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1032,f503,f1033,f1015,f848]) ).
fof(f1037,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ58_spl
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1034,f880]) ).
fof(f1039,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f1034,f593]) ).
fof(f1043,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK47_skl)) ),
inference(backward_demodulation,[status(thm)],[f1039,f543]) ).
fof(f1044,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ssList(app(sK53_skl,sK47_skl)) ),
inference(backward_demodulation,[status(thm)],[f1039,f667]) ).
fof(f1046,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ58_spl
| cons(sK51_skl,X0) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1039,f380]) ).
fof(f1047,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f495]) ).
fof(f1048,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f495]) ).
fof(f1050,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1039,f472]) ).
fof(f1051,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1039,f472]) ).
fof(f1053,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| hd(sK47_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1039,f239]) ).
fof(f1054,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ58_spl
| memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1039,f275]) ).
fof(f1055,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ58_spl
| cons(sK51_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1039,f247]) ).
fof(f1062,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f1039,f1043]) ).
fof(f1063,definition,
! [X0] :
( sQ59_spl
<=> ( cons(sK51_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1046,f1063,f503,f1033,f454]) ).
fof(f1067,definition,
! [X0,X1] :
( sQ60_spl
<=> ( ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1070,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1047,f1067,f503,f1033,f454]) ).
fof(f1071,definition,
! [X0,X1] :
( sQ61_spl
<=> ( ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1074,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1048,f1071,f503,f1033,f454]) ).
fof(f1076,definition,
! [X0,X1,X2] :
( sQ62_spl
<=> ( ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1050,f1076,f503,f611,f1033,f454]) ).
fof(f1080,definition,
! [X0,X1,X2] :
( sQ63_spl
<=> ( ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1083,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1051,f1080,f503,f611,f1033,f454]) ).
fof(f1085,definition,
( sQ64_spl
<=> hd(sK47_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1086,plain,
( ~ sQ64_spl
| hd(sK47_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f1085]) ).
fof(f1088,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| sQ64_spl
| ~ sQ3_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1053,f611,f503,f1085,f1033,f454]) ).
fof(f1089,definition,
! [X0] :
( sQ65_spl
<=> ( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1092,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1054,f1089,f503,f611,f1033,f454]) ).
fof(f1093,definition,
! [X0] :
( sQ66_spl
<=> ( cons(sK51_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1096,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| ~ sQ20_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1055,f1093,f611,f503,f1033,f454]) ).
fof(f1144,plain,
! [X0] :
( ~ sQ52_spl
| ~ memberP(sK53_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1007,f271]) ).
fof(f1145,plain,
! [X0] :
( ~ sQ52_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1007,f272]) ).
fof(f1146,definition,
! [X0] :
( sQ67_spl
<=> ( ~ memberP(sK53_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1147,plain,
! [X0] :
( ~ sQ67_spl
| ~ memberP(sK53_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1146]) ).
fof(f1149,plain,
( ~ sQ52_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1144,f1146,f739,f669,f999]) ).
fof(f1150,plain,
( ~ sQ52_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1145,f1003,f739,f669,f999]) ).
fof(f1151,plain,
! [X0] :
( ~ sQ67_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1147]) ).
fof(f1178,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ58_spl
| cons(sK51_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f1034,f904]) ).
fof(f1202,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ memberP(app(sK53_skl,sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1039,f1007]) ).
fof(f1204,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| memberP(X1,sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f496]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| memberP(X1,sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f496]) ).
fof(f1222,definition,
! [X0,X1] :
( sQ71_spl
<=> ( memberP(X1,sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1225,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1204,f1222,f503,f1033,f454]) ).
fof(f1226,definition,
! [X0,X1] :
( sQ72_spl
<=> ( memberP(X1,sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1229,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1205,f1226,f503,f1033,f454]) ).
fof(f1258,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f129]) ).
fof(f1259,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f1260,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f111]) ).
fof(f1262,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f385,f136]) ).
fof(f1265,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f385,f123]) ).
fof(f1279,definition,
! [X0] :
( sQ77_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
( ~ sQ20_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1258,f1279,f611]) ).
fof(f1283,plain,
( sQ49_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1259,f611,f917]) ).
fof(f1284,definition,
! [X0] :
( sQ78_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1287,plain,
( ~ sQ20_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1260,f1284,f611]) ).
fof(f1301,definition,
! [X0] :
( sQ83_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1304,plain,
( ~ sQ20_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1262,f1301,f611]) ).
fof(f1307,definition,
! [X0] :
( sQ84_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1310,plain,
( ~ sQ20_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1265,f1307,f611]) ).
fof(f1381,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1202,f272]) ).
fof(f1383,definition,
! [X0] :
( sQ97_spl
<=> ( ~ memberP(sK47_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( ~ sQ52_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ10_spl
| ~ sQ28_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1381,f1383,f739,f548,f1033,f454,f999]) ).
fof(f1468,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1039,f473]) ).
fof(f1469,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1039,f473]) ).
fof(f1470,definition,
! [X0,X1,X2] :
( sQ114_spl
<=> ( leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1473,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1468,f1470,f503,f611,f1033,f454]) ).
fof(f1474,definition,
! [X0,X1,X2] :
( sQ115_spl
<=> ( leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1477,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1469,f1474,f503,f611,f1033,f454]) ).
fof(f1480,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ58_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f1039,f653]) ).
fof(f1481,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ58_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f1039,f1480]) ).
fof(f1482,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ58_spl
| memberP(sK47_skl,X0)
| memberP(app(sK53_skl,sK47_skl),X0)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1481,f270]) ).
fof(f1483,definition,
! [X0] :
( sQ116_spl
<=> ( memberP(sK47_skl,X0)
| memberP(app(sK53_skl,sK47_skl),X0)
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1486,definition,
( sQ117_spl
<=> ssList(app(sK53_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1488,plain,
( sQ117_spl
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1486]) ).
fof(f1489,plain,
( ~ sQ23_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ10_spl
| ~ sQ117_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1482,f1483,f1486,f548,f1033,f454,f652]) ).
fof(f1495,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| lt(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)),sK51_skl)
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f497]) ).
fof(f1496,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| lt(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)),sK51_skl)
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1039,f497]) ).
fof(f1498,definition,
! [X0,X1] :
( sQ118_spl
<=> ( lt(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)),sK51_skl)
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1501,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1495,f1498,f503,f1033,f454]) ).
fof(f1502,definition,
! [X0,X1] :
( sQ119_spl
<=> ( lt(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)),sK51_skl)
| ~ sP1_prd(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl),X0,sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1505,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1496,f1502,f503,f1033,f454]) ).
fof(f1520,plain,
( sQ117_spl
| ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1488,f1044]) ).
fof(f1521,plain,
( sQ117_spl
| ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1520]) ).
fof(f1526,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f129]) ).
fof(f1528,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f111]) ).
fof(f1531,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f386,f136]) ).
fof(f1534,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f386,f123]) ).
fof(f1539,definition,
! [X0] :
( sQ121_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1542,plain,
( ~ sQ20_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1526,f1539,f611]) ).
fof(f1544,definition,
! [X0] :
( sQ122_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1547,plain,
( ~ sQ20_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1528,f1544,f611]) ).
fof(f1556,definition,
! [X0] :
( sQ125_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1559,plain,
( ~ sQ20_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1531,f1556,f611]) ).
fof(f1562,definition,
! [X0] :
( sQ126_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ20_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1534,f1562,f611]) ).
fof(f1575,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f578]) ).
fof(f1577,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ58_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1039,f467]) ).
fof(f1579,definition,
! [X0] :
( sQ127_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1582,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1577,f1579,f503,f611,f1033,f454]) ).
fof(f1584,plain,
( ~ sQ30_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f419,f757]) ).
fof(f1594,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1584]) ).
fof(f1597,plain,
( ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f1575]) ).
fof(f1600,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1597]) ).
fof(f1601,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1039,f474]) ).
fof(f1602,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ58_spl
| lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1039,f474]) ).
fof(f1603,definition,
! [X0,X1,X2] :
( sQ128_spl
<=> ( lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1606,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f1601,f1603,f503,f611,f1033,f454]) ).
fof(f1607,definition,
! [X0,X1,X2] :
( sQ129_spl
<=> ( lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1610,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1602,f1607,f503,f611,f1033,f454]) ).
fof(f1616,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| app(app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f1039,f531]) ).
fof(f1617,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| app(app(app(sK53_skl,sK47_skl),sK47_skl),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f1039,f1616]) ).
fof(f1629,definition,
( sQ130_spl
<=> ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1631,plain,
( sQ130_spl
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(component_clause,[status(thm)],[f1629]) ).
fof(f1639,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ58_spl
| X0 = nil
| sK47_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1039,f228]) ).
fof(f1642,definition,
! [X0,X1] :
( sQ131_spl
<=> ( X0 = nil
| sK47_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1643,plain,
! [X0,X1] :
( ~ sQ131_spl
| X0 = nil
| sK47_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1642]) ).
fof(f1645,plain,
( ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ3_spl
| sQ131_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1639,f611,f1642,f503,f1033,f454]) ).
fof(f1651,definition,
! [X0,X1] :
( sQ132_spl
<=> ( sK51_skl = X1
| sK47_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1652,plain,
! [X0,X1] :
( ~ sQ132_spl
| sK51_skl = X1
| sK47_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1651]) ).
fof(f1673,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1617,f271]) ).
fof(f1675,definition,
! [X0] :
( sQ133_spl
<=> ( ~ memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1678,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ9_spl
| ~ sQ130_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1673,f1675,f1629,f545,f1033,f454,f509]) ).
fof(f1720,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1617,f270]) ).
fof(f1722,definition,
! [X0] :
( sQ134_spl
<=> ( memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1725,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ9_spl
| ~ sQ130_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1720,f1722,f1629,f545,f1033,f454,f509]) ).
fof(f1813,definition,
( sQ139_spl
<=> nil = app(app(sK53_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1814,plain,
( ~ sQ139_spl
| nil = app(app(sK53_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f1813]) ).
fof(f1819,definition,
! [X0,X1,X2] :
( sQ140_spl
<=> ( leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1823,definition,
! [X0,X1,X2] :
( sQ141_spl
<=> ( leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1845,plain,
( sQ130_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1631,f1062]) ).
fof(f1846,plain,
( sQ130_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1845]) ).
fof(f1881,definition,
( sQ148_spl
<=> nil = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1882,plain,
( ~ sQ148_spl
| nil = sK54_skl ),
inference(component_clause,[status(thm)],[f1881]) ).
fof(f1885,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| sK47_skl = app(app(sK53_skl,sK47_skl),app(sK47_skl,sK54_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f1617,f382]) ).
fof(f1886,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| app(sK47_skl,X0) = app(app(app(sK53_skl,sK47_skl),sK47_skl),app(sK54_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f1617,f382]) ).
fof(f1887,definition,
( sQ149_spl
<=> sK47_skl = app(app(sK53_skl,sK47_skl),app(sK47_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1888,plain,
( ~ sQ149_spl
| sK47_skl = app(app(sK53_skl,sK47_skl),app(sK47_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f1887]) ).
fof(f1890,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| sQ149_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f1885,f1486,f548,f545,f1887,f1033,f454,f509]) ).
fof(f1891,definition,
! [X0] :
( sQ150_spl
<=> ( app(sK47_skl,X0) = app(app(app(sK53_skl,sK47_skl),sK47_skl),app(sK54_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1894,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| sQ150_spl
| ~ sQ9_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f1886,f1629,f545,f1891,f1033,f454,f509]) ).
fof(f1901,plain,
! [X0,X1] :
( sK4_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f117,f227]) ).
fof(f1902,plain,
! [X0,X1] :
( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f117,f228]) ).
fof(f1907,definition,
! [X0,X1] :
( sQ151_spl
<=> ( sK4_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1910,plain,
( ~ sQ20_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1901,f1907,f611]) ).
fof(f1911,definition,
! [X0,X1] :
( sQ152_spl
<=> ( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1914,plain,
( ~ sQ20_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f1902,f1911,f611]) ).
fof(f1942,definition,
! [X0,X1,X2] :
( sQ153_spl
<=> ( lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1946,definition,
! [X0,X1,X2] :
( sQ154_spl
<=> ( lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1977,plain,
( ~ sQ131_spl
| nil = sK47_skl
| ~ ssList(sK47_skl)
| sK43_skl(sK47_skl) = nil
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f1643,f233]) ).
fof(f1981,definition,
( sQ160_spl
<=> ssList(sK43_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1983,plain,
( sQ160_spl
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f1981]) ).
fof(f1984,definition,
( sQ161_spl
<=> ssItem(sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( sQ161_spl
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f1984]) ).
fof(f1987,definition,
( sQ162_spl
<=> sK43_skl(sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1988,plain,
( ~ sQ162_spl
| sK43_skl(sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f1987]) ).
fof(f1990,plain,
( ~ sQ131_spl
| sQ45_spl
| ~ sQ10_spl
| sQ162_spl
| ~ sQ161_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f1977,f1981,f1984,f1987,f548,f865,f1642]) ).
fof(f1991,definition,
( sQ163_spl
<=> ssItem(sK4_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1993,plain,
( sQ163_spl
| ~ ssItem(sK4_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f1991]) ).
fof(f1996,definition,
( sQ164_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2000,plain,
( ~ sQ162_spl
| cons(sK44_skl(sK47_skl),nil) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1988,f233]) ).
fof(f2002,definition,
( sQ165_spl
<=> cons(sK44_skl(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2003,plain,
( ~ sQ165_spl
| cons(sK44_skl(sK47_skl),nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f2002]) ).
fof(f2005,plain,
( ~ sQ162_spl
| sQ165_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2000,f548,f865,f2002,f1987]) ).
fof(f2007,plain,
( sQ161_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1986,f232]) ).
fof(f2008,plain,
( sQ161_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2007,f548,f865,f1984]) ).
fof(f2018,plain,
( sQ160_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1983,f231]) ).
fof(f2019,plain,
( sQ160_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2018,f548,f865,f1981]) ).
fof(f2026,plain,
! [X0,X1] :
( ~ sQ165_spl
| memberP(X1,sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),sK47_skl),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ),
inference(paramodulation,[status(thm)],[f2003,f496]) ).
fof(f2027,plain,
! [X0,X1] :
( ~ sQ165_spl
| memberP(X1,sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,sK47_skl),X1),cons(sK44_skl(sK47_skl),nil)),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ),
inference(paramodulation,[status(thm)],[f2003,f496]) ).
fof(f2028,plain,
! [X0,X1] :
( ~ sQ165_spl
| lt(sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)),sK44_skl(sK47_skl))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),sK47_skl),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ),
inference(paramodulation,[status(thm)],[f2003,f497]) ).
fof(f2029,plain,
! [X0,X1] :
( ~ sQ165_spl
| lt(sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)),sK44_skl(sK47_skl))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,sK47_skl),X1),cons(sK44_skl(sK47_skl),nil)),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ),
inference(paramodulation,[status(thm)],[f2003,f497]) ).
fof(f2031,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| lt(X1,sK44_skl(sK47_skl))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ),
inference(paramodulation,[status(thm)],[f2003,f476]) ).
fof(f2032,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| lt(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2003,f476]) ).
fof(f2033,plain,
( ~ sQ165_spl
| hd(sK47_skl) = sK44_skl(sK47_skl)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2003,f239]) ).
fof(f2035,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| leq(X1,sK44_skl(sK47_skl))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ),
inference(paramodulation,[status(thm)],[f2003,f475]) ).
fof(f2036,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| leq(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2003,f475]) ).
fof(f2037,plain,
! [X0] :
( ~ sQ165_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK44_skl(sK47_skl))
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssList(app(X0,cons(sK44_skl(sK47_skl),nil))) ),
inference(paramodulation,[status(thm)],[f2003,f467]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ sQ165_spl
| X1 = sK44_skl(sK47_skl)
| cons(X1,X0) != sK47_skl
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2003,f227]) ).
fof(f2043,plain,
( ~ sQ165_spl
| memberP(sK47_skl,sK44_skl(sK47_skl))
| ~ ssList(nil)
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f2003,f483]) ).
fof(f2047,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| lt(sK44_skl(sK47_skl),X1)
| lt(X1,sK44_skl(sK47_skl))
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ),
inference(paramodulation,[status(thm)],[f2003,f474]) ).
fof(f2048,plain,
! [X0,X1,X2] :
( ~ sQ165_spl
| lt(X1,sK44_skl(sK47_skl))
| lt(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2003,f474]) ).
fof(f2050,definition,
! [X0,X1] :
( sQ166_spl
<=> ( memberP(X1,sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),sK47_skl),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2053,plain,
( ~ sQ165_spl
| ~ sQ161_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f2026,f2050,f1984,f2002]) ).
fof(f2054,definition,
! [X0,X1] :
( sQ167_spl
<=> ( memberP(X1,sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,sK47_skl),X1),cons(sK44_skl(sK47_skl),nil)),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2057,plain,
( ~ sQ165_spl
| ~ sQ161_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f2027,f2054,f1984,f2002]) ).
fof(f2058,definition,
! [X0,X1] :
( sQ168_spl
<=> ( lt(sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)),sK44_skl(sK47_skl))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),sK47_skl),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2061,plain,
( ~ sQ165_spl
| ~ sQ161_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f2028,f2058,f1984,f2002]) ).
fof(f2062,definition,
! [X0,X1] :
( sQ169_spl
<=> ( lt(sK59_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)),sK44_skl(sK47_skl))
| ~ sP1_prd(sK58_skl(X1,X0,sK44_skl(sK47_skl),app(app(X0,sK47_skl),X1),cons(sK44_skl(sK47_skl),nil)),X0,sK44_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK44_skl(sK47_skl),app(app(X0,cons(sK44_skl(sK47_skl),nil)),X1),cons(sK44_skl(sK47_skl),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2065,plain,
( ~ sQ165_spl
| ~ sQ161_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f2029,f2062,f1984,f2002]) ).
fof(f2067,definition,
! [X0,X1,X2] :
( sQ170_spl
<=> ( lt(X1,sK44_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2070,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f2031,f2067,f1984,f611,f2002]) ).
fof(f2071,definition,
! [X0,X1,X2] :
( sQ171_spl
<=> ( lt(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2074,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f2032,f2071,f1984,f611,f2002]) ).
fof(f2075,definition,
( sQ172_spl
<=> hd(sK47_skl) = sK44_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2076,plain,
( ~ sQ172_spl
| hd(sK47_skl) = sK44_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f2075]) ).
fof(f2078,plain,
( ~ sQ165_spl
| sQ172_spl
| ~ sQ161_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2033,f611,f1984,f2075,f2002]) ).
fof(f2080,definition,
! [X0,X1,X2] :
( sQ173_spl
<=> ( leq(X1,sK44_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f2083,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f2035,f2080,f1984,f611,f2002]) ).
fof(f2084,definition,
! [X0,X1,X2] :
( sQ174_spl
<=> ( leq(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2087,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f2036,f2084,f1984,f611,f2002]) ).
fof(f2088,definition,
! [X0] :
( sQ175_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK44_skl(sK47_skl))
| ~ ssList(app(X0,cons(sK44_skl(sK47_skl),nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f2037,f2088,f1984,f611,f2002]) ).
fof(f2093,definition,
! [X0,X1] :
( sQ176_spl
<=> ( X1 = sK44_skl(sK47_skl)
| cons(X1,X0) != sK47_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2096,plain,
( ~ sQ165_spl
| ~ sQ161_spl
| ~ sQ20_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f2039,f2093,f611,f1984,f2002]) ).
fof(f2100,definition,
( sQ177_spl
<=> memberP(sK47_skl,sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2103,plain,
( ~ sQ165_spl
| sQ177_spl
| ~ sQ20_spl
| ~ sQ161_spl ),
inference(split_clause,[status(thm)],[f2043,f1984,f611,f2100,f2002]) ).
fof(f2107,definition,
! [X0,X1,X2] :
( sQ178_spl
<=> ( lt(sK44_skl(sK47_skl),X1)
| lt(X1,sK44_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK44_skl(sK47_skl),nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2110,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f2047,f2107,f1984,f611,f2002]) ).
fof(f2111,definition,
! [X0,X1,X2] :
( sQ179_spl
<=> ( lt(X1,sK44_skl(sK47_skl))
| lt(sK44_skl(sK47_skl),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK44_skl(sK47_skl),nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2114,plain,
( ~ sQ165_spl
| ~ sQ20_spl
| ~ sQ161_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f2048,f2111,f1984,f611,f2002]) ).
fof(f2137,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| sK51_skl = sK44_skl(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f1086,f2076]) ).
fof(f2145,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| cons(sK51_skl,sK43_skl(sK47_skl)) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2137,f233]) ).
fof(f2147,definition,
( sQ180_spl
<=> cons(sK51_skl,sK43_skl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2148,plain,
( ~ sQ180_spl
| cons(sK51_skl,sK43_skl(sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f2147]) ).
fof(f2150,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| sQ180_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2145,f548,f865,f2147,f1085,f2075]) ).
fof(f2170,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| sK54_skl = X0
| sK47_skl != app(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1617,f378]) ).
fof(f2175,definition,
! [X0] :
( sQ183_spl
<=> ( sK54_skl = X0
| sK47_skl != app(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2178,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ58_spl
| ~ sQ9_spl
| ~ sQ130_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f2170,f2175,f1629,f545,f1033,f454,f509]) ).
fof(f2370,definition,
! [X0,X1] :
( sQ216_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK47_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(sK51_skl,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2374,definition,
! [X0,X1] :
( sQ217_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK47_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2399,plain,
( ~ sQ132_spl
| nil = sK47_skl
| ~ ssList(sK47_skl)
| sK51_skl = sK44_skl(sK47_skl)
| ~ ssItem(sK44_skl(sK47_skl))
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f1652,f233]) ).
fof(f2400,plain,
( ~ sQ132_spl
| ~ singletonP(sK47_skl)
| ~ ssList(sK47_skl)
| sK51_skl = sK4_skl(sK47_skl)
| ~ ssItem(sK4_skl(sK47_skl))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1652,f117]) ).
fof(f2403,definition,
( sQ223_spl
<=> sK51_skl = sK44_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2406,plain,
( ~ sQ132_spl
| sQ45_spl
| ~ sQ10_spl
| sQ223_spl
| ~ sQ161_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f2399,f1981,f1984,f2403,f548,f865,f1651]) ).
fof(f2407,definition,
( sQ224_spl
<=> sK51_skl = sK4_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2408,plain,
( ~ sQ224_spl
| sK51_skl = sK4_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f2407]) ).
fof(f2410,plain,
( ~ sQ132_spl
| ~ sQ18_spl
| ~ sQ10_spl
| sQ224_spl
| ~ sQ163_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2400,f611,f1991,f2407,f548,f598,f1651]) ).
fof(f2413,plain,
( sQ163_spl
| ~ singletonP(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1993,f116]) ).
fof(f2414,plain,
( sQ163_spl
| ~ sQ18_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2413,f548,f598,f1991]) ).
fof(f2415,plain,
( ~ sQ224_spl
| cons(sK51_skl,nil) = sK47_skl
| ~ singletonP(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2408,f117]) ).
fof(f2417,definition,
( sQ225_spl
<=> cons(sK51_skl,nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2418,plain,
( ~ sQ225_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f2417]) ).
fof(f2420,plain,
( ~ sQ224_spl
| sQ225_spl
| ~ sQ18_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2415,f548,f598,f2417,f2407]) ).
fof(f2423,plain,
( ~ sQ149_spl
| sK47_skl = app(sK53_skl,app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f1888,f382]) ).
fof(f2424,plain,
! [X0] :
( ~ sQ149_spl
| X0 = app(sK47_skl,sK54_skl)
| app(app(sK53_skl,sK47_skl),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssList(app(sK47_skl,sK54_skl)) ),
inference(paramodulation,[status(thm)],[f1888,f378]) ).
fof(f2426,plain,
! [X0] :
( ~ sQ149_spl
| app(sK47_skl,X0) = app(app(sK53_skl,sK47_skl),app(app(sK47_skl,sK54_skl),X0))
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f1888,f382]) ).
fof(f2429,plain,
! [X0] :
( ~ sQ149_spl
| memberP(app(sK47_skl,sK54_skl),X0)
| memberP(app(sK53_skl,sK47_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1888,f270]) ).
fof(f2430,plain,
! [X0] :
( ~ sQ149_spl
| ~ memberP(app(sK47_skl,sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1888,f272]) ).
fof(f2431,plain,
! [X0] :
( ~ sQ149_spl
| ~ memberP(app(sK53_skl,sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1888,f271]) ).
fof(f2433,definition,
( sQ226_spl
<=> ssList(app(sK47_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2435,plain,
( sQ226_spl
| ~ ssList(app(sK47_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f2433]) ).
fof(f2436,definition,
( sQ227_spl
<=> sK47_skl = app(sK53_skl,app(sK47_skl,app(sK47_skl,sK54_skl))) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2437,plain,
( ~ sQ227_spl
| sK47_skl = app(sK53_skl,app(sK47_skl,app(sK47_skl,sK54_skl))) ),
inference(component_clause,[status(thm)],[f2436]) ).
fof(f2439,plain,
( ~ sQ149_spl
| sQ227_spl
| ~ sQ226_spl
| ~ sQ10_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f2423,f739,f548,f2433,f2436,f1887]) ).
fof(f2440,definition,
! [X0] :
( sQ228_spl
<=> ( X0 = app(sK47_skl,sK54_skl)
| app(app(sK53_skl,sK47_skl),X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2443,plain,
( ~ sQ149_spl
| sQ228_spl
| ~ sQ117_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f2424,f2433,f1486,f2440,f1887]) ).
fof(f2445,definition,
! [X0] :
( sQ229_spl
<=> ( app(sK47_skl,X0) = app(app(sK53_skl,sK47_skl),app(app(sK47_skl,sK54_skl),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2448,plain,
( ~ sQ149_spl
| sQ229_spl
| ~ sQ226_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f2426,f1486,f2433,f2445,f1887]) ).
fof(f2449,definition,
( sQ230_spl
<=> nil = app(sK47_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2450,plain,
( ~ sQ230_spl
| nil = app(sK47_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f2449]) ).
fof(f2453,definition,
( sQ231_spl
<=> nil = app(sK53_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2454,plain,
( ~ sQ231_spl
| nil = app(sK53_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f2453]) ).
fof(f2457,definition,
! [X0] :
( sQ232_spl
<=> ( memberP(app(sK47_skl,sK54_skl),X0)
| memberP(app(sK53_skl,sK47_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2460,plain,
( ~ sQ149_spl
| ~ sQ226_spl
| ~ sQ117_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2429,f2457,f1486,f2433,f1887]) ).
fof(f2461,definition,
! [X0] :
( sQ233_spl
<=> ( ~ memberP(app(sK47_skl,sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2462,plain,
! [X0] :
( ~ sQ233_spl
| ~ memberP(app(sK47_skl,sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2461]) ).
fof(f2464,plain,
( ~ sQ149_spl
| ~ sQ226_spl
| ~ sQ117_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2430,f2461,f1486,f2433,f1887]) ).
fof(f2465,definition,
! [X0] :
( sQ234_spl
<=> ( ~ memberP(app(sK53_skl,sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2466,plain,
! [X0] :
( ~ sQ234_spl
| ~ memberP(app(sK53_skl,sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2465]) ).
fof(f2468,plain,
( ~ sQ149_spl
| ~ sQ226_spl
| ~ sQ117_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2431,f2465,f1486,f2433,f1887]) ).
fof(f2470,plain,
( sQ226_spl
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2435,f245]) ).
fof(f2471,plain,
( sQ226_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2470,f548,f545,f2433]) ).
fof(f2481,plain,
! [X0] :
( ~ sQ233_spl
| ~ memberP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2462,f272]) ).
fof(f2483,definition,
! [X0] :
( sQ235_spl
<=> ( ~ memberP(sK54_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2486,plain,
( ~ sQ233_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2481,f2483,f548,f545,f2461]) ).
fof(f2491,definition,
! [X0] :
( sQ236_spl
<=> ( memberP(sK47_skl,X0)
| memberP(sK53_skl,X0)
| ~ ssItem(X0)
| memberP(app(sK47_skl,sK54_skl),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2529,plain,
! [X0] :
( ~ sQ231_spl
| ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2454,f272]) ).
fof(f2534,definition,
( sQ239_spl
<=> nil = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2535,plain,
( ~ sQ239_spl
| nil = sK53_skl ),
inference(component_clause,[status(thm)],[f2534]) ).
fof(f2553,definition,
! [X0] :
( sQ243_spl
<=> ( ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2554,plain,
! [X0] :
( ~ sQ243_spl
| ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2553]) ).
fof(f2556,plain,
( ~ sQ231_spl
| ~ sQ10_spl
| ~ sQ28_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f2529,f2553,f739,f548,f2453]) ).
fof(f2563,plain,
! [X0] :
( ~ sQ243_spl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2554,f279]) ).
fof(f2585,plain,
! [X0] :
( ~ sQ230_spl
| ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2450,f271]) ).
fof(f2589,definition,
( sQ245_spl
<=> cons(sK51_skl,sK54_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2590,plain,
( ~ sQ245_spl
| cons(sK51_skl,sK54_skl) = nil ),
inference(component_clause,[status(thm)],[f2589]) ).
fof(f2615,plain,
( ~ sQ230_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f2585,f2553,f548,f545,f2449]) ).
fof(f2623,plain,
( ~ sQ55_spl
| ~ sQ243_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2563,f1016]) ).
fof(f2624,plain,
( ~ sQ55_spl
| ~ sQ243_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2623,f503,f2553,f1015]) ).
fof(f2625,plain,
( ~ sQ245_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2590,f235]) ).
fof(f2647,plain,
( ~ sQ245_spl
| ~ sQ3_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2625,f545,f503,f2589]) ).
fof(f2727,plain,
! [X0,X1] :
( ~ sQ225_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK47_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2418,f478]) ).
fof(f2728,plain,
! [X0,X1] :
( ~ sQ225_spl
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,sK47_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(sK51_skl,X1))) ),
inference(paramodulation,[status(thm)],[f2418,f478]) ).
fof(f2730,plain,
! [X0,X1,X2] :
( ~ sQ225_spl
| lt(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2418,f476]) ).
fof(f2731,plain,
! [X0,X1,X2] :
( ~ sQ225_spl
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2418,f476]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( ~ sQ225_spl
| leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2418,f475]) ).
fof(f2735,plain,
! [X0,X1,X2] :
( ~ sQ225_spl
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2418,f475]) ).
fof(f2756,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f2727,f2374,f503,f611,f2417]) ).
fof(f2757,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f2728,f2370,f503,f611,f2417]) ).
fof(f2759,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f2730,f1946,f503,f611,f2417]) ).
fof(f2760,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f2731,f1942,f503,f611,f2417]) ).
fof(f2763,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f2734,f1823,f503,f611,f2417]) ).
fof(f2764,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f2735,f1819,f503,f611,f2417]) ).
fof(f2778,plain,
! [X0,X1] :
( ~ sQ225_spl
| X1 = sK51_skl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK47_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,nil)))) ),
inference(paramodulation,[status(thm)],[f2418,f479]) ).
fof(f2779,definition,
! [X0,X1] :
( sQ264_spl
<=> ( X1 = sK51_skl
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK47_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,nil)))) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2782,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f2778,f2779,f503,f611,f2417]) ).
fof(f2784,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| hd(sK47_skl) = sK51_skl ),
inference(forward_demodulation,[status(thm)],[f2137,f2076]) ).
fof(f2788,plain,
! [X0,X1] :
( ~ sQ180_spl
| X1 = sK51_skl
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK47_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,sK43_skl(sK47_skl))))) ),
inference(paramodulation,[status(thm)],[f2148,f479]) ).
fof(f2789,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK47_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,sK43_skl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f2148,f478]) ).
fof(f2790,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ ssList(X1)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,sK47_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(sK51_skl,X1))) ),
inference(paramodulation,[status(thm)],[f2148,f478]) ).
fof(f2792,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| lt(X1,sK51_skl)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f2148,f476]) ).
fof(f2793,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2148,f476]) ).
fof(f2795,plain,
( ~ sQ180_spl
| tl(sK47_skl) = sK43_skl(sK47_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f2148,f243]) ).
fof(f2796,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| leq(X1,sK51_skl)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f2148,f475]) ).
fof(f2797,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2148,f475]) ).
fof(f2798,plain,
! [X0] :
( ~ sQ180_spl
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,sK43_skl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f2148,f467]) ).
fof(f2799,plain,
! [X0] :
( ~ sQ180_spl
| ~ memberP(sK43_skl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2148,f277]) ).
fof(f2802,plain,
! [X0,X1] :
( ~ sQ180_spl
| sK43_skl(sK47_skl) = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2148,f228]) ).
fof(f2807,plain,
( ~ sQ180_spl
| sK47_skl != sK43_skl(sK47_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f2148,f225]) ).
fof(f2808,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f2148,f474]) ).
fof(f2809,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2148,f474]) ).
fof(f2811,definition,
! [X0,X1] :
( sQ265_spl
<=> ( X1 = sK51_skl
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK47_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,sK43_skl(sK47_skl))))) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2814,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f2788,f2811,f503,f1981,f2147]) ).
fof(f2815,definition,
! [X0,X1] :
( sQ266_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK47_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,sK43_skl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2818,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f2789,f2815,f503,f1981,f2147]) ).
fof(f2819,definition,
! [X0,X1] :
( sQ267_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK47_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(sK51_skl,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2822,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f2790,f2819,f503,f1981,f2147]) ).
fof(f2824,definition,
! [X0,X1,X2] :
( sQ268_spl
<=> ( lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f2792,f2824,f503,f1981,f2147]) ).
fof(f2828,definition,
! [X0,X1,X2] :
( sQ269_spl
<=> ( lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2831,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2793,f2828,f503,f1981,f2147]) ).
fof(f2833,definition,
( sQ270_spl
<=> tl(sK47_skl) = sK43_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2834,plain,
( ~ sQ270_spl
| tl(sK47_skl) = sK43_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f2833]) ).
fof(f2836,plain,
( ~ sQ180_spl
| sQ270_spl
| ~ sQ3_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f2795,f1981,f503,f2833,f2147]) ).
fof(f2837,definition,
! [X0,X1,X2] :
( sQ271_spl
<=> ( leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2840,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f2796,f2837,f503,f1981,f2147]) ).
fof(f2841,definition,
! [X0,X1,X2] :
( sQ272_spl
<=> ( leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2844,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f2797,f2841,f503,f1981,f2147]) ).
fof(f2845,definition,
! [X0] :
( sQ273_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,sK43_skl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2848,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f2798,f2845,f503,f1981,f2147]) ).
fof(f2849,definition,
! [X0] :
( sQ274_spl
<=> ( ~ memberP(sK43_skl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2850,plain,
! [X0] :
( ~ sQ274_spl
| ~ memberP(sK43_skl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2849]) ).
fof(f2852,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f2799,f2849,f503,f1981,f2147]) ).
fof(f2855,definition,
! [X0,X1] :
( sQ275_spl
<=> ( sK43_skl(sK47_skl) = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2858,plain,
( ~ sQ180_spl
| ~ sQ3_spl
| ~ sQ160_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2802,f2855,f1981,f503,f2147]) ).
fof(f2863,definition,
( sQ276_spl
<=> sK47_skl = sK43_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2866,plain,
( ~ sQ180_spl
| ~ sQ276_spl
| ~ sQ3_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f2807,f1981,f503,f2863,f2147]) ).
fof(f2867,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> ( lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,sK43_skl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2870,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f2808,f2867,f503,f1981,f2147]) ).
fof(f2871,definition,
! [X0,X1,X2] :
( sQ278_spl
<=> ( lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,sK43_skl(sK47_skl))),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2874,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f2809,f2871,f503,f1981,f2147]) ).
fof(f2996,plain,
! [X0] :
( ~ sQ180_spl
| memberP(sK43_skl(sK47_skl),X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2148,f275]) ).
fof(f2998,definition,
! [X0] :
( sQ297_spl
<=> ( memberP(sK43_skl(sK47_skl),X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f3001,plain,
( ~ sQ180_spl
| ~ sQ160_spl
| ~ sQ3_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2996,f2998,f503,f1981,f2147]) ).
fof(f3093,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ225_spl
| ~ memberP(app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f2418,f554]) ).
fof(f3094,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ225_spl
| ~ memberP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f2418,f3093]) ).
fof(f3097,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ225_spl
| ~ memberP(app(sK53_skl,sK47_skl),X0)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3094,f271]) ).
fof(f3099,definition,
! [X0] :
( sQ298_spl
<=> ( ~ memberP(app(sK53_skl,sK47_skl),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f3102,plain,
( ~ sQ11_spl
| ~ sQ225_spl
| ~ sQ10_spl
| ~ sQ117_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f3097,f3099,f1486,f548,f2417,f553]) ).
fof(f3145,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| app(app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f2418,f531]) ).
fof(f3146,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| app(app(app(sK53_skl,sK47_skl),sK47_skl),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f2418,f3145]) ).
fof(f3148,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| ~ ssList(sK54_skl)
| frontsegP(sK47_skl,app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3146,f656]) ).
fof(f3149,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ225_spl
| X0 = app(app(sK53_skl,sK47_skl),sK47_skl)
| app(X0,sK54_skl) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3146,f376]) ).
fof(f3162,definition,
( sQ299_spl
<=> frontsegP(sK47_skl,app(app(sK53_skl,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3163,plain,
( ~ sQ299_spl
| frontsegP(sK47_skl,app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(component_clause,[status(thm)],[f3162]) ).
fof(f3165,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| ~ sQ9_spl
| sQ299_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f3148,f1629,f3162,f545,f2417,f509]) ).
fof(f3166,definition,
! [X0] :
( sQ300_spl
<=> ( X0 = app(app(sK53_skl,sK47_skl),sK47_skl)
| app(X0,sK54_skl) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f3169,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| sQ300_spl
| ~ sQ9_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f3149,f1629,f545,f3166,f2417,f509]) ).
fof(f3171,definition,
( sQ301_spl
<=> rearsegP(sK47_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f3172,plain,
( ~ sQ301_spl
| rearsegP(sK47_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f3171]) ).
fof(f3195,plain,
! [X0] :
( ~ sQ180_spl
| cons(sK51_skl,app(sK43_skl(sK47_skl),X0)) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(sK43_skl(sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2148,f247]) ).
fof(f3197,definition,
! [X0] :
( sQ302_spl
<=> ( cons(sK51_skl,app(sK43_skl(sK47_skl),X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3200,plain,
( ~ sQ180_spl
| ~ sQ3_spl
| ~ sQ160_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f3195,f3197,f1981,f503,f2147]) ).
fof(f3219,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f3225,definition,
! [X0,X1] :
( sQ303_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3228,plain,
( ~ sQ20_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f3219,f3225,f611]) ).
fof(f3238,plain,
( ~ sQ139_spl
| nil = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f1814,f385]) ).
fof(f3255,plain,
( ~ sQ139_spl
| sQ45_spl
| ~ sQ10_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f3238,f1486,f548,f865,f1813]) ).
fof(f3270,definition,
( sQ307_spl
<=> rearsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3272,plain,
( sQ307_spl
| ~ rearsegP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f3270]) ).
fof(f3325,plain,
! [X0] :
( ~ sQ299_spl
| frontsegP(X0,app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3163,f282]) ).
fof(f3326,definition,
! [X0] :
( sQ312_spl
<=> ( frontsegP(X0,app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f3329,plain,
( ~ sQ299_spl
| ~ sQ130_spl
| ~ sQ10_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f3325,f3326,f548,f1629,f3162]) ).
fof(f3338,plain,
( ~ sQ227_spl
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| frontsegP(sK47_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f2437,f656]) ).
fof(f3339,plain,
! [X0] :
( ~ sQ227_spl
| X0 = sK53_skl
| app(X0,app(sK47_skl,app(sK47_skl,sK54_skl))) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f2437,f376]) ).
fof(f3341,plain,
( ~ sQ227_spl
| ~ ssList(sK53_skl)
| rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl))) ),
inference(paramodulation,[status(thm)],[f2437,f769]) ).
fof(f3342,plain,
! [X0] :
( ~ sQ227_spl
| X0 = app(sK47_skl,app(sK47_skl,sK54_skl))
| app(sK53_skl,X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl))) ),
inference(paramodulation,[status(thm)],[f2437,f378]) ).
fof(f3344,plain,
! [X0] :
( ~ sQ227_spl
| app(sK47_skl,X0) = app(sK53_skl,app(app(sK47_skl,app(sK47_skl,sK54_skl)),X0))
| ~ ssList(X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f2437,f382]) ).
fof(f3347,plain,
! [X0] :
( ~ sQ227_spl
| memberP(app(sK47_skl,app(sK47_skl,sK54_skl)),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2437,f270]) ).
fof(f3348,plain,
! [X0] :
( ~ sQ227_spl
| ~ memberP(app(sK47_skl,app(sK47_skl,sK54_skl)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2437,f272]) ).
fof(f3349,plain,
! [X0] :
( ~ sQ227_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2437,f271]) ).
fof(f3351,definition,
( sQ313_spl
<=> frontsegP(sK47_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f3352,plain,
( ~ sQ313_spl
| frontsegP(sK47_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f3351]) ).
fof(f3354,definition,
( sQ314_spl
<=> ssList(app(sK47_skl,app(sK47_skl,sK54_skl))) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f3356,plain,
( sQ314_spl
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl))) ),
inference(component_clause,[status(thm)],[f3354]) ).
fof(f3357,plain,
( ~ sQ227_spl
| ~ sQ314_spl
| sQ313_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3338,f739,f3351,f3354,f2436]) ).
fof(f3358,definition,
! [X0] :
( sQ315_spl
<=> ( X0 = sK53_skl
| app(X0,app(sK47_skl,app(sK47_skl,sK54_skl))) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f3361,plain,
( ~ sQ227_spl
| sQ315_spl
| ~ sQ314_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3339,f739,f3354,f3358,f2436]) ).
fof(f3363,definition,
( sQ316_spl
<=> rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK54_skl))) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f3364,plain,
( ~ sQ316_spl
| rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK54_skl))) ),
inference(component_clause,[status(thm)],[f3363]) ).
fof(f3366,plain,
( ~ sQ227_spl
| ~ sQ28_spl
| sQ316_spl
| ~ sQ314_spl ),
inference(split_clause,[status(thm)],[f3341,f3354,f3363,f739,f2436]) ).
fof(f3367,definition,
! [X0] :
( sQ317_spl
<=> ( X0 = app(sK47_skl,app(sK47_skl,sK54_skl))
| app(sK53_skl,X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f3370,plain,
( ~ sQ227_spl
| sQ317_spl
| ~ sQ28_spl
| ~ sQ314_spl ),
inference(split_clause,[status(thm)],[f3342,f3354,f739,f3367,f2436]) ).
fof(f3372,definition,
! [X0] :
( sQ318_spl
<=> ( app(sK47_skl,X0) = app(sK53_skl,app(app(sK47_skl,app(sK47_skl,sK54_skl)),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f3375,plain,
( ~ sQ227_spl
| sQ318_spl
| ~ sQ314_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3344,f739,f3354,f3372,f2436]) ).
fof(f3381,definition,
! [X0] :
( sQ320_spl
<=> ( memberP(app(sK47_skl,app(sK47_skl,sK54_skl)),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f3382,plain,
! [X0] :
( ~ sQ320_spl
| memberP(app(sK47_skl,app(sK47_skl,sK54_skl)),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3381]) ).
fof(f3384,plain,
( ~ sQ227_spl
| ~ sQ314_spl
| ~ sQ28_spl
| sQ320_spl ),
inference(split_clause,[status(thm)],[f3347,f3381,f739,f3354,f2436]) ).
fof(f3385,definition,
! [X0] :
( sQ321_spl
<=> ( ~ memberP(app(sK47_skl,app(sK47_skl,sK54_skl)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f3388,plain,
( ~ sQ227_spl
| ~ sQ314_spl
| ~ sQ28_spl
| sQ321_spl ),
inference(split_clause,[status(thm)],[f3348,f3385,f739,f3354,f2436]) ).
fof(f3389,definition,
! [X0] :
( sQ322_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3392,plain,
( ~ sQ227_spl
| ~ sQ314_spl
| ~ sQ28_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f3349,f3389,f739,f3354,f2436]) ).
fof(f3447,plain,
( ~ sQ225_spl
| cyclefreeP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f329]) ).
fof(f3448,definition,
( sQ323_spl
<=> cyclefreeP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3451,plain,
( ~ sQ225_spl
| sQ323_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3447,f503,f3448,f2417]) ).
fof(f3452,plain,
( ~ sQ225_spl
| totalorderP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f332]) ).
fof(f3453,definition,
( sQ324_spl
<=> totalorderP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f3456,plain,
( ~ sQ225_spl
| sQ324_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3452,f503,f3453,f2417]) ).
fof(f3457,plain,
( ~ sQ225_spl
| strictorderP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f335]) ).
fof(f3458,definition,
( sQ325_spl
<=> strictorderP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f3461,plain,
( ~ sQ225_spl
| sQ325_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3457,f503,f3458,f2417]) ).
fof(f3462,plain,
( ~ sQ225_spl
| totalorderedP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f338]) ).
fof(f3463,definition,
( sQ326_spl
<=> totalorderedP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f3466,plain,
( ~ sQ225_spl
| sQ326_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3462,f503,f3463,f2417]) ).
fof(f3467,plain,
( ~ sQ225_spl
| strictorderedP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f348]) ).
fof(f3468,definition,
( sQ327_spl
<=> strictorderedP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f3471,plain,
( ~ sQ225_spl
| sQ327_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3467,f503,f3468,f2417]) ).
fof(f3472,plain,
( ~ sQ225_spl
| duplicatefreeP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f358]) ).
fof(f3473,definition,
( sQ328_spl
<=> duplicatefreeP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3476,plain,
( ~ sQ225_spl
| sQ328_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3472,f503,f3473,f2417]) ).
fof(f3478,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f3483,definition,
! [X0] :
( sQ329_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3486,plain,
( sQ329_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3478,f611,f3483]) ).
fof(f3491,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ225_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3146,f288]) ).
fof(f3496,definition,
! [X0] :
( sQ330_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(app(app(sK53_skl,sK47_skl),sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3499,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| ~ sQ9_spl
| sQ330_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f3491,f1629,f3496,f545,f2417,f509]) ).
fof(f3505,definition,
! [X0,X1] :
( sQ331_spl
<=> ( sK51_skl = X0
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f3509,definition,
! [X0,X1] :
( sQ332_spl
<=> ( X0 = sK51_skl
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f3513,plain,
( sQ314_spl
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3356,f245]) ).
fof(f3514,plain,
( sQ314_spl
| ~ sQ226_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3513,f548,f2433,f3354]) ).
fof(f3515,plain,
( ~ sQ313_spl
| sK53_skl = sK47_skl
| ~ frontsegP(sK53_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f3352,f284]) ).
fof(f3516,plain,
! [X0] :
( ~ sQ313_spl
| frontsegP(X0,sK53_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3352,f282]) ).
fof(f3517,definition,
( sQ333_spl
<=> frontsegP(sK53_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f3519,plain,
( sQ333_spl
| ~ frontsegP(sK53_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3517]) ).
fof(f3520,definition,
( sQ334_spl
<=> sK53_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f3521,plain,
( ~ sQ334_spl
| sK53_skl = sK47_skl ),
inference(component_clause,[status(thm)],[f3520]) ).
fof(f3523,plain,
( ~ sQ313_spl
| sQ334_spl
| ~ sQ333_spl
| ~ sQ10_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3515,f739,f548,f3517,f3520,f3351]) ).
fof(f3524,definition,
! [X0] :
( sQ335_spl
<=> ( frontsegP(X0,sK53_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f3525,plain,
! [X0] :
( ~ sQ335_spl
| frontsegP(X0,sK53_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3524]) ).
fof(f3527,plain,
( ~ sQ313_spl
| ~ sQ28_spl
| ~ sQ10_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f3516,f3524,f548,f739,f3351]) ).
fof(f3528,plain,
! [X0] :
( ~ sQ320_spl
| memberP(app(sK47_skl,sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(sK47_skl)
| ~ ssItem(X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3382,f270]) ).
fof(f3529,plain,
( ~ sQ320_spl
| ~ sQ226_spl
| ~ sQ10_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f3528,f2491,f548,f2433,f3381]) ).
fof(f3530,plain,
! [X0] :
( sQ333_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f3519,f282]) ).
fof(f3531,definition,
! [X0] :
( sQ336_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f3532,plain,
! [X0] :
( ~ sQ336_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3531]) ).
fof(f3534,plain,
( sQ333_spl
| ~ sQ10_spl
| sQ336_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3530,f739,f3531,f548,f3517]) ).
fof(f3560,definition,
( sQ337_spl
<=> ssList(app(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f3562,plain,
( sQ337_spl
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f3560]) ).
fof(f3567,definition,
( sQ339_spl
<=> ssList(app(app(sK47_skl,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f3569,plain,
( sQ339_spl
| ~ ssList(app(app(sK47_skl,sK47_skl),sK47_skl)) ),
inference(component_clause,[status(thm)],[f3567]) ).
fof(f3610,definition,
( sQ348_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f3611,plain,
( ~ sQ348_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3610]) ).
fof(f3614,definition,
! [X0] :
( sQ349_spl
<=> ( frontsegP(X0,sK47_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f3675,plain,
! [X0,X1] :
( sK6_skl(X0,app(X1,X0)) = X1
| ~ ssList(sK6_skl(X0,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f769]) ).
fof(f3677,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| sK6_skl(sK54_skl,app(app(app(sK53_skl,sK47_skl),sK47_skl),sK54_skl)) = app(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(sK6_skl(sK54_skl,sK47_skl))
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl))
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f3146,f3675]) ).
fof(f3680,definition,
( sQ351_spl
<=> ssList(sK6_skl(sK54_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f3682,plain,
( sQ351_spl
| ~ ssList(sK6_skl(sK54_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f3680]) ).
fof(f3683,definition,
( sQ352_spl
<=> sK6_skl(sK54_skl,app(app(app(sK53_skl,sK47_skl),sK47_skl),sK54_skl)) = app(app(sK53_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f3686,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| sQ352_spl
| ~ sQ351_spl
| ~ sQ130_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3677,f545,f1629,f3680,f3683,f2417,f509]) ).
fof(f3689,plain,
( sQ351_spl
| ~ rearsegP(sK47_skl,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3682,f128]) ).
fof(f3690,plain,
( sQ351_spl
| ~ sQ301_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3689,f548,f545,f3171,f3680]) ).
fof(f3692,plain,
( ~ sQ225_spl
| equalelemsP(sK47_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f361]) ).
fof(f3693,definition,
( sQ353_spl
<=> equalelemsP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f3696,plain,
( ~ sQ225_spl
| sQ353_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3692,f503,f3693,f2417]) ).
fof(f3698,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f282]) ).
fof(f3701,definition,
! [X0,X1] :
( sQ354_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3704,plain,
( ~ sQ20_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f3698,f3701,f611]) ).
fof(f3707,plain,
( ~ sQ31_spl
| nil = sK54_skl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f312,f787]) ).
fof(f3710,plain,
( ~ sQ31_spl
| sQ148_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3707,f545,f1881,f786]) ).
fof(f3729,plain,
! [X0,X1] :
( ~ sQ225_spl
| frontsegP(nil,X1)
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f292]) ).
fof(f3730,plain,
! [X0,X1] :
( ~ sQ225_spl
| frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2418,f292]) ).
fof(f3733,definition,
! [X0,X1] :
( sQ356_spl
<=> ( frontsegP(nil,X1)
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f3736,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| sQ356_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3729,f503,f3733,f611,f2417]) ).
fof(f3737,definition,
! [X0,X1] :
( sQ357_spl
<=> ( frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f3740,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sQ357_spl ),
inference(split_clause,[status(thm)],[f3730,f3737,f503,f611,f2417]) ).
fof(f3745,plain,
! [X0] :
( ~ sQ225_spl
| ~ frontsegP(nil,X0)
| frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f485]) ).
fof(f3746,plain,
! [X0] :
( ~ sQ225_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f2418,f485]) ).
fof(f3763,definition,
! [X0] :
( sQ362_spl
<=> ( ~ frontsegP(nil,X0)
| frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f3766,plain,
( ~ sQ225_spl
| sQ362_spl
| ~ sQ20_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3745,f503,f611,f3763,f2417]) ).
fof(f3767,definition,
! [X0] :
( sQ363_spl
<=> ( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f3768,plain,
! [X0] :
( ~ sQ363_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3767]) ).
fof(f3770,plain,
( ~ sQ225_spl
| ~ sQ20_spl
| sQ363_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3746,f503,f3767,f611,f2417]) ).
fof(f3771,plain,
! [X0] :
( ~ sQ363_spl
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3768,f295]) ).
fof(f3773,plain,
! [X0] :
( ~ sQ301_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f3172]) ).
fof(f3775,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f3779,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f312]) ).
fof(f3781,definition,
! [X0] :
( sQ364_spl
<=> ( rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f3782,plain,
! [X0] :
( ~ sQ364_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3781]) ).
fof(f3784,plain,
( ~ sQ301_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f3773,f3781,f548,f545,f3171]) ).
fof(f3787,definition,
! [X0,X1] :
( sQ365_spl
<=> ( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f3790,plain,
( ~ sQ20_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f3775,f3787,f611]) ).
fof(f3796,definition,
! [X0,X1] :
( sQ367_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f3799,plain,
( sQ367_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3779,f611,f3796]) ).
fof(f3803,plain,
( sQ339_spl
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f3569,f245]) ).
fof(f3804,plain,
( sQ339_spl
| ~ sQ10_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f3803,f3560,f548,f3567]) ).
fof(f3805,plain,
( sQ337_spl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3562,f245]) ).
fof(f3806,plain,
( sQ337_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3805,f548,f3560]) ).
fof(f3807,plain,
! [X0] :
( ~ sQ363_spl
| sK47_skl = cons(sK51_skl,X0)
| ~ frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(cons(sK51_skl,X0))
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3771,f284]) ).
fof(f3808,plain,
! [X0,X1] :
( ~ sQ363_spl
| frontsegP(X1,sK47_skl)
| ~ frontsegP(X1,cons(sK51_skl,X0))
| ~ ssList(sK47_skl)
| ~ ssList(cons(sK51_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3771,f282]) ).
fof(f3809,plain,
( ~ sQ225_spl
| ~ sQ363_spl
| frontsegP(sK47_skl,sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2418,f3771]) ).
fof(f3810,definition,
! [X0] :
( sQ368_spl
<=> ( sK47_skl = cons(sK51_skl,X0)
| ~ frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(cons(sK51_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f3813,plain,
( ~ sQ363_spl
| ~ sQ10_spl
| sQ368_spl ),
inference(split_clause,[status(thm)],[f3807,f3810,f548,f3767]) ).
fof(f3814,definition,
! [X0,X1] :
( sQ369_spl
<=> ( frontsegP(X1,sK47_skl)
| ~ frontsegP(X1,cons(sK51_skl,X0))
| ~ ssList(cons(sK51_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3817,plain,
( ~ sQ363_spl
| ~ sQ10_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f3808,f3814,f548,f3767]) ).
fof(f3818,plain,
( ~ sQ225_spl
| ~ sQ363_spl
| sQ348_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3809,f611,f3610,f3767,f2417]) ).
fof(f3820,plain,
! [X0] :
( ~ sQ348_spl
| frontsegP(X0,sK47_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3611,f282]) ).
fof(f3822,plain,
( ~ sQ348_spl
| ~ sQ10_spl
| sQ349_spl ),
inference(split_clause,[status(thm)],[f3820,f3614,f548,f3610]) ).
fof(f3823,plain,
( ~ sQ24_spl
| ~ sQ225_spl
| frontsegP(sK47_skl,app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil))) ),
inference(forward_demodulation,[status(thm)],[f2418,f659]) ).
fof(f3824,plain,
( ~ sQ24_spl
| ~ sQ225_spl
| frontsegP(sK47_skl,app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f2418,f3823]) ).
fof(f3825,plain,
( ~ sQ24_spl
| ~ sQ225_spl
| app(app(sK53_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ frontsegP(app(app(sK53_skl,sK47_skl),sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(resolution,[status(thm)],[f3824,f284]) ).
fof(f3827,definition,
( sQ370_spl
<=> frontsegP(app(app(sK53_skl,sK47_skl),sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f3829,plain,
( sQ370_spl
| ~ frontsegP(app(app(sK53_skl,sK47_skl),sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f3827]) ).
fof(f3830,definition,
( sQ371_spl
<=> app(app(sK53_skl,sK47_skl),sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f3831,plain,
( ~ sQ371_spl
| app(app(sK53_skl,sK47_skl),sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f3830]) ).
fof(f3833,plain,
( ~ sQ24_spl
| ~ sQ225_spl
| sQ371_spl
| ~ sQ370_spl
| ~ sQ10_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f3825,f1629,f548,f3827,f3830,f2417,f658]) ).
fof(f3836,plain,
! [X0] :
( ~ sQ335_spl
| sK53_skl = X0
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3525,f284]) ).
fof(f3837,plain,
! [X0,X1] :
( ~ sQ335_spl
| frontsegP(X1,sK53_skl)
| ~ frontsegP(X1,X0)
| ~ ssList(sK53_skl)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3525,f282]) ).
fof(f3838,definition,
( sQ372_spl
<=> frontsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f3839,plain,
( ~ sQ372_spl
| frontsegP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f3838]) ).
fof(f3840,plain,
( sQ372_spl
| ~ frontsegP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f3838]) ).
fof(f3842,definition,
! [X0] :
( sQ373_spl
<=> ( sK53_skl = X0
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3845,plain,
( ~ sQ335_spl
| ~ sQ28_spl
| sQ373_spl ),
inference(split_clause,[status(thm)],[f3836,f3842,f739,f3524]) ).
fof(f3846,definition,
! [X0,X1] :
( sQ374_spl
<=> ( frontsegP(X1,sK53_skl)
| ~ frontsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3849,plain,
( ~ sQ335_spl
| ~ sQ28_spl
| sQ374_spl ),
inference(split_clause,[status(thm)],[f3837,f3846,f739,f3524]) ).
fof(f3852,plain,
! [X0] :
( sQ372_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3840,f282]) ).
fof(f3853,definition,
! [X0] :
( sQ375_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f3854,plain,
! [X0] :
( ~ sQ375_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3853]) ).
fof(f3856,plain,
( sQ372_spl
| ~ sQ10_spl
| sQ375_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3852,f611,f3853,f548,f3838]) ).
fof(f3865,definition,
( sQ377_spl
<=> ssList(app(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f3867,plain,
( sQ377_spl
| ~ ssList(app(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f3865]) ).
fof(f3869,plain,
( sQ377_spl
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3867,f245]) ).
fof(f3870,plain,
( sQ377_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3869,f611,f548,f3865]) ).
fof(f3875,plain,
! [X0,X1] :
( ~ sQ336_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(sK53_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK53_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3532,f282]) ).
fof(f3879,definition,
! [X0,X1] :
( sQ378_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(sK53_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f3882,plain,
( ~ sQ336_spl
| ~ sQ28_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f3875,f3879,f739,f3531]) ).
fof(f3885,plain,
( sQ31_spl
| ~ sQ364_spl
| ~ rearsegP(nil,sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3782,f788]) ).
fof(f3887,plain,
! [X0,X1] :
( ~ sQ364_spl
| rearsegP(X1,sK54_skl)
| ~ rearsegP(X1,X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3782,f301]) ).
fof(f3888,plain,
( sQ31_spl
| ~ sQ364_spl
| ~ sQ307_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3885,f611,f3270,f3781,f786]) ).
fof(f3890,definition,
! [X0,X1] :
( sQ379_spl
<=> ( rearsegP(X1,sK54_skl)
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f3893,plain,
( ~ sQ364_spl
| ~ sQ9_spl
| sQ379_spl ),
inference(split_clause,[status(thm)],[f3887,f3890,f545,f3781]) ).
fof(f3948,plain,
( ~ sQ301_spl
| sK54_skl = sK47_skl
| ~ rearsegP(sK54_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f303,f3172]) ).
fof(f3950,plain,
! [X0] :
( ~ sQ364_spl
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0)
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f303,f3782]) ).
fof(f3951,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f3954,definition,
( sQ382_spl
<=> rearsegP(sK54_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f3956,plain,
( sQ382_spl
| ~ rearsegP(sK54_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3954]) ).
fof(f3957,definition,
( sQ383_spl
<=> sK54_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f3958,plain,
( ~ sQ383_spl
| sK54_skl = sK47_skl ),
inference(component_clause,[status(thm)],[f3957]) ).
fof(f3959,plain,
( sQ383_spl
| sK54_skl != sK47_skl ),
inference(component_clause,[status(thm)],[f3957]) ).
fof(f3960,plain,
( ~ sQ301_spl
| sQ383_spl
| ~ sQ382_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3948,f545,f548,f3954,f3957,f3171]) ).
fof(f3963,definition,
! [X0] :
( sQ384_spl
<=> ( ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0)
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f3966,plain,
( ~ sQ364_spl
| sQ384_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3950,f545,f3963,f3781]) ).
fof(f3967,definition,
! [X0] :
( sQ385_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f3970,plain,
( sQ385_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3951,f611,f3967]) ).
fof(f3981,definition,
! [X0] :
( sQ386_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f3982,plain,
! [X0] :
( ~ sQ386_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3981]) ).
fof(f3985,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f3988,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f315,f326]) ).
fof(f3990,definition,
! [X0,X1] :
( sQ387_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f3993,plain,
( ~ sQ20_spl
| sQ387_spl ),
inference(split_clause,[status(thm)],[f3985,f3990,f611]) ).
fof(f3995,definition,
! [X0,X1] :
( sQ388_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f3998,plain,
( sQ388_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3988,f611,f3995]) ).
fof(f4073,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f4076,definition,
! [X0] :
( sQ389_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f4079,plain,
( sQ389_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4073,f611,f4076]) ).
fof(f4084,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ225_spl
| segmentP(sK47_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f3146,f321]) ).
fof(f4088,definition,
! [X0] :
( sQ390_spl
<=> ( segmentP(sK47_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f4091,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| ~ sQ9_spl
| ~ sQ117_spl
| sQ390_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4084,f548,f4088,f1486,f545,f2417,f509]) ).
fof(f4092,definition,
! [X0,X1] :
( sQ391_spl
<=> ( segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f4099,plain,
! [X0] :
( sQ307_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3272,f301]) ).
fof(f4100,definition,
! [X0] :
( sQ392_spl
<=> ( ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f4101,plain,
! [X0] :
( ~ sQ392_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4100]) ).
fof(f4103,plain,
( sQ307_spl
| ~ sQ10_spl
| sQ392_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4099,f611,f4100,f548,f3270]) ).
fof(f4330,plain,
( ~ sQ301_spl
| ~ sQ148_spl
| rearsegP(sK47_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f1882,f3172]) ).
fof(f4334,plain,
( ~ sQ301_spl
| ~ sQ148_spl
| nil = sK47_skl
| ~ rearsegP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f4330,f303]) ).
fof(f4336,plain,
( ~ sQ301_spl
| ~ sQ148_spl
| sQ45_spl
| ~ sQ307_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f4334,f611,f548,f3270,f865,f1881,f3171]) ).
fof(f4337,definition,
! [X0] :
( sQ395_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f4384,plain,
! [X0] :
( sQ382_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3956,f301]) ).
fof(f4385,definition,
! [X0] :
( sQ398_spl
<=> ( ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f4386,plain,
! [X0] :
( ~ sQ398_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4385]) ).
fof(f4388,plain,
( sQ382_spl
| ~ sQ10_spl
| sQ398_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f4384,f545,f4385,f548,f3954]) ).
fof(f4400,definition,
( sQ399_spl
<=> rearsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f4401,plain,
( ~ sQ399_spl
| rearsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f4400]) ).
fof(f4404,definition,
! [X0] :
( sQ400_spl
<=> ( rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f4468,plain,
! [X0,X1] :
( ~ sQ375_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3854,f282]) ).
fof(f4472,definition,
! [X0,X1] :
( sQ402_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f4475,plain,
( ~ sQ375_spl
| ~ sQ20_spl
| sQ402_spl ),
inference(split_clause,[status(thm)],[f4468,f4472,f611,f3853]) ).
fof(f4479,plain,
! [X0,X1] :
( ~ sQ392_spl
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4101,f301]) ).
fof(f4482,definition,
! [X0,X1] :
( sQ403_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f4485,plain,
( ~ sQ392_spl
| ~ sQ20_spl
| sQ403_spl ),
inference(split_clause,[status(thm)],[f4479,f4482,f611,f4100]) ).
fof(f4489,plain,
! [X0] :
( ~ sQ398_spl
| ~ sQ383_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f3958,f4386]) ).
fof(f4493,plain,
( ~ sQ398_spl
| ~ sQ383_spl
| ~ ssList(sK47_skl)
| ~ rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4489,f305]) ).
fof(f4500,plain,
( ~ sQ398_spl
| ~ sQ383_spl
| ~ sQ399_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4493,f548,f4400,f3957,f4385]) ).
fof(f4516,plain,
( ~ sQ316_spl
| ~ sQ383_spl
| rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK47_skl))) ),
inference(forward_demodulation,[status(thm)],[f3958,f3364]) ).
fof(f4517,plain,
( ~ sQ316_spl
| ~ sQ383_spl
| app(sK47_skl,app(sK47_skl,sK47_skl)) = sK47_skl
| ~ rearsegP(app(sK47_skl,app(sK47_skl,sK47_skl)),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK47_skl))) ),
inference(resolution,[status(thm)],[f4516,f303]) ).
fof(f4519,definition,
( sQ407_spl
<=> ssList(app(sK47_skl,app(sK47_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f4521,plain,
( sQ407_spl
| ~ ssList(app(sK47_skl,app(sK47_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f4519]) ).
fof(f4522,definition,
( sQ408_spl
<=> rearsegP(app(sK47_skl,app(sK47_skl,sK47_skl)),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f4523,plain,
( ~ sQ408_spl
| rearsegP(app(sK47_skl,app(sK47_skl,sK47_skl)),sK47_skl) ),
inference(component_clause,[status(thm)],[f4522]) ).
fof(f4524,plain,
( sQ408_spl
| ~ rearsegP(app(sK47_skl,app(sK47_skl,sK47_skl)),sK47_skl) ),
inference(component_clause,[status(thm)],[f4522]) ).
fof(f4525,definition,
( sQ409_spl
<=> app(sK47_skl,app(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f4526,plain,
( ~ sQ409_spl
| app(sK47_skl,app(sK47_skl,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f4525]) ).
fof(f4528,plain,
( ~ sQ316_spl
| ~ sQ383_spl
| sQ409_spl
| ~ sQ408_spl
| ~ sQ10_spl
| ~ sQ407_spl ),
inference(split_clause,[status(thm)],[f4517,f4519,f548,f4522,f4525,f3957,f3363]) ).
fof(f4535,plain,
( sQ370_spl
| ~ frontsegP(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f3829,f288]) ).
fof(f4537,definition,
( sQ411_spl
<=> frontsegP(app(sK53_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f4539,plain,
( sQ411_spl
| ~ frontsegP(app(sK53_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f4537]) ).
fof(f4540,plain,
( sQ370_spl
| ~ sQ411_spl
| ~ sQ10_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f4535,f1486,f548,f4537,f3827]) ).
fof(f4545,plain,
( sQ411_spl
| ~ frontsegP(sK53_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f4539,f288]) ).
fof(f4547,plain,
( sQ411_spl
| ~ sQ333_spl
| ~ sQ10_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f4545,f739,f548,f3517,f4537]) ).
fof(f4552,plain,
( sQ408_spl
| ~ rearsegP(app(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f4524,f307]) ).
fof(f4554,definition,
( sQ414_spl
<=> rearsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f4555,plain,
( ~ sQ414_spl
| rearsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f4554]) ).
fof(f4556,plain,
( sQ414_spl
| ~ rearsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f4554]) ).
fof(f4557,plain,
( sQ408_spl
| ~ sQ414_spl
| ~ sQ10_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f4552,f3560,f548,f4554,f4522]) ).
fof(f4563,plain,
( sQ414_spl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4556,f769]) ).
fof(f4566,plain,
( sQ414_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4563,f548,f4554]) ).
fof(f4602,definition,
! [X0,X1] :
( sQ419_spl
<=> ( segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f4607,definition,
! [X0] :
( sQ420_spl
<=> ( ~ memberP(sK47_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f4611,definition,
! [X0] :
( sQ421_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4615,definition,
( sQ422_spl
<=> ssList(sK6_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f4617,plain,
( sQ422_spl
| ~ ssList(sK6_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f4615]) ).
fof(f4715,plain,
( ~ sQ414_spl
| sK47_skl = app(sK47_skl,sK47_skl)
| ~ rearsegP(sK47_skl,app(sK47_skl,sK47_skl))
| ~ ssList(app(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4555,f303]) ).
fof(f4716,plain,
! [X0] :
( ~ sQ414_spl
| rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,app(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4555,f301]) ).
fof(f4717,definition,
( sQ427_spl
<=> rearsegP(sK47_skl,app(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f4719,plain,
( sQ427_spl
| ~ rearsegP(sK47_skl,app(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f4717]) ).
fof(f4720,definition,
( sQ428_spl
<=> sK47_skl = app(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f4721,plain,
( ~ sQ428_spl
| sK47_skl = app(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f4720]) ).
fof(f4722,plain,
( sQ428_spl
| sK47_skl != app(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f4720]) ).
fof(f4723,plain,
( ~ sQ414_spl
| sQ428_spl
| ~ sQ427_spl
| ~ sQ337_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4715,f548,f3560,f4717,f4720,f4554]) ).
fof(f4724,definition,
! [X0] :
( sQ429_spl
<=> ( rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,app(sK47_skl,sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f4727,plain,
( ~ sQ414_spl
| ~ sQ10_spl
| ~ sQ337_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f4716,f4724,f3560,f548,f4554]) ).
fof(f4728,plain,
! [X0] :
( sQ427_spl
| ~ rearsegP(X0,app(sK47_skl,sK47_skl))
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,sK47_skl))
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4719,f301]) ).
fof(f4729,definition,
! [X0] :
( sQ430_spl
<=> ( ~ rearsegP(X0,app(sK47_skl,sK47_skl))
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f4732,plain,
( sQ427_spl
| ~ sQ337_spl
| sQ430_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4728,f548,f4729,f3560,f4717]) ).
fof(f4736,plain,
( ~ sQ428_spl
| ~ sQ48_spl
| ~ sQ58_spl
| cons(sK51_skl,sK47_skl) = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f4721,f1178]) ).
fof(f4755,definition,
( sQ431_spl
<=> cons(sK51_skl,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f4756,plain,
( ~ sQ431_spl
| cons(sK51_skl,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f4755]) ).
fof(f4758,plain,
( ~ sQ428_spl
| ~ sQ48_spl
| ~ sQ58_spl
| sQ431_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4736,f548,f4755,f1033,f903,f4720]) ).
fof(f4801,plain,
! [X0,X1] :
( ~ sQ398_spl
| ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4386,f301]) ).
fof(f4804,definition,
! [X0,X1] :
( sQ438_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f4807,plain,
( ~ sQ398_spl
| ~ sQ9_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f4801,f4804,f545,f4385]) ).
fof(f4854,plain,
! [X0] :
( ~ sQ39_spl
| sK47_skl = X0
| nil != tl(X0)
| hd(sK47_skl) != hd(X0)
| nil = X0
| nil = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f841,f372]) ).
fof(f4859,definition,
! [X0] :
( sQ441_spl
<=> ( sK47_skl = X0
| nil != tl(X0)
| hd(sK47_skl) != hd(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f4862,plain,
( ~ sQ39_spl
| sQ45_spl
| ~ sQ10_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f4854,f4859,f548,f865,f840]) ).
fof(f4870,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| cons(sK51_skl,tl(sK47_skl)) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2784,f374]) ).
fof(f4871,plain,
( ~ sQ39_spl
| cons(hd(sK47_skl),nil) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f841,f374]) ).
fof(f4879,definition,
( sQ444_spl
<=> cons(sK51_skl,tl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f4882,plain,
( ~ sQ172_spl
| ~ sQ64_spl
| sQ444_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4870,f548,f865,f4879,f1085,f2075]) ).
fof(f4883,definition,
( sQ445_spl
<=> cons(hd(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f4886,plain,
( ~ sQ39_spl
| sQ445_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4871,f548,f865,f4883,f840]) ).
fof(f4890,definition,
( sQ446_spl
<=> ssList(app(sK47_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f4892,plain,
( sQ446_spl
| ~ ssList(app(sK47_skl,nil)) ),
inference(component_clause,[status(thm)],[f4890]) ).
fof(f4903,plain,
( sQ383_spl
| ~ sQ148_spl
| nil != sK47_skl ),
inference(backward_demodulation,[status(thm)],[f1882,f3959]) ).
fof(f4998,plain,
! [X0,X1] :
( ~ sQ225_spl
| lt(sK51_skl,sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f813]) ).
fof(f4999,plain,
! [X0,X1] :
( ~ sQ225_spl
| lt(sK51_skl,sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f813]) ).
fof(f5016,definition,
! [X0,X1] :
( sQ448_spl
<=> ( lt(sK51_skl,sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f5019,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f4998,f5016,f503,f2417]) ).
fof(f5020,definition,
! [X0,X1] :
( sQ449_spl
<=> ( lt(sK51_skl,sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f5023,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ449_spl ),
inference(split_clause,[status(thm)],[f4999,f5020,f503,f2417]) ).
fof(f5034,plain,
! [X0,X1] :
( ~ sQ12_spl
| memberP(sK47_skl,sK58_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f561]) ).
fof(f5037,plain,
! [X0,X1] :
( ~ sQ233_spl
| memberP(sK47_skl,sK58_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssItem(X0)
| sP0_prd(X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f2462]) ).
fof(f5038,plain,
! [X0,X1] :
( ~ sQ234_spl
| memberP(sK47_skl,sK58_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(app(sK53_skl,sK47_skl))
| ~ ssItem(X0)
| sP0_prd(X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f2466]) ).
fof(f5040,plain,
! [X0,X1] :
( ~ sQ67_spl
| memberP(sK47_skl,sK58_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(sK53_skl)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f1151]) ).
fof(f5041,plain,
! [X0,X1] :
( ~ sQ41_spl
| ~ sQ58_spl
| sK58_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)) = sK51_skl
| ~ ssItem(sK58_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f1037]) ).
fof(f5042,plain,
! [X0,X1] :
( ~ ssItem(sK58_skl(X1,nil,X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,nil,X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f814,f279]) ).
fof(f5043,plain,
! [X0,X1] :
( ~ sQ225_spl
| memberP(X0,sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f814]) ).
fof(f5044,plain,
! [X0,X1] :
( ~ sQ225_spl
| memberP(X0,sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f814]) ).
fof(f5045,definition,
! [X0,X1] :
( sQ450_spl
<=> ( memberP(sK47_skl,sK58_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK54_skl,X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK54_skl,cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f5048,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f5034,f5045,f545,f560]) ).
fof(f5051,definition,
! [X0,X1] :
( sQ451_spl
<=> ( memberP(sK47_skl,sK58_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,app(sK47_skl,sK54_skl),X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(app(sK47_skl,sK54_skl),cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f5054,plain,
( ~ sQ233_spl
| ~ sQ226_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f5037,f5051,f2433,f2461]) ).
fof(f5055,definition,
! [X0,X1] :
( sQ452_spl
<=> ( memberP(sK47_skl,sK58_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,app(sK53_skl,sK47_skl),X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(app(sK53_skl,sK47_skl),cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f5058,plain,
( ~ sQ234_spl
| ~ sQ117_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f5038,f5055,f1486,f2465]) ).
fof(f5060,definition,
! [X0,X1] :
( sQ453_spl
<=> ( memberP(sK47_skl,sK58_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssItem(sK58_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK53_skl,X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK53_skl,cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f5063,plain,
( ~ sQ67_spl
| ~ sQ28_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f5040,f5060,f739,f1146]) ).
fof(f5064,definition,
! [X0,X1] :
( sQ454_spl
<=> ( sK58_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)) = sK51_skl
| ~ ssItem(sK58_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,sK47_skl,X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(sK47_skl,cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f5067,plain,
( ~ sQ41_spl
| ~ sQ58_spl
| ~ sQ10_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f5041,f5064,f548,f1033,f848]) ).
fof(f5068,definition,
! [X0,X1] :
( sQ455_spl
<=> ( ~ ssItem(sK58_skl(X1,nil,X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)))
| ssItem(sK59_skl(X1,nil,X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)))
| ~ ssList(X1)
| ~ ssItem(X0)
| sP0_prd(X0,app(app(nil,cons(X0,nil)),X1),cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f5071,plain,
( ~ sQ20_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f5042,f5068,f611]) ).
fof(f5072,definition,
! [X0,X1] :
( sQ456_spl
<=> ( memberP(X0,sK58_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f5075,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ456_spl ),
inference(split_clause,[status(thm)],[f5043,f5072,f503,f2417]) ).
fof(f5076,definition,
! [X0,X1] :
( sQ457_spl
<=> ( memberP(X0,sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f5079,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ457_spl ),
inference(split_clause,[status(thm)],[f5044,f5076,f503,f2417]) ).
fof(f5090,plain,
( ~ sQ386_spl
| ~ ssList(sK54_skl)
| rearsegP(sK47_skl,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3982,f309]) ).
fof(f5091,plain,
! [X0,X1] :
( ~ sQ386_spl
| ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| rearsegP(sK47_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3982,f301]) ).
fof(f5092,plain,
( ~ sQ386_spl
| ~ ssList(sK54_skl)
| rearsegP(sK47_skl,sK54_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3982,f305]) ).
fof(f5093,definition,
( sQ458_spl
<=> rearsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f5094,plain,
( ~ sQ458_spl
| rearsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5093]) ).
fof(f5096,plain,
( ~ sQ386_spl
| ~ sQ9_spl
| sQ458_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5090,f611,f5093,f545,f3981]) ).
fof(f5097,definition,
! [X0,X1] :
( sQ459_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f5100,plain,
( ~ sQ386_spl
| ~ sQ9_spl
| sQ459_spl ),
inference(split_clause,[status(thm)],[f5091,f5097,f545,f3981]) ).
fof(f5101,plain,
( ~ sQ386_spl
| sQ301_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5092,f545,f3171,f3981]) ).
fof(f5104,plain,
! [X0] :
( ~ sQ458_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5094,f301]) ).
fof(f5106,plain,
( ~ sQ458_spl
| ~ sQ20_spl
| ~ sQ10_spl
| sQ395_spl ),
inference(split_clause,[status(thm)],[f5104,f4337,f548,f611,f5093]) ).
fof(f5165,plain,
( ~ sQ408_spl
| sK47_skl = app(sK47_skl,app(sK47_skl,sK47_skl))
| ~ rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4523,f303]) ).
fof(f5166,plain,
! [X0] :
( ~ sQ408_spl
| rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4523,f301]) ).
fof(f5167,definition,
( sQ461_spl
<=> rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f5169,plain,
( sQ461_spl
| ~ rearsegP(sK47_skl,app(sK47_skl,app(sK47_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f5167]) ).
fof(f5170,plain,
( ~ sQ408_spl
| sQ409_spl
| ~ sQ461_spl
| ~ sQ407_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5165,f548,f4519,f5167,f4525,f4522]) ).
fof(f5171,definition,
! [X0] :
( sQ462_spl
<=> ( rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f5174,plain,
( ~ sQ408_spl
| ~ sQ10_spl
| ~ sQ407_spl
| sQ462_spl ),
inference(split_clause,[status(thm)],[f5166,f5171,f4519,f548,f4522]) ).
fof(f5175,plain,
( sQ407_spl
| ~ ssList(app(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4521,f245]) ).
fof(f5176,plain,
( sQ407_spl
| ~ sQ337_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5175,f548,f3560,f4519]) ).
fof(f5177,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| hd(sK47_skl) = hd(app(app(sK53_skl,sK47_skl),sK47_skl))
| nil = app(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3146,f391]) ).
fof(f5178,definition,
( sQ463_spl
<=> hd(sK47_skl) = hd(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f5179,plain,
( ~ sQ463_spl
| hd(sK47_skl) = hd(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(component_clause,[status(thm)],[f5178]) ).
fof(f5181,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| sQ463_spl
| sQ139_spl
| ~ sQ9_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f5177,f1629,f545,f1813,f5178,f2417,f509]) ).
fof(f5182,plain,
( ~ sQ463_spl
| ~ sQ172_spl
| ~ sQ64_spl
| sK51_skl = hd(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f2784,f5179]) ).
fof(f5183,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| tl(sK47_skl) = app(tl(app(app(sK53_skl,sK47_skl),sK47_skl)),sK54_skl)
| nil = app(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f3146,f393]) ).
fof(f5184,definition,
( sQ464_spl
<=> tl(sK47_skl) = app(tl(app(app(sK53_skl,sK47_skl),sK47_skl)),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f5187,plain,
( ~ sQ5_spl
| ~ sQ225_spl
| sQ464_spl
| sQ139_spl
| ~ sQ9_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f5183,f1629,f545,f1813,f5184,f2417,f509]) ).
fof(f5206,plain,
( ~ sQ409_spl
| ~ ssList(sK47_skl)
| rearsegP(sK47_skl,app(sK47_skl,sK47_skl))
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f4526,f769]) ).
fof(f5256,plain,
( ~ sQ409_spl
| ~ sQ10_spl
| sQ427_spl
| ~ sQ337_spl ),
inference(split_clause,[status(thm)],[f5206,f3560,f4717,f548,f4525]) ).
fof(f5273,plain,
! [X0] :
( ~ sQ316_spl
| rearsegP(X0,app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3364,f301]) ).
fof(f5281,definition,
! [X0] :
( sQ480_spl
<=> ( rearsegP(X0,app(sK47_skl,app(sK47_skl,sK54_skl)))
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f5284,plain,
( ~ sQ316_spl
| ~ sQ314_spl
| ~ sQ10_spl
| sQ480_spl ),
inference(split_clause,[status(thm)],[f5273,f5281,f548,f3354,f3363]) ).
fof(f5285,plain,
( ~ sQ463_spl
| ~ sQ172_spl
| ~ sQ64_spl
| sK51_skl = hd(app(sK53_skl,sK47_skl))
| nil = app(sK53_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f5182,f391]) ).
fof(f5286,plain,
( ~ sQ463_spl
| ~ sQ172_spl
| ~ sQ64_spl
| cons(sK51_skl,tl(app(app(sK53_skl,sK47_skl),sK47_skl))) = app(app(sK53_skl,sK47_skl),sK47_skl)
| nil = app(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(app(app(sK53_skl,sK47_skl),sK47_skl)) ),
inference(paramodulation,[status(thm)],[f5182,f374]) ).
fof(f5288,definition,
( sQ481_spl
<=> sK51_skl = hd(app(sK53_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f5289,plain,
( ~ sQ481_spl
| sK51_skl = hd(app(sK53_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f5288]) ).
fof(f5291,plain,
( ~ sQ463_spl
| ~ sQ172_spl
| ~ sQ64_spl
| sQ481_spl
| sQ231_spl
| ~ sQ10_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f5285,f1486,f548,f2453,f5288,f1085,f2075,f5178]) ).
fof(f5292,definition,
( sQ482_spl
<=> cons(sK51_skl,tl(app(app(sK53_skl,sK47_skl),sK47_skl))) = app(app(sK53_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f5295,plain,
( ~ sQ463_spl
| ~ sQ172_spl
| ~ sQ64_spl
| sQ482_spl
| sQ139_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f5286,f1629,f1813,f5292,f1085,f2075,f5178]) ).
fof(f5297,plain,
( ~ sQ481_spl
| sK51_skl = hd(sK53_skl)
| nil = sK53_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f5289,f391]) ).
fof(f5298,plain,
( ~ sQ481_spl
| cons(sK51_skl,tl(app(sK53_skl,sK47_skl))) = app(sK53_skl,sK47_skl)
| nil = app(sK53_skl,sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f5289,f374]) ).
fof(f5300,definition,
( sQ483_spl
<=> sK51_skl = hd(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f5301,plain,
( ~ sQ483_spl
| sK51_skl = hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f5300]) ).
fof(f5303,plain,
( ~ sQ481_spl
| sQ483_spl
| sQ239_spl
| ~ sQ10_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f5297,f739,f548,f2534,f5300,f5288]) ).
fof(f5304,definition,
( sQ484_spl
<=> cons(sK51_skl,tl(app(sK53_skl,sK47_skl))) = app(sK53_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f5307,plain,
( ~ sQ481_spl
| sQ484_spl
| sQ231_spl
| ~ sQ117_spl ),
inference(split_clause,[status(thm)],[f5298,f1486,f2453,f5304,f5288]) ).
fof(f5406,plain,
( sQ446_spl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4892,f245]) ).
fof(f5407,plain,
( sQ446_spl
| ~ sQ20_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5406,f548,f611,f4890]) ).
fof(f5429,plain,
( sQ370_spl
| ~ sQ239_spl
| ~ frontsegP(app(app(nil,sK47_skl),sK47_skl),sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f2535,f3829]) ).
fof(f5447,definition,
! [X0] :
( sQ499_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f5455,plain,
! [X0,X1] :
( ~ sQ225_spl
| ssItem(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f815]) ).
fof(f5456,plain,
! [X0,X1] :
( ~ sQ225_spl
| ssItem(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f2418,f815]) ).
fof(f5457,definition,
! [X0,X1] :
( sQ500_spl
<=> ( ssItem(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,sK47_skl),X1),cons(sK51_skl,nil)))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f5460,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ500_spl ),
inference(split_clause,[status(thm)],[f5455,f5457,f503,f2417]) ).
fof(f5461,definition,
! [X0,X1] :
( sQ501_spl
<=> ( ssItem(sK58_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)))
| ssItem(sK59_skl(X1,X0,sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| sP0_prd(sK51_skl,app(app(X0,cons(sK51_skl,nil)),X1),cons(sK51_skl,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f5464,plain,
( ~ sQ225_spl
| ~ sQ3_spl
| sQ501_spl ),
inference(split_clause,[status(thm)],[f5456,f5461,f503,f2417]) ).
fof(f5475,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f896,f245]) ).
fof(f5505,plain,
( ~ sQ371_spl
| ~ sQ239_spl
| app(app(nil,sK47_skl),sK47_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f2535,f3831]) ).
fof(f5513,definition,
( sQ508_spl
<=> sK47_skl = app(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f5514,plain,
( ~ sQ508_spl
| sK47_skl = app(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f5513]) ).
fof(f5515,plain,
( sQ508_spl
| sK47_skl != app(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f5513]) ).
fof(f5556,plain,
! [X0] :
( sQ461_spl
| ~ rearsegP(X0,app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5169,f301]) ).
fof(f5557,definition,
! [X0] :
( sQ512_spl
<=> ( ~ rearsegP(X0,app(sK47_skl,app(sK47_skl,sK47_skl)))
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f5560,plain,
( sQ461_spl
| ~ sQ407_spl
| sQ512_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5556,f548,f5557,f4519,f5167]) ).
fof(f5607,plain,
( sQ370_spl
| ~ sQ239_spl
| ~ frontsegP(app(nil,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(nil,sK47_skl)) ),
inference(resolution,[status(thm)],[f5429,f288]) ).
fof(f5609,definition,
( sQ521_spl
<=> frontsegP(app(nil,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f5611,plain,
( sQ521_spl
| ~ frontsegP(app(nil,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f5609]) ).
fof(f5612,plain,
( sQ370_spl
| ~ sQ239_spl
| ~ sQ521_spl
| ~ sQ10_spl
| ~ sQ377_spl ),
inference(split_clause,[status(thm)],[f5607,f3865,f548,f5609,f2534,f3827]) ).
fof(f5683,plain,
( ~ sQ508_spl
| sK47_skl = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f249]) ).
fof(f5684,plain,
( ~ sQ508_spl
| ~ frontsegP(app(nil,sK47_skl),nil)
| sK5_skl(nil,sK47_skl) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f5475]) ).
fof(f5687,plain,
! [X0] :
( ~ sQ508_spl
| memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5514,f270]) ).
fof(f5688,plain,
! [X0,X1] :
( ~ sQ508_spl
| segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f321]) ).
fof(f5689,plain,
! [X0] :
( ~ sQ508_spl
| ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5514,f271]) ).
fof(f5690,plain,
! [X0] :
( ~ sQ508_spl
| ~ memberP(sK47_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5514,f272]) ).
fof(f5691,plain,
! [X0] :
( ~ sQ508_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f307]) ).
fof(f5692,plain,
( ~ sQ508_spl
| sK6_skl(sK47_skl,app(nil,sK47_skl)) = nil
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f3675]) ).
fof(f5693,plain,
! [X0] :
( ~ sQ508_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5514,f288]) ).
fof(f5694,plain,
( ~ sQ508_spl
| ~ ssList(sK47_skl)
| frontsegP(sK47_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5514,f656]) ).
fof(f5695,plain,
! [X0] :
( ~ sQ508_spl
| X0 = nil
| app(X0,sK47_skl) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5514,f376]) ).
fof(f5697,plain,
( ~ sQ508_spl
| ~ ssList(nil)
| rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f769]) ).
fof(f5698,plain,
! [X0] :
( ~ sQ508_spl
| X0 = sK47_skl
| app(nil,X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5514,f378]) ).
fof(f5700,plain,
! [X0] :
( ~ sQ508_spl
| app(sK47_skl,X0) = app(nil,app(sK47_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5514,f382]) ).
fof(f5704,plain,
( ~ sQ508_spl
| sQ164_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5683,f548,f1996,f5513]) ).
fof(f5705,definition,
( sQ523_spl
<=> sK5_skl(nil,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f5708,definition,
( sQ524_spl
<=> frontsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f5710,plain,
( sQ524_spl
| ~ frontsegP(app(nil,sK47_skl),nil) ),
inference(component_clause,[status(thm)],[f5708]) ).
fof(f5711,plain,
( ~ sQ508_spl
| ~ sQ524_spl
| sQ523_spl
| ~ sQ20_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5684,f548,f611,f5705,f5708,f5513]) ).
fof(f5720,definition,
! [X0] :
( sQ527_spl
<=> ( memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f5723,plain,
( ~ sQ508_spl
| ~ sQ10_spl
| ~ sQ20_spl
| sQ527_spl ),
inference(split_clause,[status(thm)],[f5687,f5720,f611,f548,f5513]) ).
fof(f5724,plain,
( ~ sQ508_spl
| ~ sQ20_spl
| sQ419_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5688,f548,f4602,f611,f5513]) ).
fof(f5725,plain,
( ~ sQ508_spl
| ~ sQ10_spl
| ~ sQ20_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f5689,f856,f611,f548,f5513]) ).
fof(f5726,plain,
( ~ sQ508_spl
| ~ sQ10_spl
| ~ sQ20_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f5690,f4607,f611,f548,f5513]) ).
fof(f5727,plain,
( ~ sQ508_spl
| ~ sQ20_spl
| sQ421_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5691,f548,f4611,f611,f5513]) ).
fof(f5728,definition,
( sQ528_spl
<=> sK6_skl(sK47_skl,app(nil,sK47_skl)) = nil ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f5731,plain,
( ~ sQ508_spl
| sQ528_spl
| ~ sQ422_spl
| ~ sQ20_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5692,f548,f611,f4615,f5728,f5513]) ).
fof(f5732,definition,
! [X0] :
( sQ529_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f5735,plain,
( ~ sQ508_spl
| ~ sQ10_spl
| sQ529_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5693,f611,f5732,f548,f5513]) ).
fof(f5736,definition,
( sQ530_spl
<=> frontsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f5737,plain,
( ~ sQ530_spl
| frontsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5736]) ).
fof(f5739,plain,
( ~ sQ508_spl
| ~ sQ10_spl
| sQ530_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5694,f611,f5736,f548,f5513]) ).
fof(f5740,definition,
! [X0] :
( sQ531_spl
<=> ( X0 = nil
| app(X0,sK47_skl) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f5743,plain,
( ~ sQ508_spl
| sQ531_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5695,f611,f548,f5740,f5513]) ).
fof(f5745,plain,
( ~ sQ508_spl
| ~ sQ20_spl
| sQ399_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5697,f548,f4400,f611,f5513]) ).
fof(f5746,definition,
! [X0] :
( sQ532_spl
<=> ( X0 = sK47_skl
| app(nil,X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f5749,plain,
( ~ sQ508_spl
| sQ532_spl
| ~ sQ20_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5698,f548,f611,f5746,f5513]) ).
fof(f5751,definition,
! [X0] :
( sQ533_spl
<=> ( app(sK47_skl,X0) = app(nil,app(sK47_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f5754,plain,
( ~ sQ508_spl
| sQ533_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f5700,f611,f548,f5751,f5513]) ).
fof(f5758,plain,
( sQ508_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5515,f249]) ).
fof(f5759,plain,
( sQ508_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5758,f419]) ).
fof(f5760,plain,
sQ508_spl,
inference(contradiction_clause,[status(thm)],[f5759]) ).
fof(f5762,plain,
! [X0] :
( ~ sQ399_spl
| rearsegP(X0,sK47_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4401,f301]) ).
fof(f5764,plain,
( ~ sQ399_spl
| ~ sQ10_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f5762,f4404,f548,f4400]) ).
fof(f5956,plain,
( sQ422_spl
| ~ rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4617,f128]) ).
fof(f5957,plain,
( sQ422_spl
| ~ sQ399_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f5956,f548,f4400,f4615]) ).
fof(f5983,plain,
! [X0] :
( ~ sQ530_spl
| frontsegP(X0,nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5737,f282]) ).
fof(f5985,plain,
( ~ sQ530_spl
| ~ sQ20_spl
| ~ sQ10_spl
| sQ499_spl ),
inference(split_clause,[status(thm)],[f5983,f5447,f548,f611,f5736]) ).
fof(f6075,plain,
( ~ sQ483_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f5301,f374]) ).
fof(f6077,definition,
( sQ553_spl
<=> cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f6078,plain,
( ~ sQ553_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
inference(component_clause,[status(thm)],[f6077]) ).
fof(f6080,plain,
( ~ sQ483_spl
| sQ553_spl
| sQ239_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f6075,f739,f2534,f6077,f5300]) ).
fof(f6084,plain,
( sQ524_spl
| ~ sQ508_spl
| ~ frontsegP(sK47_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f5514,f5710]) ).
fof(f6085,plain,
( sQ524_spl
| ~ sQ508_spl
| ~ sQ530_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6084,f5737]) ).
fof(f6086,plain,
( sQ524_spl
| ~ sQ508_spl
| ~ sQ530_spl ),
inference(contradiction_clause,[status(thm)],[f6085]) ).
fof(f6102,plain,
( ~ sQ553_spl
| ~ sQ363_spl
| frontsegP(sK53_skl,sK47_skl)
| ~ ssList(tl(sK53_skl)) ),
inference(paramodulation,[status(thm)],[f6078,f3771]) ).
fof(f6127,definition,
( sQ554_spl
<=> ssList(tl(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f6129,plain,
( sQ554_spl
| ~ ssList(tl(sK53_skl)) ),
inference(component_clause,[status(thm)],[f6127]) ).
fof(f6130,plain,
( ~ sQ553_spl
| ~ sQ363_spl
| sQ333_spl
| ~ sQ554_spl ),
inference(split_clause,[status(thm)],[f6102,f6127,f3517,f3767,f6077]) ).
fof(f6215,plain,
( sQ554_spl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f6129,f241]) ).
fof(f6216,plain,
( sQ554_spl
| sQ239_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f6215,f739,f2534,f6127]) ).
fof(f6347,plain,
! [X0] :
( ~ sQ508_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(sK47_skl,X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(app(nil,sK47_skl),X0)) ),
inference(paramodulation,[status(thm)],[f5514,f471]) ).
fof(f6358,definition,
! [X0] :
( sQ584_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK47_skl,X0),sK47_skl)
| ~ ssList(app(app(nil,sK47_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ584_spl])],[split_symbol_definition]) ).
fof(f6361,plain,
( ~ sQ508_spl
| ~ sQ20_spl
| ~ sQ10_spl
| sQ584_spl ),
inference(split_clause,[status(thm)],[f6347,f6358,f548,f611,f5513]) ).
fof(f6485,plain,
( ~ sQ371_spl
| ~ sQ334_spl
| app(app(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f3521,f3831]) ).
fof(f6488,plain,
( ~ sQ371_spl
| ~ sQ334_spl
| sK47_skl = app(sK47_skl,app(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f6485,f382]) ).
fof(f6512,plain,
( ~ sQ371_spl
| ~ sQ334_spl
| sQ409_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6488,f548,f4525,f3520,f3830]) ).
fof(f6601,plain,
( ~ sQ371_spl
| ~ sQ239_spl
| ~ sQ508_spl
| app(sK47_skl,sK47_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f5514,f5505]) ).
fof(f6602,plain,
( ~ sQ371_spl
| ~ sQ239_spl
| ~ sQ508_spl
| sQ428_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6601,f4722]) ).
fof(f6603,plain,
( ~ sQ371_spl
| ~ sQ239_spl
| ~ sQ508_spl
| sQ428_spl ),
inference(contradiction_clause,[status(thm)],[f6602]) ).
fof(f6608,plain,
( sQ521_spl
| ~ sQ508_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f5514,f5611]) ).
fof(f6609,plain,
( sQ521_spl
| ~ sQ508_spl
| ~ sQ348_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6608,f3611]) ).
fof(f6610,plain,
( sQ521_spl
| ~ sQ508_spl
| ~ sQ348_spl ),
inference(contradiction_clause,[status(thm)],[f6609]) ).
fof(f6679,plain,
( ~ sQ431_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f4756,f225]) ).
fof(f6705,plain,
( ~ sQ431_spl
| ~ sQ3_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6679,f548,f503,f4755]) ).
fof(f6745,definition,
( sQ619_spl
<=> tl(sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f6764,plain,
( sQ383_spl
| ~ sQ148_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f4903,f865,f1881,f3957]) ).
fof(f6772,plain,
( ~ sQ372_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3839,f298]) ).
fof(f6775,plain,
( ~ sQ372_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6772,f548,f865,f3838]) ).
fof(f6809,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ383_spl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f3958,f775]) ).
fof(f6811,plain,
( ~ sQ55_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ383_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f6809,f1016]) ).
fof(f6813,plain,
( ~ sQ55_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ383_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6811,f503,f3957,f461,f560,f1015]) ).
fof(f6855,plain,
( ~ sQ270_spl
| cons(sK44_skl(sK47_skl),tl(sK47_skl)) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2834,f233]) ).
fof(f6856,plain,
( ~ sQ270_spl
| ssList(tl(sK47_skl))
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2834,f231]) ).
fof(f6857,definition,
( sQ627_spl
<=> cons(sK44_skl(sK47_skl),tl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ627_spl])],[split_symbol_definition]) ).
fof(f6860,plain,
( ~ sQ270_spl
| sQ627_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6855,f548,f865,f6857,f2833]) ).
fof(f6861,definition,
( sQ628_spl
<=> ssList(tl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ628_spl])],[split_symbol_definition]) ).
fof(f6864,plain,
( ~ sQ270_spl
| sQ628_spl
| sQ45_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f6856,f548,f865,f6861,f2833]) ).
fof(f6872,plain,
( ~ sQ5_spl
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| segmentP(sK47_skl,cons(sK51_skl,nil))
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(paramodulation,[status(thm)],[f531,f471]) ).
fof(f6873,plain,
! [X0] :
( ~ sQ5_spl
| segmentP(sK47_skl,X0)
| ~ segmentP(cons(sK51_skl,nil),X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssList(X0)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f531,f321]) ).
fof(f6874,plain,
( ~ sQ5_spl
| sK47_skl = app(app(sK53_skl,cons(sK51_skl,nil)),app(cons(sK51_skl,nil),sK54_skl))
| ~ ssList(sK54_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f382]) ).
fof(f6875,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| segmentP(app(sK47_skl,X0),sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl),X0)) ),
inference(paramodulation,[status(thm)],[f531,f471]) ).
fof(f6880,plain,
! [X0,X1] :
( ~ sQ5_spl
| segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f531,f321]) ).
fof(f6883,plain,
! [X0] :
( ~ sQ5_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f531,f307]) ).
fof(f6884,plain,
( ~ sQ5_spl
| sK6_skl(sK54_skl,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))
| ~ ssList(sK6_skl(sK54_skl,sK47_skl))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f531,f3675]) ).
fof(f6885,plain,
! [X0] :
( ~ sQ5_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f288]) ).
fof(f6887,plain,
! [X0] :
( ~ sQ5_spl
| X0 = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))
| app(X0,sK54_skl) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f376]) ).
fof(f6890,plain,
! [X0] :
( ~ sQ5_spl
| X0 = sK54_skl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f531,f378]) ).
fof(f6892,plain,
! [X0] :
( ~ sQ5_spl
| app(sK47_skl,X0) = app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),app(sK54_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f382]) ).
fof(f6893,plain,
( ~ sQ5_spl
| nil = sK54_skl
| nil != sK47_skl
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f531,f385]) ).
fof(f6929,definition,
( sQ638_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f6931,plain,
( sQ638_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f6929]) ).
fof(f6932,definition,
( sQ639_spl
<=> segmentP(sK47_skl,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f6935,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ26_spl
| sQ639_spl
| ~ sQ27_spl
| ~ sQ638_spl ),
inference(split_clause,[status(thm)],[f6872,f6929,f669,f6932,f666,f545,f509]) ).
fof(f6936,definition,
! [X0] :
( sQ640_spl
<=> ( segmentP(sK47_skl,X0)
| ~ segmentP(cons(sK51_skl,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f6939,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ26_spl
| sQ640_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6873,f669,f6936,f666,f545,f509]) ).
fof(f6940,definition,
( sQ641_spl
<=> sK47_skl = app(app(sK53_skl,cons(sK51_skl,nil)),app(cons(sK51_skl,nil),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f6943,plain,
( ~ sQ5_spl
| sQ641_spl
| ~ sQ9_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f6874,f666,f669,f545,f6940,f509]) ).
fof(f6944,definition,
! [X0] :
( sQ642_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK47_skl,X0),sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f6947,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ642_spl ),
inference(split_clause,[status(thm)],[f6875,f6944,f545,f542,f509]) ).
fof(f6967,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| sQ391_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6880,f545,f4092,f542,f509]) ).
fof(f6970,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| sQ386_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6883,f545,f3981,f542,f509]) ).
fof(f6971,definition,
( sQ648_spl
<=> sK6_skl(sK54_skl,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f6974,plain,
( ~ sQ5_spl
| sQ648_spl
| ~ sQ351_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6884,f545,f542,f3680,f6971,f509]) ).
fof(f6975,definition,
! [X0] :
( sQ649_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f6978,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ649_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6885,f542,f6975,f545,f509]) ).
fof(f6980,definition,
! [X0] :
( sQ650_spl
<=> ( X0 = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))
| app(X0,sK54_skl) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f6983,plain,
( ~ sQ5_spl
| sQ650_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6887,f542,f545,f6980,f509]) ).
fof(f6986,definition,
! [X0] :
( sQ651_spl
<=> ( X0 = sK54_skl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f6989,plain,
( ~ sQ5_spl
| sQ651_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f6890,f545,f542,f6986,f509]) ).
fof(f6991,definition,
! [X0] :
( sQ652_spl
<=> ( app(sK47_skl,X0) = app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),app(sK54_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f6994,plain,
( ~ sQ5_spl
| sQ652_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6892,f542,f545,f6991,f509]) ).
fof(f6995,plain,
( ~ sQ5_spl
| sQ148_spl
| ~ sQ45_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6893,f542,f545,f865,f1881,f509]) ).
fof(f7002,plain,
( sQ638_spl
| ~ sQ5_spl
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f531,f6931]) ).
fof(f7003,plain,
( sQ638_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7002,f419]) ).
fof(f7004,plain,
( sQ638_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f7003]) ).
fof(f7018,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| cons(sK51_skl,tl(sK47_skl)) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f2834,f2148]) ).
fof(f7019,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| X0 = sK51_skl
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f7018,f291]) ).
fof(f7020,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| sK51_skl = X0
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f7018,f291]) ).
fof(f7021,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| frontsegP(X1,tl(sK47_skl))
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f7018,f292]) ).
fof(f7022,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| frontsegP(tl(sK47_skl),X1)
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f7018,f292]) ).
fof(f7023,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ frontsegP(X0,tl(sK47_skl))
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f7018,f485]) ).
fof(f7024,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ frontsegP(tl(sK47_skl),X0)
| frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(X0)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f7018,f485]) ).
fof(f7025,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,tl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f7018,f472]) ).
fof(f7026,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,tl(sK47_skl))),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f7018,f472]) ).
fof(f7027,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| ~ sQ270_spl
| leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,tl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f7018,f473]) ).
fof(f7028,plain,
! [X0,X1,X2] :
( ~ sQ180_spl
| ~ sQ270_spl
| leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,tl(sK47_skl))),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f7018,f473]) ).
fof(f7030,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| tl(sK47_skl) = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f7018,f228]) ).
fof(f7034,plain,
! [X0,X1] :
( ~ sQ180_spl
| ~ sQ270_spl
| X1 = sK51_skl
| cons(X1,X0) != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f7018,f227]) ).
fof(f7036,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,tl(sK47_skl)))) ),
inference(paramodulation,[status(thm)],[f7018,f467]) ).
fof(f7039,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| tl(sK47_skl) = tl(sK47_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(tl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f7018,f243]) ).
fof(f7042,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| memberP(tl(sK47_skl),X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f7018,f275]) ).
fof(f7043,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| cons(sK51_skl,app(tl(sK47_skl),X0)) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(tl(sK47_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f7018,f247]) ).
fof(f7044,plain,
! [X0] :
( ~ sQ180_spl
| ~ sQ270_spl
| ~ memberP(tl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f7018,f277]) ).
fof(f7048,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| sK47_skl != tl(sK47_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(tl(sK47_skl)) ),
inference(paramodulation,[status(thm)],[f7018,f225]) ).
fof(f7049,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f7019,f3509,f503,f6861,f2833,f2147]) ).
fof(f7050,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| sQ331_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7020,f503,f3505,f6861,f2833,f2147]) ).
fof(f7051,definition,
! [X0,X1] :
( sQ653_spl
<=> ( frontsegP(X1,tl(sK47_skl))
| ~ frontsegP(cons(X0,X1),sK47_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f7054,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ653_spl ),
inference(split_clause,[status(thm)],[f7021,f7051,f503,f6861,f2833,f2147]) ).
fof(f7055,definition,
! [X0,X1] :
( sQ654_spl
<=> ( frontsegP(tl(sK47_skl),X1)
| ~ frontsegP(sK47_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f7058,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| sQ654_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7022,f503,f7055,f6861,f2833,f2147]) ).
fof(f7059,definition,
! [X0] :
( sQ655_spl
<=> ( ~ frontsegP(X0,tl(sK47_skl))
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f7062,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| sQ655_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7023,f503,f7059,f6861,f2833,f2147]) ).
fof(f7063,definition,
! [X0] :
( sQ656_spl
<=> ( ~ frontsegP(tl(sK47_skl),X0)
| frontsegP(sK47_skl,cons(sK51_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f7066,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| sQ656_spl
| ~ sQ628_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f7024,f503,f6861,f7063,f2833,f2147]) ).
fof(f7067,definition,
! [X0,X1,X2] :
( sQ657_spl
<=> ( ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,tl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ657_spl])],[split_symbol_definition]) ).
fof(f7070,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ657_spl ),
inference(split_clause,[status(thm)],[f7025,f7067,f503,f6861,f2833,f2147]) ).
fof(f7071,definition,
! [X0,X1,X2] :
( sQ658_spl
<=> ( ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,tl(sK47_skl))),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ658_spl])],[split_symbol_definition]) ).
fof(f7074,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ658_spl ),
inference(split_clause,[status(thm)],[f7026,f7071,f503,f6861,f2833,f2147]) ).
fof(f7075,definition,
! [X0,X1,X2] :
( sQ659_spl
<=> ( leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,tl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ659_spl])],[split_symbol_definition]) ).
fof(f7078,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ659_spl ),
inference(split_clause,[status(thm)],[f7027,f7075,f503,f6861,f2833,f2147]) ).
fof(f7079,definition,
! [X0,X1,X2] :
( sQ660_spl
<=> ( leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,tl(sK47_skl))),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f7082,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ660_spl ),
inference(split_clause,[status(thm)],[f7028,f7079,f503,f6861,f2833,f2147]) ).
fof(f7090,definition,
! [X0,X1] :
( sQ663_spl
<=> ( tl(sK47_skl) = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f7093,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ3_spl
| ~ sQ628_spl
| sQ663_spl ),
inference(split_clause,[status(thm)],[f7030,f7090,f6861,f503,f2833,f2147]) ).
fof(f7097,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ3_spl
| ~ sQ628_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f7034,f1651,f6861,f503,f2833,f2147]) ).
fof(f7099,definition,
! [X0] :
( sQ664_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,tl(sK47_skl)))) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f7102,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ664_spl ),
inference(split_clause,[status(thm)],[f7036,f7099,f503,f6861,f2833,f2147]) ).
fof(f7111,definition,
( sQ667_spl
<=> tl(sK47_skl) = tl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f7114,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| sQ667_spl
| ~ sQ3_spl
| ~ sQ628_spl ),
inference(split_clause,[status(thm)],[f7039,f6861,f503,f7111,f2833,f2147]) ).
fof(f7117,definition,
! [X0] :
( sQ668_spl
<=> ( memberP(tl(sK47_skl),X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ668_spl])],[split_symbol_definition]) ).
fof(f7120,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ668_spl ),
inference(split_clause,[status(thm)],[f7042,f7117,f503,f6861,f2833,f2147]) ).
fof(f7121,definition,
! [X0] :
( sQ669_spl
<=> ( cons(sK51_skl,app(tl(sK47_skl),X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ669_spl])],[split_symbol_definition]) ).
fof(f7124,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ3_spl
| ~ sQ628_spl
| sQ669_spl ),
inference(split_clause,[status(thm)],[f7043,f7121,f6861,f503,f2833,f2147]) ).
fof(f7125,definition,
! [X0] :
( sQ670_spl
<=> ( ~ memberP(tl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f7128,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ628_spl
| ~ sQ3_spl
| sQ670_spl ),
inference(split_clause,[status(thm)],[f7044,f7125,f503,f6861,f2833,f2147]) ).
fof(f7132,plain,
( ~ sQ180_spl
| ~ sQ270_spl
| ~ sQ619_spl
| ~ sQ3_spl
| ~ sQ628_spl ),
inference(split_clause,[status(thm)],[f7048,f6861,f503,f6745,f2833,f2147]) ).
fof(f7141,plain,
! [X0] :
( ~ sQ274_spl
| ~ sQ270_spl
| ~ memberP(tl(sK47_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f2834,f2850]) ).
fof(f7142,plain,
! [X0,X1] :
( ~ sQ274_spl
| ~ sQ270_spl
| ssItem(sK59_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssList(tl(sK47_skl))
| ~ ssItem(X1)
| sP0_prd(X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil))) ),
inference(resolution,[status(thm)],[f7141,f814]) ).
fof(f7143,definition,
! [X0,X1] :
( sQ671_spl
<=> ( ssItem(sK59_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,tl(sK47_skl),X1,app(app(tl(sK47_skl),cons(X1,nil)),X0),cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f7146,plain,
( ~ sQ274_spl
| ~ sQ270_spl
| ~ sQ628_spl
| sQ671_spl ),
inference(split_clause,[status(thm)],[f7142,f7143,f6861,f2833,f2849]) ).
fof(f7159,plain,
! [X0,X1] :
( ~ sQ53_spl
| ssItem(sK59_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssItem(X1)
| sP0_prd(X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil))) ),
inference(resolution,[status(thm)],[f1008,f814]) ).
fof(f7162,definition,
! [X0,X1] :
( sQ672_spl
<=> ( ssItem(sK59_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,cons(sK51_skl,nil),X1,app(app(cons(sK51_skl,nil),cons(X1,nil)),X0),cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f7165,plain,
( ~ sQ53_spl
| ~ sQ27_spl
| sQ672_spl ),
inference(split_clause,[status(thm)],[f7159,f7162,f669,f1003]) ).
fof(f7177,plain,
! [X0,X1] :
( ~ sQ52_spl
| ssItem(sK59_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X1)
| sP0_prd(X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))) ),
inference(resolution,[status(thm)],[f1007,f814]) ).
fof(f7181,definition,
! [X0,X1] :
( sQ673_spl
<=> ( ssItem(sK59_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,app(sK53_skl,cons(sK51_skl,nil)),X1,app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f7184,plain,
( ~ sQ52_spl
| ~ sQ26_spl
| sQ673_spl ),
inference(split_clause,[status(thm)],[f7177,f7181,f666,f999]) ).
fof(f7191,plain,
! [X0,X1] :
( ~ sQ11_spl
| ssItem(sK59_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X1)
| sP0_prd(X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))) ),
inference(resolution,[status(thm)],[f554,f814]) ).
fof(f7195,definition,
! [X0,X1] :
( sQ674_spl
<=> ( ssItem(sK59_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))
| memberP(sK47_skl,sK58_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil)))
| ~ ssItem(sK58_skl(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X1,app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),cons(X1,nil)),X0),cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f7198,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| sQ674_spl ),
inference(split_clause,[status(thm)],[f7191,f7195,f542,f553]) ).
fof(f7207,plain,
( ~ sQ2_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f462,f424]) ).
fof(f7208,plain,
( ~ sQ2_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f7207,f865,f461]) ).
fof(f7209,plain,
$false,
inference(sat_refutation,[status(thm)],[f464,f512,f519,f521,f528,f551,f556,f558,f563,f571,f588,f604,f606,f655,f661,f672,f675,f677,f742,f744,f754,f759,f771,f818,f834,f838,f843,f847,f851,f855,f863,f868,f885,f894,f906,f1002,f1014,f1018,f1025,f1029,f1036,f1066,f1070,f1074,f1079,f1083,f1088,f1092,f1096,f1149,f1150,f1225,f1229,f1282,f1283,f1287,f1304,f1310,f1386,f1473,f1477,f1489,f1501,f1505,f1521,f1542,f1547,f1559,f1565,f1582,f1594,f1600,f1606,f1610,f1645,f1678,f1725,f1846,f1890,f1894,f1910,f1914,f1990,f2005,f2008,f2019,f2053,f2057,f2061,f2065,f2070,f2074,f2078,f2083,f2087,f2091,f2096,f2103,f2110,f2114,f2150,f2178,f2406,f2410,f2414,f2420,f2439,f2443,f2448,f2460,f2464,f2468,f2471,f2486,f2556,f2615,f2624,f2647,f2756,f2757,f2759,f2760,f2763,f2764,f2782,f2814,f2818,f2822,f2827,f2831,f2836,f2840,f2844,f2848,f2852,f2858,f2866,f2870,f2874,f3001,f3102,f3165,f3169,f3200,f3228,f3255,f3329,f3357,f3361,f3366,f3370,f3375,f3384,f3388,f3392,f3451,f3456,f3461,f3466,f3471,f3476,f3486,f3499,f3514,f3523,f3527,f3529,f3534,f3686,f3690,f3696,f3704,f3710,f3736,f3740,f3766,f3770,f3784,f3790,f3799,f3804,f3806,f3813,f3817,f3818,f3822,f3833,f3845,f3849,f3856,f3870,f3882,f3888,f3893,f3960,f3966,f3970,f3993,f3998,f4079,f4091,f4103,f4336,f4388,f4475,f4485,f4500,f4528,f4540,f4547,f4557,f4566,f4723,f4727,f4732,f4758,f4807,f4862,f4882,f4886,f5019,f5023,f5048,f5054,f5058,f5063,f5067,f5071,f5075,f5079,f5096,f5100,f5101,f5106,f5170,f5174,f5176,f5181,f5187,f5256,f5284,f5291,f5295,f5303,f5307,f5407,f5460,f5464,f5560,f5612,f5704,f5711,f5723,f5724,f5725,f5726,f5727,f5731,f5735,f5739,f5743,f5745,f5749,f5754,f5760,f5764,f5957,f5985,f6080,f6086,f6130,f6216,f6361,f6512,f6603,f6610,f6705,f6764,f6775,f6813,f6860,f6864,f6935,f6939,f6943,f6947,f6967,f6970,f6974,f6978,f6983,f6989,f6994,f6995,f7004,f7049,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7093,f7097,f7102,f7114,f7120,f7124,f7128,f7132,f7146,f7165,f7184,f7198,f7208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC165+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n009.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.64 % CPULimit : 300
% 0.16/0.64 % WCLimit : 300
% 0.16/0.64 % DateTime : Mon Sep 21 08:00:28 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.68 % Drodi V4.1.1
% 71.60/9.85 % Refutation found
% 71.60/9.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 71.60/9.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.19/9.95 % Elapsed time: 9.294922 seconds
% 4.19/9.95 % CPU time: 72.849148 seconds
% 4.19/9.95 % Total memory used: 341.201 MB
% 4.19/9.95 % Net memory used: 323.874 MB
%------------------------------------------------------------------------------