%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC109+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 : n013.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 02:40:00 PM UTC 2026
% Result : Theorem 11.01s 1.82s
% Output : CNFRefutation 11.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 307
% Syntax : Number of formulae : 1166 ( 35 unt; 240 def)
% Number of atoms : 5818 ( 730 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 8569 (3917 ~;3913 |; 277 &)
% ( 281 <=>; 181 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 258 ( 256 usr; 238 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 8 con; 0-5 aty)
% Number of variables : 1741 (1652 !; 89 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/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(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(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(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,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(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( leq(V,U)
& leq(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(V,W)
& leq(U,V) )
=> leq(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] :
( ssItem(U)
=> leq(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(V,W)
& lt(U,V) )
=> lt(U,W) ) ) ) ),
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(f39,axiom,
~ singletonP(nil),
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(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
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(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
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(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
duplicatefreeP(nil),
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(f90,axiom,
! [U] :
( ssItem(U)
=> ~ lt(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(V,W)
& leq(U,V) )
=> lt(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( leq(U,V)
=> ( lt(U,V)
| U = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ( segmentP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [U] :
( ( cyclefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f139,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [U] :
( ( ( ( leq(sK10_skl(U),sK9_skl(U))
& leq(sK9_skl(U),sK10_skl(U))
& app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U))) = U
& ssList(sK13_skl(U))
& ssList(sK12_skl(U))
& ssList(sK11_skl(U))
& ssItem(sK10_skl(U))
& ssItem(sK9_skl(U)) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
! [U] :
( ( totalorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f151,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(W,V)
& ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [U] :
( ( ( ( ~ leq(sK15_skl(U),sK14_skl(U))
& ~ leq(sK14_skl(U),sK15_skl(U))
& app(app(sK16_skl(U),cons(sK14_skl(U),sK17_skl(U))),cons(sK15_skl(U),sK18_skl(U))) = U
& ssList(sK18_skl(U))
& ssList(sK17_skl(U))
& ssList(sK16_skl(U))
& ssItem(sK15_skl(U))
& ssItem(sK14_skl(U)) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(V,sK14_skl(U)),skolemize(W,sK15_skl(U)),skolemize(X,sK16_skl(U)),skolemize(Y,sK17_skl(U)),skolemize(Z,sK18_skl(U))],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(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(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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(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(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(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(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(f250,plain,
! [U] :
( ! [V] :
( U = V
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f251,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
! [U] :
( ! [V] :
( ! [W] :
( leq(U,W)
| ~ leq(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f253,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
! [U] :
( leq(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f255,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f260,plain,
! [U] :
( ! [V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f261,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f262,plain,
! [U] :
( ! [V] :
( ! [W] :
( lt(U,W)
| ~ lt(V,W)
| ~ lt(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f263,plain,
! [X0,X1,X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f262]) ).
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(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(f280,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
! [X0,X1,X2,X3] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f299,plain,
! [X0] :
( nil != X0
| frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f300,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(U,W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f301,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
! [U] :
( ! [V] :
( U = V
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f303,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(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(f313,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(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f327,plain,
! [X0] :
( nil != X0
| segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f330,plain,
cyclefreeP(nil),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f333,plain,
totalorderP(nil),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f359,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[status(thm)],[f72]) ).
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(f387,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| 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(f400,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f401,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f402,plain,
! [U] :
( ! [V] :
( ! [W] :
( lt(U,W)
| ~ lt(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f403,plain,
! [X0,X1,X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f404,plain,
! [U] :
( ! [V] :
( lt(U,V)
| U = V
| ~ leq(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f405,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f404]) ).
fof(f406,plain,
! [U] :
( ! [V] :
( ( lt(U,V)
<=> ( leq(U,V)
& U != V ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f407,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f406]) ).
fof(f409,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f407]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& 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,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [U,V] :
( sP1_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| sP1_prd(V,U) )
& ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
? [U] :
( ? [V] :
( ? [W] :
( ( ( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| sP1_prd(V,U) )
& ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f418]) ).
fof(f420,plain,
( ( ( ( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) )
& neq(sK48_skl,nil) )
| sP1_prd(sK48_skl,sK47_skl) )
& ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f419]) ).
fof(f421,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f422,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f425,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f426,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f427,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f428,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f429,plain,
( neq(sK48_skl,nil)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f430,plain,
( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil)
| sP1_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f431,definition,
! [Y,Z,X2] :
( sP2_prd(X2,Z,Y)
<=> ( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f432,plain,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP2_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
inference(formula_renaming,[status(thm)],[f416,f431]) ).
fof(f433,plain,
! [W,X,Y] :
( ( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP2_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP2_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f432]) ).
fof(f434,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP2_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP2_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ( lt(sK55_skl(X1,Z,Y,X,W),Y)
& memberP(X1,sK55_skl(X1,Z,Y,X,W))
& ssItem(sK55_skl(X1,Z,Y,X,W)) )
| ~ sP2_prd(sK54_skl(X1,Z,Y,X,W),Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(sK53_skl(Y,X,W),X3)
| ~ ssItem(X3) )
& ! [X2] : sP2_prd(X2,sK52_skl(Y,X,W),Y)
& app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W)) = X
& cons(Y,nil) = W
& ssList(sK53_skl(Y,X,W))
& ssList(sK52_skl(Y,X,W))
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f439,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f440,plain,
! [X0,X1,X2] :
( app(app(sK52_skl(X0,X1,X2),X2),sK53_skl(X0,X1,X2)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f441,plain,
! [X0,X1,X2,X3] :
( sP2_prd(X3,sK52_skl(X0,X1,X2),X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f443,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK55_skl(X4,X3,X0,X1,X2))
| ~ sP2_prd(sK54_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f444,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X4,sK55_skl(X4,X3,X0,X1,X2))
| ~ sP2_prd(sK54_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f445,plain,
! [X0,X1,X2,X3,X4] :
( lt(sK55_skl(X4,X3,X0,X1,X2),X0)
| ~ sP2_prd(sK54_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f446,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP1_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP1_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f447,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP1_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP1_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f446]) ).
fof(f448,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f447]) ).
fof(f449,plain,
! [X0,X1] :
( nil != X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f447]) ).
fof(f450,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f447]) ).
fof(f451,plain,
! [Y,Z,X2] :
( ( ( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| sP2_prd(X2,Z,Y) )
& ( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2)
| ~ sP2_prd(X2,Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f431]) ).
fof(f452,plain,
( ! [Y,Z,X2] :
( ( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| sP2_prd(X2,Z,Y) )
& ! [Y,Z,X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2)
| ~ sP2_prd(X2,Z,Y) ) ),
inference(miniscoping,[status(thm)],[f451]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ssItem(X0)
| sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f452]) ).
fof(f455,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f452]) ).
fof(f456,plain,
! [X0,X1,X2] :
( lt(X2,X0)
| sP2_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f452]) ).
fof(f457,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f457,f460]) ).
fof(f464,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f457,f464]) ).
fof(f468,definition,
( sQ3_spl
<=> sP1_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ3_spl
| sP1_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( sQ3_spl
| ~ sP1_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,definition,
( sQ4_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ4_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f429,f468,f471]) ).
fof(f475,definition,
( sQ5_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ5_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
( sQ6_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ6_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f430,f468,f475,f478]) ).
fof(f484,plain,
! [X0,X2,X3,X4,X5] :
( app(app(X3,cons(X2,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f199]) ).
fof(f485,plain,
! [X0,X1,X2,X3,X4] :
( app(app(X2,cons(X1,X3)),cons(X1,X4)) != X0
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f484]) ).
fof(f486,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f487,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f486]) ).
fof(f490,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(f491,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)],[f490]) ).
fof(f500,plain,
! [X0,X1,X2,X3] :
( ~ memberP(app(app(X1,X2),X3),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(X1,X2),X3))
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(sK2_skl(X0,app(app(X1,X2),X3)),cons(X0,sK3_skl(X0,app(app(X1,X2),X3)))),X2)
| ~ ssList(X2)
| ~ ssList(app(sK2_skl(X0,app(app(X1,X2),X3)),cons(X0,sK3_skl(X0,app(app(X1,X2),X3))))) ),
inference(resolution,[status(thm)],[f137,f111]) ).
fof(f501,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(equality_resolution,[status(thm)],[f137]) ).
fof(f502,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(cons(sK4_skl(app(app(X0,X1),X2)),nil),X1)
| ~ ssList(X1)
| ~ ssList(cons(sK4_skl(app(app(X0,X1),X2)),nil))
| ~ singletonP(app(app(X0,X1),X2))
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f117,f137]) ).
fof(f503,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(cons(sK4_skl(app(X0,cons(X1,X2))),nil),X1)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f117,f112]) ).
fof(f508,plain,
( ~ sQ3_spl
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f448,f469]) ).
fof(f509,plain,
( ~ sQ3_spl
| sP1_prd(nil,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f508,f469]) ).
fof(f510,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f508,f425]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ~ ssList(sK5_skl(app(X1,X2),X0))
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f137]) ).
fof(f517,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(X3,sK5_skl(X3,app(app(X0,X1),X2))),X1)
| ~ ssList(X1)
| ~ ssList(app(X3,sK5_skl(X3,app(app(X0,X1),X2))))
| ~ frontsegP(app(app(X0,X1),X2),X3)
| ~ ssList(X3)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f123,f137]) ).
fof(f519,plain,
! [X0,X1,X2] :
( ~ ssList(sK5_skl(app(X1,X2),X0))
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f515]) ).
fof(f520,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f122]) ).
fof(f523,plain,
! [X0,X1] :
( ~ singletonP(app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| frontsegP(cons(sK4_skl(app(X0,X1)),nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4_skl(app(X0,X1)),nil)) ),
inference(resolution,[status(thm)],[f124,f117]) ).
fof(f531,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f542,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,sK6_skl(X1,X0))
| ~ ssList(sK6_skl(X1,X0))
| ~ ssList(X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f124]) ).
fof(f544,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(sK6_skl(X3,app(app(X0,X1),X2)),X3),X1)
| ~ ssList(X1)
| ~ ssList(app(sK6_skl(X3,app(app(X0,X1),X2)),X3))
| ~ rearsegP(app(app(X0,X1),X2),X3)
| ~ ssList(X3)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f129,f137]) ).
fof(f549,plain,
! [X0,X1] :
( frontsegP(X0,sK6_skl(X1,X0))
| ~ ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f542]) ).
fof(f550,plain,
! [X0,X1] :
( frontsegP(X0,sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f128]) ).
fof(f563,plain,
( ~ sQ3_spl
| nil != sK47_skl ),
inference(resolution,[status(thm)],[f449,f509]) ).
fof(f564,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f227,f117]) ).
fof(f566,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f567,definition,
! [X0,X1] :
( sQ10_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ10_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f564,f531,f567]) ).
fof(f572,definition,
! [X0] :
( sQ11_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f573,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,definition,
! [X1] :
( sQ12_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f566,f572,f575]) ).
fof(f579,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f223]) ).
fof(f580,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f573]) ).
fof(f583,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f228,f117]) ).
fof(f586,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ13_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f583,f531,f586]) ).
fof(f591,definition,
! [X0] :
( sQ14_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f581]) ).
fof(f603,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f620,definition,
( sQ17_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( sQ17_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f632,definition,
( sQ20_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( ~ sQ2_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f465,f426]) ).
fof(f641,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f563]) ).
fof(f642,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f641]) ).
fof(f643,plain,
! [X0,X1,X2,X3] :
( ~ lt(X3,X2)
| ~ lt(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssItem(X1)
| lt(X0,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f263,f263]) ).
fof(f645,plain,
! [X0,X1,X2] :
( ~ lt(X2,X0)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f263,f261]) ).
fof(f647,plain,
! [X0,X1,X2,X3] :
( ~ lt(X3,X2)
| ~ lt(X1,X3)
| ~ ssItem(X3)
| lt(X0,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f643]) ).
fof(f649,plain,
! [X0,X1,X2] :
( ~ lt(X2,X0)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f645]) ).
fof(f678,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sP0_prd(sK51_skl,nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f510,f458]) ).
fof(f679,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sP0_prd(sK51_skl,nil,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f678]) ).
fof(f682,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X3,X4)
| memberP(X5,sK55_skl(X5,sK52_skl(X0,X3,X4),X0,X1,X2))
| app(app(sK52_skl(X0,X3,X4),X2),X5) != X1
| cons(X0,nil) != X2
| ~ ssList(X5)
| ~ ssList(sK52_skl(X0,X3,X4))
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f444,f441]) ).
fof(f683,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK54_skl(X4,X3,X0,X1,X2))
| memberP(X4,sK55_skl(X4,X3,X0,X1,X2))
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f444,f454]) ).
fof(f684,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X3,X4)
| memberP(X5,sK55_skl(X5,sK52_skl(X0,X3,X4),X0,X1,X2))
| app(app(sK52_skl(X0,X3,X4),X2),X5) != X1
| cons(X0,nil) != X2
| ~ ssList(X5)
| ~ ssList(sK52_skl(X0,X3,X4))
| sP0_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f682,f436]) ).
fof(f717,definition,
! [X0] :
( sQ27_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f729,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X1,sK55_skl(X1,X0,X2,X3,X4))
| app(app(X0,X4),X1) != X3
| cons(X2,nil) != X4
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sP0_prd(X2,X3,X4)
| memberP(X0,sK54_skl(X1,X0,X2,X3,X4)) ),
inference(resolution,[status(thm)],[f455,f444]) ).
fof(f730,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK55_skl(X1,X0,X2,X3,X4))
| app(app(X0,X4),X1) != X3
| cons(X2,nil) != X4
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sP0_prd(X2,X3,X4)
| memberP(X0,sK54_skl(X1,X0,X2,X3,X4)) ),
inference(resolution,[status(thm)],[f455,f443]) ).
fof(f732,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X3,sK54_skl(X4,X3,X0,X1,X2))
| lt(sK55_skl(X4,X3,X0,X1,X2),X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f445,f455]) ).
fof(f733,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK54_skl(X4,X3,X0,X1,X2))
| lt(sK55_skl(X4,X3,X0,X1,X2),X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f445,f454]) ).
fof(f735,plain,
! [X0,X1,X2,X3,X4] :
( lt(sK55_skl(X1,X2,X0,X3,X4),X0)
| app(app(X2,X4),X1) != X3
| cons(X0,nil) != X4
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| sP0_prd(X0,X3,X4)
| lt(X0,sK54_skl(X1,X2,X0,X3,X4)) ),
inference(resolution,[status(thm)],[f456,f445]) ).
fof(f736,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X1,sK55_skl(X1,X2,X0,X3,X4))
| app(app(X2,X4),X1) != X3
| cons(X0,nil) != X4
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| sP0_prd(X0,X3,X4)
| lt(X0,sK54_skl(X1,X2,X0,X3,X4)) ),
inference(resolution,[status(thm)],[f456,f444]) ).
fof(f737,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK55_skl(X1,X2,X0,X3,X4))
| app(app(X2,X4),X1) != X3
| cons(X0,nil) != X4
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssItem(X0)
| sP0_prd(X0,X3,X4)
| lt(X0,sK54_skl(X1,X2,X0,X3,X4)) ),
inference(resolution,[status(thm)],[f456,f443]) ).
fof(f738,plain,
! [X0,X1] :
( nil != X1
| nil = X1
| nil != X0 ),
inference(resolution,[status(thm)],[f450,f449]) ).
fof(f740,definition,
! [X0] :
( sQ28_spl
<=> nil != X0 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f741,plain,
! [X0] :
( ~ sQ28_spl
| nil != X0 ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f743,definition,
! [X1] :
( sQ29_spl
<=> ( nil != X1
| nil = X1 ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f746,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f738,f740,f743]) ).
fof(f751,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f752,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f315]) ).
fof(f755,definition,
! [X0,X1] :
( sQ31_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( ~ sQ7_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f751,f755,f531]) ).
fof(f759,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X3)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f752]) ).
fof(f762,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f317,f315]) ).
fof(f765,definition,
! [X0] :
( sQ32_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f766,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f765]) ).
fof(f768,plain,
( sQ32_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f762,f531,f765]) ).
fof(f769,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f763]) ).
fof(f770,plain,
! [X0] :
( ~ sQ32_spl
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f766]) ).
fof(f798,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f458]) ).
fof(f805,plain,
( ~ sQ28_spl
| $false ),
inference(equality_resolution,[status(thm)],[f741]) ).
fof(f807,definition,
( sQ33_spl
<=> totalorderP(nil) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f809,plain,
( sQ33_spl
| ~ totalorderP(nil) ),
inference(component_clause,[status(thm)],[f807]) ).
fof(f811,definition,
( sQ34_spl
<=> cyclefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f813,plain,
( sQ34_spl
| ~ cyclefreeP(nil) ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f820,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f805]) ).
fof(f839,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f317]) ).
fof(f840,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f315]) ).
fof(f841,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f839]) ).
fof(f842,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f840]) ).
fof(f843,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f326,f323]) ).
fof(f844,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f326,f315]) ).
fof(f846,definition,
( sQ36_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( sQ36_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f843,f531,f846]) ).
fof(f850,definition,
! [X0,X1] :
( sQ37_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f851,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f850]) ).
fof(f853,plain,
( ~ sQ7_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f844,f850,f531]) ).
fof(f855,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f851]) ).
fof(f858,plain,
! [X0] :
( X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f327,f317]) ).
fof(f859,plain,
! [X0,X1] :
( segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f327,f315]) ).
fof(f860,definition,
! [X0] :
( sQ38_spl
<=> ( X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f863,plain,
( ~ sQ7_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f858,f860,f531]) ).
fof(f864,definition,
! [X0,X1] :
( sQ39_spl
<=> ( segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f865,plain,
! [X0,X1] :
( ~ sQ39_spl
| segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f867,plain,
( ~ sQ7_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f859,f864,f531]) ).
fof(f868,plain,
! [X0,X1] :
( ~ sQ39_spl
| segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f865]) ).
fof(f869,plain,
! [X0,X1] :
( ~ sQ39_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f868,f323]) ).
fof(f870,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(f872,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f376]) ).
fof(f873,definition,
! [X0] :
( sQ40_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( ~ sQ7_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f870,f873,f531]) ).
fof(f878,definition,
! [X1] :
( sQ41_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f879,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f878]) ).
fof(f881,plain,
( sQ41_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f872,f591,f878]) ).
fof(f884,plain,
( ~ sQ41_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f421,f879]) ).
fof(f886,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f884]) ).
fof(f904,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f798,f439]) ).
fof(f905,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f798,f436]) ).
fof(f906,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f425,f798]) ).
fof(f939,plain,
( sQ17_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f905]) ).
fof(f940,plain,
( sQ17_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f943,plain,
( sQ3_spl
| nil = sK47_skl
| nil != sK48_skl ),
inference(resolution,[status(thm)],[f450,f470]) ).
fof(f946,definition,
( sQ49_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( ~ sQ49_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f946]) ).
fof(f948,plain,
( sQ49_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f946]) ).
fof(f949,plain,
( sQ3_spl
| sQ20_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f943,f946,f632,f468]) ).
fof(f952,plain,
( ~ sQ1_spl
| sK48_skl = nil ),
inference(backward_demodulation,[status(thm)],[f461,f425]) ).
fof(f961,plain,
! [X0,X1,X2,X3,X4] :
( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderedP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f177]) ).
fof(f962,definition,
! [X0] :
( sQ51_spl
<=> ( nil = X0
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f965,definition,
! [X1] :
( sQ52_spl
<=> ( ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f966,plain,
! [X0] :
( ~ sQ52_spl
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f965]) ).
fof(f970,definition,
! [X0,X1,X2,X3,X4] :
( sQ53_spl
<=> ( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f973,definition,
( sQ54_spl
<=> totalorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f975,plain,
( sQ54_spl
| ~ totalorderedP(nil) ),
inference(component_clause,[status(thm)],[f973]) ).
fof(f976,plain,
( ~ sQ54_spl
| ~ sQ7_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f961,f970,f531,f973]) ).
fof(f977,plain,
( sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f975,f339]) ).
fof(f978,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f979,plain,
! [X0] :
( ~ sQ52_spl
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f966]) ).
fof(f980,plain,
( ~ sQ1_spl
| sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f952,f948]) ).
fof(f981,plain,
( ~ sQ1_spl
| sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f980]) ).
fof(f1003,plain,
! [X0,X1,X2,X3,X4] :
( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| lt(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ strictorderedP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f188,f387]) ).
fof(f1013,definition,
( sQ59_spl
<=> strictorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1015,plain,
( sQ59_spl
| ~ strictorderedP(nil) ),
inference(component_clause,[status(thm)],[f1013]) ).
fof(f1016,definition,
! [X0,X1,X2,X3,X4] :
( sQ60_spl
<=> ( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| lt(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1019,plain,
( sQ60_spl
| ~ sQ59_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1003,f531,f1013,f1016]) ).
fof(f1020,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1015,f349]) ).
fof(f1021,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f1020]) ).
fof(f1031,plain,
( ~ sQ4_spl
| ~ sQ49_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f947,f472]) ).
fof(f1042,plain,
( ~ sQ4_spl
| ~ sQ49_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1031,f487]) ).
fof(f1044,plain,
( ~ sQ4_spl
| ~ sQ49_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1042,f531,f946,f471]) ).
fof(f1090,plain,
( ~ sQ52_spl
| nil != nil ),
inference(resolution,[status(thm)],[f979,f223]) ).
fof(f1091,plain,
( ~ sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1090]) ).
fof(f1092,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1091]) ).
fof(f1098,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| ~ ssList(sK53_skl(X2,X0,X1))
| ~ ssList(sK52_skl(X2,X0,X1))
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f137,f440]) ).
fof(f1111,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| ~ ssList(sK53_skl(X2,X0,X1))
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1098,f437]) ).
fof(f1149,plain,
( ~ sQ0_spl
| nil != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f904,f235]) ).
fof(f1153,plain,
( ~ sQ0_spl
| ssList(sK47_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f904,f222]) ).
fof(f1180,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1149,f531,f620,f632,f457]) ).
fof(f1193,definition,
( sQ72_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1196,plain,
( ~ sQ0_spl
| sQ72_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1153,f531,f620,f1193,f457]) ).
fof(f1236,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X0)
| segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f389,f137]) ).
fof(f1244,definition,
! [X0,X1] :
( sQ77_spl
<=> ( ~ ssList(X0)
| segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1247,plain,
( ~ sQ7_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1236,f1244,f531]) ).
fof(f1269,definition,
( sQ78_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1309,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(nil)
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f249,f112]) ).
fof(f1310,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(f1317,definition,
! [X0,X1] :
( sQ83_spl
<=> ( ~ ssList(X1)
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1320,plain,
( ~ sQ7_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1309,f1317,f531]) ).
fof(f1321,definition,
! [X0] :
( sQ84_spl
<=> ( app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1324,plain,
( ~ sQ7_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1310,f1321,f531]) ).
fof(f1344,plain,
! [X0,X1,X2] :
( ~ ssList(cons(X0,cons(X1,X2)))
| X0 = X1
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ equalelemsP(cons(X0,cons(X1,X2)))
| ~ ssList(cons(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f210,f249]) ).
fof(f1356,definition,
! [X0,X1,X2] :
( sQ87_spl
<=> ( ~ ssList(cons(X0,cons(X1,X2)))
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ equalelemsP(cons(X0,cons(X1,X2)))
| ~ ssList(cons(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1359,plain,
( ~ sQ7_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1344,f1356,f531]) ).
fof(f1388,plain,
! [X0] :
( sQ6_spl
| ~ segmentP(X0,sK47_skl)
| ~ segmentP(sK48_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f315,f480]) ).
fof(f1396,definition,
( sQ91_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( sQ91_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f1396]) ).
fof(f1399,definition,
! [X0] :
( sQ92_spl
<=> ( ~ segmentP(X0,sK47_skl)
| ~ segmentP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1400,plain,
! [X0] :
( ~ sQ92_spl
| ~ segmentP(X0,sK47_skl)
| ~ segmentP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1399]) ).
fof(f1402,plain,
( sQ6_spl
| ~ sQ72_spl
| sQ92_spl
| ~ sQ91_spl ),
inference(split_clause,[status(thm)],[f1388,f1396,f1399,f1193,f478]) ).
fof(f1405,plain,
( sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1398,f422]) ).
fof(f1406,plain,
sQ91_spl,
inference(contradiction_clause,[status(thm)],[f1405]) ).
fof(f1422,plain,
( sQ5_spl
| sK47_skl = nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f477,f220]) ).
fof(f1424,plain,
( sQ5_spl
| sQ20_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f1422,f1193,f531,f632,f475]) ).
fof(f1470,plain,
( ~ sQ0_spl
| tl(sK47_skl) = nil
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f904,f243]) ).
fof(f1471,definition,
( sQ94_spl
<=> tl(sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1472,plain,
( ~ sQ94_spl
| tl(sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f1471]) ).
fof(f1474,plain,
( ~ sQ0_spl
| sQ94_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1470,f531,f620,f1471,f457]) ).
fof(f1490,definition,
! [X0,X1] :
( sQ95_spl
<=> ( ~ ssList(X0)
| segmentP(nil,X1)
| ~ ssList(X1)
| nil != app(X0,X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1554,definition,
( sQ105_spl
<=> duplicatefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( sQ105_spl
| ~ duplicatefreeP(nil) ),
inference(component_clause,[status(thm)],[f1554]) ).
fof(f1602,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f1606,definition,
! [X0,X1] :
( sQ110_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1609,plain,
( ~ sQ7_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1602,f1606,f531]) ).
fof(f1685,plain,
! [X0,X1,X2] :
( nil != X1
| nil != cons(X0,X2)
| ~ ssList(cons(X0,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X1)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f112,f387]) ).
fof(f1711,definition,
! [X0,X2] :
( sQ123_spl
<=> ( nil != cons(X0,X2)
| ~ ssList(cons(X0,X2))
| ~ ssList(X2)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1714,plain,
( sQ52_spl
| sQ123_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1685,f531,f1711,f965]) ).
fof(f1718,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f1721,definition,
! [X0] :
( sQ124_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1724,plain,
( sQ124_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1718,f531,f1721]) ).
fof(f1799,plain,
! [X0,X1,X2] :
( frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f491,f292]) ).
fof(f1800,plain,
! [X0,X1,X2] :
( X0 = X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f491,f291]) ).
fof(f1805,definition,
! [X0] :
( sQ134_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1806,plain,
! [X0] :
( ~ sQ134_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1805]) ).
fof(f1808,definition,
! [X1,X2] :
( sQ135_spl
<=> ( frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1811,plain,
( sQ135_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f1799,f1805,f1808]) ).
fof(f1812,definition,
! [X0] :
( sQ136_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1815,definition,
! [X1,X2] :
( sQ137_spl
<=> ( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1816,plain,
! [X0,X1] :
( ~ sQ137_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1815]) ).
fof(f1818,plain,
( sQ137_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1800,f1812,f1815]) ).
fof(f1830,plain,
! [X0] :
( ~ sQ134_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1806]) ).
fof(f1831,plain,
! [X0,X1] :
( ~ sQ137_spl
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1816]) ).
fof(f1833,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f282]) ).
fof(f1836,definition,
! [X0,X1] :
( sQ140_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1839,plain,
( ~ sQ7_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1833,f1836,f531]) ).
fof(f1853,definition,
( sQ143_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1854,plain,
( ~ sQ143_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f1853]) ).
fof(f1858,plain,
! [X0] :
( ~ sQ143_spl
| frontsegP(X0,sK47_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1854,f282]) ).
fof(f1859,definition,
( sQ144_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1863,definition,
! [X0] :
( sQ145_spl
<=> ( frontsegP(X0,sK47_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1866,plain,
( ~ sQ143_spl
| ~ sQ72_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1858,f1863,f1193,f1853]) ).
fof(f1884,plain,
( ~ sQ134_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f103,f1830]) ).
fof(f1888,plain,
~ sQ134_spl,
inference(contradiction_clause,[status(thm)],[f1884]) ).
fof(f1890,plain,
! [X0] :
( X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f299,f284]) ).
fof(f1891,plain,
! [X0,X1] :
( frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f299,f282]) ).
fof(f1892,definition,
! [X0] :
( sQ146_spl
<=> ( X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1895,plain,
( ~ sQ7_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f1890,f1892,f531]) ).
fof(f1896,definition,
! [X0,X1] :
( sQ147_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1899,plain,
( ~ sQ7_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1891,f1896,f531]) ).
fof(f1902,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f1906,definition,
! [X0,X1] :
( sQ148_spl
<=> ( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1909,plain,
( ~ sQ7_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1902,f1906,f531]) ).
fof(f1913,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f1916,definition,
! [X0] :
( sQ149_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1919,plain,
( sQ149_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1913,f531,f1916]) ).
fof(f1938,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f312,f301]) ).
fof(f1941,definition,
! [X0,X1] :
( sQ150_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1944,plain,
( ~ sQ7_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f1938,f1941,f531]) ).
fof(f1948,plain,
! [X0] :
( X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f313,f303]) ).
fof(f1949,plain,
! [X0,X1] :
( rearsegP(X1,X0)
| ~ rearsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f313,f301]) ).
fof(f1950,definition,
! [X0] :
( sQ151_spl
<=> ( X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( ~ sQ7_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1948,f1950,f531]) ).
fof(f1954,definition,
! [X0,X1] :
( sQ152_spl
<=> ( rearsegP(X1,X0)
| ~ rearsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1957,plain,
( ~ sQ7_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f1949,f1954,f531]) ).
fof(f2034,definition,
( sQ157_spl
<=> lt(sK51_skl,hd(nil)) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2035,plain,
( ~ sQ157_spl
| lt(sK51_skl,hd(nil)) ),
inference(component_clause,[status(thm)],[f2034]) ).
fof(f2036,plain,
( sQ157_spl
| ~ lt(sK51_skl,hd(nil)) ),
inference(component_clause,[status(thm)],[f2034]) ).
fof(f2084,plain,
( ~ sQ157_spl
| ~ lt(hd(nil),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2035,f261]) ).
fof(f2085,plain,
! [X0] :
( ~ sQ157_spl
| lt(X0,hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(hd(nil))
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2035,f263]) ).
fof(f2086,definition,
( sQ158_spl
<=> ssItem(hd(nil)) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2088,plain,
( sQ158_spl
| ~ ssItem(hd(nil)) ),
inference(component_clause,[status(thm)],[f2086]) ).
fof(f2089,definition,
( sQ159_spl
<=> lt(hd(nil),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( sQ159_spl
| ~ lt(hd(nil),sK51_skl) ),
inference(component_clause,[status(thm)],[f2089]) ).
fof(f2092,plain,
( ~ sQ157_spl
| ~ sQ159_spl
| ~ sQ17_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2084,f2086,f620,f2089,f2034]) ).
fof(f2093,definition,
! [X0] :
( sQ160_spl
<=> ( lt(X0,hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2094,plain,
! [X0] :
( ~ sQ160_spl
| lt(X0,hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2093]) ).
fof(f2096,plain,
( ~ sQ157_spl
| ~ sQ158_spl
| ~ sQ17_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f2085,f2093,f620,f2086,f2034]) ).
fof(f2120,plain,
! [X0] :
( sQ159_spl
| ~ lt(X0,sK51_skl)
| ~ lt(hd(nil),X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2091,f263]) ).
fof(f2121,definition,
! [X0] :
( sQ163_spl
<=> ( ~ lt(X0,sK51_skl)
| ~ lt(hd(nil),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2122,plain,
! [X0] :
( ~ sQ163_spl
| ~ lt(X0,sK51_skl)
| ~ lt(hd(nil),X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2121]) ).
fof(f2124,plain,
( sQ159_spl
| ~ sQ17_spl
| sQ163_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2120,f2086,f2121,f620,f2089]) ).
fof(f2125,plain,
! [X0] :
( sQ157_spl
| ~ lt(X0,hd(nil))
| ~ lt(sK51_skl,X0)
| ~ ssItem(hd(nil))
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2036,f263]) ).
fof(f2126,definition,
! [X0] :
( sQ164_spl
<=> ( ~ lt(X0,hd(nil))
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2127,plain,
! [X0] :
( ~ sQ164_spl
| ~ lt(X0,hd(nil))
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2126]) ).
fof(f2129,plain,
( sQ157_spl
| ~ sQ158_spl
| sQ164_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2125,f620,f2126,f2086,f2034]) ).
fof(f2147,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X4,X5)
| memberP(X3,sK55_skl(X3,sK52_skl(X0,X4,X5),X0,X1,X2))
| app(app(sK52_skl(X0,X4,X5),X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| sP0_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f684,f437]) ).
fof(f2149,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssItem(sK55_skl(nil,sK52_skl(X0,X3,X4),X0,X1,X2))
| ~ sP0_prd(X0,X3,X4)
| app(app(sK52_skl(X0,X3,X4),X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(nil)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f2147,f279]) ).
fof(f2155,definition,
! [X0,X1,X2,X3,X4] :
( sQ167_spl
<=> ( ~ ssItem(sK55_skl(nil,sK52_skl(X0,X3,X4),X0,X1,X2))
| ~ sP0_prd(X0,X3,X4)
| app(app(sK52_skl(X0,X3,X4),X2),nil) != X1
| cons(X0,nil) != X2
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2158,plain,
( ~ sQ7_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f2149,f2155,f531]) ).
fof(f2179,plain,
! [X0] :
( ~ sQ137_spl
| nil != X0
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1831,f299]) ).
fof(f2184,plain,
( ~ sQ137_spl
| sQ52_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2179,f531,f965,f1815]) ).
fof(f2186,definition,
! [X0] :
( sQ171_spl
<=> ( ~ ssList(X0)
| ~ ssList(cons(sK51_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f2187,plain,
! [X0] :
( ~ sQ171_spl
| ~ ssList(X0)
| ~ ssList(cons(sK51_skl,X0)) ),
inference(component_clause,[status(thm)],[f2186]) ).
fof(f2192,plain,
! [X0] :
( ~ sQ94_spl
| sK47_skl = X0
| nil != tl(X0)
| hd(sK47_skl) != hd(X0)
| nil = X0
| nil = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1472,f372]) ).
fof(f2195,definition,
! [X0] :
( sQ172_spl
<=> ( sK47_skl = X0
| nil != tl(X0)
| hd(sK47_skl) != hd(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2198,plain,
( ~ sQ94_spl
| sQ20_spl
| ~ sQ72_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f2192,f2195,f1193,f632,f1471]) ).
fof(f2209,plain,
( ~ sQ94_spl
| cons(hd(sK47_skl),nil) = sK47_skl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1472,f374]) ).
fof(f2219,definition,
( sQ174_spl
<=> cons(hd(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2222,plain,
( ~ sQ94_spl
| sQ174_spl
| sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f2209,f1193,f632,f2219,f1471]) ).
fof(f2225,plain,
! [X0] :
( ~ sQ171_spl
| ~ ssItem(sK51_skl)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2187,f222]) ).
fof(f2227,plain,
( ~ sQ171_spl
| ~ sQ17_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2225,f572,f620,f2186]) ).
fof(f2231,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK55_skl(nil,X3,X0,X1,X2))
| ssItem(sK54_skl(nil,X3,X0,X1,X2))
| app(app(X3,X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f683,f279]) ).
fof(f2238,definition,
! [X0,X1,X2,X3] :
( sQ176_spl
<=> ( ~ ssItem(sK55_skl(nil,X3,X0,X1,X2))
| ssItem(sK54_skl(nil,X3,X0,X1,X2))
| app(app(X3,X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2241,plain,
( ~ sQ7_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f2231,f2238,f531]) ).
fof(f2316,definition,
! [X0] :
( sQ187_spl
<=> ( lt(X0,hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2317,plain,
! [X0] :
( ~ sQ187_spl
| lt(X0,hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2316]) ).
fof(f2322,plain,
! [X0] :
( ~ sQ187_spl
| lt(X0,hd(nil))
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2317]) ).
fof(f2326,definition,
! [X0] :
( sQ188_spl
<=> ( leq(X0,hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2327,plain,
! [X0] :
( ~ sQ188_spl
| leq(X0,hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2326]) ).
fof(f2332,plain,
! [X0] :
( ~ sQ188_spl
| leq(X0,hd(nil))
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2327]) ).
fof(f2341,definition,
( sQ189_spl
<=> segmentP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2343,plain,
( sQ189_spl
| ~ segmentP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f2341]) ).
fof(f2353,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK55_skl(nil,X0,X1,X2,X3))
| app(app(X0,X3),nil) != X2
| cons(X1,nil) != X3
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,X2,X3)
| memberP(X0,sK54_skl(nil,X0,X1,X2,X3)) ),
inference(resolution,[status(thm)],[f729,f279]) ).
fof(f2360,definition,
! [X0,X1,X2,X3] :
( sQ192_spl
<=> ( ~ ssItem(sK55_skl(nil,X0,X1,X2,X3))
| app(app(X0,X3),nil) != X2
| cons(X1,nil) != X3
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,X2,X3)
| memberP(X0,sK54_skl(nil,X0,X1,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( ~ sQ7_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f2353,f2360,f531]) ).
fof(f2366,plain,
! [X0] :
( sQ189_spl
| ~ segmentP(X0,sK47_skl)
| ~ segmentP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2343,f315]) ).
fof(f2368,definition,
! [X0] :
( sQ193_spl
<=> ( ~ segmentP(X0,sK47_skl)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2369,plain,
! [X0] :
( ~ sQ193_spl
| ~ segmentP(X0,sK47_skl)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2368]) ).
fof(f2371,plain,
( sQ189_spl
| ~ sQ72_spl
| sQ193_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2366,f531,f2368,f1193,f2341]) ).
fof(f2451,plain,
( ~ sQ187_spl
| ~ ssItem(hd(nil))
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2322,f401]) ).
fof(f2454,plain,
( ~ sQ187_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2451,f2086,f2316]) ).
fof(f2455,definition,
! [X0] :
( sQ204_spl
<=> ( ~ lt(hd(nil),X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2456,plain,
! [X0] :
( ~ sQ204_spl
| ~ lt(hd(nil),X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2455]) ).
fof(f2464,plain,
! [X0] :
( ~ sQ204_spl
| ~ lt(hd(nil),X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2456]) ).
fof(f2465,plain,
! [X0,X1] :
( ~ sQ204_spl
| ~ lt(X1,X0)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2464,f263]) ).
fof(f2466,definition,
! [X0,X1] :
( sQ206_spl
<=> ( ~ lt(X1,X0)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2469,plain,
( ~ sQ204_spl
| ~ sQ158_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2465,f2466,f2086,f2455]) ).
fof(f2505,plain,
! [X0,X1] :
( ~ sQ193_spl
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2369,f315]) ).
fof(f2509,definition,
! [X0,X1] :
( sQ207_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2512,plain,
( ~ sQ193_spl
| ~ sQ7_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2505,f2509,f531,f2368]) ).
fof(f2518,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK54_skl(X3,nil,X0,X1,X2))
| ssItem(sK55_skl(X3,nil,X0,X1,X2))
| app(app(nil,X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f730,f279]) ).
fof(f2526,definition,
! [X0,X1,X2,X3] :
( sQ209_spl
<=> ( ~ ssItem(sK54_skl(X3,nil,X0,X1,X2))
| ssItem(sK55_skl(X3,nil,X0,X1,X2))
| app(app(nil,X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2529,plain,
( ~ sQ7_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2518,f2526,f531]) ).
fof(f2535,definition,
! [X0,X1,X2] :
( sQ210_spl
<=> ( ~ segmentP(X1,sK47_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(app(X0,X1),X2)
| ~ ssList(app(app(X0,X1),X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2540,definition,
! [X0,X1] :
( sQ211_spl
<=> ( ~ segmentP(X1,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2593,definition,
( sQ216_spl
<=> ssList(tl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2595,plain,
( sQ216_spl
| ~ ssList(tl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f2593]) ).
fof(f2600,definition,
( sQ218_spl
<=> ssList(sK43_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2602,plain,
( sQ218_spl
| ~ ssList(sK43_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f2600]) ).
fof(f2603,definition,
( sQ219_spl
<=> ssItem(sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2605,plain,
( sQ219_spl
| ~ ssItem(sK44_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f2603]) ).
fof(f2615,plain,
( sQ216_spl
| ~ sQ94_spl
| ~ ssList(nil) ),
inference(forward_demodulation,[status(thm)],[f1472,f2595]) ).
fof(f2616,plain,
( sQ216_spl
| ~ sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2615,f223]) ).
fof(f2617,plain,
( sQ216_spl
| ~ sQ94_spl ),
inference(contradiction_clause,[status(thm)],[f2616]) ).
fof(f2645,definition,
! [X0,X1,X2] :
( sQ223_spl
<=> ( nil != app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2))))
| ~ ssList(app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2)))))
| ~ memberP(app(app(X1,sK47_skl),X2),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(X1,sK47_skl),X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2))))) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2652,plain,
( sQ218_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2602,f231]) ).
fof(f2653,plain,
( sQ218_spl
| sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f2652,f1193,f632,f2600]) ).
fof(f2752,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| rearsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f130,f249]) ).
fof(f2759,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(X0)
| rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f130,f389]) ).
fof(f2760,plain,
! [X0,X1] :
( nil != X1
| nil != X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X1)
| rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f130,f387]) ).
fof(f2779,definition,
! [X0] :
( sQ237_spl
<=> ( ~ ssList(X0)
| rearsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2782,plain,
( ~ sQ7_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2752,f2779,f531]) ).
fof(f2790,definition,
! [X0] :
( sQ238_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2793,plain,
( ~ sQ7_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2759,f2790,f531]) ).
fof(f2794,definition,
! [X0] :
( sQ239_spl
<=> ( nil != X0
| ~ ssList(X0)
| rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2797,plain,
( sQ52_spl
| sQ239_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2760,f531,f2794,f965]) ).
fof(f2827,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(f2828,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(f2837,definition,
! [X0] :
( sQ241_spl
<=> ( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2840,plain,
( sQ241_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2827,f531,f2837]) ).
fof(f2841,definition,
! [X0] :
( sQ242_spl
<=> ( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2844,plain,
( sQ242_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2828,f531,f2841]) ).
fof(f2865,definition,
! [X0,X1] :
( sQ243_spl
<=> ( nil != app(app(X0,sK47_skl),X1)
| ~ ssList(app(app(X0,sK47_skl),X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,sK47_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2875,definition,
! [X0,X1] :
( sQ244_spl
<=> ( nil != cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil)
| ~ ssList(cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil))
| ~ singletonP(app(app(X0,sK47_skl),X1))
| ~ ssList(app(app(X0,sK47_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2886,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(X0)
| frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f124,f249]) ).
fof(f2893,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f124,f389]) ).
fof(f2894,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f124,f387]) ).
fof(f2916,definition,
! [X0] :
( sQ245_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2919,plain,
( ~ sQ7_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f2886,f2916,f531]) ).
fof(f2927,definition,
! [X0] :
( sQ246_spl
<=> ( ~ ssList(X0)
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2930,plain,
( ~ sQ7_spl
| sQ246_spl ),
inference(split_clause,[status(thm)],[f2893,f2927,f531]) ).
fof(f2931,definition,
! [X0] :
( sQ247_spl
<=> ( nil != X0
| ~ ssList(X0)
| frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2934,plain,
( sQ52_spl
| sQ247_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2894,f531,f2931,f965]) ).
fof(f2966,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(f2967,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(f2978,definition,
! [X0] :
( sQ249_spl
<=> ( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2981,plain,
( sQ249_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2966,f531,f2978]) ).
fof(f2982,definition,
! [X0] :
( sQ250_spl
<=> ( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2985,plain,
( sQ250_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f2967,f531,f2982]) ).
fof(f3016,plain,
! [X0,X1,X2] :
( memberP(nil,X1)
| X1 = sK4_skl(app(X0,cons(X1,X2)))
| ~ ssList(nil)
| ~ ssItem(sK4_skl(app(X0,cons(X1,X2))))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f503,f275]) ).
fof(f3018,definition,
! [X0,X1,X2] :
( sQ251_spl
<=> ( memberP(nil,X1)
| X1 = sK4_skl(app(X0,cons(X1,X2)))
| ~ ssItem(sK4_skl(app(X0,cons(X1,X2))))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3021,plain,
( ~ sQ7_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f3016,f3018,f531]) ).
fof(f3031,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f245]) ).
fof(f3032,plain,
! [X0,X1] :
( nil != app(X1,X0)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3031,f299]) ).
fof(f3034,plain,
( sQ95_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3032,f531,f1490]) ).
fof(f3039,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil)) ),
inference(resolution,[status(thm)],[f118,f380]) ).
fof(f3058,definition,
( sQ254_spl
<=> ssList(app(sK47_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3060,plain,
( sQ254_spl
| ~ ssList(app(sK47_skl,nil)) ),
inference(component_clause,[status(thm)],[f3058]) ).
fof(f3065,definition,
! [X0] :
( sQ256_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3068,plain,
( ~ sQ7_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f3039,f3065,f531]) ).
fof(f3069,definition,
! [X0] :
( sQ257_spl
<=> ( sK47_skl != X0
| singletonP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3070,plain,
! [X0] :
( ~ sQ257_spl
| sK47_skl != X0
| singletonP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3069]) ).
fof(f3124,definition,
! [X0,X1,X2] :
( sQ261_spl
<=> ( nil != app(X2,sK5_skl(X2,app(app(X0,sK47_skl),X1)))
| ~ ssList(app(X2,sK5_skl(X2,app(app(X0,sK47_skl),X1))))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X2,sK5_skl(X2,app(app(X0,sK47_skl),X1))))
| ~ frontsegP(app(app(X0,sK47_skl),X1),X2)
| ~ ssList(X2)
| ~ ssList(app(app(X0,sK47_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3143,plain,
( sQ254_spl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3060,f245]) ).
fof(f3144,plain,
( sQ254_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f3143,f1193,f531,f3058]) ).
fof(f3149,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(f3150,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(f3157,definition,
! [X0] :
( sQ263_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,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3160,plain,
( sQ263_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3149,f531,f3157]) ).
fof(f3161,definition,
! [X0] :
( sQ264_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,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3164,plain,
( sQ264_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3150,f531,f3161]) ).
fof(f3179,plain,
( ~ sQ257_spl
| sK47_skl != nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3070,f280]) ).
fof(f3180,plain,
( ~ sQ257_spl
| ~ sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3179,f531,f632,f3069]) ).
fof(f3309,definition,
! [X0,X1,X2] :
( sQ285_spl
<=> ( nil != app(sK6_skl(X2,app(app(X0,sK47_skl),X1)),X2)
| ~ ssList(app(sK6_skl(X2,app(app(X0,sK47_skl),X1)),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK6_skl(X2,app(app(X0,sK47_skl),X1)),X2))
| ~ rearsegP(app(app(X0,sK47_skl),X1),X2)
| ~ ssList(X2)
| ~ ssList(app(app(X0,sK47_skl),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3381,plain,
! [X0] :
( ~ sQ160_spl
| leq(X0,hd(nil))
| ~ ssItem(hd(nil))
| ~ ssItem(X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2094,f409]) ).
fof(f3382,plain,
! [X0,X1] :
( ~ sQ160_spl
| lt(X1,hd(nil))
| ~ leq(X1,X0)
| ~ ssItem(hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2094,f403]) ).
fof(f3383,plain,
( ~ sQ160_spl
| ~ ssItem(hd(nil))
| ~ lt(hd(nil),sK51_skl)
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2094,f401]) ).
fof(f3384,plain,
! [X0] :
( ~ sQ160_spl
| ~ lt(hd(nil),X0)
| ~ ssItem(X0)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2094,f261]) ).
fof(f3385,plain,
! [X0,X1] :
( ~ sQ160_spl
| lt(X1,hd(nil))
| ~ lt(X1,X0)
| ~ ssItem(hd(nil))
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2094,f263]) ).
fof(f3386,definition,
! [X0] :
( sQ293_spl
<=> ( leq(X0,hd(nil))
| ~ ssItem(X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3389,plain,
( ~ sQ160_spl
| ~ sQ158_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f3381,f3386,f2086,f2093]) ).
fof(f3390,definition,
! [X0,X1] :
( sQ294_spl
<=> ( lt(X1,hd(nil))
| ~ leq(X1,X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3393,plain,
( ~ sQ160_spl
| ~ sQ158_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f3382,f3390,f2086,f2093]) ).
fof(f3394,plain,
( ~ sQ160_spl
| ~ sQ159_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f3383,f2086,f2089,f2093]) ).
fof(f3395,definition,
! [X0] :
( sQ295_spl
<=> ( ~ lt(hd(nil),X0)
| ~ ssItem(X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f3396,plain,
! [X0] :
( ~ sQ295_spl
| ~ lt(hd(nil),X0)
| ~ ssItem(X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3395]) ).
fof(f3398,plain,
( ~ sQ160_spl
| ~ sQ158_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f3384,f3395,f2086,f2093]) ).
fof(f3399,definition,
! [X0,X1] :
( sQ296_spl
<=> ( lt(X1,hd(nil))
| ~ lt(X1,X0)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f3402,plain,
( ~ sQ160_spl
| ~ sQ158_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f3385,f3399,f2086,f2093]) ).
fof(f3404,plain,
! [X0] :
( ~ sQ295_spl
| ~ lt(hd(nil),X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3396]) ).
fof(f3479,plain,
! [X0,X1,X2,X3] :
( ~ sQ163_spl
| ssItem(sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f2122,f737]) ).
fof(f3480,plain,
! [X0,X1,X2,X3] :
( ~ sQ163_spl
| memberP(X0,sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f2122,f736]) ).
fof(f3481,plain,
! [X0] :
( ~ sQ163_spl
| hd(nil) = X0
| ~ leq(hd(nil),X0)
| ~ ssItem(X0)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2122,f405]) ).
fof(f3482,plain,
! [X0,X1] :
( ~ sQ163_spl
| ~ lt(X1,X0)
| ~ leq(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2122,f403]) ).
fof(f3483,plain,
! [X0,X1] :
( ~ sQ163_spl
| ~ lt(X1,X0)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2122,f263]) ).
fof(f3484,definition,
! [X0,X1,X2,X3] :
( sQ303_spl
<=> ( ssItem(sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3487,plain,
( ~ sQ163_spl
| ~ sQ158_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f3479,f3484,f2086,f2121]) ).
fof(f3488,definition,
! [X0,X1,X2,X3] :
( sQ304_spl
<=> ( memberP(X0,sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3491,plain,
( ~ sQ163_spl
| ~ sQ158_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f3480,f3488,f2086,f2121]) ).
fof(f3492,definition,
! [X0] :
( sQ305_spl
<=> ( hd(nil) = X0
| ~ leq(hd(nil),X0)
| ~ ssItem(X0)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f3495,plain,
( ~ sQ163_spl
| ~ sQ158_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f3481,f3492,f2086,f2121]) ).
fof(f3496,definition,
! [X0,X1] :
( sQ306_spl
<=> ( ~ lt(X1,X0)
| ~ leq(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f3499,plain,
( ~ sQ163_spl
| ~ sQ158_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f3482,f3496,f2086,f2121]) ).
fof(f3500,definition,
! [X0,X1] :
( sQ307_spl
<=> ( ~ lt(X1,X0)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3503,plain,
( ~ sQ163_spl
| ~ sQ158_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f3483,f3500,f2086,f2121]) ).
fof(f3568,plain,
! [X0,X1,X2,X3,X4] :
( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| leq(X1,X0)
| leq(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ totalorderP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f153,f387]) ).
fof(f3597,definition,
! [X0,X1,X2,X3,X4] :
( sQ314_spl
<=> ( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| leq(X1,X0)
| leq(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f3600,plain,
( sQ314_spl
| ~ sQ33_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3568,f531,f807,f3597]) ).
fof(f3603,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f809,f333]) ).
fof(f3604,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f3603]) ).
fof(f3606,plain,
! [X0,X1,X2,X3] :
( ~ sQ164_spl
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| lt(hd(nil),sK54_skl(X0,X1,hd(nil),X2,X3))
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f2127,f735]) ).
fof(f3607,plain,
! [X0,X1,X2,X3] :
( ~ sQ164_spl
| ssItem(sK54_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f2127,f733]) ).
fof(f3608,plain,
! [X0,X1,X2,X3] :
( ~ sQ164_spl
| memberP(X1,sK54_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f2127,f732]) ).
fof(f3609,plain,
! [X0] :
( ~ sQ164_spl
| X0 = hd(nil)
| ~ leq(X0,hd(nil))
| ~ ssItem(hd(nil))
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2127,f405]) ).
fof(f3610,plain,
! [X0,X1] :
( ~ sQ164_spl
| ~ lt(X1,hd(nil))
| ~ leq(X0,X1)
| ~ ssItem(hd(nil))
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2127,f403]) ).
fof(f3611,plain,
! [X0,X1] :
( ~ sQ164_spl
| ~ lt(X1,hd(nil))
| ~ lt(X0,X1)
| ~ ssItem(hd(nil))
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2127,f263]) ).
fof(f3612,definition,
! [X0,X1,X2,X3] :
( sQ315_spl
<=> ( app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(hd(nil),X2,X3)
| lt(hd(nil),sK54_skl(X0,X1,hd(nil),X2,X3))
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f3615,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ315_spl ),
inference(split_clause,[status(thm)],[f3606,f3612,f2086,f2126]) ).
fof(f3616,definition,
! [X0,X1,X2,X3] :
( sQ316_spl
<=> ( ssItem(sK54_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f3619,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ316_spl ),
inference(split_clause,[status(thm)],[f3607,f3616,f2086,f2126]) ).
fof(f3620,definition,
! [X0,X1,X2,X3] :
( sQ317_spl
<=> ( memberP(X1,sK54_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK51_skl,sK55_skl(X0,X1,hd(nil),X2,X3))
| ~ ssItem(sK55_skl(X0,X1,hd(nil),X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f3623,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ317_spl ),
inference(split_clause,[status(thm)],[f3608,f3620,f2086,f2126]) ).
fof(f3624,definition,
! [X0] :
( sQ318_spl
<=> ( X0 = hd(nil)
| ~ leq(X0,hd(nil))
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f3625,plain,
! [X0] :
( ~ sQ318_spl
| X0 = hd(nil)
| ~ leq(X0,hd(nil))
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3624]) ).
fof(f3627,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f3609,f3624,f2086,f2126]) ).
fof(f3628,definition,
! [X0,X1] :
( sQ319_spl
<=> ( ~ lt(X1,hd(nil))
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f3631,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ319_spl ),
inference(split_clause,[status(thm)],[f3610,f3628,f2086,f2126]) ).
fof(f3632,definition,
! [X0,X1] :
( sQ320_spl
<=> ( ~ lt(X1,hd(nil))
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f3635,plain,
( ~ sQ164_spl
| ~ sQ158_spl
| sQ320_spl ),
inference(split_clause,[status(thm)],[f3611,f3632,f2086,f2126]) ).
fof(f3638,plain,
! [X0] :
( ~ sQ318_spl
| X0 = hd(nil)
| ~ leq(X0,hd(nil))
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3625]) ).
fof(f3639,plain,
! [X0] :
( ~ sQ318_spl
| ~ sQ188_spl
| X0 = hd(nil)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3638,f2332]) ).
fof(f3773,plain,
! [X0,X1,X2,X3] :
( ~ sQ318_spl
| ~ sQ188_spl
| ssItem(sK55_skl(X0,X1,sK51_skl,X2,X3))
| app(app(X1,X3),X0) != X2
| cons(sK51_skl,nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,X2,X3)
| sK54_skl(X0,X1,sK51_skl,X2,X3) = hd(nil)
| ~ ssItem(sK54_skl(X0,X1,sK51_skl,X2,X3)) ),
inference(resolution,[status(thm)],[f3639,f737]) ).
fof(f3774,plain,
! [X0,X1,X2,X3] :
( ~ sQ318_spl
| ~ sQ188_spl
| memberP(X0,sK55_skl(X0,X1,sK51_skl,X2,X3))
| app(app(X1,X3),X0) != X2
| cons(sK51_skl,nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,X2,X3)
| sK54_skl(X0,X1,sK51_skl,X2,X3) = hd(nil)
| ~ ssItem(sK54_skl(X0,X1,sK51_skl,X2,X3)) ),
inference(resolution,[status(thm)],[f3639,f736]) ).
fof(f3775,plain,
! [X0,X1,X2] :
( ~ sQ318_spl
| ~ sQ188_spl
| ~ lt(X2,X0)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ lt(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| X0 = hd(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3639,f647]) ).
fof(f3776,plain,
! [X0] :
( ~ sQ318_spl
| ~ sQ188_spl
| sK51_skl = X0
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl)
| X0 = hd(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3639,f405]) ).
fof(f3777,plain,
! [X0,X1] :
( ~ sQ318_spl
| ~ sQ188_spl
| ~ lt(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| X0 = hd(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3639,f403]) ).
fof(f3778,plain,
! [X0,X1] :
( ~ sQ318_spl
| ~ sQ188_spl
| ~ lt(X1,X0)
| ~ lt(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| X0 = hd(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3639,f263]) ).
fof(f3779,definition,
! [X0,X1,X2,X3] :
( sQ327_spl
<=> ( ssItem(sK55_skl(X0,X1,sK51_skl,X2,X3))
| app(app(X1,X3),X0) != X2
| cons(sK51_skl,nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(sK51_skl,X2,X3)
| sK54_skl(X0,X1,sK51_skl,X2,X3) = hd(nil)
| ~ ssItem(sK54_skl(X0,X1,sK51_skl,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f3782,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f3773,f3779,f620,f2326,f3624]) ).
fof(f3783,definition,
! [X0,X1,X2,X3] :
( sQ328_spl
<=> ( memberP(X0,sK55_skl(X0,X1,sK51_skl,X2,X3))
| app(app(X1,X3),X0) != X2
| cons(sK51_skl,nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| sP0_prd(sK51_skl,X2,X3)
| sK54_skl(X0,X1,sK51_skl,X2,X3) = hd(nil)
| ~ ssItem(sK54_skl(X0,X1,sK51_skl,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3786,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f3774,f3783,f620,f2326,f3624]) ).
fof(f3787,definition,
! [X0,X1,X2] :
( sQ329_spl
<=> ( ~ lt(X2,X0)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ lt(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = hd(nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3790,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f3775,f3787,f620,f2326,f3624]) ).
fof(f3791,definition,
! [X0] :
( sQ330_spl
<=> ( sK51_skl = X0
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0)
| X0 = hd(nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3794,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f3776,f3791,f620,f2326,f3624]) ).
fof(f3795,definition,
! [X0,X1] :
( sQ331_spl
<=> ( ~ lt(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = hd(nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f3798,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ331_spl ),
inference(split_clause,[status(thm)],[f3777,f3795,f620,f2326,f3624]) ).
fof(f3799,definition,
! [X0,X1] :
( sQ332_spl
<=> ( ~ lt(X1,X0)
| ~ lt(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = hd(nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f3802,plain,
( ~ sQ318_spl
| ~ sQ188_spl
| ~ sQ17_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f3778,f3799,f620,f2326,f3624]) ).
fof(f4150,plain,
! [X0,X1,X2,X3,X4] :
( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ cyclefreeP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f141,f387]) ).
fof(f4180,definition,
! [X0,X1,X2,X3,X4] :
( sQ380_spl
<=> ( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f4183,plain,
( sQ380_spl
| ~ sQ34_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4150,f531,f811,f4180]) ).
fof(f4186,plain,
( sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f813,f330]) ).
fof(f4187,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f4186]) ).
fof(f4192,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(f4193,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(f4203,definition,
! [X0] :
( sQ381_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,[sQ381_spl])],[split_symbol_definition]) ).
fof(f4206,plain,
( sQ381_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4192,f531,f4203]) ).
fof(f4207,definition,
! [X0] :
( sQ382_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,[sQ382_spl])],[split_symbol_definition]) ).
fof(f4210,plain,
( sQ382_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4193,f531,f4207]) ).
fof(f4325,plain,
! [X0,X1,X2,X3] :
( nil != app(X1,cons(X0,X2))
| nil != cons(X0,X3)
| ~ ssList(cons(X0,X3))
| ~ ssList(app(X1,cons(X0,X2)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ duplicatefreeP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f485,f387]) ).
fof(f4348,definition,
! [X0,X1,X2,X3] :
( sQ395_spl
<=> ( nil != app(X1,cons(X0,X2))
| nil != cons(X0,X3)
| ~ ssList(cons(X0,X3))
| ~ ssList(app(X1,cons(X0,X2)))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f4351,plain,
( sQ395_spl
| ~ sQ105_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4325,f531,f1554,f4348]) ).
fof(f4354,plain,
( sQ105_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1556,f359]) ).
fof(f4355,plain,
sQ105_spl,
inference(contradiction_clause,[status(thm)],[f4354]) ).
fof(f4356,plain,
! [X0,X1,X2,X3] :
( ~ sQ295_spl
| ssItem(sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f3404,f737]) ).
fof(f4357,plain,
! [X0,X1,X2,X3] :
( ~ sQ295_spl
| memberP(X0,sK55_skl(X0,X1,hd(nil),X2,X3))
| app(app(X1,X3),X0) != X2
| cons(hd(nil),nil) != X3
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(hd(nil))
| sP0_prd(hd(nil),X2,X3)
| ~ lt(sK54_skl(X0,X1,hd(nil),X2,X3),sK51_skl)
| ~ ssItem(sK54_skl(X0,X1,hd(nil),X2,X3)) ),
inference(resolution,[status(thm)],[f3404,f736]) ).
fof(f4358,plain,
! [X0,X1,X2] :
( ~ sQ295_spl
| ~ lt(X2,X0)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3404,f647]) ).
fof(f4359,plain,
! [X0] :
( ~ sQ295_spl
| hd(nil) = X0
| ~ leq(hd(nil),X0)
| ~ ssItem(X0)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3404,f405]) ).
fof(f4360,plain,
! [X0,X1] :
( ~ sQ295_spl
| ~ lt(X1,X0)
| ~ leq(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3404,f403]) ).
fof(f4361,plain,
! [X0,X1] :
( ~ sQ295_spl
| ~ lt(X1,X0)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(hd(nil))
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3404,f263]) ).
fof(f4362,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f4356,f3484,f2086,f3395]) ).
fof(f4363,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f4357,f3488,f2086,f3395]) ).
fof(f4364,definition,
! [X0,X1,X2] :
( sQ396_spl
<=> ( ~ lt(X2,X0)
| ~ lt(X1,X2)
| ~ ssItem(X2)
| ~ lt(hd(nil),X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f4367,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f4358,f4364,f2086,f3395]) ).
fof(f4368,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f4359,f3492,f2086,f3395]) ).
fof(f4369,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f4360,f3496,f2086,f3395]) ).
fof(f4370,plain,
( ~ sQ295_spl
| ~ sQ158_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4361,f3500,f2086,f3395]) ).
fof(f4640,plain,
! [X0,X1] :
( sQ189_spl
| ~ segmentP(X1,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f759,f2343]) ).
fof(f4641,plain,
! [X0,X1,X2] :
( ~ sQ193_spl
| ~ segmentP(X1,sK47_skl)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f759,f2369]) ).
fof(f4642,plain,
! [X0,X1,X2] :
( ~ sQ32_spl
| nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f759,f770]) ).
fof(f4658,plain,
! [X0,X1,X2] :
( nil != X2
| ~ ssList(X2)
| ~ segmentP(X2,X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f759,f327]) ).
fof(f4659,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f759,f323]) ).
fof(f4660,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ segmentP(nil,X2)
| ~ ssList(nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f759,f323]) ).
fof(f4673,plain,
! [X0,X1,X2] :
( nil != X2
| ~ ssList(X2)
| ~ segmentP(X1,nil)
| ~ ssList(nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f759,f327]) ).
fof(f4674,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f759,f323]) ).
fof(f4687,definition,
! [X0,X1] :
( sQ447_spl
<=> ( ~ segmentP(X1,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f4690,plain,
( sQ189_spl
| ~ sQ72_spl
| sQ447_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4640,f531,f4687,f1193,f2341]) ).
fof(f4691,definition,
! [X0,X1,X2] :
( sQ448_spl
<=> ( ~ segmentP(X1,sK47_skl)
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4694,plain,
( ~ sQ193_spl
| sQ448_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4641,f531,f4691,f2368]) ).
fof(f4695,definition,
! [X0,X1,X2] :
( sQ449_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4698,plain,
( ~ sQ32_spl
| sQ449_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4642,f531,f4695,f765]) ).
fof(f4699,definition,
! [X0,X1,X2] :
( sQ450_spl
<=> ( nil != X0
| ~ ssList(X0)
| ~ segmentP(X2,sK47_skl)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f4713,definition,
! [X0] :
( sQ451_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f4717,definition,
! [X0,X1,X2] :
( sQ452_spl
<=> ( nil != X2
| ~ ssList(X2)
| ~ segmentP(X2,X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f4720,plain,
( ~ sQ7_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f4658,f4717,f531]) ).
fof(f4721,plain,
( ~ sQ7_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f4659,f4713,f531]) ).
fof(f4722,definition,
! [X0,X1,X2] :
( sQ453_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f4725,plain,
( ~ sQ7_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f4660,f4722,f531]) ).
fof(f4735,definition,
! [X0,X1,X2] :
( sQ454_spl
<=> ( nil != X2
| ~ ssList(X2)
| ~ segmentP(X1,nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f4738,plain,
( ~ sQ7_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f4673,f4735,f531]) ).
fof(f4739,definition,
! [X0,X1,X2] :
( sQ455_spl
<=> ( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f4742,plain,
( ~ sQ7_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f4674,f4739,f531]) ).
fof(f4911,plain,
! [X0,X1] :
( nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f769,f327]) ).
fof(f4913,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f769,f323]) ).
fof(f4926,plain,
! [X0,X1] :
( nil != X0
| ~ ssList(X0)
| ~ segmentP(X1,nil)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f769,f327]) ).
fof(f4927,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f769,f323]) ).
fof(f4942,definition,
! [X0,X1] :
( sQ465_spl
<=> ( nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f4945,plain,
( ~ sQ7_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f4911,f4942,f531]) ).
fof(f4947,definition,
! [X0,X1] :
( sQ466_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f4950,plain,
( ~ sQ7_spl
| sQ466_spl ),
inference(split_clause,[status(thm)],[f4913,f4947,f531]) ).
fof(f4960,definition,
! [X0,X1] :
( sQ467_spl
<=> ( nil != X0
| ~ ssList(X0)
| ~ segmentP(X1,nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f4963,plain,
( ~ sQ7_spl
| sQ467_spl ),
inference(split_clause,[status(thm)],[f4926,f4960,f531]) ).
fof(f4964,definition,
! [X0,X1] :
( sQ468_spl
<=> ( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f4967,plain,
( sQ468_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f4927,f531,f4964]) ).
fof(f5007,definition,
( sQ472_spl
<=> sK51_skl = hd(nil) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f5008,plain,
( ~ sQ472_spl
| sK51_skl = hd(nil) ),
inference(component_clause,[status(thm)],[f5007]) ).
fof(f5011,definition,
( sQ473_spl
<=> lt(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f5012,plain,
( ~ sQ473_spl
| lt(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f5011]) ).
fof(f5013,plain,
( sQ473_spl
| ~ lt(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f5011]) ).
fof(f5016,plain,
( sQ158_spl
| ~ sQ472_spl
| ~ ssItem(sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f5008,f2088]) ).
fof(f5018,plain,
( sQ158_spl
| ~ sQ472_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5016,f620,f5007,f2086]) ).
fof(f5023,plain,
! [X0,X1] :
( sQ473_spl
| ~ lt(X1,sK51_skl)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ lt(sK51_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f5013,f647]) ).
fof(f5025,plain,
! [X0] :
( sQ473_spl
| ~ lt(X0,sK51_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f5013,f403]) ).
fof(f5026,plain,
! [X0] :
( sQ473_spl
| ~ lt(X0,sK51_skl)
| ~ lt(sK51_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f5013,f263]) ).
fof(f5027,definition,
! [X0,X1] :
( sQ475_spl
<=> ( ~ lt(X1,sK51_skl)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f5030,plain,
( sQ473_spl
| sQ475_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5023,f620,f5027,f5011]) ).
fof(f5031,definition,
( sQ476_spl
<=> leq(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f5032,plain,
( ~ sQ476_spl
| leq(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f5031]) ).
fof(f5033,plain,
( sQ476_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f5031]) ).
fof(f5035,definition,
! [X0] :
( sQ477_spl
<=> ( ~ lt(X0,sK51_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f5038,plain,
( sQ473_spl
| sQ477_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5025,f620,f5035,f5011]) ).
fof(f5039,definition,
! [X0] :
( sQ478_spl
<=> ( ~ lt(X0,sK51_skl)
| ~ lt(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f5042,plain,
( sQ473_spl
| sQ478_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5026,f620,f5039,f5011]) ).
fof(f5063,plain,
! [X0,X1,X2] :
( nil != app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| nil = app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| ~ segmentP(X0,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f841,f327]) ).
fof(f5073,definition,
! [X0,X1,X2] :
( sQ481_spl
<=> ( nil != app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| nil = app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| ~ segmentP(X0,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f5076,plain,
( ~ sQ7_spl
| sQ481_spl ),
inference(split_clause,[status(thm)],[f5063,f5073,f531]) ).
fof(f5079,plain,
( sQ476_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f5033,f255]) ).
fof(f5080,plain,
( sQ476_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5079,f620,f5031]) ).
fof(f5081,plain,
( ~ sQ473_spl
| ~ lt(sK51_skl,sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f5012,f649]) ).
fof(f5094,plain,
( ~ sQ473_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5081,f620,f5011]) ).
fof(f5146,plain,
! [X0,X1] :
( sQ159_spl
| ~ lt(X1,sK51_skl)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ lt(hd(nil),X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2091,f647]) ).
fof(f5148,plain,
! [X0] :
( sQ159_spl
| ~ lt(X0,sK51_skl)
| ~ leq(hd(nil),X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(hd(nil)) ),
inference(resolution,[status(thm)],[f2091,f403]) ).
fof(f5150,definition,
! [X0,X1] :
( sQ486_spl
<=> ( ~ lt(X1,sK51_skl)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ lt(hd(nil),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f5153,plain,
( sQ159_spl
| ~ sQ17_spl
| sQ486_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f5146,f2086,f5150,f620,f2089]) ).
fof(f5154,definition,
( sQ487_spl
<=> leq(hd(nil),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f5156,plain,
( sQ487_spl
| ~ leq(hd(nil),sK51_skl) ),
inference(component_clause,[status(thm)],[f5154]) ).
fof(f5158,definition,
! [X0] :
( sQ488_spl
<=> ( ~ lt(X0,sK51_skl)
| ~ leq(hd(nil),X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f5161,plain,
( sQ159_spl
| ~ sQ17_spl
| sQ488_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f5148,f2086,f5158,f620,f2089]) ).
fof(f5169,plain,
! [X0,X1,X2,X3] :
( nil != app(app(X2,X0),X3)
| ~ ssList(app(app(X2,X0),X3))
| segmentP(nil,X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(nil)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f842,f327]) ).
fof(f5179,definition,
! [X0,X1,X2,X3] :
( sQ489_spl
<=> ( nil != app(app(X2,X0),X3)
| ~ ssList(app(app(X2,X0),X3))
| segmentP(nil,X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f5182,plain,
( ~ sQ7_spl
| sQ489_spl ),
inference(split_clause,[status(thm)],[f5169,f5179,f531]) ).
fof(f5188,plain,
! [X0] :
( ~ sQ37_spl
| ~ ssList(nil)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f855,f323]) ).
fof(f5189,plain,
! [X0,X1,X2,X3] :
( ~ sQ37_spl
| ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f855,f759]) ).
fof(f5190,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f855,f315]) ).
fof(f5193,definition,
! [X0] :
( sQ490_spl
<=> ( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f5196,plain,
( ~ sQ37_spl
| ~ sQ7_spl
| sQ490_spl ),
inference(split_clause,[status(thm)],[f5188,f5193,f531,f850]) ).
fof(f5197,definition,
! [X0,X1,X2,X3] :
( sQ491_spl
<=> ( ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f5200,plain,
( ~ sQ37_spl
| ~ sQ7_spl
| sQ491_spl ),
inference(split_clause,[status(thm)],[f5189,f5197,f531,f850]) ).
fof(f5201,definition,
! [X0,X1,X2] :
( sQ492_spl
<=> ( ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f5204,plain,
( ~ sQ37_spl
| ~ sQ7_spl
| sQ492_spl ),
inference(split_clause,[status(thm)],[f5190,f5201,f531,f850]) ).
fof(f5212,plain,
( sQ487_spl
| ~ sQ472_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f5008,f5156]) ).
fof(f5213,plain,
( sQ487_spl
| ~ sQ472_spl
| ~ sQ476_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5212,f5032]) ).
fof(f5214,plain,
( sQ487_spl
| ~ sQ472_spl
| ~ sQ476_spl ),
inference(contradiction_clause,[status(thm)],[f5213]) ).
fof(f5228,plain,
! [X0] :
( ~ sQ92_spl
| ~ sQ39_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f869,f1400]) ).
fof(f5230,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ sQ39_spl
| ~ segmentP(X0,X1)
| ~ ssList(X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f869,f855]) ).
fof(f5231,plain,
! [X0] :
( ~ sQ193_spl
| ~ sQ39_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f869,f2369]) ).
fof(f5232,plain,
! [X0] :
( ~ sQ32_spl
| ~ sQ39_spl
| nil = X0
| ~ ssList(X0)
| ~ ssList(nil)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f869,f770]) ).
fof(f5247,definition,
! [X0] :
( sQ493_spl
<=> ( ~ segmentP(X0,sK47_skl)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f5248,plain,
! [X0] :
( ~ sQ493_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5247]) ).
fof(f5250,plain,
( ~ sQ92_spl
| ~ sQ39_spl
| ~ sQ91_spl
| sQ493_spl ),
inference(split_clause,[status(thm)],[f5228,f5247,f1396,f864,f1399]) ).
fof(f5252,definition,
! [X0,X1] :
( sQ494_spl
<=> ( ~ segmentP(X0,X1)
| ~ ssList(X0)
| nil = X1
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f5255,plain,
( ~ sQ37_spl
| ~ sQ39_spl
| ~ sQ7_spl
| sQ494_spl ),
inference(split_clause,[status(thm)],[f5230,f5252,f531,f864,f850]) ).
fof(f5256,plain,
( ~ sQ193_spl
| ~ sQ39_spl
| ~ sQ7_spl
| sQ493_spl ),
inference(split_clause,[status(thm)],[f5231,f5247,f531,f864,f2368]) ).
fof(f5257,plain,
( ~ sQ32_spl
| ~ sQ39_spl
| ~ sQ7_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f5232,f962,f531,f864,f765]) ).
fof(f5267,plain,
! [X0] :
( ~ sQ493_spl
| ~ segmentP(X0,sK47_skl)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5248]) ).
fof(f5276,plain,
! [X0] :
( ~ sQ476_spl
| leq(X0,sK51_skl)
| ~ leq(X0,sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f253,f5032]) ).
fof(f5285,definition,
! [X0] :
( sQ495_spl
<=> ( leq(X0,sK51_skl)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f5288,plain,
( ~ sQ476_spl
| ~ sQ17_spl
| sQ495_spl ),
inference(split_clause,[status(thm)],[f5276,f5285,f620,f5031]) ).
fof(f5296,plain,
( ~ sQ476_spl
| sK51_skl = sK51_skl
| ~ leq(sK51_skl,sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f251,f5032]) ).
fof(f5301,plain,
( sQ78_spl
| ~ sQ476_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f5296,f620,f5031,f1269]) ).
fof(f5346,definition,
! [X0] :
( sQ497_spl
<=> ( ~ segmentP(X0,nil)
| sK47_skl = X0
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f5347,plain,
! [X0] :
( ~ sQ497_spl
| ~ segmentP(X0,nil)
| sK47_skl = X0
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5346]) ).
fof(f5350,definition,
! [X0] :
( sQ498_spl
<=> ( ~ segmentP(sK47_skl,X0)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f5351,plain,
! [X0] :
( ~ sQ498_spl
| ~ segmentP(sK47_skl,X0)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5350]) ).
fof(f5362,definition,
! [X0] :
( sQ501_spl
<=> ( segmentP(X0,sK47_skl)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f5363,plain,
! [X0] :
( ~ sQ501_spl
| segmentP(X0,sK47_skl)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5362]) ).
fof(f5366,definition,
( sQ502_spl
<=> segmentP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f5367,plain,
( ~ sQ502_spl
| segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5366]) ).
fof(f5368,plain,
( sQ502_spl
| ~ segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5366]) ).
fof(f5370,plain,
! [X0] :
( ~ sQ501_spl
| segmentP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5363,f323]) ).
fof(f5373,plain,
! [X0] :
( ~ sQ498_spl
| ~ segmentP(sK47_skl,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5351,f323]) ).
fof(f5374,plain,
! [X0] :
( ~ sQ497_spl
| sK47_skl = X0
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5347,f323]) ).
fof(f5385,plain,
( sQ502_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5368,f323]) ).
fof(f5389,plain,
( sQ502_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5385,f421]) ).
fof(f5390,plain,
sQ502_spl,
inference(contradiction_clause,[status(thm)],[f5389]) ).
fof(f5391,plain,
! [X0] :
( ~ sQ502_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5367,f769]) ).
fof(f5392,plain,
! [X0] :
( ~ sQ502_spl
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = sK47_skl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5367,f769]) ).
fof(f5393,plain,
! [X0,X1] :
( ~ sQ502_spl
| ~ segmentP(X1,sK47_skl)
| ~ ssList(sK47_skl)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5367,f759]) ).
fof(f5394,plain,
! [X0,X1] :
( ~ sQ502_spl
| ~ segmentP(nil,X1)
| ~ ssList(nil)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5367,f759]) ).
fof(f5395,plain,
! [X0] :
( ~ sQ502_spl
| segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5367,f315]) ).
fof(f5396,plain,
( ~ sQ502_spl
| nil = sK47_skl
| ~ segmentP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5367,f317]) ).
fof(f5397,definition,
! [X0] :
( sQ503_spl
<=> ( ~ segmentP(X0,sK47_skl)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f5400,plain,
( ~ sQ502_spl
| ~ sQ72_spl
| sQ503_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5391,f531,f5397,f1193,f5366]) ).
fof(f5401,definition,
! [X0] :
( sQ504_spl
<=> ( ~ segmentP(nil,X0)
| X0 = sK47_skl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f5404,plain,
( ~ sQ502_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ504_spl ),
inference(split_clause,[status(thm)],[f5392,f5401,f1193,f531,f5366]) ).
fof(f5405,definition,
! [X0,X1] :
( sQ505_spl
<=> ( ~ segmentP(X1,sK47_skl)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f5408,plain,
( ~ sQ502_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f5393,f5405,f531,f1193,f5366]) ).
fof(f5409,definition,
! [X0,X1] :
( sQ506_spl
<=> ( ~ segmentP(nil,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f5412,plain,
( ~ sQ502_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ506_spl ),
inference(split_clause,[status(thm)],[f5394,f5409,f1193,f531,f5366]) ).
fof(f5413,definition,
! [X0] :
( sQ507_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f5416,plain,
( ~ sQ502_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f5395,f5413,f1193,f531,f5366]) ).
fof(f5417,plain,
( ~ sQ502_spl
| sQ20_spl
| ~ sQ189_spl
| ~ sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5396,f531,f1193,f2341,f632,f5366]) ).
fof(f5436,plain,
( sQ219_spl
| nil = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f232,f2605]) ).
fof(f5438,plain,
( sQ219_spl
| sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5436,f1193,f632,f2603]) ).
fof(f5492,plain,
( ~ sQ32_spl
| ~ sQ501_spl
| nil = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5370,f770]) ).
fof(f5505,plain,
( ~ sQ32_spl
| ~ sQ501_spl
| sQ20_spl
| ~ sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5492,f531,f1193,f632,f5362,f765]) ).
fof(f5506,definition,
( sQ509_spl
<=> segmentP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f5507,plain,
( ~ sQ509_spl
| segmentP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f5506]) ).
fof(f5508,plain,
( sQ509_spl
| ~ segmentP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f5506]) ).
fof(f5519,definition,
! [X0] :
( sQ512_spl
<=> ( segmentP(X0,sK47_skl)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f5549,plain,
( sQ509_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5508,f319]) ).
fof(f5559,plain,
( sQ509_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5549,f421]) ).
fof(f5560,plain,
sQ509_spl,
inference(contradiction_clause,[status(thm)],[f5559]) ).
fof(f5561,plain,
( ~ sQ509_spl
| ~ ssList(sK47_skl)
| sK47_skl = sK47_skl
| ~ segmentP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5507,f769]) ).
fof(f5562,plain,
! [X0] :
( ~ sQ509_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| sK47_skl = X0
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5507,f769]) ).
fof(f5565,plain,
! [X0] :
( ~ sQ509_spl
| ~ ssList(sK47_skl)
| segmentP(X0,sK47_skl)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5507,f759]) ).
fof(f5566,plain,
! [X0,X1] :
( ~ sQ509_spl
| ~ segmentP(X1,sK47_skl)
| ~ ssList(sK47_skl)
| segmentP(X0,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5507,f759]) ).
fof(f5568,plain,
! [X0,X1] :
( ~ sQ509_spl
| ~ segmentP(sK47_skl,X1)
| ~ ssList(sK47_skl)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5507,f759]) ).
fof(f5571,plain,
( sQ144_spl
| ~ sQ509_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5561,f1193,f5506,f1859]) ).
fof(f5572,definition,
! [X0] :
( sQ519_spl
<=> ( ~ segmentP(X0,sK47_skl)
| sK47_skl = X0
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f5575,plain,
( ~ sQ509_spl
| sQ519_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5562,f1193,f5572,f5506]) ).
fof(f5578,plain,
( ~ sQ509_spl
| ~ sQ72_spl
| sQ512_spl ),
inference(split_clause,[status(thm)],[f5565,f5519,f1193,f5506]) ).
fof(f5579,definition,
! [X0,X1] :
( sQ520_spl
<=> ( ~ segmentP(X1,sK47_skl)
| segmentP(X0,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f5582,plain,
( ~ sQ509_spl
| ~ sQ72_spl
| sQ520_spl ),
inference(split_clause,[status(thm)],[f5566,f5579,f1193,f5506]) ).
fof(f5584,definition,
! [X0,X1] :
( sQ521_spl
<=> ( ~ segmentP(sK47_skl,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f5587,plain,
( ~ sQ509_spl
| ~ sQ72_spl
| sQ521_spl ),
inference(split_clause,[status(thm)],[f5568,f5584,f1193,f5506]) ).
fof(f5638,plain,
! [X0,X1] :
( ~ sQ493_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil))
| ~ singletonP(app(app(X0,sK47_skl),X1))
| ~ ssList(app(app(X0,sK47_skl),X1))
| nil != cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil)
| ~ ssList(cons(sK4_skl(app(app(X0,sK47_skl),X1)),nil)) ),
inference(resolution,[status(thm)],[f5267,f502]) ).
fof(f5639,plain,
! [X0,X1,X2] :
( ~ sQ493_spl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK6_skl(X0,app(app(X1,sK47_skl),X2)),X0))
| ~ rearsegP(app(app(X1,sK47_skl),X2),X0)
| ~ ssList(X0)
| ~ ssList(app(app(X1,sK47_skl),X2))
| nil != app(sK6_skl(X0,app(app(X1,sK47_skl),X2)),X0)
| ~ ssList(app(sK6_skl(X0,app(app(X1,sK47_skl),X2)),X0)) ),
inference(resolution,[status(thm)],[f5267,f544]) ).
fof(f5640,plain,
! [X0,X1,X2] :
( ~ sQ493_spl
| ~ memberP(app(app(X1,sK47_skl),X2),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(X1,sK47_skl),X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2)))))
| nil != app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2))))
| ~ ssList(app(sK2_skl(X0,app(app(X1,sK47_skl),X2)),cons(X0,sK3_skl(X0,app(app(X1,sK47_skl),X2))))) ),
inference(resolution,[status(thm)],[f5267,f500]) ).
fof(f5641,plain,
! [X0,X1] :
( ~ sQ493_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(app(app(X0,sK47_skl),X1))
| nil != app(app(X0,sK47_skl),X1)
| ~ ssList(app(app(X0,sK47_skl),X1)) ),
inference(resolution,[status(thm)],[f5267,f501]) ).
fof(f5642,plain,
! [X0,X1,X2] :
( ~ sQ493_spl
| ~ segmentP(X1,sK47_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(X1)
| nil != app(app(X0,X1),X2)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f5267,f321]) ).
fof(f5643,plain,
! [X0,X1,X2] :
( ~ sQ493_spl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(app(X0,sK5_skl(X0,app(app(X1,sK47_skl),X2))))
| ~ frontsegP(app(app(X1,sK47_skl),X2),X0)
| ~ ssList(X0)
| ~ ssList(app(app(X1,sK47_skl),X2))
| nil != app(X0,sK5_skl(X0,app(app(X1,sK47_skl),X2)))
| ~ ssList(app(X0,sK5_skl(X0,app(app(X1,sK47_skl),X2)))) ),
inference(resolution,[status(thm)],[f5267,f517]) ).
fof(f5646,plain,
! [X0,X1,X2] :
( ~ sQ493_spl
| ~ segmentP(X2,sK47_skl)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ segmentP(X0,X1)
| ~ ssList(sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5267,f759]) ).
fof(f5647,plain,
! [X0,X1] :
( ~ sQ493_spl
| ~ segmentP(X1,sK47_skl)
| ~ segmentP(X0,X1)
| ~ ssList(sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5267,f315]) ).
fof(f5648,plain,
( ~ sQ493_spl
| ~ ssList(sK47_skl)
| nil != sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5267,f319]) ).
fof(f5650,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ244_spl ),
inference(split_clause,[status(thm)],[f5638,f2875,f1193,f5247]) ).
fof(f5651,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f5639,f3309,f1193,f5247]) ).
fof(f5652,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f5640,f2645,f1193,f5247]) ).
fof(f5653,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f5641,f2865,f1193,f5247]) ).
fof(f5654,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f5642,f2535,f1193,f5247]) ).
fof(f5655,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f5643,f3124,f1193,f5247]) ).
fof(f5658,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f5646,f4699,f1193,f5247]) ).
fof(f5659,plain,
( ~ sQ493_spl
| ~ sQ72_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f5647,f2540,f1193,f5247]) ).
fof(f5660,plain,
( ~ sQ493_spl
| ~ sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5648,f1193,f632,f5247]) ).
fof(f5685,plain,
( ~ sQ498_spl
| ~ ssList(sK47_skl)
| sK47_skl = nil
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5373,f319]) ).
fof(f5698,plain,
( ~ sQ498_spl
| sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5685,f1193,f632,f5350]) ).
fof(f5702,plain,
( ~ sQ502_spl
| ~ sQ497_spl
| sK47_skl = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5374,f5367]) ).
fof(f5709,plain,
( ~ sQ502_spl
| ~ sQ497_spl
| sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5702,f531,f632,f5346,f5366]) ).
fof(f5711,definition,
! [X0] :
( sQ524_spl
<=> ( nil != X0
| ~ ssList(X0)
| sK47_skl = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f5712,plain,
! [X0] :
( ~ sQ524_spl
| nil != X0
| ~ ssList(X0)
| sK47_skl = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5711]) ).
fof(f5726,plain,
! [X0] :
( ~ sQ524_spl
| nil != X0
| sK47_skl = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5712]) ).
fof(f5786,plain,
( ~ sQ524_spl
| nil != nil
| sK47_skl = nil ),
inference(resolution,[status(thm)],[f5726,f223]) ).
fof(f5802,definition,
( sQ534_spl
<=> sK47_skl = app(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f5803,plain,
( ~ sQ534_spl
| sK47_skl = app(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5802]) ).
fof(f5804,plain,
( sQ534_spl
| sK47_skl != app(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5802]) ).
fof(f5805,definition,
( sQ535_spl
<=> nil = app(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f5807,plain,
( sQ535_spl
| nil != app(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5805]) ).
fof(f5810,plain,
( ~ sQ524_spl
| ~ sQ36_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f5786,f632,f846,f5711]) ).
fof(f5932,plain,
( sQ535_spl
| nil != sK47_skl
| nil != nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5807,f387]) ).
fof(f5933,plain,
( sQ535_spl
| ~ sQ20_spl
| ~ sQ36_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5932,f1193,f531,f846,f632,f5805]) ).
fof(f5936,plain,
( ~ sQ534_spl
| ~ ssList(nil)
| frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5803,f124]) ).
fof(f5937,plain,
( ~ sQ534_spl
| ~ ssList(sK47_skl)
| rearsegP(sK47_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5803,f130]) ).
fof(f5940,plain,
! [X0] :
( ~ sQ534_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5803,f288]) ).
fof(f5941,plain,
! [X0,X1,X2] :
( ~ sQ534_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(sK47_skl,X1))
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5803,f842]) ).
fof(f5942,plain,
! [X0,X1] :
( ~ sQ534_spl
| X0 = app(app(sK47_skl,nil),X1)
| ~ segmentP(X0,app(sK47_skl,X1))
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5803,f841]) ).
fof(f5943,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(sK6_skl(X1,app(sK47_skl,X0)),X1),nil)
| ~ ssList(nil)
| ~ ssList(app(sK6_skl(X1,app(app(sK47_skl,nil),X0)),X1))
| ~ rearsegP(app(app(sK47_skl,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(sK47_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5803,f544]) ).
fof(f5944,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(X1,sK5_skl(X1,app(sK47_skl,X0))),nil)
| ~ ssList(nil)
| ~ ssList(app(X1,sK5_skl(X1,app(app(sK47_skl,nil),X0))))
| ~ frontsegP(app(app(sK47_skl,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(sK47_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5803,f517]) ).
fof(f5945,plain,
! [X0] :
( ~ sQ534_spl
| ~ ssList(sK47_skl)
| segmentP(X0,nil)
| ~ ssList(nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5803,f3031]) ).
fof(f5946,plain,
! [X0] :
( ~ sQ534_spl
| sK47_skl != X0
| ~ ssList(nil)
| frontsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5803,f124]) ).
fof(f5947,plain,
! [X0] :
( ~ sQ534_spl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(cons(sK4_skl(app(sK47_skl,X0)),nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK4_skl(app(app(sK47_skl,nil),X0)),nil))
| ~ singletonP(app(app(sK47_skl,nil),X0))
| ~ ssList(app(app(sK47_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5803,f502]) ).
fof(f5948,plain,
! [X0] :
( ~ sQ534_spl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(sK47_skl,X0),nil)
| ~ ssList(nil)
| ~ ssList(app(app(sK47_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5803,f501]) ).
fof(f5949,plain,
! [X0] :
( ~ sQ534_spl
| sK47_skl != X0
| ~ ssList(sK47_skl)
| rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5803,f130]) ).
fof(f5950,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ memberP(app(app(sK47_skl,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| segmentP(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(sK47_skl,X1)))),nil)
| ~ ssList(nil)
| ~ ssList(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1))))) ),
inference(paramodulation,[status(thm)],[f5803,f500]) ).
fof(f5951,plain,
! [X0,X1] :
( ~ sQ534_spl
| ~ memberP(app(app(sK47_skl,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| segmentP(app(sK2_skl(X0,app(sK47_skl,X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1)))),nil)
| ~ ssList(nil)
| ~ ssList(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1))))) ),
inference(paramodulation,[status(thm)],[f5803,f500]) ).
fof(f5952,plain,
( ~ sQ534_spl
| tl(sK47_skl) = app(tl(sK47_skl),nil)
| nil = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5803,f393]) ).
fof(f5953,plain,
( ~ sQ534_spl
| hd(sK47_skl) = hd(sK47_skl)
| nil = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5803,f391]) ).
fof(f5954,plain,
! [X0] :
( ~ sQ534_spl
| ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5803,f272]) ).
fof(f5955,plain,
! [X0] :
( ~ sQ534_spl
| ~ memberP(sK47_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5803,f271]) ).
fof(f5956,plain,
! [X0] :
( ~ sQ534_spl
| memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5803,f270]) ).
fof(f5957,plain,
! [X0] :
( ~ sQ534_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5803,f307]) ).
fof(f5962,plain,
! [X0,X1] :
( ~ sQ534_spl
| segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5803,f321]) ).
fof(f5963,plain,
! [X0] :
( ~ sQ534_spl
| X0 = sK47_skl
| app(X0,nil) != sK47_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5803,f376]) ).
fof(f5965,plain,
! [X0,X1] :
( ~ sQ534_spl
| app(sK47_skl,X1) != X0
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5803,f137]) ).
fof(f5966,plain,
! [X0] :
( ~ sQ534_spl
| app(sK47_skl,X0) = app(sK47_skl,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f5803,f382]) ).
fof(f5967,plain,
! [X0] :
( ~ sQ534_spl
| X0 = nil
| app(sK47_skl,X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5803,f378]) ).
fof(f5969,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| sQ143_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5936,f1193,f1853,f531,f5802]) ).
fof(f5970,definition,
( sQ549_spl
<=> rearsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f5971,plain,
( ~ sQ549_spl
| rearsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f5970]) ).
fof(f5973,plain,
( ~ sQ534_spl
| sQ549_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5937,f1193,f531,f5970,f5802]) ).
fof(f5976,definition,
! [X0] :
( sQ550_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f5979,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| sQ550_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5940,f1193,f5976,f531,f5802]) ).
fof(f5980,definition,
! [X0,X1,X2] :
( sQ551_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(sK47_skl,X1))
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f5983,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| sQ551_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5941,f531,f5980,f1193,f5802]) ).
fof(f5984,definition,
! [X0,X1] :
( sQ552_spl
<=> ( X0 = app(app(sK47_skl,nil),X1)
| ~ segmentP(X0,app(sK47_skl,X1))
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ552_spl])],[split_symbol_definition]) ).
fof(f5987,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| sQ552_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5942,f531,f5984,f1193,f5802]) ).
fof(f5988,definition,
! [X0,X1] :
( sQ553_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK6_skl(X1,app(sK47_skl,X0)),X1),nil)
| ~ ssList(app(sK6_skl(X1,app(app(sK47_skl,nil),X0)),X1))
| ~ rearsegP(app(app(sK47_skl,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(sK47_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f5991,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ553_spl ),
inference(split_clause,[status(thm)],[f5943,f5988,f531,f1193,f5802]) ).
fof(f5992,definition,
! [X0,X1] :
( sQ554_spl
<=> ( ~ ssList(X0)
| segmentP(app(X1,sK5_skl(X1,app(sK47_skl,X0))),nil)
| ~ ssList(app(X1,sK5_skl(X1,app(app(sK47_skl,nil),X0))))
| ~ frontsegP(app(app(sK47_skl,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(sK47_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f5995,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ554_spl ),
inference(split_clause,[status(thm)],[f5944,f5992,f531,f1193,f5802]) ).
fof(f5996,definition,
! [X0] :
( sQ555_spl
<=> ( segmentP(X0,nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f5999,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ555_spl ),
inference(split_clause,[status(thm)],[f5945,f5996,f531,f1193,f5802]) ).
fof(f6000,definition,
! [X0] :
( sQ556_spl
<=> ( sK47_skl != X0
| frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f6003,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ556_spl ),
inference(split_clause,[status(thm)],[f5946,f6000,f1193,f531,f5802]) ).
fof(f6004,definition,
! [X0] :
( sQ557_spl
<=> ( ~ ssList(X0)
| segmentP(cons(sK4_skl(app(sK47_skl,X0)),nil),nil)
| ~ ssList(cons(sK4_skl(app(app(sK47_skl,nil),X0)),nil))
| ~ singletonP(app(app(sK47_skl,nil),X0))
| ~ ssList(app(app(sK47_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f6007,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ557_spl ),
inference(split_clause,[status(thm)],[f5947,f6004,f531,f1193,f5802]) ).
fof(f6008,definition,
! [X0] :
( sQ558_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK47_skl,X0),nil)
| ~ ssList(app(app(sK47_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f6011,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ558_spl ),
inference(split_clause,[status(thm)],[f5948,f6008,f531,f1193,f5802]) ).
fof(f6012,definition,
! [X0] :
( sQ559_spl
<=> ( sK47_skl != X0
| rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f6015,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ559_spl ),
inference(split_clause,[status(thm)],[f5949,f6012,f531,f1193,f5802]) ).
fof(f6016,definition,
! [X0,X1] :
( sQ560_spl
<=> ( ~ memberP(app(app(sK47_skl,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X1)
| segmentP(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(sK47_skl,X1)))),nil)
| ~ ssList(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1))))) ) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f6019,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ560_spl ),
inference(split_clause,[status(thm)],[f5950,f6016,f531,f1193,f5802]) ).
fof(f6020,definition,
! [X0,X1] :
( sQ561_spl
<=> ( ~ memberP(app(app(sK47_skl,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sK47_skl,nil),X1))
| ~ ssList(X1)
| segmentP(app(sK2_skl(X0,app(sK47_skl,X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1)))),nil)
| ~ ssList(app(sK2_skl(X0,app(app(sK47_skl,nil),X1)),cons(X0,sK3_skl(X0,app(app(sK47_skl,nil),X1))))) ) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f6023,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ561_spl ),
inference(split_clause,[status(thm)],[f5951,f6020,f531,f1193,f5802]) ).
fof(f6024,definition,
( sQ562_spl
<=> tl(sK47_skl) = app(tl(sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f6025,plain,
( ~ sQ562_spl
| tl(sK47_skl) = app(tl(sK47_skl),nil) ),
inference(component_clause,[status(thm)],[f6024]) ).
fof(f6027,plain,
( ~ sQ534_spl
| sQ562_spl
| sQ20_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5952,f1193,f531,f632,f6024,f5802]) ).
fof(f6028,definition,
( sQ563_spl
<=> hd(sK47_skl) = hd(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f6031,plain,
( ~ sQ534_spl
| sQ563_spl
| sQ20_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5953,f1193,f531,f632,f6028,f5802]) ).
fof(f6032,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f5954,f717,f1193,f531,f5802]) ).
fof(f6033,definition,
! [X0] :
( sQ564_spl
<=> ( ~ memberP(sK47_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f6036,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ564_spl ),
inference(split_clause,[status(thm)],[f5955,f6033,f1193,f531,f5802]) ).
fof(f6037,definition,
! [X0] :
( sQ565_spl
<=> ( memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f6040,plain,
( ~ sQ534_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ565_spl ),
inference(split_clause,[status(thm)],[f5956,f6037,f1193,f531,f5802]) ).
fof(f6041,definition,
! [X0] :
( sQ566_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f6044,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| sQ566_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5957,f531,f6041,f1193,f5802]) ).
fof(f6049,definition,
! [X0,X1] :
( sQ567_spl
<=> ( segmentP(app(sK47_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition]) ).
fof(f6052,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| sQ567_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5962,f531,f6049,f1193,f5802]) ).
fof(f6053,definition,
! [X0] :
( sQ568_spl
<=> ( X0 = sK47_skl
| app(X0,nil) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f6056,plain,
( ~ sQ534_spl
| sQ568_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5963,f1193,f531,f6053,f5802]) ).
fof(f6058,definition,
! [X0,X1] :
( sQ569_spl
<=> ( app(sK47_skl,X1) != X0
| ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f6061,plain,
( ~ sQ534_spl
| ~ sQ72_spl
| ~ sQ7_spl
| sQ569_spl ),
inference(split_clause,[status(thm)],[f5965,f6058,f531,f1193,f5802]) ).
fof(f6062,definition,
! [X0] :
( sQ570_spl
<=> ( app(sK47_skl,X0) = app(sK47_skl,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f6065,plain,
( ~ sQ534_spl
| sQ570_spl
| ~ sQ7_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f5966,f1193,f531,f6062,f5802]) ).
fof(f6066,definition,
! [X0] :
( sQ571_spl
<=> ( X0 = nil
| app(sK47_skl,X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f6069,plain,
( ~ sQ534_spl
| sQ571_spl
| ~ sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f5967,f531,f1193,f6066,f5802]) ).
fof(f6071,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| nil = app(tl(sK47_skl),nil) ),
inference(forward_demodulation,[status(thm)],[f1472,f6025]) ).
fof(f6072,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| nil = app(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f1472,f6071]) ).
fof(f6083,plain,
! [X0,X1] :
( ~ singletonP(app(X0,X1))
| ~ ssList(X1)
| frontsegP(cons(sK4_skl(app(X0,X1)),nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4_skl(app(X0,X1)),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f245]) ).
fof(f6084,plain,
! [X0,X1,X2] :
( sK4_skl(app(cons(X0,X1),X2)) = X0
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ),
inference(resolution,[status(thm)],[f6083,f291]) ).
fof(f6085,plain,
! [X0,X1,X2] :
( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ),
inference(resolution,[status(thm)],[f6083,f292]) ).
fof(f6089,definition,
! [X0,X1,X2] :
( sQ573_spl
<=> ( sK4_skl(app(cons(X0,X1),X2)) = X0
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f6092,plain,
( ~ sQ7_spl
| sQ573_spl ),
inference(split_clause,[status(thm)],[f6084,f6089,f531]) ).
fof(f6093,definition,
! [X0,X1,X2] :
( sQ574_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f6096,plain,
( ~ sQ7_spl
| sQ574_spl ),
inference(split_clause,[status(thm)],[f6085,f6093,f531]) ).
fof(f6103,plain,
( ~ sQ549_spl
| nil = sK47_skl
| ~ rearsegP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5971,f303]) ).
fof(f6104,plain,
! [X0] :
( ~ sQ549_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5971,f301]) ).
fof(f6105,definition,
( sQ575_spl
<=> rearsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f6107,plain,
( sQ575_spl
| ~ rearsegP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f6105]) ).
fof(f6108,plain,
( ~ sQ549_spl
| sQ20_spl
| ~ sQ575_spl
| ~ sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6103,f531,f1193,f6105,f632,f5970]) ).
fof(f6109,definition,
! [X0] :
( sQ576_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ576_spl])],[split_symbol_definition]) ).
fof(f6112,plain,
( ~ sQ549_spl
| ~ sQ7_spl
| ~ sQ72_spl
| sQ576_spl ),
inference(split_clause,[status(thm)],[f6104,f6109,f1193,f531,f5970]) ).
fof(f6113,plain,
( sQ575_spl
| nil != sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6107,f313]) ).
fof(f6114,plain,
! [X0] :
( sQ575_spl
| ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6107,f301]) ).
fof(f6115,plain,
( sQ575_spl
| ~ sQ20_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f6113,f1193,f632,f6105]) ).
fof(f6116,definition,
! [X0] :
( sQ577_spl
<=> ( ~ rearsegP(X0,sK47_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f6119,plain,
( sQ575_spl
| ~ sQ72_spl
| sQ577_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6114,f531,f6116,f1193,f6105]) ).
fof(f6122,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6072,f124]) ).
fof(f6123,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6072,f130]) ).
fof(f6127,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f288]) ).
fof(f6128,plain,
! [X0,X1,X2] :
( ~ sQ562_spl
| ~ sQ94_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f842]) ).
fof(f6129,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| X0 = app(app(nil,nil),X1)
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f841]) ).
fof(f6130,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(sK6_skl(X1,app(nil,X0)),X1),nil)
| ~ ssList(nil)
| ~ ssList(app(sK6_skl(X1,app(app(nil,nil),X0)),X1))
| ~ rearsegP(app(app(nil,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f6072,f544]) ).
fof(f6131,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(X1,sK5_skl(X1,app(nil,X0))),nil)
| ~ ssList(nil)
| ~ ssList(app(X1,sK5_skl(X1,app(app(nil,nil),X0))))
| ~ frontsegP(app(app(nil,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f6072,f517]) ).
fof(f6132,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6072,f3031]) ).
fof(f6133,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| nil != X0
| ~ ssList(nil)
| frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6072,f124]) ).
fof(f6134,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(cons(sK4_skl(app(nil,X0)),nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK4_skl(app(app(nil,nil),X0)),nil))
| ~ singletonP(app(app(nil,nil),X0))
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f6072,f502]) ).
fof(f6135,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f6072,f501]) ).
fof(f6136,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| nil != X0
| ~ ssList(nil)
| rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6072,f130]) ).
fof(f6137,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ memberP(app(app(nil,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X1)
| ~ ssList(nil)
| segmentP(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(nil,X1)))),nil)
| ~ ssList(nil)
| ~ ssList(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1))))) ),
inference(paramodulation,[status(thm)],[f6072,f500]) ).
fof(f6138,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ memberP(app(app(nil,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X1)
| ~ ssList(nil)
| segmentP(app(sK2_skl(X0,app(nil,X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1)))),nil)
| ~ ssList(nil)
| ~ ssList(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1))))) ),
inference(paramodulation,[status(thm)],[f6072,f500]) ).
fof(f6141,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f6072,f272]) ).
fof(f6143,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f6072,f270]) ).
fof(f6144,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f307]) ).
fof(f6149,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| segmentP(app(nil,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f321]) ).
fof(f6150,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f376]) ).
fof(f6152,plain,
! [X0,X1] :
( ~ sQ562_spl
| ~ sQ94_spl
| app(nil,X1) != X0
| ~ ssList(X1)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6072,f137]) ).
fof(f6153,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f382]) ).
fof(f6154,plain,
! [X0] :
( ~ sQ562_spl
| ~ sQ94_spl
| X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6072,f378]) ).
fof(f6158,definition,
( sQ578_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ578_spl])],[split_symbol_definition]) ).
fof(f6159,plain,
( ~ sQ578_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f6158]) ).
fof(f6161,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ578_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6122,f531,f6158,f1471,f6024]) ).
fof(f6162,definition,
( sQ579_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f6163,plain,
( ~ sQ579_spl
| rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f6162]) ).
fof(f6165,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ579_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6123,f531,f6162,f1471,f6024]) ).
fof(f6178,definition,
! [X0] :
( sQ583_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ583_spl])],[split_symbol_definition]) ).
fof(f6181,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ583_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6127,f531,f6178,f1471,f6024]) ).
fof(f6182,definition,
! [X0,X1,X2] :
( sQ584_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ584_spl])],[split_symbol_definition]) ).
fof(f6185,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ584_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6128,f531,f6182,f1471,f6024]) ).
fof(f6186,definition,
! [X0,X1] :
( sQ585_spl
<=> ( X0 = app(app(nil,nil),X1)
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f6189,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ585_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6129,f531,f6186,f1471,f6024]) ).
fof(f6190,definition,
! [X0,X1] :
( sQ586_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK6_skl(X1,app(nil,X0)),X1),nil)
| ~ ssList(app(sK6_skl(X1,app(app(nil,nil),X0)),X1))
| ~ rearsegP(app(app(nil,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ586_spl])],[split_symbol_definition]) ).
fof(f6193,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ586_spl ),
inference(split_clause,[status(thm)],[f6130,f6190,f531,f1471,f6024]) ).
fof(f6194,definition,
! [X0,X1] :
( sQ587_spl
<=> ( ~ ssList(X0)
| segmentP(app(X1,sK5_skl(X1,app(nil,X0))),nil)
| ~ ssList(app(X1,sK5_skl(X1,app(app(nil,nil),X0))))
| ~ frontsegP(app(app(nil,nil),X0),X1)
| ~ ssList(X1)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ587_spl])],[split_symbol_definition]) ).
fof(f6197,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ587_spl ),
inference(split_clause,[status(thm)],[f6131,f6194,f531,f1471,f6024]) ).
fof(f6198,definition,
! [X0] :
( sQ588_spl
<=> ( segmentP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ588_spl])],[split_symbol_definition]) ).
fof(f6201,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ588_spl ),
inference(split_clause,[status(thm)],[f6132,f6198,f531,f1471,f6024]) ).
fof(f6202,definition,
! [X0] :
( sQ589_spl
<=> ( nil != X0
| frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f6205,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ589_spl ),
inference(split_clause,[status(thm)],[f6133,f6202,f531,f1471,f6024]) ).
fof(f6206,definition,
! [X0] :
( sQ590_spl
<=> ( ~ ssList(X0)
| segmentP(cons(sK4_skl(app(nil,X0)),nil),nil)
| ~ ssList(cons(sK4_skl(app(app(nil,nil),X0)),nil))
| ~ singletonP(app(app(nil,nil),X0))
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ590_spl])],[split_symbol_definition]) ).
fof(f6209,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ590_spl ),
inference(split_clause,[status(thm)],[f6134,f6206,f531,f1471,f6024]) ).
fof(f6210,definition,
! [X0] :
( sQ591_spl
<=> ( ~ ssList(X0)
| segmentP(app(nil,X0),nil)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f6213,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ591_spl ),
inference(split_clause,[status(thm)],[f6135,f6210,f531,f1471,f6024]) ).
fof(f6214,definition,
! [X0] :
( sQ592_spl
<=> ( nil != X0
| rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f6217,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ592_spl ),
inference(split_clause,[status(thm)],[f6136,f6214,f531,f1471,f6024]) ).
fof(f6218,definition,
! [X0,X1] :
( sQ593_spl
<=> ( ~ memberP(app(app(nil,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X1)
| segmentP(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(nil,X1)))),nil)
| ~ ssList(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1))))) ) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f6221,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ593_spl ),
inference(split_clause,[status(thm)],[f6137,f6218,f531,f1471,f6024]) ).
fof(f6222,definition,
! [X0,X1] :
( sQ594_spl
<=> ( ~ memberP(app(app(nil,nil),X1),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X1)
| segmentP(app(sK2_skl(X0,app(nil,X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1)))),nil)
| ~ ssList(app(sK2_skl(X0,app(app(nil,nil),X1)),cons(X0,sK3_skl(X0,app(app(nil,nil),X1))))) ) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f6225,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ594_spl ),
inference(split_clause,[status(thm)],[f6138,f6222,f531,f1471,f6024]) ).
fof(f6231,definition,
! [X0] :
( sQ596_spl
<=> ( ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f6234,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ596_spl ),
inference(split_clause,[status(thm)],[f6141,f6231,f531,f1471,f6024]) ).
fof(f6236,definition,
! [X0] :
( sQ597_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f6239,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ597_spl ),
inference(split_clause,[status(thm)],[f6143,f6236,f531,f1471,f6024]) ).
fof(f6240,definition,
! [X0] :
( sQ598_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f6243,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ598_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6144,f531,f6240,f1471,f6024]) ).
fof(f6248,definition,
! [X0,X1] :
( sQ599_spl
<=> ( segmentP(app(nil,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f6251,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ599_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6149,f531,f6248,f1471,f6024]) ).
fof(f6252,definition,
! [X0] :
( sQ600_spl
<=> ( X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f6255,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ600_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6150,f531,f6252,f1471,f6024]) ).
fof(f6257,definition,
! [X0,X1] :
( sQ601_spl
<=> ( app(nil,X1) != X0
| ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f6260,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| ~ sQ7_spl
| sQ601_spl ),
inference(split_clause,[status(thm)],[f6152,f6257,f531,f1471,f6024]) ).
fof(f6261,definition,
! [X0] :
( sQ602_spl
<=> ( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f6264,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ602_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6153,f531,f6261,f1471,f6024]) ).
fof(f6265,definition,
! [X0] :
( sQ603_spl
<=> ( X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f6268,plain,
( ~ sQ562_spl
| ~ sQ94_spl
| sQ603_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6154,f531,f6265,f1471,f6024]) ).
fof(f6290,plain,
! [X0] :
( ~ sQ579_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f6163,f301]) ).
fof(f6293,definition,
! [X0] :
( sQ608_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f6296,plain,
( ~ sQ579_spl
| ~ sQ7_spl
| sQ608_spl ),
inference(split_clause,[status(thm)],[f6290,f6293,f531,f6162]) ).
fof(f6298,plain,
! [X0] :
( ~ sQ578_spl
| frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f6159,f282]) ).
fof(f6301,definition,
! [X0] :
( sQ609_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ609_spl])],[split_symbol_definition]) ).
fof(f6304,plain,
( ~ sQ578_spl
| ~ sQ7_spl
| sQ609_spl ),
inference(split_clause,[status(thm)],[f6298,f6301,f531,f6158]) ).
fof(f6335,plain,
( sQ534_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5804,f389]) ).
fof(f6336,plain,
( sQ534_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6335,f421]) ).
fof(f6337,plain,
sQ534_spl,
inference(contradiction_clause,[status(thm)],[f6336]) ).
fof(f6368,plain,
! [X0] :
( nil = sK6_skl(X0,nil)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f550,f298]) ).
fof(f6371,definition,
! [X0] :
( sQ610_spl
<=> ( nil = sK6_skl(X0,nil)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f6374,plain,
( sQ610_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6368,f531,f6371]) ).
fof(f6402,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f438]) ).
fof(f6403,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| segmentP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6402,f679]) ).
fof(f6404,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ189_spl
| ~ sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f6403,f531,f1193,f2341,f468,f457]) ).
fof(f6411,plain,
( ~ sQ0_spl
| segmentP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f906,f6402]) ).
fof(f6414,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ72_spl
| ~ sQ91_spl ),
inference(split_clause,[status(thm)],[f6411,f1396,f1193,f478,f457]) ).
fof(f6415,plain,
$false,
inference(sat_refutation,[status(thm)],[f463,f467,f474,f481,f570,f578,f580,f589,f603,f642,f746,f758,f768,f820,f849,f853,f863,f867,f876,f881,f886,f940,f949,f976,f978,f981,f1019,f1021,f1044,f1092,f1180,f1196,f1247,f1320,f1324,f1359,f1402,f1406,f1424,f1474,f1609,f1714,f1724,f1811,f1818,f1839,f1866,f1888,f1895,f1899,f1909,f1919,f1944,f1953,f1957,f2092,f2096,f2124,f2129,f2158,f2184,f2198,f2222,f2227,f2241,f2363,f2371,f2454,f2469,f2512,f2529,f2617,f2653,f2782,f2793,f2797,f2840,f2844,f2919,f2930,f2934,f2981,f2985,f3021,f3034,f3068,f3144,f3160,f3164,f3180,f3389,f3393,f3394,f3398,f3402,f3487,f3491,f3495,f3499,f3503,f3600,f3604,f3615,f3619,f3623,f3627,f3631,f3635,f3782,f3786,f3790,f3794,f3798,f3802,f4183,f4187,f4206,f4210,f4351,f4355,f4362,f4363,f4367,f4368,f4369,f4370,f4690,f4694,f4698,f4720,f4721,f4725,f4738,f4742,f4945,f4950,f4963,f4967,f5018,f5030,f5038,f5042,f5076,f5080,f5094,f5153,f5161,f5182,f5196,f5200,f5204,f5214,f5250,f5255,f5256,f5257,f5288,f5301,f5390,f5400,f5404,f5408,f5412,f5416,f5417,f5438,f5505,f5560,f5571,f5575,f5578,f5582,f5587,f5650,f5651,f5652,f5653,f5654,f5655,f5658,f5659,f5660,f5698,f5709,f5810,f5933,f5969,f5973,f5979,f5983,f5987,f5991,f5995,f5999,f6003,f6007,f6011,f6015,f6019,f6023,f6027,f6031,f6032,f6036,f6040,f6044,f6052,f6056,f6061,f6065,f6069,f6092,f6096,f6108,f6112,f6115,f6119,f6161,f6165,f6181,f6185,f6189,f6193,f6197,f6201,f6205,f6209,f6213,f6217,f6221,f6225,f6234,f6239,f6243,f6251,f6255,f6260,f6264,f6268,f6296,f6304,f6337,f6374,f6404,f6414]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC109+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:55:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 11.01/1.82 % Refutation found
% 11.01/1.82 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.01/1.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.01/1.85 % Elapsed time: 1.469852 seconds
% 11.01/1.85 % CPU time: 11.227912 seconds
% 11.01/1.85 % Total memory used: 209.199 MB
% 11.01/1.85 % Net memory used: 200.941 MB
%------------------------------------------------------------------------------