%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC297+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:41 PM UTC 2026
% Result : Theorem 17.11s 2.60s
% Output : CNFRefutation 17.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 307
% Syntax : Number of formulae : 1196 ( 21 unt; 246 def)
% Number of atoms : 5418 ( 677 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 7690 (3468 ~;3516 |; 238 &)
% ( 282 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 265 ( 263 usr; 246 prp; 0-3 aty)
% Number of functors : 59 ( 59 usr; 10 con; 0-2 aty)
% Number of variables : 1219 (1138 !; 81 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( ssItem(U)
=> totalorderP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( hd(U) = V
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( tl(U) = V
& ssList(V) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ! [X2] :
( ssItem(X2)
=> ( ( lt(Y,X2)
| ~ memberP(X1,X2) )
& ( lt(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ! [X2] :
( ssItem(X2)
=> ( ( lt(Y,X2)
| ~ memberP(X1,X2) )
& ( lt(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ 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(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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(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(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(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(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(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(f363,plain,
! [U] :
( ? [V] :
( hd(U) = V
& ssItem(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f364,plain,
! [U] :
( ( hd(U) = sK45_skl(U)
& ssItem(sK45_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl]),skolemize(V,sK45_skl(U))],[f363]) ).
fof(f366,plain,
! [X0] :
( hd(X0) = sK45_skl(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f367,plain,
! [U] :
( ? [V] :
( tl(U) = V
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f368,plain,
! [U] :
( ( tl(U) = sK46_skl(U)
& ssList(sK46_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl]),skolemize(V,sK46_skl(U))],[f367]) ).
fof(f370,plain,
! [X0] :
( tl(X0) = sK46_skl(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
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] :
( ( ~ neq(X,nil)
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ lt(Y,X2)
& memberP(X1,X2) )
| ( ~ lt(X2,Y)
& memberP(Z,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(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,
! [Y,Z,X2] :
( sP0_prd(X2,Z,Y)
<=> ( ~ lt(X2,Y)
& memberP(Z,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ lt(Y,X2)
& memberP(X1,X2) )
| sP0_prd(X2,Z,Y) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(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,
( ( ~ neq(sK50_skl,nil)
| ( memberP(sK50_skl,sK55_skl)
& cons(sK55_skl,nil) = sK49_skl
& ssItem(sK55_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ( ( ~ lt(sK51_skl,sK54_skl)
& memberP(sK53_skl,sK54_skl) )
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) )
& ssItem(sK54_skl)
& app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl
& ssList(sK53_skl)
& ssList(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(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f422,plain,
ssList(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,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
ssItem(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( memberP(sK53_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
( ~ lt(sK51_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK55_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f434,plain,
( ~ neq(sK50_skl,nil)
| cons(sK55_skl,nil) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f435,plain,
( ~ neq(sK50_skl,nil)
| memberP(sK50_skl,sK55_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f436,plain,
! [Y,Z,X2] :
( ( lt(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ( ( ~ lt(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f437,plain,
( ! [Y,Z,X2] :
( lt(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ! [Y,Z,X2] :
( ( ~ lt(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(miniscoping,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f441,definition,
( sQ0_spl
<=> sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ0_spl
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ1_spl
<=> memberP(sK53_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ1_spl
| memberP(sK53_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f446,plain,
( sQ1_spl
| ~ memberP(sK53_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f430,f441,f444]) ).
fof(f448,definition,
( sQ2_spl
<=> lt(sK51_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f431,f441,f448]) ).
fof(f452,definition,
( sQ3_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ3_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f454,plain,
( sQ3_spl
| nil != sK49_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
( sQ4_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ4_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f432,f452,f455]) ).
fof(f459,definition,
( sQ5_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ5_spl
| ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,definition,
( sQ6_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ6_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f433,f459,f462]) ).
fof(f466,definition,
( sQ7_spl
<=> cons(sK55_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ7_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f434,f466,f462]) ).
fof(f470,definition,
( sQ8_spl
<=> memberP(sK50_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f435,f470,f462]) ).
fof(f476,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(f478,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f480,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(f481,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(f482,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(f483,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(f484,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(f485,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(f486,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(f487,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)],[f486]) ).
fof(f488,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(f491,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f479,f245]) ).
fof(f492,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f478,f245]) ).
fof(f493,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f494,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f493]) ).
fof(f495,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(f496,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)],[f495]) ).
fof(f508,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f510,plain,
( ~ sQ3_spl
| app(app(sK52_skl,cons(sK51_skl,sK49_skl)),sK53_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f453,f508]) ).
fof(f648,plain,
( ~ sQ0_spl
| memberP(sK52_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f442,f438]) ).
fof(f653,definition,
( sQ13_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( sQ13_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f653]) ).
fof(f661,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f655,f421]) ).
fof(f662,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f666,definition,
( sQ15_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f668,plain,
( sQ15_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f678,definition,
( sQ16_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ16_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f686,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f680,f223]) ).
fof(f687,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f691,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssItem(sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f467,f476]) ).
fof(f693,definition,
! [X0] :
( sQ18_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f691,f693,f459,f678,f466]) ).
fof(f697,plain,
! [X0] :
( ~ sQ3_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f453,f279]) ).
fof(f750,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f668,f422]) ).
fof(f751,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f752,plain,
( sQ6_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f464,f220]) ).
fof(f754,plain,
( sQ6_spl
| sQ4_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f752,f666,f678,f455,f462]) ).
fof(f782,plain,
! [X0] :
( ~ sQ3_spl
| sK49_skl = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f453,f312]) ).
fof(f818,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sK50_skl = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f456,f453]) ).
fof(f822,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| sK49_skl = X0
| ~ rearsegP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f456,f782]) ).
fof(f833,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| sK50_skl = X0
| ~ rearsegP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f818,f822]) ).
fof(f848,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f818,f697]) ).
fof(f886,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| app(app(sK52_skl,cons(sK51_skl,sK49_skl)),sK53_skl) = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f818,f510]) ).
fof(f897,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| app(app(sK52_skl,cons(sK51_skl,sK50_skl)),sK53_skl) = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f818,f886]) ).
fof(f899,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f900,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f901,plain,
! [X0] :
( ~ sQ19_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,definition,
! [X1] :
( sQ20_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f906,plain,
( sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f899,f900,f903]) ).
fof(f907,plain,
( ~ sQ19_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f427,f910]) ).
fof(f910,plain,
! [X0] :
( ~ sQ19_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f901]) ).
fof(f911,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f907]) ).
fof(f975,definition,
( sQ26_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,sK50_skl))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( ~ sQ26_spl
| ssList(app(sK52_skl,cons(sK51_skl,sK50_skl))) ),
inference(component_clause,[status(thm)],[f975]) ).
fof(f977,plain,
( sQ26_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK50_skl))) ),
inference(component_clause,[status(thm)],[f975]) ).
fof(f978,definition,
( sQ27_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f980,plain,
( sQ27_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f978]) ).
fof(f982,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f980,f427]) ).
fof(f983,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f984,plain,
( sQ26_spl
| ~ ssList(cons(sK51_skl,sK50_skl))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f977,f245]) ).
fof(f985,definition,
( sQ28_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f987,plain,
( sQ28_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f985]) ).
fof(f988,definition,
( sQ29_spl
<=> ssList(cons(sK51_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f990,plain,
( sQ29_spl
| ~ ssList(cons(sK51_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f988]) ).
fof(f991,plain,
( sQ26_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f984,f985,f988,f975]) ).
fof(f992,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f987,f426]) ).
fof(f993,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f994,plain,
( sQ29_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f990,f222]) ).
fof(f995,definition,
( sQ30_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f997,plain,
( sQ30_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f998,plain,
( sQ29_spl
| ~ sQ30_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f994,f666,f995,f988]) ).
fof(f999,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f997,f425]) ).
fof(f1000,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1006,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK50_skl)))
| rearsegP(sK50_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f897,f491]) ).
fof(f1007,definition,
( sQ32_spl
<=> rearsegP(sK50_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1008,plain,
( ~ sQ32_spl
| rearsegP(sK50_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f1007]) ).
fof(f1010,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ26_spl
| sQ32_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1006,f978,f1007,f975,f455,f452]) ).
fof(f1011,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ32_spl
| sK50_skl = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f1008,f833]) ).
fof(f1012,definition,
( sQ33_spl
<=> sK50_skl = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
( ~ sQ33_spl
| sK50_skl = sK53_skl ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ32_spl
| sQ33_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1011,f978,f1012,f1007,f455,f452]) ).
fof(f1017,plain,
( ~ sQ26_spl
| ~ sQ33_spl
| ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
inference(backward_demodulation,[status(thm)],[f1013,f976]) ).
fof(f1046,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ memberP(sK53_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1013,f848]) ).
fof(f1060,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ33_spl
| sK53_skl = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1013,f818]) ).
fof(f1094,definition,
( sQ34_spl
<=> sK53_skl = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1110,definition,
( sQ36_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( sQ36_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,sK53_skl))) ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1126,plain,
( sQ36_spl
| ~ sQ26_spl
| ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1112,f1017]) ).
fof(f1127,plain,
( sQ36_spl
| ~ sQ26_spl
| ~ sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f1126]) ).
fof(f1130,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f378]) ).
fof(f1131,definition,
! [X0] :
( sQ40_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1134,definition,
! [X1] :
( sQ41_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1135,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1134]) ).
fof(f1137,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1130,f1131,f1134]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ sQ7_spl
| X1 = sK55_skl
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f467,f227]) ).
fof(f1142,plain,
( ~ sQ7_spl
| sK49_skl != nil
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f467,f225]) ).
fof(f1143,definition,
! [X0,X1] :
( sQ42_spl
<=> ( X1 = sK55_skl
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
! [X0,X1] :
( ~ sQ42_spl
| X1 = sK55_skl
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1143]) ).
fof(f1146,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ16_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1138,f1143,f678,f459,f466]) ).
fof(f1150,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1142,f678,f459,f452,f466]) ).
fof(f1151,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ),
inference(resolution,[status(thm)],[f249,f378]) ).
fof(f1153,definition,
! [X0] :
( sQ43_spl
<=> ( app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1156,plain,
( ~ sQ16_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1151,f1153,f678]) ).
fof(f1159,plain,
( ~ sQ7_spl
| cyclefreeP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f329]) ).
fof(f1160,definition,
( sQ44_spl
<=> cyclefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1163,plain,
( ~ sQ7_spl
| sQ44_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1159,f459,f1160,f466]) ).
fof(f1165,plain,
( ~ sQ7_spl
| ~ sQ42_spl
| sK55_skl = sK55_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1144,f467]) ).
fof(f1167,definition,
( sQ45_spl
<=> sK55_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1170,plain,
( ~ sQ7_spl
| ~ sQ42_spl
| sQ45_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1165,f678,f459,f1167,f1143,f466]) ).
fof(f1171,definition,
( sQ46_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1175,plain,
( sK49_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f508,f382]) ).
fof(f1176,plain,
! [X0] :
( X0 = sK53_skl
| app(app(sK52_skl,cons(sK51_skl,nil)),X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f508,f378]) ).
fof(f1178,plain,
! [X0] :
( app(sK49_skl,X0) = app(app(sK52_skl,cons(sK51_skl,nil)),app(sK53_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f508,f382]) ).
fof(f1179,plain,
( ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| rearsegP(sK49_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f508,f491]) ).
fof(f1180,plain,
( ~ ssList(sK53_skl)
| frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f508,f492]) ).
fof(f1182,definition,
( sQ47_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1184,plain,
( sQ47_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f1182]) ).
fof(f1185,definition,
( sQ48_spl
<=> sK49_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1186,plain,
( ~ sQ48_spl
| sK49_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl)) ),
inference(component_clause,[status(thm)],[f1185]) ).
fof(f1188,plain,
( sQ48_spl
| ~ sQ27_spl
| ~ sQ47_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1175,f985,f1182,f978,f1185]) ).
fof(f1189,definition,
( sQ49_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1190,plain,
( ~ sQ49_spl
| ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1191,plain,
( sQ49_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f1189]) ).
fof(f1192,definition,
! [X0] :
( sQ50_spl
<=> ( X0 = sK53_skl
| app(app(sK52_skl,cons(sK51_skl,nil)),X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1193,plain,
! [X0] :
( ~ sQ50_spl
| X0 = sK53_skl
| app(app(sK52_skl,cons(sK51_skl,nil)),X0) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1192]) ).
fof(f1195,plain,
( sQ50_spl
| ~ sQ49_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1176,f978,f1189,f1192]) ).
fof(f1197,definition,
! [X0] :
( sQ51_spl
<=> ( app(sK49_skl,X0) = app(app(sK52_skl,cons(sK51_skl,nil)),app(sK53_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1200,plain,
( sQ51_spl
| ~ sQ27_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f1178,f1189,f978,f1197]) ).
fof(f1201,definition,
( sQ52_spl
<=> rearsegP(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( ~ sQ52_spl
| rearsegP(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f1201]) ).
fof(f1204,plain,
( ~ sQ49_spl
| sQ52_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1179,f978,f1201,f1189]) ).
fof(f1205,definition,
( sQ53_spl
<=> frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( ~ sQ53_spl
| frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1208,plain,
( ~ sQ27_spl
| sQ53_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f1180,f1189,f1205,f978]) ).
fof(f1210,plain,
( sQ47_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1184,f222]) ).
fof(f1211,plain,
( sQ47_spl
| ~ sQ30_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1210,f678,f995,f1182]) ).
fof(f1212,plain,
( sQ49_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f1191,f245]) ).
fof(f1213,plain,
( sQ49_spl
| ~ sQ47_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1212,f985,f1182,f1189]) ).
fof(f1216,plain,
( ~ sQ7_spl
| memberP(sK49_skl,sK55_skl)
| ~ ssList(nil)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f494]) ).
fof(f1217,definition,
( sQ54_spl
<=> memberP(sK49_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( ~ sQ7_spl
| sQ54_spl
| ~ sQ16_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1216,f459,f678,f1217,f466]) ).
fof(f1221,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f1224,definition,
( sQ55_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1227,plain,
( sQ55_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1221,f678,f1224]) ).
fof(f1229,definition,
( sQ56_spl
<=> nil = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1230,plain,
( ~ sQ56_spl
| nil = sK53_skl ),
inference(component_clause,[status(thm)],[f1229]) ).
fof(f1244,plain,
! [X0] :
( ~ sQ48_spl
| X0 = app(cons(sK51_skl,nil),sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK52_skl)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1186,f378]) ).
fof(f1246,plain,
! [X0] :
( ~ sQ48_spl
| app(sK49_skl,X0) = app(sK52_skl,app(app(cons(sK51_skl,nil),sK53_skl),X0))
| ~ ssList(X0)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1186,f382]) ).
fof(f1247,plain,
( ~ sQ48_spl
| ~ ssList(sK52_skl)
| rearsegP(sK49_skl,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1186,f491]) ).
fof(f1248,plain,
( ~ sQ48_spl
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1186,f492]) ).
fof(f1250,definition,
( sQ58_spl
<=> ssList(app(cons(sK51_skl,nil),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1251,plain,
( ~ sQ58_spl
| ssList(app(cons(sK51_skl,nil),sK53_skl)) ),
inference(component_clause,[status(thm)],[f1250]) ).
fof(f1252,plain,
( sQ58_spl
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl)) ),
inference(component_clause,[status(thm)],[f1250]) ).
fof(f1253,definition,
( sQ59_spl
<=> nil = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1254,plain,
( ~ sQ59_spl
| nil = sK52_skl ),
inference(component_clause,[status(thm)],[f1253]) ).
fof(f1261,definition,
! [X0] :
( sQ61_spl
<=> ( X0 = app(cons(sK51_skl,nil),sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
! [X0] :
( ~ sQ61_spl
| X0 = app(cons(sK51_skl,nil),sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1261]) ).
fof(f1264,plain,
( ~ sQ48_spl
| sQ61_spl
| ~ sQ28_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f1244,f1250,f985,f1261,f1185]) ).
fof(f1266,definition,
! [X0] :
( sQ62_spl
<=> ( app(sK49_skl,X0) = app(sK52_skl,app(app(cons(sK51_skl,nil),sK53_skl),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1269,plain,
( ~ sQ48_spl
| sQ62_spl
| ~ sQ58_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1246,f985,f1250,f1266,f1185]) ).
fof(f1270,definition,
( sQ63_spl
<=> rearsegP(sK49_skl,app(cons(sK51_skl,nil),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1271,plain,
( ~ sQ63_spl
| rearsegP(sK49_skl,app(cons(sK51_skl,nil),sK53_skl)) ),
inference(component_clause,[status(thm)],[f1270]) ).
fof(f1273,plain,
( ~ sQ48_spl
| ~ sQ28_spl
| sQ63_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f1247,f1250,f1270,f985,f1185]) ).
fof(f1274,definition,
( sQ64_spl
<=> frontsegP(sK49_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1275,plain,
( ~ sQ64_spl
| frontsegP(sK49_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f1274]) ).
fof(f1277,plain,
( ~ sQ48_spl
| ~ sQ58_spl
| sQ64_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1248,f985,f1274,f1250,f1185]) ).
fof(f1279,plain,
( sQ58_spl
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(resolution,[status(thm)],[f1252,f245]) ).
fof(f1280,plain,
( sQ58_spl
| ~ sQ27_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f1279,f1182,f978,f1250]) ).
fof(f1281,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(f1283,plain,
! [X0] :
( ~ sQ48_spl
| sK52_skl = X0
| sK49_skl != app(X0,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK52_skl)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1186,f376]) ).
fof(f1284,plain,
! [X0] :
( app(sK52_skl,cons(sK51_skl,nil)) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK53_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f508,f376]) ).
fof(f1288,definition,
! [X0] :
( sQ65_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1291,plain,
( ~ sQ16_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1281,f1288,f678]) ).
fof(f1293,definition,
! [X0] :
( sQ66_spl
<=> ( sK52_skl = X0
| sK49_skl != app(X0,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1294,plain,
! [X0] :
( ~ sQ66_spl
| sK52_skl = X0
| sK49_skl != app(X0,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1293]) ).
fof(f1296,plain,
( ~ sQ48_spl
| ~ sQ28_spl
| ~ sQ58_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1283,f1293,f1250,f985,f1185]) ).
fof(f1297,definition,
! [X0] :
( sQ67_spl
<=> ( app(sK52_skl,cons(sK51_skl,nil)) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1298,plain,
! [X0] :
( ~ sQ67_spl
| app(sK52_skl,cons(sK51_skl,nil)) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1297]) ).
fof(f1300,plain,
( ~ sQ49_spl
| ~ sQ27_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1284,f1297,f978,f1189]) ).
fof(f1305,plain,
! [X0] :
( ~ sQ7_spl
| ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f467,f277]) ).
fof(f1306,definition,
! [X0] :
( sQ68_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1309,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1305,f1306,f459,f678,f466]) ).
fof(f1310,plain,
( ~ sQ7_spl
| totalorderP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f332]) ).
fof(f1311,definition,
( sQ69_spl
<=> totalorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1314,plain,
( ~ sQ7_spl
| sQ69_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1310,f459,f1311,f466]) ).
fof(f1315,plain,
( ~ sQ7_spl
| strictorderP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f335]) ).
fof(f1316,definition,
( sQ70_spl
<=> strictorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1319,plain,
( ~ sQ7_spl
| sQ70_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1315,f459,f1316,f466]) ).
fof(f1320,plain,
( ~ sQ7_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f338]) ).
fof(f1321,definition,
( sQ71_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1324,plain,
( ~ sQ7_spl
| sQ71_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1320,f459,f1321,f466]) ).
fof(f1325,plain,
( ~ sQ7_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f348]) ).
fof(f1326,definition,
( sQ72_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1329,plain,
( ~ sQ7_spl
| sQ72_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1325,f459,f1326,f466]) ).
fof(f1330,plain,
( ~ sQ7_spl
| duplicatefreeP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f358]) ).
fof(f1331,definition,
( sQ73_spl
<=> duplicatefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( ~ sQ7_spl
| sQ73_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1330,f459,f1331,f466]) ).
fof(f1335,plain,
( ~ sQ7_spl
| equalelemsP(sK49_skl)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f361]) ).
fof(f1336,definition,
( sQ74_spl
<=> equalelemsP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1339,plain,
( ~ sQ7_spl
| sQ74_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1335,f459,f1336,f466]) ).
fof(f1342,plain,
! [X0] :
( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f386]) ).
fof(f1343,plain,
! [X0] :
( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f385]) ).
fof(f1347,definition,
! [X0] :
( sQ75_spl
<=> ( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1350,plain,
( sQ75_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1342,f678,f1347]) ).
fof(f1351,definition,
! [X0] :
( sQ76_spl
<=> ( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1354,plain,
( sQ76_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1343,f678,f1351]) ).
fof(f1357,plain,
( ~ sQ50_spl
| sK53_skl = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f1193,f508]) ).
fof(f1358,plain,
( ~ sQ50_spl
| ~ frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK49_skl)
| sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl) = sK53_skl
| ~ ssList(sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl)) ),
inference(resolution,[status(thm)],[f1193,f123]) ).
fof(f1360,plain,
( ~ sQ50_spl
| sQ34_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1357,f978,f1094,f1192]) ).
fof(f1361,definition,
( sQ77_spl
<=> ssList(sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1363,plain,
( sQ77_spl
| ~ ssList(sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1361]) ).
fof(f1364,definition,
( sQ78_spl
<=> sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1365,plain,
( ~ sQ78_spl
| sK5_skl(app(sK52_skl,cons(sK51_skl,nil)),sK49_skl) = sK53_skl ),
inference(component_clause,[status(thm)],[f1364]) ).
fof(f1367,plain,
( ~ sQ50_spl
| ~ sQ53_spl
| ~ sQ49_spl
| ~ sQ13_spl
| sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1358,f1361,f1364,f653,f1189,f1205,f1192]) ).
fof(f1369,plain,
( sQ77_spl
| ~ frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1363,f122]) ).
fof(f1370,plain,
( sQ77_spl
| ~ sQ53_spl
| ~ sQ49_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1369,f653,f1189,f1205,f1361]) ).
fof(f1373,plain,
( ~ sQ78_spl
| app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl
| ~ frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1365,f123]) ).
fof(f1375,definition,
( sQ79_spl
<=> app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( ~ sQ78_spl
| sQ79_spl
| ~ sQ53_spl
| ~ sQ49_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1373,f653,f1189,f1205,f1375,f1364]) ).
fof(f1379,plain,
! [X0] :
( ~ sQ61_spl
| X0 = cons(sK51_skl,nil)
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil))
| app(sK52_skl,app(X0,sK53_skl)) != sK49_skl
| ~ ssList(app(X0,sK53_skl)) ),
inference(resolution,[status(thm)],[f1262,f376]) ).
fof(f1380,plain,
! [X0] :
( ~ sQ61_spl
| X0 = sK53_skl
| ~ ssList(X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl)
| app(sK52_skl,app(cons(sK51_skl,nil),X0)) != sK49_skl
| ~ ssList(app(cons(sK51_skl,nil),X0)) ),
inference(resolution,[status(thm)],[f1262,f378]) ).
fof(f1383,plain,
! [X0] :
( ~ sQ61_spl
| ~ ssItem(X0)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| app(sK52_skl,cons(X0,app(cons(sK51_skl,nil),sK53_skl))) != sK49_skl
| ~ ssList(cons(X0,app(cons(sK51_skl,nil),sK53_skl))) ),
inference(resolution,[status(thm)],[f1262,f225]) ).
fof(f1386,definition,
! [X0] :
( sQ80_spl
<=> ( X0 = cons(sK51_skl,nil)
| ~ ssList(X0)
| app(sK52_skl,app(X0,sK53_skl)) != sK49_skl
| ~ ssList(app(X0,sK53_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1389,plain,
( ~ sQ61_spl
| ~ sQ27_spl
| ~ sQ47_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1379,f1386,f1182,f978,f1261]) ).
fof(f1390,definition,
! [X0] :
( sQ81_spl
<=> ( X0 = sK53_skl
| ~ ssList(X0)
| app(sK52_skl,app(cons(sK51_skl,nil),X0)) != sK49_skl
| ~ ssList(app(cons(sK51_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1393,plain,
( ~ sQ61_spl
| ~ sQ47_spl
| ~ sQ27_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1380,f1390,f978,f1182,f1261]) ).
fof(f1394,definition,
( sQ82_spl
<=> app(sK52_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1396,plain,
( sQ82_spl
| app(sK52_skl,nil) != sK49_skl ),
inference(component_clause,[status(thm)],[f1394]) ).
fof(f1397,definition,
( sQ83_spl
<=> nil = cons(sK51_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( ~ sQ83_spl
| nil = cons(sK51_skl,nil) ),
inference(component_clause,[status(thm)],[f1397]) ).
fof(f1402,definition,
! [X0] :
( sQ84_spl
<=> ( ~ ssItem(X0)
| app(sK52_skl,cons(X0,app(cons(sK51_skl,nil),sK53_skl))) != sK49_skl
| ~ ssList(cons(X0,app(cons(sK51_skl,nil),sK53_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( ~ sQ61_spl
| ~ sQ58_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1383,f1402,f1250,f1261]) ).
fof(f1408,plain,
! [X0] :
( ~ sQ7_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f467,f380]) ).
fof(f1409,definition,
! [X0] :
( sQ85_spl
<=> ( cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1410,plain,
! [X0] :
( ~ sQ85_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1409]) ).
fof(f1412,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1408,f1409,f459,f466]) ).
fof(f1413,plain,
( ~ sQ7_spl
| ~ sQ85_spl
| sK49_skl = app(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f467,f1410]) ).
fof(f1414,definition,
( sQ86_spl
<=> sK49_skl = app(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1415,plain,
( ~ sQ86_spl
| sK49_skl = app(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1414]) ).
fof(f1417,plain,
( ~ sQ7_spl
| ~ sQ85_spl
| sQ86_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1413,f678,f1414,f1409,f466]) ).
fof(f1418,plain,
( ~ sQ86_spl
| sK49_skl = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f389]) ).
fof(f1419,plain,
! [X0] :
( ~ sQ86_spl
| X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f376]) ).
fof(f1423,plain,
! [X0] :
( ~ sQ86_spl
| X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f378]) ).
fof(f1425,plain,
! [X0] :
( ~ sQ86_spl
| app(sK49_skl,X0) = app(sK49_skl,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f382]) ).
fof(f1426,plain,
( ~ sQ86_spl
| ~ ssList(sK49_skl)
| rearsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f491]) ).
fof(f1427,plain,
( ~ sQ86_spl
| ~ ssList(nil)
| frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f492]) ).
fof(f1429,plain,
( ~ sQ86_spl
| sQ46_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1418,f653,f1171,f1414]) ).
fof(f1430,definition,
! [X0] :
( sQ87_spl
<=> ( X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1431,plain,
! [X0] :
( ~ sQ87_spl
| X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1433,plain,
( ~ sQ86_spl
| sQ87_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1419,f653,f678,f1430,f1414]) ).
fof(f1437,definition,
! [X0] :
( sQ88_spl
<=> ( X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1438,plain,
! [X0] :
( ~ sQ88_spl
| X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1437]) ).
fof(f1440,plain,
( ~ sQ86_spl
| sQ88_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1423,f678,f653,f1437,f1414]) ).
fof(f1442,definition,
! [X0] :
( sQ89_spl
<=> ( app(sK49_skl,X0) = app(sK49_skl,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1443,plain,
! [X0] :
( ~ sQ89_spl
| app(sK49_skl,X0) = app(sK49_skl,app(nil,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1442]) ).
fof(f1445,plain,
( ~ sQ86_spl
| sQ89_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1425,f653,f678,f1442,f1414]) ).
fof(f1446,definition,
( sQ90_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1447,plain,
( ~ sQ90_spl
| rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1446]) ).
fof(f1449,plain,
( ~ sQ86_spl
| ~ sQ13_spl
| sQ90_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1426,f678,f1446,f653,f1414]) ).
fof(f1450,definition,
( sQ91_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1451,plain,
( ~ sQ91_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1450]) ).
fof(f1453,plain,
( ~ sQ86_spl
| ~ sQ16_spl
| sQ91_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1427,f653,f1450,f678,f1414]) ).
fof(f1461,plain,
( ~ sQ88_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| sK5_skl(sK49_skl,sK49_skl) = nil
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f1438,f123]) ).
fof(f1465,definition,
( sQ92_spl
<=> ssList(sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1467,plain,
( sQ92_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1465]) ).
fof(f1468,definition,
( sQ93_spl
<=> sK5_skl(sK49_skl,sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1469,plain,
( ~ sQ93_spl
| sK5_skl(sK49_skl,sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f1468]) ).
fof(f1471,plain,
( ~ sQ88_spl
| ~ sQ91_spl
| ~ sQ13_spl
| sQ93_spl
| ~ sQ92_spl ),
inference(split_clause,[status(thm)],[f1461,f1465,f1468,f653,f1450,f1437]) ).
fof(f1475,plain,
( sQ92_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1467,f122]) ).
fof(f1476,plain,
( sQ92_spl
| ~ sQ91_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1475,f653,f1450,f1465]) ).
fof(f1482,plain,
! [X0] :
( ~ sQ89_spl
| X0 = app(nil,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1443,f378]) ).
fof(f1484,definition,
! [X0] :
( sQ94_spl
<=> ( X0 = app(nil,X0)
| ~ ssList(X0)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1487,plain,
( ~ sQ89_spl
| ~ sQ13_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1482,f1484,f653,f1442]) ).
fof(f1491,plain,
! [X0] :
( ~ sQ48_spl
| ~ memberP(app(cons(sK51_skl,nil),sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1186,f272]) ).
fof(f1492,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f508,f272]) ).
fof(f1494,definition,
! [X0] :
( sQ95_spl
<=> ( ~ memberP(app(cons(sK51_skl,nil),sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1495,plain,
! [X0] :
( ~ sQ95_spl
| ~ memberP(app(cons(sK51_skl,nil),sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1494]) ).
fof(f1497,plain,
( ~ sQ48_spl
| ~ sQ58_spl
| ~ sQ28_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1491,f1494,f985,f1250,f1185]) ).
fof(f1498,definition,
! [X0] :
( sQ96_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1501,plain,
( ~ sQ27_spl
| ~ sQ49_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f1492,f1498,f1189,f978]) ).
fof(f1504,plain,
! [X0] :
( ~ sQ7_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f467,f275]) ).
fof(f1505,definition,
! [X0] :
( sQ97_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
! [X0] :
( ~ sQ97_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1505]) ).
fof(f1508,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1504,f1505,f459,f678,f466]) ).
fof(f1509,plain,
! [X0] :
( ~ sQ97_spl
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1506,f279]) ).
fof(f1510,plain,
! [X0] :
( ~ sQ86_spl
| ~ memberP(sK49_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1415,f271]) ).
fof(f1511,plain,
! [X0] :
( ~ sQ48_spl
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1186,f271]) ).
fof(f1512,plain,
! [X0] :
( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f508,f271]) ).
fof(f1513,definition,
! [X0] :
( sQ98_spl
<=> ( ~ memberP(sK49_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1516,plain,
( ~ sQ86_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1510,f1513,f653,f678,f1414]) ).
fof(f1517,definition,
! [X0] :
( sQ99_spl
<=> ( ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1518,plain,
! [X0] :
( ~ sQ99_spl
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1517]) ).
fof(f1520,plain,
( ~ sQ48_spl
| ~ sQ58_spl
| ~ sQ28_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1511,f1517,f985,f1250,f1185]) ).
fof(f1521,definition,
! [X0] :
( sQ100_spl
<=> ( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1522,plain,
! [X0] :
( ~ sQ100_spl
| ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1521]) ).
fof(f1524,plain,
( ~ sQ27_spl
| ~ sQ49_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1512,f1521,f1189,f978]) ).
fof(f1525,plain,
! [X0] :
( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f386]) ).
fof(f1526,plain,
! [X0] :
( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f385]) ).
fof(f1527,definition,
! [X0] :
( sQ101_spl
<=> ( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( sQ101_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1525,f678,f1527]) ).
fof(f1531,definition,
! [X0] :
( sQ102_spl
<=> ( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1534,plain,
( sQ102_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1526,f678,f1531]) ).
fof(f1537,plain,
( ~ sQ0_spl
| ~ sQ99_spl
| memberP(sK49_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1518,f648]) ).
fof(f1538,definition,
( sQ103_spl
<=> ssItem(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1540,plain,
( sQ103_spl
| ~ ssItem(sK54_skl) ),
inference(component_clause,[status(thm)],[f1538]) ).
fof(f1541,definition,
( sQ104_spl
<=> memberP(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1542,plain,
( ~ sQ104_spl
| memberP(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f1541]) ).
fof(f1544,plain,
( ~ sQ0_spl
| ~ sQ99_spl
| sQ104_spl
| ~ sQ103_spl ),
inference(split_clause,[status(thm)],[f1537,f1538,f1541,f1517,f441]) ).
fof(f1545,plain,
( sQ103_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1540,f429]) ).
fof(f1546,plain,
sQ103_spl,
inference(contradiction_clause,[status(thm)],[f1545]) ).
fof(f1547,plain,
( ~ sQ97_spl
| ~ sQ104_spl
| sK54_skl = sK55_skl
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1542,f1509]) ).
fof(f1548,definition,
( sQ105_spl
<=> sK54_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1549,plain,
( ~ sQ105_spl
| sK54_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1548]) ).
fof(f1551,plain,
( ~ sQ97_spl
| ~ sQ104_spl
| sQ105_spl
| ~ sQ103_spl ),
inference(split_clause,[status(thm)],[f1547,f1538,f1548,f1541,f1505]) ).
fof(f1566,plain,
! [X0] :
( ~ sQ67_spl
| sK52_skl = X0
| ~ ssList(sK52_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(X0)
| sK49_skl != app(app(X0,cons(sK51_skl,nil)),sK53_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f1298,f376]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ67_spl
| cons(sK51_skl,nil) = X0
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| sK49_skl != app(app(sK52_skl,X0),sK53_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(resolution,[status(thm)],[f1298,f378]) ).
fof(f1571,plain,
( ~ sQ67_spl
| nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| sK49_skl != app(nil,sK53_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1298,f385]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ67_spl
| ~ ssItem(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| sK49_skl != app(cons(X0,app(sK52_skl,cons(sK51_skl,nil))),sK53_skl)
| ~ ssList(cons(X0,app(sK52_skl,cons(sK51_skl,nil)))) ),
inference(resolution,[status(thm)],[f1298,f225]) ).
fof(f1573,definition,
! [X0] :
( sQ108_spl
<=> ( sK52_skl = X0
| ~ ssList(X0)
| sK49_skl != app(app(X0,cons(sK51_skl,nil)),sK53_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1576,plain,
( ~ sQ67_spl
| ~ sQ28_spl
| ~ sQ47_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1566,f1573,f1182,f985,f1297]) ).
fof(f1577,definition,
! [X0] :
( sQ109_spl
<=> ( cons(sK51_skl,nil) = X0
| ~ ssList(X0)
| sK49_skl != app(app(sK52_skl,X0),sK53_skl)
| ~ ssList(app(sK52_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1580,plain,
( ~ sQ67_spl
| ~ sQ47_spl
| ~ sQ28_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1567,f1577,f985,f1182,f1297]) ).
fof(f1583,definition,
( sQ110_spl
<=> sK49_skl = app(nil,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1585,plain,
( sQ110_spl
| sK49_skl != app(nil,sK53_skl) ),
inference(component_clause,[status(thm)],[f1583]) ).
fof(f1587,plain,
( ~ sQ67_spl
| sQ83_spl
| ~ sQ47_spl
| ~ sQ28_spl
| ~ sQ110_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1571,f678,f1583,f985,f1182,f1397,f1297]) ).
fof(f1588,definition,
! [X0] :
( sQ111_spl
<=> ( ~ ssItem(X0)
| sK49_skl != app(cons(X0,app(sK52_skl,cons(sK51_skl,nil))),sK53_skl)
| ~ ssList(cons(X0,app(sK52_skl,cons(sK51_skl,nil)))) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1591,plain,
( ~ sQ67_spl
| ~ sQ49_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1572,f1588,f1189,f1297]) ).
fof(f1592,plain,
( ~ sQ48_spl
| ~ sQ66_spl
| sK52_skl = sK52_skl
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f1294,f1186]) ).
fof(f1594,definition,
( sQ112_spl
<=> sK52_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1597,plain,
( ~ sQ48_spl
| ~ sQ66_spl
| sQ112_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1592,f985,f1594,f1293,f1185]) ).
fof(f1599,plain,
! [X0] :
( ~ sQ95_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1495,f271]) ).
fof(f1600,plain,
! [X0] :
( ~ sQ95_spl
| ~ memberP(sK53_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1495,f272]) ).
fof(f1601,definition,
! [X0] :
( sQ113_spl
<=> ( ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1602,plain,
! [X0] :
( ~ sQ113_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1601]) ).
fof(f1604,plain,
( ~ sQ95_spl
| ~ sQ27_spl
| ~ sQ47_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1599,f1601,f1182,f978,f1494]) ).
fof(f1605,definition,
! [X0] :
( sQ114_spl
<=> ( ~ memberP(sK53_skl,X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1608,plain,
( ~ sQ95_spl
| ~ sQ27_spl
| ~ sQ47_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1600,f1605,f1182,f978,f1494]) ).
fof(f1609,plain,
! [X0] :
( ~ sQ113_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1602]) ).
fof(f1611,plain,
! [X0] :
( ~ sQ113_spl
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1609,f277]) ).
fof(f1612,plain,
( ~ sQ113_spl
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1609,f494]) ).
fof(f1613,definition,
! [X0] :
( sQ115_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1616,plain,
( ~ sQ113_spl
| ~ sQ16_spl
| ~ sQ30_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1611,f1613,f995,f678,f1601]) ).
fof(f1617,definition,
( sQ116_spl
<=> memberP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1618,plain,
( ~ sQ116_spl
| memberP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1617]) ).
fof(f1620,plain,
( ~ sQ113_spl
| ~ sQ16_spl
| sQ116_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1612,f995,f1617,f678,f1601]) ).
fof(f1622,plain,
( ~ sQ97_spl
| ~ sQ116_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1618,f1509]) ).
fof(f1623,definition,
( sQ117_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1624,plain,
( ~ sQ117_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1623]) ).
fof(f1626,plain,
( ~ sQ97_spl
| ~ sQ116_spl
| sQ117_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1622,f995,f1623,f1617,f1505]) ).
fof(f1629,plain,
! [X0] :
( ~ sQ95_spl
| ~ sQ117_spl
| ~ memberP(app(cons(sK55_skl,nil),sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1495]) ).
fof(f1630,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ117_spl
| sK52_skl = X0
| sK49_skl != app(X0,app(cons(sK55_skl,nil),sK53_skl))
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1294]) ).
fof(f1631,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ117_spl
| app(sK52_skl,cons(sK55_skl,nil)) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1298]) ).
fof(f1635,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ117_spl
| X0 = app(cons(sK55_skl,nil),sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1262]) ).
fof(f1636,plain,
( ~ sQ78_spl
| ~ sQ117_spl
| sK5_skl(app(sK52_skl,cons(sK55_skl,nil)),sK49_skl) = sK53_skl ),
inference(backward_demodulation,[status(thm)],[f1624,f1365]) ).
fof(f1637,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ117_spl
| X0 = sK53_skl
| app(app(sK52_skl,cons(sK55_skl,nil)),X0) != sK49_skl
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1193]) ).
fof(f1638,plain,
( ~ sQ63_spl
| ~ sQ117_spl
| rearsegP(sK49_skl,app(cons(sK55_skl,nil),sK53_skl)) ),
inference(backward_demodulation,[status(thm)],[f1624,f1271]) ).
fof(f1639,plain,
( ~ sQ58_spl
| ~ sQ117_spl
| ssList(app(cons(sK55_skl,nil),sK53_skl)) ),
inference(backward_demodulation,[status(thm)],[f1624,f1251]) ).
fof(f1640,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| sK49_skl = app(sK52_skl,app(cons(sK55_skl,nil),sK53_skl)) ),
inference(backward_demodulation,[status(thm)],[f1624,f1186]) ).
fof(f1641,plain,
( ~ sQ53_spl
| ~ sQ117_spl
| frontsegP(sK49_skl,app(sK52_skl,cons(sK55_skl,nil))) ),
inference(backward_demodulation,[status(thm)],[f1624,f1206]) ).
fof(f1642,plain,
( ~ sQ49_spl
| ~ sQ117_spl
| ssList(app(sK52_skl,cons(sK55_skl,nil))) ),
inference(backward_demodulation,[status(thm)],[f1624,f1190]) ).
fof(f1644,plain,
( ~ sQ117_spl
| app(app(sK52_skl,cons(sK55_skl,nil)),sK53_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1624,f508]) ).
fof(f1651,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ117_spl
| ~ memberP(app(sK52_skl,cons(sK55_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1624,f1522]) ).
fof(f1656,plain,
! [X0] :
( ~ sQ95_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ memberP(app(sK49_skl,sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1629]) ).
fof(f1657,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK52_skl = X0
| sK49_skl != app(X0,app(sK49_skl,sK53_skl))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1630]) ).
fof(f1658,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| app(sK52_skl,sK49_skl) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1631]) ).
fof(f1660,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = app(sK49_skl,sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1635]) ).
fof(f1661,plain,
( ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK5_skl(app(sK52_skl,sK49_skl),sK49_skl) = sK53_skl ),
inference(forward_demodulation,[status(thm)],[f467,f1636]) ).
fof(f1662,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = sK53_skl
| app(app(sK52_skl,sK49_skl),X0) != sK49_skl
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1637]) ).
fof(f1663,plain,
( ~ sQ63_spl
| ~ sQ117_spl
| ~ sQ7_spl
| rearsegP(sK49_skl,app(sK49_skl,sK53_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1638]) ).
fof(f1664,plain,
( ~ sQ58_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ssList(app(sK49_skl,sK53_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1639]) ).
fof(f1665,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK49_skl = app(sK52_skl,app(sK49_skl,sK53_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1640]) ).
fof(f1666,plain,
( ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| frontsegP(sK49_skl,app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1641]) ).
fof(f1667,plain,
( ~ sQ49_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1642]) ).
fof(f1669,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| app(app(sK52_skl,sK49_skl),sK53_skl) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f467,f1644]) ).
fof(f1677,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ memberP(app(sK52_skl,sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f467,f1651]) ).
fof(f1696,plain,
! [X0] :
( ~ sQ86_spl
| memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1415,f270]) ).
fof(f1703,definition,
! [X0] :
( sQ120_spl
<=> ( memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1706,plain,
( ~ sQ86_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1696,f1703,f653,f678,f1414]) ).
fof(f1707,plain,
! [X0] :
( ~ sQ86_spl
| cons(X0,sK49_skl) = app(cons(X0,sK49_skl),nil)
| ~ ssItem(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f247]) ).
fof(f1708,definition,
! [X0] :
( sQ121_spl
<=> ( cons(X0,sK49_skl) = app(cons(X0,sK49_skl),nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( ~ sQ86_spl
| sQ121_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1707,f678,f653,f1708,f1414]) ).
fof(f1725,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,nil)),cons(sK55_skl,X1)))
| ~ ssList(app(app(X0,sK49_skl),cons(sK55_skl,X1))) ),
inference(paramodulation,[status(thm)],[f467,f487]) ).
fof(f1726,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f487]) ).
fof(f1728,definition,
! [X0,X1] :
( sQ122_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,nil)),cons(sK55_skl,X1)))
| ~ ssList(app(app(X0,sK49_skl),cons(sK55_skl,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1729,plain,
! [X0,X1] :
( ~ sQ122_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,nil)),cons(sK55_skl,X1)))
| ~ ssList(app(app(X0,sK49_skl),cons(sK55_skl,X1))) ),
inference(component_clause,[status(thm)],[f1728]) ).
fof(f1731,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1725,f1728,f459,f678,f466]) ).
fof(f1732,definition,
! [X0,X1] :
( sQ123_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1733,plain,
! [X0,X1] :
( ~ sQ123_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1732]) ).
fof(f1735,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1726,f1732,f459,f678,f466]) ).
fof(f1736,plain,
! [X0,X1] :
( ~ sQ122_spl
| ~ sQ7_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK49_skl),cons(sK55_skl,X1)))
| ~ ssList(app(app(X0,sK49_skl),cons(sK55_skl,X1))) ),
inference(forward_demodulation,[status(thm)],[f467,f1729]) ).
fof(f1737,plain,
! [X0,X1] :
( ~ sQ123_spl
| ~ sQ7_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),sK49_skl))
| ~ ssList(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f467,f1733]) ).
fof(f1739,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ strictorderedP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f467,f485]) ).
fof(f1740,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| lt(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f485]) ).
fof(f1742,definition,
! [X0,X1,X2] :
( sQ124_spl
<=> ( lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1739,f1742,f459,f678,f466]) ).
fof(f1746,definition,
! [X0,X1,X2] :
( sQ125_spl
<=> ( lt(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1749,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1740,f1746,f459,f678,f466]) ).
fof(f1753,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ totalorderedP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f467,f484]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f484]) ).
fof(f1756,definition,
! [X0,X1,X2] :
( sQ126_spl
<=> ( leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1759,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1753,f1756,f459,f678,f466]) ).
fof(f1760,definition,
! [X0,X1,X2] :
( sQ127_spl
<=> ( leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1763,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1754,f1760,f459,f678,f466]) ).
fof(f1767,plain,
( ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| app(app(sK52_skl,sK49_skl),sK53_skl) = sK49_skl
| ~ frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1661,f123]) ).
fof(f1768,definition,
( sQ128_spl
<=> ssList(app(sK52_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1770,plain,
( sQ128_spl
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1768]) ).
fof(f1771,definition,
( sQ129_spl
<=> frontsegP(sK49_skl,app(sK52_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1773,plain,
( sQ129_spl
| ~ frontsegP(sK49_skl,app(sK52_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1771]) ).
fof(f1775,definition,
( sQ130_spl
<=> app(app(sK52_skl,sK49_skl),sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
( ~ sQ130_spl
| app(app(sK52_skl,sK49_skl),sK53_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f1775]) ).
fof(f1778,plain,
( ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ130_spl
| ~ sQ129_spl
| ~ sQ128_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1767,f653,f1768,f1771,f1775,f466,f1623,f1364]) ).
fof(f1779,plain,
( sQ129_spl
| ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1773,f1666]) ).
fof(f1780,plain,
( sQ129_spl
| ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1779]) ).
fof(f1781,plain,
( sQ128_spl
| ~ sQ49_spl
| ~ sQ117_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1770,f1667]) ).
fof(f1782,plain,
( sQ128_spl
| ~ sQ49_spl
| ~ sQ117_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1781]) ).
fof(f1783,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| cons(X0,sK49_skl) = app(cons(X0,sK52_skl),app(sK49_skl,sK53_skl))
| ~ ssItem(X0)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f247]) ).
fof(f1784,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| memberP(app(sK49_skl,sK53_skl),X0)
| memberP(sK52_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1665,f270]) ).
fof(f1786,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ memberP(app(sK49_skl,sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1665,f272]) ).
fof(f1787,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = sK52_skl
| app(X0,app(sK49_skl,sK53_skl)) != sK49_skl
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1665,f376]) ).
fof(f1791,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = app(sK49_skl,sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f378]) ).
fof(f1793,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| app(sK49_skl,X0) = app(sK52_skl,app(app(sK49_skl,sK53_skl),X0))
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1665,f382]) ).
fof(f1794,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(sK52_skl)
| rearsegP(sK49_skl,app(sK49_skl,sK53_skl))
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f491]) ).
fof(f1797,definition,
( sQ131_spl
<=> ssList(app(sK49_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1799,plain,
( sQ131_spl
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(component_clause,[status(thm)],[f1797]) ).
fof(f1800,definition,
! [X0] :
( sQ132_spl
<=> ( cons(X0,sK49_skl) = app(cons(X0,sK52_skl),app(sK49_skl,sK53_skl))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1803,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ132_spl
| ~ sQ28_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f1783,f1797,f985,f1800,f466,f1623,f1185]) ).
fof(f1804,definition,
! [X0] :
( sQ133_spl
<=> ( memberP(app(sK49_skl,sK53_skl),X0)
| memberP(sK52_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1807,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ131_spl
| ~ sQ28_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1784,f1804,f985,f1797,f466,f1623,f1185]) ).
fof(f1809,definition,
! [X0] :
( sQ134_spl
<=> ( ~ memberP(app(sK49_skl,sK53_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1812,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ131_spl
| ~ sQ28_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1786,f1809,f985,f1797,f466,f1623,f1185]) ).
fof(f1813,definition,
! [X0] :
( sQ135_spl
<=> ( X0 = sK52_skl
| app(X0,app(sK49_skl,sK53_skl)) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1816,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ135_spl
| ~ sQ131_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1787,f985,f1797,f1813,f466,f1623,f1185]) ).
fof(f1819,definition,
( sQ136_spl
<=> nil = app(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1820,plain,
( ~ sQ136_spl
| nil = app(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f1819]) ).
fof(f1823,definition,
! [X0] :
( sQ137_spl
<=> ( X0 = app(sK49_skl,sK53_skl)
| app(sK52_skl,X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1826,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ137_spl
| ~ sQ28_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f1791,f1797,f985,f1823,f466,f1623,f1185]) ).
fof(f1828,definition,
! [X0] :
( sQ138_spl
<=> ( app(sK49_skl,X0) = app(sK52_skl,app(app(sK49_skl,sK53_skl),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1831,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ138_spl
| ~ sQ131_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1793,f985,f1797,f1828,f466,f1623,f1185]) ).
fof(f1832,definition,
( sQ139_spl
<=> rearsegP(sK49_skl,app(sK49_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1835,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ28_spl
| sQ139_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f1794,f1797,f1832,f985,f466,f1623,f1185]) ).
fof(f1838,plain,
( sQ131_spl
| ~ sQ58_spl
| ~ sQ117_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1799,f1664]) ).
fof(f1839,plain,
( sQ131_spl
| ~ sQ58_spl
| ~ sQ117_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1838]) ).
fof(f1853,plain,
( ~ sQ93_spl
| ~ sQ59_spl
| sK5_skl(sK49_skl,sK49_skl) = sK52_skl ),
inference(backward_demodulation,[status(thm)],[f1254,f1469]) ).
fof(f1871,plain,
! [X0] :
( ~ sQ59_spl
| app(sK52_skl,X0) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1254,f249]) ).
fof(f1872,plain,
! [X0] :
( ~ sQ59_spl
| ~ memberP(sK52_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1254,f279]) ).
fof(f1916,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| cons(X0,sK49_skl) = app(cons(X0,app(sK52_skl,sK49_skl)),sK53_skl)
| ~ ssItem(X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f1669,f247]) ).
fof(f1917,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| memberP(sK53_skl,X0)
| memberP(app(sK52_skl,sK49_skl),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1669,f270]) ).
fof(f1918,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| ~ memberP(app(sK52_skl,sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1669,f271]) ).
fof(f1920,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| X0 = app(sK52_skl,sK49_skl)
| app(X0,sK53_skl) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1669,f376]) ).
fof(f1922,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| X0 = sK53_skl
| app(app(sK52_skl,sK49_skl),X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f1669,f378]) ).
fof(f1924,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| app(sK49_skl,X0) = app(app(sK52_skl,sK49_skl),app(sK53_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1669,f382]) ).
fof(f1928,definition,
( sQ140_spl
<=> sK49_skl = app(sK52_skl,app(sK49_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1932,definition,
! [X0] :
( sQ141_spl
<=> ( cons(X0,sK49_skl) = app(cons(X0,app(sK52_skl,sK49_skl)),sK53_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1935,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| sQ141_spl
| ~ sQ128_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1916,f978,f1768,f1932,f466,f1623]) ).
fof(f1936,definition,
! [X0] :
( sQ142_spl
<=> ( memberP(sK53_skl,X0)
| memberP(app(sK52_skl,sK49_skl),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1939,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ128_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1917,f1936,f1768,f978,f466,f1623]) ).
fof(f1940,definition,
! [X0] :
( sQ143_spl
<=> ( ~ memberP(app(sK52_skl,sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1943,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ128_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1918,f1940,f1768,f978,f466,f1623]) ).
fof(f1945,definition,
! [X0] :
( sQ144_spl
<=> ( X0 = app(sK52_skl,sK49_skl)
| app(X0,sK53_skl) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1948,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| sQ144_spl
| ~ sQ27_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f1920,f1768,f978,f1945,f466,f1623]) ).
fof(f1950,definition,
! [X0] :
( sQ145_spl
<=> ( X0 = sK53_skl
| app(app(sK52_skl,sK49_skl),X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| sQ145_spl
| ~ sQ128_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f1922,f978,f1768,f1950,f466,f1623]) ).
fof(f1955,definition,
! [X0] :
( sQ146_spl
<=> ( app(sK49_skl,X0) = app(app(sK52_skl,sK49_skl),app(sK53_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1958,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| sQ146_spl
| ~ sQ27_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f1924,f1768,f978,f1955,f466,f1623]) ).
fof(f1970,definition,
! [X1] :
( sQ148_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1971,plain,
! [X0] :
( ~ sQ148_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1970]) ).
fof(f2053,plain,
! [X0,X1,X2] :
( ~ sQ7_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)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f481]) ).
fof(f2054,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ cyclefreeP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f467,f481]) ).
fof(f2055,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f482]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ totalorderP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f467,f482]) ).
fof(f2057,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| lt(sK55_skl,X1)
| lt(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f483]) ).
fof(f2058,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| lt(X1,sK55_skl)
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ strictorderP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f467,f483]) ).
fof(f2059,plain,
! [X0,X1] :
( ~ sQ7_spl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f467,f228]) ).
fof(f2079,definition,
! [X0,X1,X2] :
( sQ155_spl
<=> ( ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2082,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f2053,f2079,f459,f678,f466]) ).
fof(f2083,definition,
! [X0,X1,X2] :
( sQ156_spl
<=> ( ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2086,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f2054,f2083,f459,f678,f466]) ).
fof(f2087,definition,
! [X0,X1,X2] :
( sQ157_spl
<=> ( leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2090,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2055,f2087,f459,f678,f466]) ).
fof(f2091,definition,
! [X0,X1,X2] :
( sQ158_spl
<=> ( leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2094,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f2056,f2091,f459,f678,f466]) ).
fof(f2095,definition,
! [X0,X1,X2] :
( sQ159_spl
<=> ( lt(sK55_skl,X1)
| lt(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,cons(X1,X2)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2098,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2057,f2095,f459,f678,f466]) ).
fof(f2099,definition,
! [X0,X1,X2] :
( sQ160_spl
<=> ( lt(X1,sK55_skl)
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2)))
| ~ ssList(app(app(X0,sK49_skl),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2102,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f2058,f2099,f459,f678,f466]) ).
fof(f2103,definition,
! [X0,X1] :
( sQ161_spl
<=> ( nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2104,plain,
! [X0,X1] :
( ~ sQ161_spl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2103]) ).
fof(f2106,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ16_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f2059,f2103,f678,f459,f466]) ).
fof(f2342,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ59_spl
| sK49_skl = app(sK49_skl,sK53_skl)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f1871]) ).
fof(f2348,definition,
( sQ180_spl
<=> sK49_skl = app(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2349,plain,
( ~ sQ180_spl
| sK49_skl = app(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f2348]) ).
fof(f2350,plain,
( sQ180_spl
| sK49_skl != app(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f2348]) ).
fof(f2351,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ59_spl
| sQ180_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f2342,f1797,f2348,f1253,f466,f1623,f1185]) ).
fof(f2353,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ180_spl
| sK49_skl = app(sK52_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f2349,f1665]) ).
fof(f2364,plain,
( ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| sK5_skl(sK49_skl,sK49_skl) = sK53_skl ),
inference(backward_demodulation,[status(thm)],[f2353,f1661]) ).
fof(f2375,plain,
( ~ sQ93_spl
| ~ sQ59_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| sK53_skl = sK52_skl ),
inference(backward_demodulation,[status(thm)],[f2364,f1853]) ).
fof(f2386,plain,
! [X0] :
( ~ sQ59_spl
| ~ sQ93_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| ~ memberP(sK53_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f2375,f1872]) ).
fof(f2497,definition,
! [X0,X1] :
( sQ182_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK53_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f2654,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ93_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f2386,f445]) ).
fof(f2655,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ93_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| ~ sQ103_spl ),
inference(split_clause,[status(thm)],[f2654,f1538,f2348,f1185,f466,f1623,f1364,f1468,f1253,f444]) ).
fof(f2659,plain,
( ~ sQ105_spl
| ssItem(sK55_skl) ),
inference(backward_demodulation,[status(thm)],[f1549,f429]) ).
fof(f2665,plain,
! [X0,X1] :
( ~ sQ7_spl
| X1 = sK55_skl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,cons(sK55_skl,nil))))
| ~ ssList(app(X0,cons(X1,sK49_skl))) ),
inference(paramodulation,[status(thm)],[f467,f488]) ).
fof(f2691,definition,
! [X0,X1] :
( sQ206_spl
<=> ( X1 = sK55_skl
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,cons(sK55_skl,nil))))
| ~ ssList(app(X0,cons(X1,sK49_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2694,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2665,f2691,f459,f678,f466]) ).
fof(f2729,plain,
! [X0] :
( ~ sQ86_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f307]) ).
fof(f2730,plain,
! [X0,X1] :
( ~ sQ86_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f321]) ).
fof(f2731,plain,
! [X0] :
( ~ sQ86_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(sK49_skl,X0),nil)
| ~ ssList(nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f1415,f480]) ).
fof(f2744,definition,
! [X0] :
( sQ207_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2747,plain,
( ~ sQ86_spl
| ~ sQ13_spl
| sQ207_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2729,f678,f2744,f653,f1414]) ).
fof(f2748,definition,
! [X0,X1] :
( sQ208_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2751,plain,
( ~ sQ86_spl
| ~ sQ13_spl
| sQ208_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2730,f678,f2748,f653,f1414]) ).
fof(f2752,definition,
! [X0] :
( sQ209_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2755,plain,
( ~ sQ86_spl
| ~ sQ13_spl
| ~ sQ16_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2731,f2752,f678,f653,f1414]) ).
fof(f2773,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| segmentP(sK49_skl,X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1669,f321]) ).
fof(f2774,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(sK52_skl,sK49_skl),sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1669,f480]) ).
fof(f2776,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK53_skl,X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f1669,f307]) ).
fof(f2777,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ sQ7_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK53_skl,X0)
| ~ ssList(X1)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f1669,f321]) ).
fof(f2778,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| segmentP(app(sK49_skl,X0),sK53_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(app(app(sK52_skl,sK49_skl),sK53_skl),X0)) ),
inference(paramodulation,[status(thm)],[f1669,f480]) ).
fof(f2791,definition,
! [X0] :
( sQ210_spl
<=> ( segmentP(sK49_skl,X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2794,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ210_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2773,f653,f2791,f985,f978,f466,f1623]) ).
fof(f2795,definition,
( sQ211_spl
<=> ssList(app(app(sK52_skl,sK49_skl),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2797,plain,
( sQ211_spl
| ~ ssList(app(app(sK52_skl,sK49_skl),sK53_skl)) ),
inference(component_clause,[status(thm)],[f2795]) ).
fof(f2798,definition,
( sQ212_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2799,plain,
( ~ sQ212_spl
| segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2798]) ).
fof(f2801,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ212_spl
| ~ sQ13_spl
| ~ sQ211_spl ),
inference(split_clause,[status(thm)],[f2774,f2795,f653,f2798,f985,f978,f466,f1623]) ).
fof(f2803,definition,
! [X0] :
( sQ213_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(sK53_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2806,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ128_spl
| sQ213_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2776,f978,f2803,f1768,f466,f1623]) ).
fof(f2807,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ128_spl
| sQ182_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f2777,f978,f2497,f1768,f466,f1623]) ).
fof(f2808,definition,
! [X0] :
( sQ214_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK53_skl)
| ~ ssList(app(app(app(sK52_skl,sK49_skl),sK53_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2809,plain,
! [X0] :
( ~ sQ214_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK53_skl)
| ~ ssList(app(app(app(sK52_skl,sK49_skl),sK53_skl),X0)) ),
inference(component_clause,[status(thm)],[f2808]) ).
fof(f2811,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ128_spl
| ~ sQ27_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f2778,f2808,f978,f1768,f466,f1623]) ).
fof(f2824,plain,
! [X0] :
( ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK53_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f1669,f2809]) ).
fof(f2825,plain,
( sQ211_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1669,f2797]) ).
fof(f2826,plain,
( sQ211_spl
| ~ sQ117_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2825,f421]) ).
fof(f2827,plain,
( sQ211_spl
| ~ sQ117_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f2826]) ).
fof(f2829,plain,
! [X0] :
( ~ sQ212_spl
| segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2799,f315]) ).
fof(f2831,definition,
! [X0] :
( sQ215_spl
<=> ( segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2834,plain,
( ~ sQ212_spl
| ~ sQ13_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f2829,f2831,f653,f2798]) ).
fof(f2848,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f307]) ).
fof(f2849,plain,
! [X0,X1] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X1)
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f1665,f321]) ).
fof(f2850,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(X0)
| ~ ssList(sK52_skl)
| segmentP(app(sK49_skl,X0),app(sK49_skl,sK53_skl))
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(app(app(sK52_skl,app(sK49_skl,sK53_skl)),X0)) ),
inference(paramodulation,[status(thm)],[f1665,f480]) ).
fof(f2863,definition,
! [X0] :
( sQ216_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2864,plain,
! [X0] :
( ~ sQ216_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2863]) ).
fof(f2866,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ28_spl
| sQ216_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f2848,f1797,f2863,f985,f466,f1623,f1185]) ).
fof(f2867,definition,
! [X0,X1] :
( sQ217_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2870,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ28_spl
| sQ217_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f2849,f1797,f2867,f985,f466,f1623,f1185]) ).
fof(f2871,definition,
! [X0] :
( sQ218_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),app(sK49_skl,sK53_skl))
| ~ ssList(app(app(sK52_skl,app(sK49_skl,sK53_skl)),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2874,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ28_spl
| ~ sQ131_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2850,f2871,f1797,f985,f466,f1623,f1185]) ).
fof(f2908,plain,
! [X0,X1] :
( segmentP(X1,nil)
| ~ segmentP(X1,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f323,f315]) ).
fof(f2909,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f323,f317]) ).
fof(f2910,definition,
! [X0,X1] :
( sQ219_spl
<=> ( segmentP(X1,nil)
| ~ segmentP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2913,plain,
( ~ sQ16_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f2908,f2910,f678]) ).
fof(f2914,definition,
! [X0] :
( sQ220_spl
<=> ( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2917,plain,
( ~ sQ16_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f2909,f2914,f678]) ).
fof(f2947,plain,
( ~ sQ90_spl
| nil = sK49_skl
| ~ rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f1447]) ).
fof(f2951,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f2957,definition,
( sQ222_spl
<=> rearsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2960,plain,
( ~ sQ90_spl
| sQ3_spl
| ~ sQ222_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2947,f678,f653,f2957,f452,f1446]) ).
fof(f2969,definition,
! [X0] :
( sQ224_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2972,plain,
( sQ224_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2951,f678,f2969]) ).
fof(f2974,plain,
! [X0] :
( ~ sQ63_spl
| ~ sQ117_spl
| ~ sQ7_spl
| rearsegP(X0,app(sK49_skl,sK53_skl))
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1663]) ).
fof(f2975,plain,
! [X0] :
( ~ sQ90_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1447]) ).
fof(f2976,plain,
! [X0] :
( ~ sQ52_spl
| rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1202]) ).
fof(f2979,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f2981,definition,
! [X0] :
( sQ225_spl
<=> ( rearsegP(X0,app(sK49_skl,sK53_skl))
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2982,plain,
! [X0] :
( ~ sQ225_spl
| rearsegP(X0,app(sK49_skl,sK53_skl))
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2981]) ).
fof(f2984,plain,
( ~ sQ63_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ131_spl
| ~ sQ13_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2974,f2981,f653,f1797,f466,f1623,f1270]) ).
fof(f2985,definition,
! [X0] :
( sQ226_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2988,plain,
( ~ sQ90_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f2975,f2985,f653,f678,f1446]) ).
fof(f2989,definition,
! [X0] :
( sQ227_spl
<=> ( rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2990,plain,
! [X0] :
( ~ sQ227_spl
| rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2989]) ).
fof(f2992,plain,
( ~ sQ52_spl
| ~ sQ27_spl
| ~ sQ13_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2976,f2989,f653,f978,f1201]) ).
fof(f2997,definition,
! [X0,X1] :
( sQ228_spl
<=> ( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f3000,plain,
( ~ sQ16_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2979,f2997,f678]) ).
fof(f3002,plain,
! [X0] :
( ~ sQ7_spl
| ~ frontsegP(nil,X0)
| frontsegP(sK49_skl,cons(sK55_skl,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f496]) ).
fof(f3003,plain,
! [X0] :
( ~ sQ7_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f496]) ).
fof(f3004,definition,
! [X0] :
( sQ229_spl
<=> ( ~ frontsegP(nil,X0)
| frontsegP(sK49_skl,cons(sK55_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f3005,plain,
! [X0] :
( ~ sQ229_spl
| ~ frontsegP(nil,X0)
| frontsegP(sK49_skl,cons(sK55_skl,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3004]) ).
fof(f3007,plain,
( ~ sQ7_spl
| sQ229_spl
| ~ sQ16_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3002,f459,f678,f3004,f466]) ).
fof(f3008,definition,
! [X0] :
( sQ230_spl
<=> ( ~ frontsegP(X0,nil)
| frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f3009,plain,
! [X0] :
( ~ sQ230_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3008]) ).
fof(f3011,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| sQ230_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3003,f459,f3008,f678,f466]) ).
fof(f3012,plain,
! [X0] :
( ~ sQ230_spl
| frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3009,f295]) ).
fof(f3020,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ122_spl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK49_skl),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f1736]) ).
fof(f3021,definition,
! [X0] :
( sQ231_spl
<=> ( ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK49_skl),cons(sK55_skl,nil)))
| ~ ssList(app(app(X0,sK49_skl),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f3024,plain,
( ~ sQ7_spl
| ~ sQ122_spl
| ~ sQ16_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f3020,f3021,f678,f1728,f466]) ).
fof(f3048,plain,
! [X0,X1] :
( ~ sQ227_spl
| ~ rearsegP(X1,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| rearsegP(app(X0,X1),sK53_skl)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f2990,f307]) ).
fof(f3049,plain,
! [X0] :
( ~ sQ227_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| rearsegP(app(X0,sK49_skl),sK53_skl)
| ~ ssList(app(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f2990,f491]) ).
fof(f3051,definition,
! [X0,X1] :
( sQ232_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| ~ ssList(X0)
| ~ ssList(X1)
| rearsegP(app(X0,X1),sK53_skl)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f3054,plain,
( ~ sQ227_spl
| ~ sQ13_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f3048,f3051,f653,f2989]) ).
fof(f3055,definition,
! [X0] :
( sQ233_spl
<=> ( ~ ssList(X0)
| rearsegP(app(X0,sK49_skl),sK53_skl)
| ~ ssList(app(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3058,plain,
( ~ sQ227_spl
| ~ sQ13_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f3049,f3055,f653,f2989]) ).
fof(f3078,definition,
( sQ234_spl
<=> nil = app(sK52_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3079,plain,
( ~ sQ234_spl
| nil = app(sK52_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3078]) ).
fof(f3086,plain,
( sQ180_spl
| ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| app(sK52_skl,sK49_skl) != sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1660,f2350]) ).
fof(f3087,plain,
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| nil = sK49_skl
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| app(sK52_skl,nil) != sK49_skl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1660,f386]) ).
fof(f3089,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = sK49_skl
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| app(sK52_skl,app(X0,sK53_skl)) != sK49_skl
| ~ ssList(app(X0,sK53_skl)) ),
inference(resolution,[status(thm)],[f1660,f376]) ).
fof(f3090,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| X0 = sK53_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl)
| app(sK52_skl,app(sK49_skl,X0)) != sK49_skl
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f1660,f378]) ).
fof(f3091,plain,
! [X0] :
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssItem(X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| app(sK52_skl,cons(X0,app(sK49_skl,sK53_skl))) != sK49_skl
| ~ ssList(cons(X0,app(sK49_skl,sK53_skl))) ),
inference(resolution,[status(thm)],[f1660,f225]) ).
fof(f3092,plain,
( ~ sQ88_spl
| ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK53_skl = nil
| ~ ssList(sK53_skl)
| app(sK52_skl,sK49_skl) != sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1660,f1438]) ).
fof(f3095,definition,
( sQ235_spl
<=> app(sK52_skl,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3098,plain,
( sQ180_spl
| ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ235_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3086,f653,f3095,f466,f1623,f1261,f2348]) ).
fof(f3099,plain,
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ3_spl
| ~ sQ27_spl
| ~ sQ13_spl
| ~ sQ82_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3087,f678,f1394,f653,f978,f452,f466,f1623,f1261]) ).
fof(f3101,definition,
! [X0] :
( sQ236_spl
<=> ( X0 = sK49_skl
| ~ ssList(X0)
| app(sK52_skl,app(X0,sK53_skl)) != sK49_skl
| ~ ssList(app(X0,sK53_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f3104,plain,
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ13_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f3089,f3101,f653,f978,f466,f1623,f1261]) ).
fof(f3105,definition,
! [X0] :
( sQ237_spl
<=> ( X0 = sK53_skl
| ~ ssList(X0)
| app(sK52_skl,app(sK49_skl,X0)) != sK49_skl
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f3108,plain,
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ27_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f3090,f3105,f978,f653,f466,f1623,f1261]) ).
fof(f3109,definition,
! [X0] :
( sQ238_spl
<=> ( ~ ssItem(X0)
| app(sK52_skl,cons(X0,app(sK49_skl,sK53_skl))) != sK49_skl
| ~ ssList(cons(X0,app(sK49_skl,sK53_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3112,plain,
( ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ131_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f3091,f3109,f1797,f466,f1623,f1261]) ).
fof(f3113,plain,
( ~ sQ88_spl
| ~ sQ61_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ56_spl
| ~ sQ27_spl
| ~ sQ235_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3092,f653,f3095,f978,f1229,f466,f1623,f1261,f1437]) ).
fof(f3151,plain,
( sQ82_spl
| ~ sQ56_spl
| app(sK52_skl,sK53_skl) != sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1230,f1396]) ).
fof(f3418,plain,
! [X0,X1,X2] :
( ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f292,f496]) ).
fof(f3420,definition,
! [X0] :
( sQ251_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3421,plain,
! [X0] :
( ~ sQ251_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3420]) ).
fof(f3423,definition,
! [X1,X2] :
( sQ252_spl
<=> ( ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3426,plain,
( sQ252_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f3418,f3420,f3423]) ).
fof(f3438,plain,
( ~ sQ5_spl
| ~ sQ251_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f460,f3449]) ).
fof(f3449,plain,
! [X0] :
( ~ sQ251_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3421]) ).
fof(f3450,plain,
( ~ sQ5_spl
| ~ sQ251_spl ),
inference(contradiction_clause,[status(thm)],[f3438]) ).
fof(f3451,plain,
! [X0] :
( ~ sQ230_spl
| ~ ssList(X0)
| sK49_skl = cons(sK55_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK55_skl,X0))
| ~ ssList(cons(sK55_skl,X0))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f284,f3012]) ).
fof(f3455,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f284,f492]) ).
fof(f3457,definition,
! [X0] :
( sQ253_spl
<=> ( ~ ssList(X0)
| sK49_skl = cons(sK55_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK55_skl,X0))
| ~ ssList(cons(sK55_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3460,plain,
( ~ sQ230_spl
| sQ253_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3451,f653,f3457,f3008]) ).
fof(f3461,definition,
( sQ254_spl
<=> frontsegP(sK52_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3468,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3455]) ).
fof(f3469,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3468,f245]) ).
fof(f3481,plain,
! [X0] :
( ~ sQ86_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f288]) ).
fof(f3493,definition,
! [X0] :
( sQ255_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3496,plain,
( ~ sQ86_spl
| ~ sQ16_spl
| sQ255_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f3481,f653,f3493,f678,f1414]) ).
fof(f3522,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f295,f284]) ).
fof(f3523,definition,
! [X0] :
( sQ256_spl
<=> ( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3526,plain,
( ~ sQ16_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f3522,f3523,f678]) ).
fof(f3542,plain,
( ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| app(sK52_skl,sK49_skl) = sK49_skl
| ~ frontsegP(app(sK52_skl,sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f1666,f284]) ).
fof(f3543,definition,
( sQ257_spl
<=> frontsegP(app(sK52_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3545,plain,
( sQ257_spl
| ~ frontsegP(app(sK52_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3543]) ).
fof(f3546,plain,
( ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ235_spl
| ~ sQ257_spl
| ~ sQ13_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f3542,f1768,f653,f3543,f3095,f466,f1623,f1205]) ).
fof(f3551,plain,
! [X0,X1] :
( ~ sQ230_spl
| ~ ssList(X1)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,cons(sK55_skl,X1))
| ~ ssList(sK49_skl)
| ~ ssList(cons(sK55_skl,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f3012]) ).
fof(f3552,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| frontsegP(X0,app(sK52_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f1666]) ).
fof(f3553,plain,
! [X0] :
( ~ sQ64_spl
| frontsegP(X0,sK52_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f1275]) ).
fof(f3554,plain,
! [X0] :
( ~ sQ91_spl
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f1451]) ).
fof(f3557,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f3559,definition,
! [X0,X1] :
( sQ258_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,cons(sK55_skl,X1))
| ~ ssList(cons(sK55_skl,X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3562,plain,
( ~ sQ230_spl
| ~ sQ13_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f3551,f3559,f653,f3008]) ).
fof(f3563,definition,
! [X0] :
( sQ259_spl
<=> ( frontsegP(X0,app(sK52_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3564,plain,
! [X0] :
( ~ sQ259_spl
| frontsegP(X0,app(sK52_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3563]) ).
fof(f3566,plain,
( ~ sQ53_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ128_spl
| ~ sQ13_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f3552,f3563,f653,f1768,f466,f1623,f1205]) ).
fof(f3567,definition,
! [X0] :
( sQ260_spl
<=> ( frontsegP(X0,sK52_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3568,plain,
! [X0] :
( ~ sQ260_spl
| frontsegP(X0,sK52_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3567]) ).
fof(f3570,plain,
( ~ sQ64_spl
| ~ sQ28_spl
| ~ sQ13_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f3553,f3567,f653,f985,f1274]) ).
fof(f3571,definition,
! [X0] :
( sQ261_spl
<=> ( frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3574,plain,
( ~ sQ91_spl
| ~ sQ13_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f3554,f3571,f653,f1450]) ).
fof(f3579,definition,
! [X0,X1] :
( sQ262_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3582,plain,
( ~ sQ16_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f3557,f3579,f678]) ).
fof(f3584,plain,
( sQ257_spl
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f3545,f288]) ).
fof(f3585,plain,
( sQ257_spl
| ~ sQ254_spl
| ~ sQ13_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f3584,f985,f653,f3461,f3543]) ).
fof(f3600,definition,
! [X0] :
( sQ263_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK52_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3601,plain,
! [X0] :
( ~ sQ263_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK52_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3600]) ).
fof(f3622,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ7_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(app(sK52_skl,sK49_skl),X0)
| ~ ssList(sK53_skl)
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1669,f288]) ).
fof(f3637,definition,
! [X0] :
( sQ264_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(app(sK52_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3638,plain,
! [X0] :
( ~ sQ264_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(app(sK52_skl,sK49_skl),X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3637]) ).
fof(f3640,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| sQ264_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f3622,f1768,f3637,f978,f466,f1623]) ).
fof(f3660,plain,
! [X0,X1] :
( ~ sQ123_spl
| ~ sQ7_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(X0,cons(sK55_skl,X1)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ),
inference(resolution,[status(thm)],[f1737,f245]) ).
fof(f3661,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ123_spl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,nil)),sK49_skl))
| ~ ssList(app(app(X0,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f467,f1737]) ).
fof(f3662,definition,
! [X0,X1] :
( sQ265_spl
<=> ( ~ ssList(app(X0,cons(sK55_skl,X1)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,X1)),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3665,plain,
( ~ sQ123_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f3660,f3662,f653,f466,f1732]) ).
fof(f3666,definition,
! [X0] :
( sQ266_spl
<=> ( ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK55_skl,nil)),sK49_skl))
| ~ ssList(app(app(X0,sK49_skl),sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3669,plain,
( ~ sQ7_spl
| ~ sQ123_spl
| ~ sQ16_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f3661,f3666,f678,f1732,f466]) ).
fof(f3701,plain,
! [X0,X1] :
( ~ sQ260_spl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| frontsegP(app(X0,X1),sK52_skl)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f3568,f288]) ).
fof(f3702,plain,
! [X0] :
( ~ sQ260_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| frontsegP(app(sK49_skl,X0),sK52_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f3568,f492]) ).
fof(f3705,definition,
! [X0,X1] :
( sQ267_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| frontsegP(app(X0,X1),sK52_skl)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3708,plain,
( ~ sQ260_spl
| ~ sQ13_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f3701,f3705,f653,f3567]) ).
fof(f3709,definition,
! [X0] :
( sQ268_spl
<=> ( ~ ssList(X0)
| frontsegP(app(sK49_skl,X0),sK52_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3712,plain,
( ~ sQ260_spl
| ~ sQ13_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3702,f3709,f653,f3567]) ).
fof(f3715,plain,
( ~ sQ263_spl
| ~ ssList(sK52_skl)
| frontsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3601,f295]) ).
fof(f3717,definition,
( sQ269_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3718,plain,
( ~ sQ269_spl
| frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f3717]) ).
fof(f3720,plain,
( ~ sQ263_spl
| ~ sQ28_spl
| sQ269_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3715,f678,f3717,f985,f3600]) ).
fof(f3763,plain,
( ~ sQ83_spl
| ~ sQ117_spl
| nil = cons(sK55_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f1624,f1398]) ).
fof(f3764,plain,
( ~ sQ83_spl
| ~ sQ117_spl
| ~ sQ7_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f467,f3763]) ).
fof(f3765,plain,
( ~ sQ83_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3764,f454]) ).
fof(f3766,plain,
( ~ sQ83_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f3765]) ).
fof(f3795,plain,
! [X0] :
( ~ sQ269_spl
| frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3718,f282]) ).
fof(f3796,plain,
( ~ sQ269_spl
| nil = sK49_skl
| ~ frontsegP(nil,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3718,f284]) ).
fof(f3797,definition,
! [X0] :
( sQ280_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3800,plain,
( ~ sQ269_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f3795,f3797,f653,f678,f3717]) ).
fof(f3801,definition,
( sQ281_spl
<=> frontsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3804,plain,
( ~ sQ269_spl
| sQ3_spl
| ~ sQ281_spl
| ~ sQ13_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3796,f678,f653,f3801,f452,f3717]) ).
fof(f3829,plain,
! [X0] :
( nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f136,f386]) ).
fof(f3830,plain,
! [X0] :
( nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f136,f385]) ).
fof(f3831,definition,
! [X0] :
( sQ282_spl
<=> ( nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3834,plain,
( sQ282_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3829,f678,f3831]) ).
fof(f3835,definition,
! [X0] :
( sQ283_spl
<=> ( nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3838,plain,
( sQ283_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3830,f678,f3835]) ).
fof(f3851,plain,
! [X0,X1] :
( ~ sQ229_spl
| frontsegP(X1,cons(sK55_skl,X0))
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(cons(sK55_skl,X0))
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3005,f282]) ).
fof(f3852,plain,
! [X0] :
( ~ sQ229_spl
| cons(sK55_skl,X0) = sK49_skl
| ~ frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(cons(sK55_skl,X0))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3005,f284]) ).
fof(f3854,definition,
! [X0,X1] :
( sQ284_spl
<=> ( frontsegP(X1,cons(sK55_skl,X0))
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(cons(sK55_skl,X0))
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3857,plain,
( ~ sQ229_spl
| ~ sQ13_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f3851,f3854,f653,f3004]) ).
fof(f3858,definition,
! [X0] :
( sQ285_spl
<=> ( cons(sK55_skl,X0) = sK49_skl
| ~ frontsegP(cons(sK55_skl,X0),sK49_skl)
| ~ ssList(cons(sK55_skl,X0))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3861,plain,
( ~ sQ229_spl
| ~ sQ13_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f3852,f3858,f653,f3004]) ).
fof(f3888,plain,
! [X0,X1] :
( ~ sQ225_spl
| rearsegP(X1,app(sK49_skl,sK53_skl))
| ~ rearsegP(X1,X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2982,f301]) ).
fof(f3889,plain,
! [X0] :
( ~ sQ225_spl
| app(sK49_skl,sK53_skl) = X0
| ~ rearsegP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2982,f303]) ).
fof(f3893,definition,
! [X0,X1] :
( sQ287_spl
<=> ( rearsegP(X1,app(sK49_skl,sK53_skl))
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3896,plain,
( ~ sQ225_spl
| ~ sQ131_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f3888,f3893,f1797,f2981]) ).
fof(f3897,definition,
! [X0] :
( sQ288_spl
<=> ( app(sK49_skl,sK53_skl) = X0
| ~ rearsegP(app(sK49_skl,sK53_skl),X0)
| ~ ssList(X0)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3900,plain,
( ~ sQ225_spl
| ~ sQ131_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f3889,f3897,f1797,f2981]) ).
fof(f3903,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ136_spl
| sK49_skl = app(sK52_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f1820,f1665]) ).
fof(f3922,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ136_spl
| sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3903,f1396]) ).
fof(f3923,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ136_spl
| sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3922]) ).
fof(f3926,plain,
! [X0,X1] :
( ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| segmentP(X1,sK53_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(sK53_skl)
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f2824,f315]) ).
fof(f3927,plain,
! [X0] :
( ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK53_skl = app(sK49_skl,X0)
| ~ segmentP(sK53_skl,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(sK53_skl)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f2824,f317]) ).
fof(f3928,plain,
( ~ sQ86_spl
| ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(nil)
| segmentP(sK49_skl,sK53_skl)
| ~ ssList(app(sK49_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1415,f2824]) ).
fof(f3929,definition,
! [X0,X1] :
( sQ289_spl
<=> ( segmentP(X1,sK53_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3932,plain,
( ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f3926,f3929,f978,f466,f1623,f2808]) ).
fof(f3933,definition,
! [X0] :
( sQ290_spl
<=> ( sK53_skl = app(sK49_skl,X0)
| ~ segmentP(sK53_skl,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3936,plain,
( ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f3927,f3933,f978,f466,f1623,f2808]) ).
fof(f3937,definition,
( sQ291_spl
<=> ssList(app(sK49_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3939,plain,
( sQ291_spl
| ~ ssList(app(sK49_skl,nil)) ),
inference(component_clause,[status(thm)],[f3937]) ).
fof(f3940,definition,
( sQ292_spl
<=> segmentP(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f3941,plain,
( ~ sQ292_spl
| segmentP(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f3940]) ).
fof(f3943,plain,
( ~ sQ86_spl
| ~ sQ214_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ16_spl
| sQ292_spl
| ~ sQ291_spl ),
inference(split_clause,[status(thm)],[f3928,f3937,f3940,f678,f466,f1623,f2808,f1414]) ).
fof(f3946,plain,
( sQ291_spl
| ~ sQ86_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1415,f3939]) ).
fof(f3947,plain,
( sQ291_spl
| ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3946,f421]) ).
fof(f3948,plain,
( sQ291_spl
| ~ sQ86_spl ),
inference(contradiction_clause,[status(thm)],[f3947]) ).
fof(f3950,plain,
! [X0] :
( ~ sQ292_spl
| segmentP(X0,sK53_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3941,f315]) ).
fof(f3952,definition,
! [X0] :
( sQ293_spl
<=> ( segmentP(X0,sK53_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3953,plain,
! [X0] :
( ~ sQ293_spl
| segmentP(X0,sK53_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3952]) ).
fof(f3955,plain,
( ~ sQ292_spl
| ~ sQ27_spl
| ~ sQ13_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f3950,f3952,f653,f978,f3940]) ).
fof(f3995,plain,
! [X0,X1,X2] :
( ~ sQ293_spl
| ~ segmentP(X1,sK49_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| segmentP(app(app(X0,X1),X2),sK53_skl)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f3953,f321]) ).
fof(f3996,plain,
! [X0,X1] :
( ~ sQ293_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(X0,sK49_skl),X1))
| segmentP(app(app(X0,sK49_skl),X1),sK53_skl)
| ~ ssList(app(app(X0,sK49_skl),X1)) ),
inference(resolution,[status(thm)],[f3953,f480]) ).
fof(f3999,definition,
! [X0,X1,X2] :
( sQ295_spl
<=> ( ~ segmentP(X1,sK49_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(app(X0,X1),X2),sK53_skl)
| ~ ssList(app(app(X0,X1),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f4002,plain,
( ~ sQ293_spl
| ~ sQ13_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f3995,f3999,f653,f3952]) ).
fof(f4003,definition,
! [X0,X1] :
( sQ296_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,sK49_skl),X1))
| segmentP(app(app(X0,sK49_skl),X1),sK53_skl)
| ~ ssList(app(app(X0,sK49_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f4006,plain,
( ~ sQ293_spl
| ~ sQ13_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f3996,f4003,f653,f3952]) ).
fof(f4010,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK52_skl = X0
| ~ ssList(sK52_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| sK49_skl != app(app(X0,sK49_skl),sK53_skl)
| ~ ssList(app(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f1658,f376]) ).
fof(f4011,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sK49_skl = X0
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| ~ ssList(X0)
| sK49_skl != app(app(sK52_skl,X0),sK53_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(resolution,[status(thm)],[f1658,f378]) ).
fof(f4012,plain,
! [X0] :
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssItem(X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| sK49_skl != app(cons(X0,app(sK52_skl,sK49_skl)),sK53_skl)
| ~ ssList(cons(X0,app(sK52_skl,sK49_skl))) ),
inference(resolution,[status(thm)],[f1658,f225]) ).
fof(f4018,definition,
! [X0] :
( sQ297_spl
<=> ( sK52_skl = X0
| ~ ssList(X0)
| sK49_skl != app(app(X0,sK49_skl),sK53_skl)
| ~ ssList(app(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f4021,plain,
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ28_spl
| ~ sQ13_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f4010,f4018,f653,f985,f466,f1623,f1297]) ).
fof(f4022,definition,
! [X0] :
( sQ298_spl
<=> ( sK49_skl = X0
| ~ ssList(X0)
| sK49_skl != app(app(sK52_skl,X0),sK53_skl)
| ~ ssList(app(sK52_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f4025,plain,
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ28_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f4011,f4022,f985,f653,f466,f1623,f1297]) ).
fof(f4026,definition,
! [X0] :
( sQ299_spl
<=> ( ~ ssItem(X0)
| sK49_skl != app(cons(X0,app(sK52_skl,sK49_skl)),sK53_skl)
| ~ ssList(cons(X0,app(sK52_skl,sK49_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f4029,plain,
( ~ sQ67_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ128_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f4012,f4026,f1768,f466,f1623,f1297]) ).
fof(f4046,plain,
( ~ sQ87_spl
| sK6_skl(nil,sK49_skl) = sK49_skl
| ~ ssList(sK6_skl(nil,sK49_skl))
| ~ rearsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f129,f1431]) ).
fof(f4048,plain,
! [X0] :
( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f386]) ).
fof(f4049,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f385]) ).
fof(f4051,definition,
( sQ300_spl
<=> ssList(sK6_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f4053,plain,
( sQ300_spl
| ~ ssList(sK6_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f4051]) ).
fof(f4054,definition,
( sQ301_spl
<=> sK6_skl(nil,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f4057,plain,
( ~ sQ87_spl
| sQ301_spl
| ~ sQ300_spl
| ~ sQ90_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4046,f653,f678,f1446,f4051,f4054,f1430]) ).
fof(f4060,definition,
! [X0] :
( sQ302_spl
<=> ( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f4063,plain,
( sQ302_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4048,f678,f4060]) ).
fof(f4064,definition,
! [X0] :
( sQ303_spl
<=> ( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f4067,plain,
( sQ303_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4049,f678,f4064]) ).
fof(f4071,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(f4077,definition,
! [X0,X1] :
( sQ304_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,[sQ304_spl])],[split_symbol_definition]) ).
fof(f4080,plain,
( ~ sQ16_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f4071,f4077,f678]) ).
fof(f4104,plain,
( sQ300_spl
| ~ rearsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4053,f128]) ).
fof(f4105,plain,
( sQ300_spl
| ~ sQ90_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4104,f653,f678,f1446,f4051]) ).
fof(f4112,plain,
( ~ sQ50_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK49_skl)
| sK5_skl(app(sK52_skl,sK49_skl),sK49_skl) = sK53_skl
| ~ ssList(sK5_skl(app(sK52_skl,sK49_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f1662,f123]) ).
fof(f4115,definition,
( sQ310_spl
<=> ssList(sK5_skl(app(sK52_skl,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f4117,plain,
( sQ310_spl
| ~ ssList(sK5_skl(app(sK52_skl,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f4115]) ).
fof(f4118,definition,
( sQ311_spl
<=> sK5_skl(app(sK52_skl,sK49_skl),sK49_skl) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4121,plain,
( ~ sQ50_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ129_spl
| ~ sQ128_spl
| ~ sQ13_spl
| sQ311_spl
| ~ sQ310_spl ),
inference(split_clause,[status(thm)],[f4112,f4115,f4118,f653,f1768,f1771,f466,f1623,f1192]) ).
fof(f4123,plain,
( sQ310_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f1661,f4117]) ).
fof(f4124,plain,
( sQ310_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4123,f427]) ).
fof(f4125,plain,
( sQ310_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f4124]) ).
fof(f4131,plain,
! [X0,X1] :
( ~ sQ259_spl
| frontsegP(X1,app(sK52_skl,sK49_skl))
| ~ frontsegP(X1,X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3564,f282]) ).
fof(f4132,plain,
! [X0] :
( ~ sQ259_spl
| app(sK52_skl,sK49_skl) = X0
| ~ frontsegP(app(sK52_skl,sK49_skl),X0)
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3564,f284]) ).
fof(f4135,definition,
! [X0,X1] :
( sQ312_spl
<=> ( frontsegP(X1,app(sK52_skl,sK49_skl))
| ~ frontsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f4138,plain,
( ~ sQ259_spl
| ~ sQ128_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f4131,f4135,f1768,f3563]) ).
fof(f4139,definition,
! [X0] :
( sQ313_spl
<=> ( app(sK52_skl,sK49_skl) = X0
| ~ frontsegP(app(sK52_skl,sK49_skl),X0)
| ~ ssList(X0)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f4142,plain,
( ~ sQ259_spl
| ~ sQ128_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f4132,f4139,f1768,f3563]) ).
fof(f4148,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ234_spl
| app(nil,sK53_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f3079,f1669]) ).
fof(f4163,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ234_spl
| sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4148,f1585]) ).
fof(f4164,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ234_spl
| sQ110_spl ),
inference(contradiction_clause,[status(thm)],[f4163]) ).
fof(f4253,plain,
! [X0] :
( ~ sQ95_spl
| ~ sQ117_spl
| ~ sQ7_spl
| memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f271,f1656]) ).
fof(f4258,definition,
! [X0] :
( sQ314_spl
<=> ( memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f4261,plain,
( ~ sQ95_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ13_spl
| sQ314_spl ),
inference(split_clause,[status(thm)],[f4253,f4258,f653,f978,f466,f1623,f1494]) ).
fof(f4265,plain,
( ~ sQ7_spl
| hd(sK49_skl) = sK55_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f467,f239]) ).
fof(f4266,definition,
( sQ315_spl
<=> hd(sK49_skl) = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f4267,plain,
( ~ sQ315_spl
| hd(sK49_skl) = sK55_skl ),
inference(component_clause,[status(thm)],[f4266]) ).
fof(f4269,plain,
( ~ sQ7_spl
| sQ315_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4265,f678,f459,f4266,f466]) ).
fof(f4270,plain,
( ~ sQ315_spl
| sK55_skl = sK45_skl(sK49_skl)
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4267,f366]) ).
fof(f4272,definition,
( sQ316_spl
<=> sK55_skl = sK45_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f4275,plain,
( ~ sQ315_spl
| sQ316_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4270,f653,f452,f4272,f4266]) ).
fof(f4279,plain,
( ~ sQ7_spl
| tl(sK49_skl) = nil
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f467,f243]) ).
fof(f4280,definition,
( sQ317_spl
<=> tl(sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f4281,plain,
( ~ sQ317_spl
| tl(sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f4280]) ).
fof(f4283,plain,
( ~ sQ7_spl
| sQ317_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4279,f678,f459,f4280,f466]) ).
fof(f4285,plain,
( ~ sQ161_spl
| nil = sK43_skl(sK49_skl)
| ~ ssItem(sK44_skl(sK49_skl))
| ~ ssList(sK43_skl(sK49_skl))
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f233,f2104]) ).
fof(f4286,plain,
( ~ sQ42_spl
| sK44_skl(sK49_skl) = sK55_skl
| ~ ssItem(sK44_skl(sK49_skl))
| ~ ssList(sK43_skl(sK49_skl))
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f233,f1144]) ).
fof(f4290,definition,
( sQ318_spl
<=> ssList(sK43_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f4292,plain,
( sQ318_spl
| ~ ssList(sK43_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4290]) ).
fof(f4293,definition,
( sQ319_spl
<=> ssItem(sK44_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f4295,plain,
( sQ319_spl
| ~ ssItem(sK44_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4293]) ).
fof(f4296,definition,
( sQ320_spl
<=> nil = sK43_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f4297,plain,
( ~ sQ320_spl
| nil = sK43_skl(sK49_skl) ),
inference(component_clause,[status(thm)],[f4296]) ).
fof(f4299,plain,
( ~ sQ161_spl
| sQ320_spl
| ~ sQ319_spl
| ~ sQ318_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4285,f653,f452,f4290,f4293,f4296,f2103]) ).
fof(f4300,definition,
( sQ321_spl
<=> sK44_skl(sK49_skl) = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f4301,plain,
( ~ sQ321_spl
| sK44_skl(sK49_skl) = sK55_skl ),
inference(component_clause,[status(thm)],[f4300]) ).
fof(f4303,plain,
( ~ sQ42_spl
| sQ321_spl
| ~ sQ319_spl
| ~ sQ318_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4286,f653,f452,f4290,f4293,f4300,f1143]) ).
fof(f4313,plain,
! [X0] :
( ~ sQ315_spl
| sK49_skl = X0
| tl(sK49_skl) != tl(X0)
| sK55_skl != hd(X0)
| nil = X0
| nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f4267,f372]) ).
fof(f4317,definition,
! [X0] :
( sQ324_spl
<=> ( sK49_skl = X0
| tl(sK49_skl) != tl(X0)
| sK55_skl != hd(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f4320,plain,
( ~ sQ315_spl
| sQ3_spl
| ~ sQ13_spl
| sQ324_spl ),
inference(split_clause,[status(thm)],[f4313,f4317,f653,f452,f4266]) ).
fof(f4328,plain,
( ~ sQ315_spl
| cons(sK55_skl,tl(sK49_skl)) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4267,f374]) ).
fof(f4329,definition,
( sQ325_spl
<=> ssList(tl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f4331,plain,
( sQ325_spl
| ~ ssList(tl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4329]) ).
fof(f4332,definition,
( sQ326_spl
<=> ssItem(hd(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f4334,plain,
( sQ326_spl
| ~ ssItem(hd(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4332]) ).
fof(f4344,definition,
( sQ329_spl
<=> cons(sK55_skl,tl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4347,plain,
( ~ sQ315_spl
| sQ329_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4328,f653,f452,f4344,f4266]) ).
fof(f4348,plain,
( sQ326_spl
| ~ sQ315_spl
| ~ ssItem(sK55_skl) ),
inference(forward_demodulation,[status(thm)],[f4267,f4334]) ).
fof(f4349,plain,
( sQ326_spl
| ~ sQ315_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4348,f460]) ).
fof(f4350,plain,
( sQ326_spl
| ~ sQ315_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f4349]) ).
fof(f4351,plain,
( sQ325_spl
| ~ sQ317_spl
| ~ ssList(nil) ),
inference(forward_demodulation,[status(thm)],[f4281,f4331]) ).
fof(f4352,plain,
( sQ325_spl
| ~ sQ317_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4351,f223]) ).
fof(f4353,plain,
( sQ325_spl
| ~ sQ317_spl ),
inference(contradiction_clause,[status(thm)],[f4352]) ).
fof(f4357,plain,
( ~ sQ317_spl
| cons(hd(sK49_skl),nil) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4281,f374]) ).
fof(f4358,plain,
( ~ sQ317_spl
| nil = sK46_skl(sK49_skl)
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4281,f370]) ).
fof(f4360,definition,
( sQ330_spl
<=> cons(hd(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f4363,plain,
( ~ sQ317_spl
| sQ330_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4357,f653,f452,f4360,f4280]) ).
fof(f4364,definition,
( sQ331_spl
<=> nil = sK46_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4367,plain,
( ~ sQ317_spl
| sQ331_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4358,f653,f452,f4364,f4280]) ).
fof(f4370,plain,
( sQ319_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4295,f232]) ).
fof(f4371,plain,
( sQ319_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4370,f653,f452,f4293]) ).
fof(f4372,plain,
( sQ318_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4292,f231]) ).
fof(f4373,plain,
( sQ318_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4372,f653,f452,f4290]) ).
fof(f4378,plain,
( ~ sQ320_spl
| cons(sK44_skl(sK49_skl),nil) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4297,f233]) ).
fof(f4380,definition,
( sQ332_spl
<=> cons(sK44_skl(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4383,plain,
( ~ sQ320_spl
| sQ332_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4378,f653,f452,f4380,f4296]) ).
fof(f4386,plain,
( ~ sQ321_spl
| cons(sK55_skl,sK43_skl(sK49_skl)) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4301,f233]) ).
fof(f4388,definition,
( sQ333_spl
<=> cons(sK55_skl,sK43_skl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4391,plain,
( ~ sQ321_spl
| sQ333_spl
| sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4386,f653,f452,f4388,f4300]) ).
fof(f4397,plain,
( ~ sQ66_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ rearsegP(sK49_skl,app(sK49_skl,sK53_skl))
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK49_skl)
| sK52_skl = sK6_skl(app(sK49_skl,sK53_skl),sK49_skl)
| ~ ssList(sK6_skl(app(sK49_skl,sK53_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f1657,f129]) ).
fof(f4400,definition,
( sQ334_spl
<=> ssList(sK6_skl(app(sK49_skl,sK53_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4402,plain,
( sQ334_spl
| ~ ssList(sK6_skl(app(sK49_skl,sK53_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f4400]) ).
fof(f4403,definition,
( sQ335_spl
<=> sK52_skl = sK6_skl(app(sK49_skl,sK53_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4404,plain,
( ~ sQ335_spl
| sK52_skl = sK6_skl(app(sK49_skl,sK53_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f4403]) ).
fof(f4406,plain,
( ~ sQ66_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ139_spl
| ~ sQ131_spl
| ~ sQ13_spl
| sQ335_spl
| ~ sQ334_spl ),
inference(split_clause,[status(thm)],[f4397,f4400,f4403,f653,f1797,f1832,f466,f1623,f1293]) ).
fof(f4408,plain,
( sQ334_spl
| ~ rearsegP(sK49_skl,app(sK49_skl,sK53_skl))
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4402,f128]) ).
fof(f4409,plain,
( sQ334_spl
| ~ sQ139_spl
| ~ sQ131_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4408,f653,f1797,f1832,f4400]) ).
fof(f4412,plain,
( ~ sQ335_spl
| app(sK52_skl,app(sK49_skl,sK53_skl)) = sK49_skl
| ~ rearsegP(sK49_skl,app(sK49_skl,sK53_skl))
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4404,f129]) ).
fof(f4414,plain,
( ~ sQ335_spl
| sQ140_spl
| ~ sQ139_spl
| ~ sQ131_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4412,f653,f1797,f1832,f1928,f4403]) ).
fof(f4415,plain,
! [X0] :
( ~ sQ216_spl
| ~ rearsegP(sK53_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2864,f307]) ).
fof(f4420,definition,
! [X0] :
( sQ336_spl
<=> ( ~ rearsegP(sK53_skl,X0)
| ~ ssList(X0)
| rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4423,plain,
( ~ sQ216_spl
| ~ sQ13_spl
| ~ sQ27_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f4415,f4420,f978,f653,f2863]) ).
fof(f4438,plain,
! [X0] :
( ~ sQ100_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ memberP(sK52_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1677,f271]) ).
fof(f4440,definition,
! [X0] :
( sQ337_spl
<=> ( ~ memberP(sK52_skl,X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4443,plain,
( ~ sQ100_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ28_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f4438,f4440,f985,f653,f466,f1623,f1521]) ).
fof(f4469,plain,
! [X0] :
( ~ sQ264_spl
| ~ frontsegP(sK52_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK52_skl)
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3638,f288]) ).
fof(f4474,definition,
! [X0] :
( sQ338_spl
<=> ( ~ frontsegP(sK52_skl,X0)
| ~ ssList(X0)
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f4475,plain,
! [X0] :
( ~ sQ338_spl
| ~ frontsegP(sK52_skl,X0)
| ~ ssList(X0)
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4474]) ).
fof(f4477,plain,
( ~ sQ264_spl
| ~ sQ13_spl
| ~ sQ28_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f4469,f4474,f985,f653,f3637]) ).
fof(f4482,plain,
! [X0] :
( ~ sQ338_spl
| ~ frontsegP(sK52_skl,X0)
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4475]) ).
fof(f4509,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ ssList(app(sK49_skl,sK53_skl))
| sK52_skl = app(sK52_skl,app(sK49_skl,sK53_skl))
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1665,f3469]) ).
fof(f4517,definition,
( sQ344_spl
<=> sK52_skl = app(sK52_skl,app(sK49_skl,sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f4518,plain,
( ~ sQ344_spl
| sK52_skl = app(sK52_skl,app(sK49_skl,sK53_skl)) ),
inference(component_clause,[status(thm)],[f4517]) ).
fof(f4520,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ131_spl
| sQ344_spl
| ~ sQ254_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f4509,f985,f3461,f4517,f1797,f466,f1623,f1185]) ).
fof(f4556,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| hd(sK49_skl) = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f1665,f391]) ).
fof(f4557,plain,
( ~ sQ86_spl
| hd(sK49_skl) = hd(sK49_skl)
| nil = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1415,f391]) ).
fof(f4558,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| hd(sK49_skl) = hd(app(sK52_skl,sK49_skl))
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1669,f391]) ).
fof(f4562,definition,
( sQ346_spl
<=> hd(sK49_skl) = hd(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f4563,plain,
( ~ sQ346_spl
| hd(sK49_skl) = hd(sK52_skl) ),
inference(component_clause,[status(thm)],[f4562]) ).
fof(f4565,plain,
( ~ sQ48_spl
| ~ sQ117_spl
| ~ sQ7_spl
| sQ346_spl
| sQ59_spl
| ~ sQ131_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f4556,f985,f1797,f1253,f4562,f466,f1623,f1185]) ).
fof(f4566,definition,
( sQ347_spl
<=> hd(sK49_skl) = hd(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f4569,plain,
( ~ sQ86_spl
| sQ347_spl
| sQ3_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4557,f653,f678,f452,f4566,f1414]) ).
fof(f4570,definition,
( sQ348_spl
<=> hd(sK49_skl) = hd(app(sK52_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f4571,plain,
( ~ sQ348_spl
| hd(sK49_skl) = hd(app(sK52_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f4570]) ).
fof(f4573,plain,
( ~ sQ117_spl
| ~ sQ7_spl
| sQ348_spl
| sQ234_spl
| ~ sQ27_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4558,f1768,f978,f3078,f4570,f466,f1623]) ).
fof(f4574,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| sK55_skl = hd(app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f4267,f4571]) ).
fof(f4575,plain,
( ~ sQ346_spl
| ~ sQ315_spl
| sK55_skl = hd(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f4267,f4563]) ).
fof(f4576,plain,
! [X0] :
( ~ sQ317_spl
| tl(app(sK49_skl,X0)) = app(nil,X0)
| nil = sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4281,f393]) ).
fof(f4577,definition,
! [X0] :
( sQ349_spl
<=> ( tl(app(sK49_skl,X0)) = app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f4580,plain,
( ~ sQ317_spl
| sQ3_spl
| sQ349_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4576,f653,f4577,f452,f4280]) ).
fof(f4582,plain,
! [X0,X1] :
( ~ sQ7_spl
| frontsegP(nil,X1)
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f467,f292]) ).
fof(f4583,plain,
! [X0,X1] :
( ~ sQ7_spl
| frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f467,f292]) ).
fof(f4585,definition,
! [X0,X1] :
( sQ350_spl
<=> ( frontsegP(nil,X1)
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f4588,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| sQ350_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f4582,f459,f4585,f678,f466]) ).
fof(f4589,definition,
! [X0,X1] :
( sQ351_spl
<=> ( frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f4592,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f4583,f4589,f459,f678,f466]) ).
fof(f4593,plain,
( ~ sQ346_spl
| ~ sQ315_spl
| cons(sK55_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f4575,f374]) ).
fof(f4598,definition,
( sQ352_spl
<=> cons(sK55_skl,tl(sK52_skl)) = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f4599,plain,
( ~ sQ352_spl
| cons(sK55_skl,tl(sK52_skl)) = sK52_skl ),
inference(component_clause,[status(thm)],[f4598]) ).
fof(f4601,plain,
( ~ sQ346_spl
| ~ sQ315_spl
| sQ352_spl
| sQ59_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f4593,f985,f1253,f4598,f4266,f4562]) ).
fof(f4615,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| cons(sK55_skl,tl(app(sK52_skl,sK49_skl))) = app(sK52_skl,sK49_skl)
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f4574,f374]) ).
fof(f4616,plain,
! [X0] :
( ~ sQ348_spl
| ~ sQ315_spl
| X0 = app(sK52_skl,sK49_skl)
| tl(X0) != tl(app(sK52_skl,sK49_skl))
| hd(X0) != sK55_skl
| nil = app(sK52_skl,sK49_skl)
| nil = X0
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f4574,f372]) ).
fof(f4618,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| sK55_skl = sK45_skl(app(sK52_skl,sK49_skl))
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f4574,f366]) ).
fof(f4624,definition,
( sQ356_spl
<=> cons(sK55_skl,tl(app(sK52_skl,sK49_skl))) = app(sK52_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4627,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| sQ356_spl
| sQ234_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4615,f1768,f3078,f4624,f4266,f4570]) ).
fof(f4628,definition,
! [X0] :
( sQ357_spl
<=> ( X0 = app(sK52_skl,sK49_skl)
| tl(X0) != tl(app(sK52_skl,sK49_skl))
| hd(X0) != sK55_skl
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f4631,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| sQ234_spl
| sQ357_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4616,f1768,f4628,f3078,f4266,f4570]) ).
fof(f4633,definition,
( sQ358_spl
<=> sK55_skl = sK45_skl(app(sK52_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f4636,plain,
( ~ sQ348_spl
| ~ sQ315_spl
| sQ358_spl
| sQ234_spl
| ~ sQ128_spl ),
inference(split_clause,[status(thm)],[f4618,f1768,f3078,f4633,f4266,f4570]) ).
fof(f4641,plain,
( ~ sQ352_spl
| ~ sQ230_spl
| frontsegP(sK52_skl,sK49_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(paramodulation,[status(thm)],[f4599,f3012]) ).
fof(f4656,definition,
( sQ359_spl
<=> ssList(tl(sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f4658,plain,
( sQ359_spl
| ~ ssList(tl(sK52_skl)) ),
inference(component_clause,[status(thm)],[f4656]) ).
fof(f4671,plain,
( ~ sQ352_spl
| ~ sQ230_spl
| sQ254_spl
| ~ sQ359_spl ),
inference(split_clause,[status(thm)],[f4641,f4656,f3461,f3008,f4598]) ).
fof(f4714,plain,
( sQ359_spl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f4658,f241]) ).
fof(f4715,plain,
( sQ359_spl
| sQ59_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f4714,f985,f1253,f4656]) ).
fof(f4856,plain,
( ~ sQ344_spl
| ~ sQ180_spl
| sK52_skl = app(sK52_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f2349,f4518]) ).
fof(f5165,plain,
( ~ sQ105_spl
| ssItem(sK55_skl) ),
inference(backward_demodulation,[status(thm)],[f1549,f429]) ).
fof(f5170,plain,
( ~ sQ0_spl
| ~ sQ93_spl
| ~ sQ59_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| memberP(sK53_skl,sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f2375,f648]) ).
fof(f5171,plain,
( ~ sQ0_spl
| ~ sQ93_spl
| ~ sQ59_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| ~ sQ105_spl
| memberP(sK53_skl,sK55_skl) ),
inference(forward_demodulation,[status(thm)],[f1549,f5170]) ).
fof(f5175,plain,
( sQ1_spl
| ~ sQ105_spl
| ~ memberP(sK53_skl,sK55_skl) ),
inference(forward_demodulation,[status(thm)],[f1549,f446]) ).
fof(f5176,plain,
( sQ1_spl
| ~ sQ105_spl
| ~ sQ0_spl
| ~ sQ93_spl
| ~ sQ59_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5175,f5171]) ).
fof(f5177,plain,
( sQ1_spl
| ~ sQ105_spl
| ~ sQ0_spl
| ~ sQ93_spl
| ~ sQ59_spl
| ~ sQ78_spl
| ~ sQ117_spl
| ~ sQ7_spl
| ~ sQ48_spl
| ~ sQ180_spl ),
inference(contradiction_clause,[status(thm)],[f5176]) ).
fof(f5194,plain,
( ~ sQ105_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f5165,f459,f1548]) ).
fof(f5220,plain,
! [X0] :
( ~ sQ148_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1971]) ).
fof(f5225,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f1135]) ).
fof(f5226,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f5225]) ).
fof(f5360,plain,
( ~ sQ130_spl
| ~ sQ344_spl
| ~ sQ180_spl
| app(sK52_skl,sK53_skl) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f4856,f1776]) ).
fof(f5361,plain,
( ~ sQ130_spl
| ~ sQ344_spl
| ~ sQ180_spl
| sQ82_spl
| ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5360,f3151]) ).
fof(f5362,plain,
( ~ sQ130_spl
| ~ sQ344_spl
| ~ sQ180_spl
| sQ82_spl
| ~ sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f5361]) ).
fof(f5368,plain,
( ~ sQ105_spl
| ~ sQ148_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2659,f5220]) ).
fof(f5369,plain,
( ~ sQ105_spl
| ~ sQ148_spl ),
inference(contradiction_clause,[status(thm)],[f5368]) ).
fof(f5585,plain,
( ~ sQ338_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f4482,f3600,f4474]) ).
fof(f5610,plain,
( ~ sQ116_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ33_spl
| memberP(sK53_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1060,f1618]) ).
fof(f6403,plain,
( ~ sQ116_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1046,f5610]) ).
fof(f6405,plain,
( ~ sQ116_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6403,f995,f1012,f455,f452,f1617]) ).
fof(f6406,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f451,f458,f465,f469,f473,f662,f687,f696,f751,f754,f906,f911,f983,f991,f993,f998,f1000,f1010,f1015,f1127,f1137,f1146,f1150,f1156,f1163,f1170,f1188,f1195,f1200,f1204,f1208,f1211,f1213,f1220,f1227,f1264,f1269,f1273,f1277,f1280,f1291,f1296,f1300,f1309,f1314,f1319,f1324,f1329,f1334,f1339,f1350,f1354,f1360,f1367,f1370,f1378,f1389,f1393,f1405,f1412,f1417,f1429,f1433,f1440,f1445,f1449,f1453,f1471,f1476,f1487,f1497,f1501,f1508,f1516,f1520,f1524,f1530,f1534,f1544,f1546,f1551,f1576,f1580,f1587,f1591,f1597,f1604,f1608,f1616,f1620,f1626,f1706,f1711,f1731,f1735,f1745,f1749,f1759,f1763,f1778,f1780,f1782,f1803,f1807,f1812,f1816,f1826,f1831,f1835,f1839,f1935,f1939,f1943,f1948,f1953,f1958,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2351,f2655,f2694,f2747,f2751,f2755,f2794,f2801,f2806,f2807,f2811,f2827,f2834,f2866,f2870,f2874,f2913,f2917,f2960,f2972,f2984,f2988,f2992,f3000,f3007,f3011,f3024,f3054,f3058,f3098,f3099,f3104,f3108,f3112,f3113,f3426,f3450,f3460,f3496,f3526,f3546,f3562,f3566,f3570,f3574,f3582,f3585,f3640,f3665,f3669,f3708,f3712,f3720,f3766,f3800,f3804,f3834,f3838,f3857,f3861,f3896,f3900,f3923,f3932,f3936,f3943,f3948,f3955,f4002,f4006,f4021,f4025,f4029,f4057,f4063,f4067,f4080,f4105,f4121,f4125,f4138,f4142,f4164,f4261,f4269,f4275,f4283,f4299,f4303,f4320,f4347,f4350,f4353,f4363,f4367,f4371,f4373,f4383,f4391,f4406,f4409,f4414,f4423,f4443,f4477,f4520,f4565,f4569,f4573,f4580,f4588,f4592,f4601,f4627,f4631,f4636,f4671,f4715,f5177,f5194,f5226,f5362,f5369,f5585,f6405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC297+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Mon Sep 21 08:12:51 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.31 % Drodi V4.1.1
% 17.11/2.60 % Refutation found
% 17.11/2.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.11/2.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.90/2.64 % Elapsed time: 2.330986 seconds
% 17.90/2.64 % CPU time: 18.232681 seconds
% 17.90/2.64 % Total memory used: 233.787 MB
% 17.90/2.64 % Net memory used: 222.917 MB
%------------------------------------------------------------------------------