%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN917+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 03:18:19 PM UTC 2026
% Result : Theorem 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 151
% Syntax : Number of formulae : 822 ( 1 unt; 150 def)
% Number of atoms : 4311 ( 0 equ)
% Maximal formula atoms : 94 ( 5 avg)
% Number of connectives : 5401 (1912 ~;2214 |; 916 &)
% ( 204 <=>; 72 =>; 0 <=; 83 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 158 ( 157 usr; 139 prp; 0-2 aty)
% Number of functors : 72 ( 72 usr; 71 con; 0-1 aty)
% Number of variables : 1460 (1024 !; 436 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [X] :
( p(X)
=> c )
<=> ( ? [X] : p(X)
=> c ) )
& ( ! [X] :
( c
=> p(X) )
<=> ( c
=> ! [X] : p(X) ) )
& ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ! [X] : c
<=> c )
& ( ? [X] : c
<=> c )
& ( ? [X] :
( c
& p(X) )
<=> ( c
& ? [X] : p(X) ) )
& ( ! [X] :
( c
| p(X) )
<=> ( c
| ! [X] : p(X) ) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ? [X] :
( q(X)
& p(X) )
=> ( ? [X] : q(X)
& ? [X] : p(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( q(X)
| p(X) )
<=> ( ? [X] : q(X)
| ? [X] : p(X) ) )
& ( ( ! [X] : q(X)
| ! [X] : p(X) )
=> ! [X] :
( q(X)
| p(X) ) )
& ( ! [X] :
( q(X)
& p(X) )
<=> ( ! [X] : q(X)
& ! [X] : p(X) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) )
& ( ( ! [X,Y,Z] :
( ( r(Y,Z)
& r(X,Y) )
=> r(X,Z) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [X] :
( p(X)
=> c )
<=> ( ? [X] : p(X)
=> c ) )
& ( ! [X] :
( c
=> p(X) )
<=> ( c
=> ! [X] : p(X) ) )
& ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ! [X] : c
<=> c )
& ( ? [X] : c
<=> c )
& ( ? [X] :
( c
& p(X) )
<=> ( c
& ? [X] : p(X) ) )
& ( ! [X] :
( c
| p(X) )
<=> ( c
| ! [X] : p(X) ) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ? [X] :
( q(X)
& p(X) )
=> ( ? [X] : q(X)
& ? [X] : p(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( q(X)
| p(X) )
<=> ( ? [X] : q(X)
| ? [X] : p(X) ) )
& ( ( ! [X] : q(X)
| ! [X] : p(X) )
=> ! [X] :
( q(X)
| p(X) ) )
& ( ! [X] :
( q(X)
& p(X) )
<=> ( ! [X] : q(X)
& ! [X] : p(X) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ( ! [X] :
( ( g(X)
& f(X) )
=> h(X) )
=> ? [X] :
( ~ g(X)
& f(X) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) )
& ( ( ! [X,Y,Z] :
( ( r(Y,Z)
& r(X,Y) )
=> r(X,Z) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [X] :
( c
| ~ p(X) )
<~> ( c
| ! [X] : ~ p(X) ) )
| ( ! [X] :
( p(X)
| ~ c )
<~> ( ! [X] : p(X)
| ~ c ) )
| ( ? [X] :
( c
| ~ p(X) )
<~> ( c
| ? [X] : ~ p(X) ) )
| ( ? [X] :
( p(X)
| ~ c )
<~> ( ? [X] : p(X)
| ~ c ) )
| ( ! [X] : c
<~> c )
| ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ( ! [X] :
( p(X)
| ~ c )
<~> ( ! [X] : p(X)
| ~ c ) )
| ( ? [X] :
( c
| ~ p(X) )
<~> ( c
| ? [X] : ~ p(X) ) )
| ( ? [X] :
( p(X)
| ~ c )
<~> ( ? [X] : p(X)
| ~ c ) )
| ( ! [X] : c
<~> c )
| ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ( ! [X] :
( c
| ~ p(X) )
<~> ( c
| ! [X] : ~ p(X) ) )
| sP0_prd ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ( ~ c
& ? [X] : p(X) )
| ? [X] :
( ~ c
& p(X) ) )
& ( c
| ! [X] : ~ p(X)
| ! [X] :
( c
| ~ p(X) ) ) )
| sP0_prd ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( ( ~ c
& ? [X] : p(X) )
| ( ~ c
& ? [X] : p(X) ) )
& ( c
| ! [X] : ~ p(X)
| c
| ! [X] : ~ p(X) ) )
| sP0_prd ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ( ( ~ c
& p(sK1_skl) )
| ( ~ c
& p(sK0_skl) ) )
& ( c
| ! [X] : ~ p(X)
| c
| ! [X] : ~ p(X) ) )
| sP0_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( c
| ~ p(X1)
| c
| ~ p(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
( p(sK1_skl)
| p(sK0_skl)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,plain,
( ~ c
| ~ c
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f14,definition,
( sP1_prd
<=> ( ( ? [X] :
( c
| ~ p(X) )
<~> ( c
| ? [X] : ~ p(X) ) )
| ( ? [X] :
( p(X)
| ~ c )
<~> ( ? [X] : p(X)
| ~ c ) )
| ( ! [X] : c
<~> c )
| ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f15,plain,
( sP0_prd
<=> ( ( ! [X] :
( p(X)
| ~ c )
<~> ( ! [X] : p(X)
| ~ c ) )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f4,f14]) ).
fof(f16,definition,
! [X] :
( sP2_prd(X)
<=> ( p(X)
| ~ c ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f17,plain,
( sP0_prd
<=> ( ( ! [X] : sP2_prd(X)
<~> ( ! [X] : p(X)
| ~ c ) )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f15,f16]) ).
fof(f18,plain,
( ( ( ( ( ? [X] : ~ p(X)
& c )
| ! [X] : sP2_prd(X) )
& ( ! [X] : p(X)
| ~ c
| ? [X] : ~ sP2_prd(X) )
& ~ sP1_prd )
| sP0_prd )
& ( ( ( ( ? [X] : ~ p(X)
& c )
| ? [X] : ~ sP2_prd(X) )
& ( ! [X] : p(X)
| ~ c
| ! [X] : sP2_prd(X) ) )
| sP1_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
( ( ( ( ( ~ p(sK5_skl)
& c )
| ! [X] : sP2_prd(X) )
& ( ! [X] : p(X)
| ~ c
| ~ sP2_prd(sK4_skl) )
& ~ sP1_prd )
| sP0_prd )
& ( ( ( ( ~ p(sK3_skl)
& c )
| ~ sP2_prd(sK2_skl) )
& ( ! [X] : p(X)
| ~ c
| ! [X] : sP2_prd(X) ) )
| sP1_prd
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(X,sK4_skl),skolemize(X,sK5_skl)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( p(X1)
| ~ c
| sP2_prd(X0)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
( c
| ~ sP2_prd(sK2_skl)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
( ~ p(sK3_skl)
| ~ sP2_prd(sK2_skl)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
( ~ sP1_prd
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f27,definition,
( sP3_prd
<=> ( ( ? [X] :
( p(X)
| ~ c )
<~> ( ? [X] : p(X)
| ~ c ) )
| ( ! [X] : c
<~> c )
| ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f28,plain,
( sP1_prd
<=> ( ( ? [X] :
( c
| ~ p(X) )
<~> ( c
| ? [X] : ~ p(X) ) )
| sP3_prd ) ),
inference(formula_renaming,[status(thm)],[f14,f27]) ).
fof(f29,definition,
! [X] :
( sP4_prd(X)
<=> ( c
| ~ p(X) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f30,plain,
( sP1_prd
<=> ( ( ? [X] : sP4_prd(X)
<~> ( c
| ? [X] : ~ p(X) ) )
| sP3_prd ) ),
inference(formula_renaming,[status(thm)],[f28,f29]) ).
fof(f31,plain,
( ( ( ( ( ~ c
& ! [X] : p(X) )
| ? [X] : sP4_prd(X) )
& ( c
| ? [X] : ~ p(X)
| ! [X] : ~ sP4_prd(X) )
& ~ sP3_prd )
| sP1_prd )
& ( ( ( ( ~ c
& ! [X] : p(X) )
| ! [X] : ~ sP4_prd(X) )
& ( c
| ? [X] : ~ p(X)
| ? [X] : sP4_prd(X) ) )
| sP3_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
( ( ( ( ( ~ c
& ! [X] : p(X) )
| sP4_prd(sK9_skl) )
& ( c
| ~ p(sK8_skl)
| ! [X] : ~ sP4_prd(X) )
& ~ sP3_prd )
| sP1_prd )
& ( ( ( ( ~ c
& ! [X] : p(X) )
| ! [X] : ~ sP4_prd(X) )
& ( c
| ~ p(sK7_skl)
| sP4_prd(sK6_skl) ) )
| sP3_prd
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(X,sK6_skl),skolemize(X,sK7_skl),skolemize(X,sK8_skl),skolemize(X,sK9_skl)],[f31]) ).
fof(f33,plain,
( c
| ~ p(sK7_skl)
| sP4_prd(sK6_skl)
| sP3_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( p(X1)
| ~ sP4_prd(X0)
| sP3_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
! [X0] :
( ~ c
| ~ sP4_prd(X0)
| sP3_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
( ~ sP3_prd
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f38,plain,
! [X0] :
( p(X0)
| sP4_prd(sK9_skl)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f40,plain,
! [X] :
( ( ( ~ p(X)
& c )
| sP2_prd(X) )
& ( p(X)
| ~ c
| ~ sP2_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
( ! [X] :
( ( ~ p(X)
& c )
| sP2_prd(X) )
& ! [X] :
( p(X)
| ~ c
| ~ sP2_prd(X) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0] :
( p(X0)
| ~ c
| ~ sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( c
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0] :
( ~ p(X0)
| sP2_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,definition,
( sP5_prd
<=> ( ( ! [X] : c
<~> c )
| ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f46,plain,
( sP3_prd
<=> ( ( ? [X] :
( p(X)
| ~ c )
<~> ( ? [X] : p(X)
| ~ c ) )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f27,f45]) ).
fof(f47,definition,
! [X] :
( sP6_prd(X)
<=> ( p(X)
| ~ c ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f48,plain,
( sP3_prd
<=> ( ( ? [X] : sP6_prd(X)
<~> ( ? [X] : p(X)
| ~ c ) )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f46,f47]) ).
fof(f49,plain,
( ( ( ( ( ! [X] : ~ p(X)
& c )
| ? [X] : sP6_prd(X) )
& ( ? [X] : p(X)
| ~ c
| ! [X] : ~ sP6_prd(X) )
& ~ sP5_prd )
| sP3_prd )
& ( ( ( ( ! [X] : ~ p(X)
& c )
| ! [X] : ~ sP6_prd(X) )
& ( ? [X] : p(X)
| ~ c
| ? [X] : sP6_prd(X) ) )
| sP5_prd
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
( ( ( ( ( ! [X] : ~ p(X)
& c )
| sP6_prd(sK13_skl) )
& ( p(sK12_skl)
| ~ c
| ! [X] : ~ sP6_prd(X) )
& ~ sP5_prd )
| sP3_prd )
& ( ( ( ( ! [X] : ~ p(X)
& c )
| ! [X] : ~ sP6_prd(X) )
& ( p(sK11_skl)
| ~ c
| sP6_prd(sK10_skl) ) )
| sP5_prd
| ~ sP3_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(X,sK10_skl),skolemize(X,sK11_skl),skolemize(X,sK12_skl),skolemize(X,sK13_skl)],[f49]) ).
fof(f51,plain,
( p(sK11_skl)
| ~ c
| sP6_prd(sK10_skl)
| sP5_prd
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0] :
( c
| ~ sP6_prd(X0)
| sP5_prd
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( ~ p(X1)
| ~ sP6_prd(X0)
| sP5_prd
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
( ~ sP5_prd
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f57,plain,
! [X0] :
( ~ p(X0)
| sP6_prd(sK13_skl)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f58,plain,
! [X] :
( ( ( ~ c
& p(X) )
| sP4_prd(X) )
& ( c
| ~ p(X)
| ~ sP4_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f59,plain,
( ! [X] :
( ( ~ c
& p(X) )
| sP4_prd(X) )
& ! [X] :
( c
| ~ p(X)
| ~ sP4_prd(X) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0] :
( c
| ~ p(X0)
| ~ sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( p(X0)
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
! [X0] :
( ~ c
| sP4_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,definition,
( sP7_prd
<=> ( ( ? [X] : c
<~> c )
| ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f64,plain,
( sP5_prd
<=> ( ( ! [X] : c
<~> c )
| sP7_prd ) ),
inference(formula_renaming,[status(thm)],[f45,f63]) ).
fof(f65,plain,
( ( ( ( ~ c
| ! [X] : c )
& ( c
| ? [X] : ~ c )
& ~ sP7_prd )
| sP5_prd )
& ( ( ( ~ c
| ? [X] : ~ c )
& ( c
| ! [X] : c ) )
| sP7_prd
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
( c
| c
| sP7_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
( ~ c
| ~ c
| sP7_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sP7_prd
| sP5_prd ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f71,plain,
! [X] :
( ( ( ~ p(X)
& c )
| sP6_prd(X) )
& ( p(X)
| ~ c
| ~ sP6_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f72,plain,
( ! [X] :
( ( ~ p(X)
& c )
| sP6_prd(X) )
& ! [X] :
( p(X)
| ~ c
| ~ sP6_prd(X) ) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0] :
( p(X0)
| ~ c
| ~ sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [X0] :
( c
| sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0] :
( ~ p(X0)
| sP6_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,definition,
( sP8_prd
<=> ( ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f77,plain,
( sP7_prd
<=> ( ( ? [X] : c
<~> c )
| sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f63,f76]) ).
fof(f78,plain,
( ( ( ( ~ c
| ? [X] : c )
& ( c
| ! [X] : ~ c )
& ~ sP8_prd )
| sP7_prd )
& ( ( ( ~ c
| ! [X] : ~ c )
& ( c
| ? [X] : c ) )
| sP8_prd
| ~ sP7_prd ) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
( c
| c
| sP8_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
( ~ c
| ~ c
| sP8_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
( ~ sP8_prd
| sP7_prd ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f84,definition,
( sP9_prd
<=> ( ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f85,plain,
( sP8_prd
<=> ( ( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f76,f84]) ).
fof(f86,definition,
! [X] :
( sP10_prd(X)
<=> ( c
& p(X) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f87,plain,
( sP8_prd
<=> ( ( ? [X] : sP10_prd(X)
<~> ( c
& ? [X] : p(X) ) )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f85,f86]) ).
fof(f88,plain,
( ( ( ( ~ c
| ! [X] : ~ p(X)
| ? [X] : sP10_prd(X) )
& ( ( c
& ? [X] : p(X) )
| ! [X] : ~ sP10_prd(X) )
& ~ sP9_prd )
| sP8_prd )
& ( ( ( ~ c
| ! [X] : ~ p(X)
| ! [X] : ~ sP10_prd(X) )
& ( ( c
& ? [X] : p(X) )
| ? [X] : sP10_prd(X) ) )
| sP9_prd
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
( ( ( ( ~ c
| ! [X] : ~ p(X)
| sP10_prd(sK17_skl) )
& ( ( c
& p(sK16_skl) )
| ! [X] : ~ sP10_prd(X) )
& ~ sP9_prd )
| sP8_prd )
& ( ( ( ~ c
| ! [X] : ~ p(X)
| ! [X] : ~ sP10_prd(X) )
& ( ( c
& p(sK15_skl) )
| sP10_prd(sK14_skl) ) )
| sP9_prd
| ~ sP8_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl]),skolemize(X,sK14_skl),skolemize(X,sK15_skl),skolemize(X,sK16_skl),skolemize(X,sK17_skl)],[f88]) ).
fof(f90,plain,
( p(sK15_skl)
| sP10_prd(sK14_skl)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( c
| sP10_prd(sK14_skl)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1] :
( ~ c
| ~ p(X1)
| ~ sP10_prd(X0)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f93,plain,
( ~ sP9_prd
| sP8_prd ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f97,definition,
( sP11_prd
<=> ( ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f98,plain,
( sP9_prd
<=> ( ( ! [X] :
( c
| p(X) )
<~> ( c
| ! [X] : p(X) ) )
| sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f84,f97]) ).
fof(f99,definition,
! [X] :
( sP12_prd(X)
<=> ( c
| p(X) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f100,plain,
( sP9_prd
<=> ( ( ! [X] : sP12_prd(X)
<~> ( c
| ! [X] : p(X) ) )
| sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f98,f99]) ).
fof(f101,plain,
( ( ( ( ( ~ c
& ? [X] : ~ p(X) )
| ! [X] : sP12_prd(X) )
& ( c
| ! [X] : p(X)
| ? [X] : ~ sP12_prd(X) )
& ~ sP11_prd )
| sP9_prd )
& ( ( ( ( ~ c
& ? [X] : ~ p(X) )
| ? [X] : ~ sP12_prd(X) )
& ( c
| ! [X] : p(X)
| ! [X] : sP12_prd(X) ) )
| sP11_prd
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
( ( ( ( ( ~ c
& ~ p(sK21_skl) )
| ! [X] : sP12_prd(X) )
& ( c
| ! [X] : p(X)
| ~ sP12_prd(sK20_skl) )
& ~ sP11_prd )
| sP9_prd )
& ( ( ( ( ~ c
& ~ p(sK19_skl) )
| ~ sP12_prd(sK18_skl) )
& ( c
| ! [X] : p(X)
| ! [X] : sP12_prd(X) ) )
| sP11_prd
| ~ sP9_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl,sK20_skl,sK21_skl]),skolemize(X,sK18_skl),skolemize(X,sK19_skl),skolemize(X,sK20_skl),skolemize(X,sK21_skl)],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( c
| p(X1)
| sP12_prd(X0)
| sP11_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
( ~ p(sK19_skl)
| ~ sP12_prd(sK18_skl)
| sP11_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
( ~ c
| ~ sP12_prd(sK18_skl)
| sP11_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
( ~ sP11_prd
| sP9_prd ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f110,plain,
! [X] :
( ( ~ c
| ~ p(X)
| sP10_prd(X) )
& ( ( c
& p(X) )
| ~ sP10_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f86]) ).
fof(f111,plain,
( ! [X] :
( ~ c
| ~ p(X)
| sP10_prd(X) )
& ! [X] :
( ( c
& p(X) )
| ~ sP10_prd(X) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0] :
( p(X0)
| ~ sP10_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( c
| ~ sP10_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
! [X0] :
( ~ c
| ~ p(X0)
| sP10_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f115,definition,
( sP13_prd
<=> ( ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f116,plain,
( sP11_prd
<=> ( ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| sP13_prd ) ),
inference(formula_renaming,[status(thm)],[f97,f115]) ).
fof(f117,plain,
( ( ( ( ! [Y] :
( p(Y)
| ! [X] : ~ p(X) )
| ? [Y] : p(Y) )
& ~ sP13_prd )
| sP11_prd )
& ( ( ? [Y] :
( ~ p(Y)
& ? [X] : p(X) )
& ! [Y] : ~ p(Y) )
| sP13_prd
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
( ( ( ( ! [Y] : p(Y)
| ! [X] : ~ p(X)
| ? [Y] : p(Y) )
& ~ sP13_prd )
| sP11_prd )
& ( ( ? [Y] : ~ p(Y)
& ? [X] : p(X)
& ! [Y] : ~ p(Y) )
| sP13_prd
| ~ sP11_prd ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
( ( ( ( ! [Y] : p(Y)
| ! [X] : ~ p(X)
| p(sK24_skl) )
& ~ sP13_prd )
| sP11_prd )
& ( ( ~ p(sK23_skl)
& p(sK22_skl)
& ! [Y] : ~ p(Y) )
| sP13_prd
| ~ sP11_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl]),skolemize(X,sK22_skl),skolemize(Y,sK23_skl),skolemize(Y,sK24_skl)],[f118]) ).
fof(f120,plain,
! [X0] :
( ~ p(X0)
| sP13_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
( p(sK22_skl)
| sP13_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f123,plain,
( ~ sP13_prd
| sP11_prd ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f124,plain,
! [X0,X1] :
( p(X1)
| ~ p(X0)
| p(sK24_skl)
| sP11_prd ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
! [X] :
( ( ( ~ c
& ~ p(X) )
| sP12_prd(X) )
& ( c
| p(X)
| ~ sP12_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f126,plain,
( ! [X] :
( ( ~ c
& ~ p(X) )
| sP12_prd(X) )
& ! [X] :
( c
| p(X)
| ~ sP12_prd(X) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0] :
( c
| p(X0)
| ~ sP12_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [X0] :
( ~ p(X0)
| sP12_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
! [X0] :
( ~ c
| sP12_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f130,definition,
( sP14_prd
<=> ( ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f131,plain,
( sP13_prd
<=> ( ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f115,f130]) ).
fof(f132,plain,
( ( ( ( ? [X] : p(X)
| ? [X] : ~ p(X) )
& ~ sP14_prd )
| sP13_prd )
& ( ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| sP14_prd
| ~ sP13_prd ) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
( ( ( ( p(sK26_skl)
| ~ p(sK25_skl) )
& ~ sP14_prd )
| sP13_prd )
& ( ( ! [X] : ~ p(X)
& ! [X] : p(X) )
| sP14_prd
| ~ sP13_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl]),skolemize(X,sK25_skl),skolemize(X,sK26_skl)],[f132]) ).
fof(f134,plain,
! [X0] :
( p(X0)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ p(X0)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
( ~ sP14_prd
| sP13_prd ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
( p(sK26_skl)
| ~ p(sK25_skl)
| sP13_prd ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,definition,
( sP15_prd
<=> ( ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f139,plain,
( sP14_prd
<=> ( ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| sP15_prd ) ),
inference(formula_renaming,[status(thm)],[f130,f138]) ).
fof(f140,plain,
( ( ( ! [Y] :
( p(Y)
| ? [X] : ~ p(X) )
& ~ sP15_prd )
| sP14_prd )
& ( ? [Y] :
( ~ p(Y)
& ! [X] : p(X) )
| sP15_prd
| ~ sP14_prd ) ),
inference(NNF_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
( ( ( ( ! [Y] : p(Y)
| ? [X] : ~ p(X) )
& ~ sP15_prd )
| sP14_prd )
& ( ( ? [Y] : ~ p(Y)
& ! [X] : p(X) )
| sP15_prd
| ~ sP14_prd ) ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f142,plain,
( ( ( ( ! [Y] : p(Y)
| ~ p(sK28_skl) )
& ~ sP15_prd )
| sP14_prd )
& ( ( ~ p(sK27_skl)
& ! [X] : p(X) )
| sP15_prd
| ~ sP14_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27_skl,sK28_skl]),skolemize(Y,sK27_skl),skolemize(X,sK28_skl)],[f141]) ).
fof(f143,plain,
! [X0] :
( p(X0)
| sP15_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
( ~ p(sK27_skl)
| sP15_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ sP15_prd
| sP14_prd ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [X0] :
( p(X0)
| ~ p(sK28_skl)
| sP14_prd ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f147,definition,
( sP16_prd
<=> ( ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f148,plain,
( sP15_prd
<=> ( ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| sP16_prd ) ),
inference(formula_renaming,[status(thm)],[f138,f147]) ).
fof(f149,plain,
( ( ( ( ( ? [X] : q(X)
& ? [X] : p(X) )
| ! [X] :
( ~ q(X)
| ~ p(X) ) )
& ~ sP16_prd )
| sP15_prd )
& ( ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& ? [X] :
( q(X)
& p(X) ) )
| sP16_prd
| ~ sP15_prd ) ),
inference(NNF_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
( ( ( ( ( q(sK31_skl)
& p(sK30_skl) )
| ! [X] :
( ~ q(X)
| ~ p(X) ) )
& ~ sP16_prd )
| sP15_prd )
& ( ( ( ! [X] : ~ q(X)
| ! [X] : ~ p(X) )
& q(sK29_skl)
& p(sK29_skl) )
| sP16_prd
| ~ sP15_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl]),skolemize(X,sK29_skl),skolemize(X,sK30_skl),skolemize(X,sK31_skl)],[f149]) ).
fof(f151,plain,
( p(sK29_skl)
| sP16_prd
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
( q(sK29_skl)
| sP16_prd
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,plain,
! [X0,X1] :
( ~ q(X1)
| ~ p(X0)
| sP16_prd
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f154,plain,
( ~ sP16_prd
| sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f155,plain,
! [X0] :
( p(sK30_skl)
| ~ q(X0)
| ~ p(X0)
| sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f156,plain,
! [X0] :
( q(sK31_skl)
| ~ q(X0)
| ~ p(X0)
| sP15_prd ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f157,definition,
( sP17_prd
<=> ( ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f158,plain,
( sP16_prd
<=> ( ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f147,f157]) ).
fof(f159,plain,
( ( ( ? [Y] :
( ! [X] : p(X)
| ~ p(Y) )
& ~ sP17_prd )
| sP16_prd )
& ( ! [Y] :
( ? [X] : ~ p(X)
& p(Y) )
| sP17_prd
| ~ sP16_prd ) ),
inference(NNF_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
( ( ( ( ! [X] : p(X)
| ? [Y] : ~ p(Y) )
& ~ sP17_prd )
| sP16_prd )
& ( ( ? [X] : ~ p(X)
& ! [Y] : p(Y) )
| sP17_prd
| ~ sP16_prd ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f161,plain,
( ( ( ( ! [X] : p(X)
| ~ p(sK33_skl) )
& ~ sP17_prd )
| sP16_prd )
& ( ( ~ p(sK32_skl)
& ! [Y] : p(Y) )
| sP17_prd
| ~ sP16_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl,sK33_skl]),skolemize(X,sK32_skl),skolemize(Y,sK33_skl)],[f160]) ).
fof(f162,plain,
! [X0] :
( p(X0)
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ p(sK32_skl)
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f164,plain,
( ~ sP17_prd
| sP16_prd ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f165,plain,
! [X0] :
( p(X0)
| ~ p(sK33_skl)
| sP16_prd ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f166,definition,
( sP18_prd
<=> ( ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f167,plain,
( sP17_prd
<=> ( ( ? [X] :
( q(X)
| p(X) )
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f157,f166]) ).
fof(f168,definition,
! [X] :
( sP19_prd(X)
<=> ( q(X)
| p(X) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f169,plain,
( sP17_prd
<=> ( ( ? [X] : sP19_prd(X)
<~> ( ? [X] : q(X)
| ? [X] : p(X) ) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f167,f168]) ).
fof(f170,plain,
( ( ( ( ( ! [X] : ~ q(X)
& ! [X] : ~ p(X) )
| ? [X] : sP19_prd(X) )
& ( ? [X] : q(X)
| ? [X] : p(X)
| ! [X] : ~ sP19_prd(X) )
& ~ sP18_prd )
| sP17_prd )
& ( ( ( ( ! [X] : ~ q(X)
& ! [X] : ~ p(X) )
| ! [X] : ~ sP19_prd(X) )
& ( ? [X] : q(X)
| ? [X] : p(X)
| ? [X] : sP19_prd(X) ) )
| sP18_prd
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f169]) ).
fof(f171,plain,
( ( ( ( ( ! [X] : ~ q(X)
& ! [X] : ~ p(X) )
| sP19_prd(sK39_skl) )
& ( q(sK38_skl)
| p(sK37_skl)
| ! [X] : ~ sP19_prd(X) )
& ~ sP18_prd )
| sP17_prd )
& ( ( ( ( ! [X] : ~ q(X)
& ! [X] : ~ p(X) )
| ! [X] : ~ sP19_prd(X) )
& ( q(sK36_skl)
| p(sK35_skl)
| sP19_prd(sK34_skl) ) )
| sP18_prd
| ~ sP17_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl,sK39_skl]),skolemize(X,sK34_skl),skolemize(X,sK35_skl),skolemize(X,sK36_skl),skolemize(X,sK37_skl),skolemize(X,sK38_skl),skolemize(X,sK39_skl)],[f170]) ).
fof(f172,plain,
( q(sK36_skl)
| p(sK35_skl)
| sP19_prd(sK34_skl)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0,X1] :
( ~ p(X1)
| ~ sP19_prd(X0)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f174,plain,
! [X0,X1] :
( ~ q(X1)
| ~ sP19_prd(X0)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
( ~ sP18_prd
| sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
! [X0] :
( q(sK38_skl)
| p(sK37_skl)
| ~ sP19_prd(X0)
| sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f177,plain,
! [X0] :
( ~ p(X0)
| sP19_prd(sK39_skl)
| sP17_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f179,definition,
( sP20_prd
<=> ( ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f180,plain,
( sP18_prd
<=> ( ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f166,f179]) ).
fof(f181,plain,
( ( ( ( ! [X] :
( q(X)
| p(X) )
| ( ? [X] : ~ q(X)
& ? [X] : ~ p(X) ) )
& ~ sP20_prd )
| sP18_prd )
& ( ( ? [X] :
( ~ q(X)
& ~ p(X) )
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| sP20_prd
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f180]) ).
fof(f182,plain,
( ( ( ( ! [X] :
( q(X)
| p(X) )
| ( ~ q(sK42_skl)
& ~ p(sK41_skl) ) )
& ~ sP20_prd )
| sP18_prd )
& ( ( ~ q(sK40_skl)
& ~ p(sK40_skl)
& ( ! [X] : q(X)
| ! [X] : p(X) ) )
| sP20_prd
| ~ sP18_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40_skl,sK41_skl,sK42_skl]),skolemize(X,sK40_skl),skolemize(X,sK41_skl),skolemize(X,sK42_skl)],[f181]) ).
fof(f183,plain,
! [X0,X1] :
( q(X1)
| p(X0)
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f184,plain,
( ~ p(sK40_skl)
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ q(sK40_skl)
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f186,plain,
( ~ sP20_prd
| sP18_prd ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f187,plain,
! [X0] :
( q(X0)
| p(X0)
| ~ p(sK41_skl)
| sP18_prd ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f189,plain,
! [X] :
( ( ( ~ q(X)
& ~ p(X) )
| sP19_prd(X) )
& ( q(X)
| p(X)
| ~ sP19_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f168]) ).
fof(f190,plain,
( ! [X] :
( ( ~ q(X)
& ~ p(X) )
| sP19_prd(X) )
& ! [X] :
( q(X)
| p(X)
| ~ sP19_prd(X) ) ),
inference(miniscoping,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0] :
( q(X0)
| p(X0)
| ~ sP19_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
! [X0] :
( ~ p(X0)
| sP19_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f193,plain,
! [X0] :
( ~ q(X0)
| sP19_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f194,definition,
( sP21_prd
<=> ( ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f195,plain,
( sP20_prd
<=> ( ( ! [X] :
( q(X)
& p(X) )
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f179,f194]) ).
fof(f196,definition,
! [X] :
( sP22_prd(X)
<=> ( q(X)
& p(X) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f197,plain,
( sP20_prd
<=> ( ( ! [X] : sP22_prd(X)
<~> ( ! [X] : q(X)
& ! [X] : p(X) ) )
| sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f195,f196]) ).
fof(f198,plain,
( ( ( ( ? [X] : ~ q(X)
| ? [X] : ~ p(X)
| ! [X] : sP22_prd(X) )
& ( ( ! [X] : q(X)
& ! [X] : p(X) )
| ? [X] : ~ sP22_prd(X) )
& ~ sP21_prd )
| sP20_prd )
& ( ( ( ? [X] : ~ q(X)
| ? [X] : ~ p(X)
| ? [X] : ~ sP22_prd(X) )
& ( ( ! [X] : q(X)
& ! [X] : p(X) )
| ! [X] : sP22_prd(X) ) )
| sP21_prd
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f197]) ).
fof(f199,plain,
( ( ( ( ~ q(sK48_skl)
| ~ p(sK47_skl)
| ! [X] : sP22_prd(X) )
& ( ( ! [X] : q(X)
& ! [X] : p(X) )
| ~ sP22_prd(sK46_skl) )
& ~ sP21_prd )
| sP20_prd )
& ( ( ( ~ q(sK45_skl)
| ~ p(sK44_skl)
| ~ sP22_prd(sK43_skl) )
& ( ( ! [X] : q(X)
& ! [X] : p(X) )
| ! [X] : sP22_prd(X) ) )
| sP21_prd
| ~ sP20_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl,sK45_skl,sK46_skl,sK47_skl,sK48_skl]),skolemize(X,sK43_skl),skolemize(X,sK44_skl),skolemize(X,sK45_skl),skolemize(X,sK46_skl),skolemize(X,sK47_skl),skolemize(X,sK48_skl)],[f198]) ).
fof(f200,plain,
! [X0,X1] :
( p(X1)
| sP22_prd(X0)
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f201,plain,
! [X0,X1] :
( q(X1)
| sP22_prd(X0)
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ q(sK45_skl)
| ~ p(sK44_skl)
| ~ sP22_prd(sK43_skl)
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f203,plain,
( ~ sP21_prd
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f204,plain,
! [X0] :
( p(X0)
| ~ sP22_prd(sK46_skl)
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f205,plain,
! [X0] :
( q(X0)
| ~ sP22_prd(sK46_skl)
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f206,plain,
! [X0] :
( ~ q(sK48_skl)
| ~ p(sK47_skl)
| sP22_prd(X0)
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f207,definition,
( sP23_prd
<=> ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f208,plain,
( sP21_prd
<=> ( ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f194,f207]) ).
fof(f209,plain,
( ( ( ? [X] :
! [Y] :
( q(X)
| ~ p(X)
| ( ~ q(X)
& p(Y) ) )
& ~ sP23_prd )
| sP21_prd )
& ( ! [X] :
? [Y] :
( ~ q(X)
& p(X)
& ( q(X)
| ~ p(Y) ) )
| sP23_prd
| ~ sP21_prd ) ),
inference(NNF_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
( ( ( ( ? [X] : q(X)
| ? [X] : ~ p(X)
| ( ? [X] : ~ q(X)
& ! [Y] : p(Y) ) )
& ~ sP23_prd )
| sP21_prd )
& ( ( ! [X] : ~ q(X)
& ! [X] : p(X)
& ( ! [X] : q(X)
| ? [Y] : ~ p(Y) ) )
| sP23_prd
| ~ sP21_prd ) ),
inference(miniscoping,[status(thm)],[f209]) ).
fof(f211,plain,
( ( ( ( q(sK52_skl)
| ~ p(sK51_skl)
| ( ~ q(sK50_skl)
& ! [Y] : p(Y) ) )
& ~ sP23_prd )
| sP21_prd )
& ( ( ! [X] : ~ q(X)
& ! [X] : p(X)
& ( ! [X] : q(X)
| ~ p(sK49_skl) ) )
| sP23_prd
| ~ sP21_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(Y,sK49_skl),skolemize(X,sK50_skl),skolemize(X,sK51_skl),skolemize(X,sK52_skl)],[f210]) ).
fof(f212,plain,
! [X0] :
( q(X0)
| ~ p(sK49_skl)
| sP23_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f213,plain,
! [X0] :
( p(X0)
| sP23_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f214,plain,
! [X0] :
( ~ q(X0)
| sP23_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f215,plain,
( ~ sP23_prd
| sP21_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f217,plain,
( q(sK52_skl)
| ~ p(sK51_skl)
| ~ q(sK50_skl)
| sP21_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f218,plain,
! [X] :
( ( ~ q(X)
| ~ p(X)
| sP22_prd(X) )
& ( ( q(X)
& p(X) )
| ~ sP22_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f196]) ).
fof(f219,plain,
( ! [X] :
( ~ q(X)
| ~ p(X)
| sP22_prd(X) )
& ! [X] :
( ( q(X)
& p(X) )
| ~ sP22_prd(X) ) ),
inference(miniscoping,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0] :
( p(X0)
| ~ sP22_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f221,plain,
! [X0] :
( q(X0)
| ~ sP22_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f222,plain,
! [X0] :
( ~ q(X0)
| ~ p(X0)
| sP22_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f219]) ).
fof(f223,definition,
( sP24_prd
<=> ( ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f224,plain,
( sP23_prd
<=> ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) )
| sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f207,f223]) ).
fof(f225,definition,
( sP25_prd
<=> ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25_prd])],[]) ).
fof(f226,plain,
( sP23_prd
<=> ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& sP25_prd )
| sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f224,f225]) ).
fof(f227,definition,
! [R] :
( sP26_prd(R)
<=> ( g(R)
| ~ h(R)
| ~ f(R) ) ),
introduced(definition,[new_symbols(definition,[sP26_prd])],[]) ).
fof(f228,plain,
( sP23_prd
<=> ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP26_prd(R)
& sP25_prd )
| sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f226,f227]) ).
fof(f229,plain,
( ( ( ( ? [V] :
( ~ h(V)
& g(V)
& f(V) )
| ? [R] : ~ sP26_prd(R)
| ~ sP25_prd )
& ~ sP24_prd )
| sP23_prd )
& ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP26_prd(R)
& sP25_prd )
| sP24_prd
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
( ( ( ( ( ~ h(sK54_skl)
& g(sK54_skl)
& f(sK54_skl) )
| ~ sP26_prd(sK53_skl)
| ~ sP25_prd )
& ~ sP24_prd )
| sP23_prd )
& ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP26_prd(R)
& sP25_prd )
| sP24_prd
| ~ sP23_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl]),skolemize(R,sK53_skl),skolemize(V,sK54_skl)],[f229]) ).
fof(f231,plain,
( sP25_prd
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [X0] :
( sP26_prd(X0)
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f233,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0)
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
( ~ sP24_prd
| sP23_prd ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f238,definition,
( sP27_prd
<=> ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP27_prd])],[]) ).
fof(f239,plain,
( sP24_prd
<=> ( ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y) ) )
| sP27_prd ) ),
inference(formula_renaming,[status(thm)],[f223,f238]) ).
fof(f240,definition,
! [X,Y] :
( sP28_prd(Y,X)
<=> ( r(Y,X)
| ~ r(X,Y) ) ),
introduced(definition,[new_symbols(definition,[sP28_prd])],[]) ).
fof(f241,plain,
( sP24_prd
<=> ( ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] : sP28_prd(Y,X) )
| sP27_prd ) ),
inference(formula_renaming,[status(thm)],[f239,f240]) ).
fof(f242,plain,
( ( ( ( ! [X,Y] :
( r(X,X)
| ~ r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(Y,Z)
& r(X,Y) )
| ? [X,Y] : ~ sP28_prd(Y,X) )
& ~ sP27_prd )
| sP24_prd )
& ( ( ? [X,Y] :
( ~ r(X,X)
& r(X,Y) )
& ! [X,Y,Z] :
( r(X,Z)
| ~ r(Y,Z)
| ~ r(X,Y) )
& ! [X,Y] : sP28_prd(Y,X) )
| sP27_prd
| ~ sP24_prd ) ),
inference(NNF_transformation,[status(thm)],[f241]) ).
fof(f243,plain,
( ( ( ( ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) )
| ? [X,Z] :
( ~ r(X,Z)
& ? [Y] :
( r(Y,Z)
& r(X,Y) ) )
| ? [X,Y] : ~ sP28_prd(Y,X) )
& ~ sP27_prd )
| sP24_prd )
& ( ( ? [X] :
( ~ r(X,X)
& ? [Y] : r(X,Y) )
& ! [X,Z] :
( r(X,Z)
| ! [Y] :
( ~ r(Y,Z)
| ~ r(X,Y) ) )
& ! [X,Y] : sP28_prd(Y,X) )
| sP27_prd
| ~ sP24_prd ) ),
inference(miniscoping,[status(thm)],[f242]) ).
fof(f244,plain,
( ( ( ( ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) )
| ( ~ r(sK59_skl,sK60_skl)
& r(sK61_skl,sK60_skl)
& r(sK59_skl,sK61_skl) )
| ~ sP28_prd(sK58_skl,sK57_skl) )
& ~ sP27_prd )
| sP24_prd )
& ( ( ~ r(sK55_skl,sK55_skl)
& r(sK55_skl,sK56_skl)
& ! [X,Z] :
( r(X,Z)
| ! [Y] :
( ~ r(Y,Z)
| ~ r(X,Y) ) )
& ! [X,Y] : sP28_prd(Y,X) )
| sP27_prd
| ~ sP24_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl,sK57_skl,sK58_skl,sK59_skl,sK60_skl,sK61_skl]),skolemize(X,sK55_skl),skolemize(Y,sK56_skl),skolemize(X,sK57_skl),skolemize(Y,sK58_skl),skolemize(X,sK59_skl),skolemize(Z,sK60_skl),skolemize(Y,sK61_skl)],[f243]) ).
fof(f245,plain,
! [X0,X1] :
( sP28_prd(X0,X1)
| sP27_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [X0,X1,X2] :
( r(X0,X2)
| ~ r(X1,X2)
| ~ r(X0,X1)
| sP27_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f247,plain,
( r(sK55_skl,sK56_skl)
| sP27_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f248,plain,
( ~ r(sK55_skl,sK55_skl)
| sP27_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f249,plain,
( ~ sP27_prd
| sP24_prd ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f253,definition,
( sP29_prd
<=> ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& g(X)
& f(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP29_prd])],[]) ).
fof(f254,plain,
( sP25_prd
<=> ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& sP29_prd ) ),
inference(formula_renaming,[status(thm)],[f225,f253]) ).
fof(f255,plain,
( ( ( ? [Z] :
( ~ h(Z)
& f(Z) )
& ? [W] :
( ~ g(W)
& f(W) ) )
| ~ sP29_prd
| sP25_prd )
& ( ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& sP29_prd )
| ~ sP25_prd ) ),
inference(NNF_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
( ( ( ~ h(sK63_skl)
& f(sK63_skl)
& ~ g(sK62_skl)
& f(sK62_skl) )
| ~ sP29_prd
| sP25_prd )
& ( ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& sP29_prd )
| ~ sP25_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62_skl,sK63_skl]),skolemize(W,sK62_skl),skolemize(Z,sK63_skl)],[f255]) ).
fof(f257,plain,
( sP29_prd
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f258,plain,
! [X0,X1] :
( h(X1)
| ~ f(X1)
| g(X0)
| ~ f(X0)
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f263,plain,
! [R] :
( ( ( ~ g(R)
& h(R)
& f(R) )
| sP26_prd(R) )
& ( g(R)
| ~ h(R)
| ~ f(R)
| ~ sP26_prd(R) ) ),
inference(NNF_transformation,[status(thm)],[f227]) ).
fof(f264,plain,
( ! [R] :
( ( ~ g(R)
& h(R)
& f(R) )
| sP26_prd(R) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R)
| ~ sP26_prd(R) ) ),
inference(miniscoping,[status(thm)],[f263]) ).
fof(f265,plain,
! [X0] :
( g(X0)
| ~ h(X0)
| ~ f(X0)
| ~ sP26_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f269,definition,
( sP30_prd
<=> ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP30_prd])],[]) ).
fof(f270,plain,
( sP27_prd
<=> ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& sP30_prd ) ),
inference(formula_renaming,[status(thm)],[f238,f269]) ).
fof(f271,definition,
! [R] :
( sP31_prd(R)
<=> ( g(R)
| ~ h(R)
| ~ f(R) ) ),
introduced(definition,[new_symbols(definition,[sP31_prd])],[]) ).
fof(f272,plain,
( sP27_prd
<=> ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP31_prd(R)
& sP30_prd ) ),
inference(formula_renaming,[status(thm)],[f270,f271]) ).
fof(f273,plain,
( ( ? [V] :
( ~ h(V)
& g(V)
& f(V) )
| ? [R] : ~ sP31_prd(R)
| ~ sP30_prd
| sP27_prd )
& ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP31_prd(R)
& sP30_prd )
| ~ sP27_prd ) ),
inference(NNF_transformation,[status(thm)],[f272]) ).
fof(f274,plain,
( ( ( ~ h(sK65_skl)
& g(sK65_skl)
& f(sK65_skl) )
| ~ sP31_prd(sK64_skl)
| ~ sP30_prd
| sP27_prd )
& ( ( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] : sP31_prd(R)
& sP30_prd )
| ~ sP27_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl,sK65_skl]),skolemize(R,sK64_skl),skolemize(V,sK65_skl)],[f273]) ).
fof(f275,plain,
( sP30_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0] :
( sP31_prd(X0)
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0)
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f281,plain,
! [X,Y] :
( ( ( ~ r(Y,X)
& r(X,Y) )
| sP28_prd(Y,X) )
& ( r(Y,X)
| ~ r(X,Y)
| ~ sP28_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f240]) ).
fof(f282,plain,
( ! [X,Y] :
( ( ~ r(Y,X)
& r(X,Y) )
| sP28_prd(Y,X) )
& ! [X,Y] :
( r(Y,X)
| ~ r(X,Y)
| ~ sP28_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f281]) ).
fof(f283,plain,
! [X0,X1] :
( r(X0,X1)
| ~ r(X1,X0)
| ~ sP28_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f282]) ).
fof(f286,definition,
! [X] :
( sP32_prd(X)
<=> ( ~ h(X)
& g(X)
& f(X) ) ),
introduced(definition,[new_symbols(definition,[sP32_prd])],[]) ).
fof(f287,plain,
( sP29_prd
<=> ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] : sP32_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f253,f286]) ).
fof(f288,plain,
( ( ( ! [X] :
( g(X)
| ~ f(X) )
& ! [X] : ~ sP32_prd(X) )
| sP29_prd )
& ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] : sP32_prd(X)
| ~ sP29_prd ) ),
inference(NNF_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
( ( ( ! [X] :
( g(X)
| ~ f(X) )
& ! [X] : ~ sP32_prd(X) )
| sP29_prd )
& ( ( ~ g(sK67_skl)
& f(sK67_skl) )
| sP32_prd(sK66_skl)
| ~ sP29_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl,sK67_skl]),skolemize(X,sK66_skl),skolemize(X,sK67_skl)],[f288]) ).
fof(f290,plain,
( f(sK67_skl)
| sP32_prd(sK66_skl)
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
( ~ g(sK67_skl)
| sP32_prd(sK66_skl)
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f294,definition,
! [X] :
( sP33_prd(X)
<=> ( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP33_prd])],[]) ).
fof(f295,plain,
( sP30_prd
<=> ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] : sP33_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f269,f294]) ).
fof(f296,plain,
( ( ( ? [Z] :
( ~ h(Z)
& f(Z) )
& ? [W] :
( ~ g(W)
& f(W) ) )
| ? [X] : ~ sP33_prd(X)
| sP30_prd )
& ( ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] : sP33_prd(X) )
| ~ sP30_prd ) ),
inference(NNF_transformation,[status(thm)],[f295]) ).
fof(f297,plain,
( ( ( ~ h(sK70_skl)
& f(sK70_skl)
& ~ g(sK69_skl)
& f(sK69_skl) )
| ~ sP33_prd(sK68_skl)
| sP30_prd )
& ( ( ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] : sP33_prd(X) )
| ~ sP30_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68_skl,sK69_skl,sK70_skl]),skolemize(X,sK68_skl),skolemize(W,sK69_skl),skolemize(Z,sK70_skl)],[f296]) ).
fof(f298,plain,
! [X0] :
( sP33_prd(X0)
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f299,plain,
! [X0,X1] :
( h(X1)
| ~ f(X1)
| g(X0)
| ~ f(X0)
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f304,plain,
! [R] :
( ( ( ~ g(R)
& h(R)
& f(R) )
| sP31_prd(R) )
& ( g(R)
| ~ h(R)
| ~ f(R)
| ~ sP31_prd(R) ) ),
inference(NNF_transformation,[status(thm)],[f271]) ).
fof(f305,plain,
( ! [R] :
( ( ~ g(R)
& h(R)
& f(R) )
| sP31_prd(R) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R)
| ~ sP31_prd(R) ) ),
inference(miniscoping,[status(thm)],[f304]) ).
fof(f306,plain,
! [X0] :
( g(X0)
| ~ h(X0)
| ~ f(X0)
| ~ sP31_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f305]) ).
fof(f310,plain,
! [X] :
( ( h(X)
| ~ g(X)
| ~ f(X)
| sP32_prd(X) )
& ( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP32_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f286]) ).
fof(f311,plain,
( ! [X] :
( h(X)
| ~ g(X)
| ~ f(X)
| sP32_prd(X) )
& ! [X] :
( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP32_prd(X) ) ),
inference(miniscoping,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( f(X0)
| ~ sP32_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f314,plain,
! [X0] :
( ~ h(X0)
| ~ sP32_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f316,definition,
! [X] :
( sP34_prd(X)
<=> ( ~ h(X)
& g(X)
& f(X) ) ),
introduced(definition,[new_symbols(definition,[sP34_prd])],[]) ).
fof(f317,plain,
! [X] :
( sP33_prd(X)
<=> ( ? [Y] :
( ~ g(Y)
& f(Y) )
| sP34_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f294,f316]) ).
fof(f318,plain,
! [X] :
( ( ( ! [Y] :
( g(Y)
| ~ f(Y) )
& ~ sP34_prd(X) )
| sP33_prd(X) )
& ( ? [Y] :
( ~ g(Y)
& f(Y) )
| sP34_prd(X)
| ~ sP33_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f317]) ).
fof(f319,plain,
( ! [X] :
( ( ! [Y] :
( g(Y)
| ~ f(Y) )
& ~ sP34_prd(X) )
| sP33_prd(X) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| sP34_prd(X)
| ~ sP33_prd(X) ) ),
inference(miniscoping,[status(thm)],[f318]) ).
fof(f320,plain,
( ! [X] :
( ( ! [Y] :
( g(Y)
| ~ f(Y) )
& ~ sP34_prd(X) )
| sP33_prd(X) )
& ! [X] :
( ( ~ g(sK71_skl(X))
& f(sK71_skl(X)) )
| sP34_prd(X)
| ~ sP33_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71_skl]),skolemize(Y,sK71_skl(X))],[f319]) ).
fof(f321,plain,
! [X0] :
( f(sK71_skl(X0))
| sP34_prd(X0)
| ~ sP33_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [X0] :
( ~ g(sK71_skl(X0))
| sP34_prd(X0)
| ~ sP33_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f325,plain,
! [X] :
( ( h(X)
| ~ g(X)
| ~ f(X)
| sP34_prd(X) )
& ( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP34_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f316]) ).
fof(f326,plain,
( ! [X] :
( h(X)
| ~ g(X)
| ~ f(X)
| sP34_prd(X) )
& ! [X] :
( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP34_prd(X) ) ),
inference(miniscoping,[status(thm)],[f325]) ).
fof(f327,plain,
! [X0] :
( f(X0)
| ~ sP34_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f329,plain,
! [X0] :
( ~ h(X0)
| ~ sP34_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f331,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f334,definition,
! [X0] :
( sQ1_spl
<=> ~ p(X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f335,plain,
! [X0] :
( ~ sQ1_spl
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
( sQ2_spl
<=> c ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f331,f334,f337]) ).
fof(f341,definition,
( sQ3_spl
<=> p(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ3_spl
| p(sK0_skl) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ4_spl
<=> p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ4_spl
| p(sK1_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( sQ4_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f331,f341,f344]) ).
fof(f350,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f331,f337]) ).
fof(f351,definition,
( sQ5_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f354,definition,
! [X0] :
( sQ6_spl
<=> sP2_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f355,plain,
! [X0] :
( ~ sQ6_spl
| sP2_prd(X0) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
! [X1] :
( sQ7_spl
<=> p(X1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f358,plain,
! [X0] :
( ~ sQ7_spl
| p(X0) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( sQ7_spl
| ~ sQ2_spl
| sQ6_spl
| sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f331,f351,f354,f337,f357]) ).
fof(f361,definition,
( sQ8_spl
<=> sP2_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ8_spl
| ~ sP2_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( sQ2_spl
| ~ sQ8_spl
| sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f331,f351,f361,f337]) ).
fof(f365,definition,
( sQ9_spl
<=> p(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ9_spl
| p(sK3_skl) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( sQ9_spl
| ~ p(sK3_skl) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f331,f351,f361,f365]) ).
fof(f369,plain,
( ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f331,f351]) ).
fof(f375,definition,
( sQ11_spl
<=> p(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ11_spl
| ~ p(sK5_skl) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f379,definition,
( sQ12_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f382,definition,
( sQ13_spl
<=> sP4_prd(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ13_spl
| sP4_prd(sK6_skl) ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,definition,
( sQ14_spl
<=> p(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( ~ sQ14_spl
| p(sK7_skl) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( sQ14_spl
| ~ p(sK7_skl) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,plain,
( sQ2_spl
| ~ sQ14_spl
| sQ13_spl
| sQ12_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f33,f351,f379,f382,f385,f337]) ).
fof(f389,definition,
! [X0] :
( sQ15_spl
<=> ~ sP4_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f390,plain,
! [X0] :
( ~ sQ15_spl
| ~ sP4_prd(X0) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( sQ7_spl
| sQ15_spl
| sQ12_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f34,f351,f379,f389,f357]) ).
fof(f393,plain,
( ~ sQ2_spl
| sQ15_spl
| sQ12_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f35,f351,f379,f389,f337]) ).
fof(f394,plain,
( ~ sQ12_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f36,f351,f379]) ).
fof(f395,definition,
( sQ16_spl
<=> p(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ16_spl
| ~ p(sK8_skl) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f399,definition,
( sQ17_spl
<=> sP4_prd(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( ~ sQ17_spl
| sP4_prd(sK9_skl) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,plain,
( sQ7_spl
| sQ17_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f38,f351,f399,f357]) ).
fof(f404,definition,
! [X0] :
( sQ18_spl
<=> ( p(X0)
| ~ sP2_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f405,plain,
! [X0] :
( ~ sQ18_spl
| p(X0)
| ~ sP2_prd(X0) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( ~ sQ2_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f42,f404,f337]) ).
fof(f408,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f354,f337]) ).
fof(f409,definition,
( sQ19_spl
<=> sP5_prd ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f412,definition,
( sQ20_spl
<=> sP6_prd(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( ~ sQ20_spl
| sP6_prd(sK10_skl) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,definition,
( sQ21_spl
<=> p(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ21_spl
| p(sK11_skl) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,plain,
( sQ21_spl
| ~ sQ2_spl
| sQ20_spl
| sQ19_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f51,f379,f409,f412,f337,f415]) ).
fof(f419,definition,
! [X0] :
( sQ22_spl
<=> ~ sP6_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f420,plain,
! [X0] :
( ~ sQ22_spl
| ~ sP6_prd(X0) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ2_spl
| sQ22_spl
| sQ19_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f52,f379,f409,f419,f337]) ).
fof(f423,plain,
( sQ1_spl
| sQ22_spl
| sQ19_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f53,f379,f409,f419,f334]) ).
fof(f424,plain,
( ~ sQ19_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f54,f379,f409]) ).
fof(f425,definition,
( sQ23_spl
<=> p(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( ~ sQ23_spl
| p(sK12_skl) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f429,definition,
( sQ24_spl
<=> sP6_prd(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ24_spl
| sP6_prd(sK13_skl) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f433,plain,
( sQ1_spl
| sQ24_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f57,f379,f429,f334]) ).
fof(f434,definition,
! [X0] :
( sQ25_spl
<=> ( ~ p(X0)
| ~ sP4_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f435,plain,
! [X0] :
( ~ sQ25_spl
| ~ p(X0)
| ~ sP4_prd(X0) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ2_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f60,f434,f337]) ).
fof(f438,definition,
! [X0] :
( sQ26_spl
<=> sP4_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f439,plain,
! [X0] :
( ~ sQ26_spl
| sP4_prd(X0) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ2_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f62,f438,f337]) ).
fof(f442,definition,
( sQ27_spl
<=> sP7_prd ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ2_spl
| sQ27_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f66,f409,f442,f337]) ).
fof(f446,plain,
( ~ sQ2_spl
| sQ27_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f67,f409,f442,f337]) ).
fof(f447,plain,
( ~ sQ27_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f68,f409,f442]) ).
fof(f450,definition,
! [X0] :
( sQ28_spl
<=> ( p(X0)
| ~ sP6_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f451,plain,
! [X0] :
( ~ sQ28_spl
| p(X0)
| ~ sP6_prd(X0) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( ~ sQ2_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f73,f450,f337]) ).
fof(f454,definition,
! [X0] :
( sQ29_spl
<=> sP6_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f455,plain,
! [X0] :
( ~ sQ29_spl
| sP6_prd(X0) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ2_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f74,f454,f337]) ).
fof(f458,definition,
( sQ30_spl
<=> sP8_prd ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ2_spl
| sQ30_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f79,f442,f458,f337]) ).
fof(f462,plain,
( ~ sQ2_spl
| sQ30_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f80,f442,f458,f337]) ).
fof(f463,plain,
( ~ sQ30_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f81,f442,f458]) ).
fof(f466,definition,
( sQ31_spl
<=> sP9_prd ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f469,definition,
( sQ32_spl
<=> sP10_prd(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( ~ sQ32_spl
| sP10_prd(sK14_skl) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,definition,
( sQ33_spl
<=> p(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ33_spl
| p(sK15_skl) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,plain,
( sQ33_spl
| sQ32_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f90,f458,f466,f469,f472]) ).
fof(f476,plain,
( sQ2_spl
| sQ32_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f91,f458,f466,f469,f337]) ).
fof(f477,definition,
! [X0] :
( sQ34_spl
<=> ~ sP10_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f478,plain,
! [X0] :
( ~ sQ34_spl
| ~ sP10_prd(X0) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f480,plain,
( ~ sQ2_spl
| sQ1_spl
| sQ34_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f92,f458,f466,f477,f334,f337]) ).
fof(f481,plain,
( ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f93,f458,f466]) ).
fof(f482,definition,
( sQ35_spl
<=> p(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ35_spl
| p(sK16_skl) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f487,definition,
( sQ36_spl
<=> sP10_prd(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( ~ sQ36_spl
| sP10_prd(sK17_skl) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f491,definition,
( sQ37_spl
<=> sP11_prd ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f494,definition,
! [X0] :
( sQ38_spl
<=> sP12_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0] :
( ~ sQ38_spl
| sP12_prd(X0) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ2_spl
| sQ7_spl
| sQ38_spl
| sQ37_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f103,f466,f491,f494,f357,f337]) ).
fof(f498,definition,
( sQ39_spl
<=> sP12_prd(sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ39_spl
| ~ sP12_prd(sK18_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ40_spl
<=> p(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ40_spl
| ~ p(sK19_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ40_spl
| ~ sQ39_spl
| sQ37_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f104,f466,f491,f498,f501]) ).
fof(f505,plain,
( ~ sQ2_spl
| ~ sQ39_spl
| sQ37_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f105,f466,f491,f498,f337]) ).
fof(f506,plain,
( ~ sQ37_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f106,f466,f491]) ).
fof(f507,definition,
( sQ41_spl
<=> sP12_prd(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ41_spl
| ~ sP12_prd(sK20_skl) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f511,definition,
( sQ42_spl
<=> p(sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ42_spl
| ~ p(sK21_skl) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f516,plain,
( sQ2_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f113,f477,f337]) ).
fof(f517,definition,
! [X0] :
( sQ43_spl
<=> ( ~ p(X0)
| sP10_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f518,plain,
! [X0] :
( ~ sQ43_spl
| ~ p(X0)
| sP10_prd(X0) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ sQ2_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f114,f517,f337]) ).
fof(f521,definition,
( sQ44_spl
<=> sP13_prd ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ1_spl
| sQ44_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f120,f491,f521,f334]) ).
fof(f525,definition,
( sQ45_spl
<=> p(sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ45_spl
| p(sK22_skl) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( sQ45_spl
| sQ44_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f121,f491,f521,f525]) ).
fof(f529,definition,
( sQ46_spl
<=> p(sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ46_spl
| ~ p(sK23_skl) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f533,plain,
( ~ sQ44_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f123,f491,f521]) ).
fof(f534,definition,
( sQ47_spl
<=> p(sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ47_spl
| p(sK24_skl) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ7_spl
| sQ1_spl
| sQ47_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f124,f491,f534,f334,f357]) ).
fof(f538,definition,
! [X0] :
( sQ48_spl
<=> ( p(X0)
| ~ sP12_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f539,plain,
! [X0] :
( ~ sQ48_spl
| p(X0)
| ~ sP12_prd(X0) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,plain,
( sQ2_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f127,f538,f337]) ).
fof(f542,plain,
( ~ sQ2_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f129,f494,f337]) ).
fof(f543,definition,
( sQ49_spl
<=> sP14_prd ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ7_spl
| sQ49_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f134,f521,f543,f357]) ).
fof(f547,plain,
( sQ1_spl
| sQ49_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f135,f521,f543,f334]) ).
fof(f548,plain,
( ~ sQ49_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f136,f521,f543]) ).
fof(f549,definition,
( sQ50_spl
<=> p(sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ50_spl
| ~ p(sK25_skl) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,definition,
( sQ51_spl
<=> p(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ51_spl
| p(sK26_skl) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ51_spl
| ~ sQ50_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f137,f521,f549,f552]) ).
fof(f556,definition,
( sQ52_spl
<=> sP15_prd ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ7_spl
| sQ52_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f143,f543,f556,f357]) ).
fof(f560,definition,
( sQ53_spl
<=> p(sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ53_spl
| p(sK27_skl) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f562,plain,
( sQ53_spl
| ~ p(sK27_skl) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( ~ sQ53_spl
| sQ52_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f144,f543,f556,f560]) ).
fof(f564,plain,
( ~ sQ52_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f145,f543,f556]) ).
fof(f565,definition,
( sQ54_spl
<=> p(sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ54_spl
| ~ p(sK28_skl) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,plain,
( sQ7_spl
| ~ sQ54_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f146,f543,f565,f357]) ).
fof(f569,definition,
( sQ55_spl
<=> sP16_prd ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f572,definition,
( sQ56_spl
<=> p(sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( ~ sQ56_spl
| p(sK29_skl) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,plain,
( sQ56_spl
| sQ55_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f151,f556,f569,f572]) ).
fof(f576,definition,
( sQ57_spl
<=> q(sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( ~ sQ57_spl
| q(sK29_skl) ),
inference(component_clause,[status(thm)],[f576]) ).
fof(f579,plain,
( sQ57_spl
| sQ55_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f152,f556,f569,f576]) ).
fof(f580,definition,
! [X1] :
( sQ58_spl
<=> ~ q(X1) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f581,plain,
! [X0] :
( ~ sQ58_spl
| ~ q(X0) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,plain,
( sQ58_spl
| sQ1_spl
| sQ55_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f153,f556,f569,f334,f580]) ).
fof(f584,plain,
( ~ sQ55_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f154,f556,f569]) ).
fof(f585,definition,
! [X0] :
( sQ59_spl
<=> ( ~ q(X0)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f586,plain,
! [X0] :
( ~ sQ59_spl
| ~ q(X0)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,definition,
( sQ60_spl
<=> p(sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ60_spl
| p(sK30_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( sQ60_spl
| sQ59_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f155,f556,f585,f588]) ).
fof(f592,definition,
( sQ61_spl
<=> q(sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ61_spl
| q(sK31_skl) ),
inference(component_clause,[status(thm)],[f592]) ).
fof(f595,plain,
( sQ61_spl
| sQ59_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f156,f556,f585,f592]) ).
fof(f596,definition,
( sQ62_spl
<=> sP17_prd ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ7_spl
| sQ62_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f162,f569,f596,f357]) ).
fof(f600,definition,
( sQ63_spl
<=> p(sK32_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ63_spl
| ~ p(sK32_skl) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ63_spl
| sQ62_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f163,f569,f596,f600]) ).
fof(f604,plain,
( ~ sQ62_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f164,f569,f596]) ).
fof(f605,definition,
( sQ64_spl
<=> p(sK33_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ64_spl
| ~ p(sK33_skl) ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f608,plain,
( sQ7_spl
| ~ sQ64_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f165,f569,f605,f357]) ).
fof(f609,definition,
( sQ65_spl
<=> sP18_prd ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f612,definition,
( sQ66_spl
<=> sP19_prd(sK34_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( ~ sQ66_spl
| sP19_prd(sK34_skl) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f614,plain,
( sQ66_spl
| ~ sP19_prd(sK34_skl) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,definition,
( sQ67_spl
<=> p(sK35_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ67_spl
| p(sK35_skl) ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,definition,
( sQ68_spl
<=> q(sK36_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f619,plain,
( ~ sQ68_spl
| q(sK36_skl) ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,plain,
( sQ68_spl
| sQ67_spl
| sQ66_spl
| sQ65_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f172,f596,f609,f612,f615,f618]) ).
fof(f622,definition,
! [X0] :
( sQ69_spl
<=> ~ sP19_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f623,plain,
! [X0] :
( ~ sQ69_spl
| ~ sP19_prd(X0) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f625,plain,
( sQ1_spl
| sQ69_spl
| sQ65_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f173,f596,f609,f622,f334]) ).
fof(f626,plain,
( sQ58_spl
| sQ69_spl
| sQ65_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f174,f596,f609,f622,f580]) ).
fof(f627,plain,
( ~ sQ65_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f175,f596,f609]) ).
fof(f628,definition,
( sQ70_spl
<=> p(sK37_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ70_spl
| p(sK37_skl) ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f631,definition,
( sQ71_spl
<=> q(sK38_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f632,plain,
( ~ sQ71_spl
| q(sK38_skl) ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( sQ71_spl
| sQ70_spl
| sQ69_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f176,f596,f622,f628,f631]) ).
fof(f635,definition,
( sQ72_spl
<=> sP19_prd(sK39_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ72_spl
| sP19_prd(sK39_skl) ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,plain,
( sQ1_spl
| sQ72_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f177,f596,f635,f334]) ).
fof(f640,definition,
( sQ73_spl
<=> sP20_prd ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f643,definition,
! [X1] :
( sQ74_spl
<=> q(X1) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f644,plain,
! [X0] :
( ~ sQ74_spl
| q(X0) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( sQ74_spl
| sQ7_spl
| sQ73_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f183,f609,f640,f357,f643]) ).
fof(f647,definition,
( sQ75_spl
<=> p(sK40_skl) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( sQ75_spl
| ~ p(sK40_skl) ),
inference(component_clause,[status(thm)],[f647]) ).
fof(f650,plain,
( ~ sQ75_spl
| sQ73_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f184,f609,f640,f647]) ).
fof(f651,definition,
( sQ76_spl
<=> q(sK40_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( sQ76_spl
| ~ q(sK40_skl) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,plain,
( ~ sQ76_spl
| sQ73_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f185,f609,f640,f651]) ).
fof(f655,plain,
( ~ sQ73_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f186,f609,f640]) ).
fof(f656,definition,
( sQ77_spl
<=> p(sK41_skl) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ77_spl
| ~ p(sK41_skl) ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,definition,
! [X0] :
( sQ78_spl
<=> ( q(X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f660,plain,
! [X0] :
( ~ sQ78_spl
| q(X0)
| p(X0) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f662,plain,
( sQ78_spl
| ~ sQ77_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f187,f609,f656,f659]) ).
fof(f663,definition,
( sQ79_spl
<=> q(sK42_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( sQ79_spl
| ~ q(sK42_skl) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f667,definition,
( sQ80_spl
<=> sP21_prd ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f670,definition,
! [X0] :
( sQ81_spl
<=> sP22_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f671,plain,
! [X0] :
( ~ sQ81_spl
| sP22_prd(X0) ),
inference(component_clause,[status(thm)],[f670]) ).
fof(f673,plain,
( sQ7_spl
| sQ81_spl
| sQ80_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f200,f640,f667,f670,f357]) ).
fof(f674,plain,
( sQ74_spl
| sQ81_spl
| sQ80_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f201,f640,f667,f670,f643]) ).
fof(f675,definition,
( sQ82_spl
<=> sP22_prd(sK43_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f676,plain,
( ~ sQ82_spl
| sP22_prd(sK43_skl) ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f677,plain,
( sQ82_spl
| ~ sP22_prd(sK43_skl) ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f678,definition,
( sQ83_spl
<=> p(sK44_skl) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ83_spl
| ~ p(sK44_skl) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,definition,
( sQ84_spl
<=> q(sK45_skl) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( sQ84_spl
| ~ q(sK45_skl) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f684,plain,
( ~ sQ84_spl
| ~ sQ83_spl
| ~ sQ82_spl
| sQ80_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f202,f640,f667,f675,f678,f681]) ).
fof(f685,plain,
( ~ sQ80_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f203,f640,f667]) ).
fof(f686,definition,
( sQ85_spl
<=> sP22_prd(sK46_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( sQ85_spl
| ~ sP22_prd(sK46_skl) ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f689,plain,
( sQ7_spl
| ~ sQ85_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f204,f640,f686,f357]) ).
fof(f690,plain,
( sQ74_spl
| ~ sQ85_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f205,f640,f686,f643]) ).
fof(f691,definition,
( sQ86_spl
<=> p(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f693,plain,
( sQ86_spl
| ~ p(sK47_skl) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f694,definition,
( sQ87_spl
<=> q(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( sQ87_spl
| ~ q(sK48_skl) ),
inference(component_clause,[status(thm)],[f694]) ).
fof(f697,plain,
( ~ sQ87_spl
| ~ sQ86_spl
| sQ81_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f206,f640,f670,f691,f694]) ).
fof(f698,definition,
( sQ88_spl
<=> sP23_prd ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f701,definition,
( sQ89_spl
<=> p(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( sQ89_spl
| ~ p(sK49_skl) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( sQ74_spl
| ~ sQ89_spl
| sQ88_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f212,f667,f698,f701,f643]) ).
fof(f705,plain,
( sQ7_spl
| sQ88_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f213,f667,f698,f357]) ).
fof(f706,plain,
( sQ58_spl
| sQ88_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f214,f667,f698,f580]) ).
fof(f707,plain,
( ~ sQ88_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f215,f667,f698]) ).
fof(f708,definition,
( sQ90_spl
<=> p(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( sQ90_spl
| ~ p(sK51_skl) ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f711,definition,
( sQ91_spl
<=> q(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f712,plain,
( ~ sQ91_spl
| q(sK52_skl) ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f715,definition,
( sQ92_spl
<=> q(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f717,plain,
( sQ92_spl
| ~ q(sK50_skl) ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,plain,
( sQ91_spl
| ~ sQ90_spl
| ~ sQ92_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f217,f667,f715,f708,f711]) ).
fof(f719,definition,
( sQ93_spl
<=> sP24_prd ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f722,definition,
( sQ94_spl
<=> sP25_prd ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( sQ94_spl
| sQ93_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f231,f698,f719,f722]) ).
fof(f726,definition,
! [X0] :
( sQ95_spl
<=> sP26_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f727,plain,
! [X0] :
( ~ sQ95_spl
| sP26_prd(X0) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( sQ95_spl
| sQ93_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f232,f698,f719,f726]) ).
fof(f730,definition,
! [X0] :
( sQ96_spl
<=> ( h(X0)
| ~ g(X0)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f731,plain,
! [X0] :
( ~ sQ96_spl
| h(X0)
| ~ g(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f733,plain,
( sQ96_spl
| sQ93_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f233,f698,f719,f730]) ).
fof(f734,plain,
( ~ sQ93_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f234,f698,f719]) ).
fof(f735,definition,
( sQ97_spl
<=> sP26_prd(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( sQ97_spl
| ~ sP26_prd(sK53_skl) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f750,definition,
( sQ101_spl
<=> sP27_prd ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f753,definition,
! [X0,X1] :
( sQ102_spl
<=> sP28_prd(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f754,plain,
! [X0,X1] :
( ~ sQ102_spl
| sP28_prd(X0,X1) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f756,plain,
( sQ102_spl
| sQ101_spl
| ~ sQ93_spl ),
inference(split_clause,[status(thm)],[f245,f719,f750,f753]) ).
fof(f757,definition,
! [X0,X1,X2] :
( sQ103_spl
<=> ( r(X0,X2)
| ~ r(X1,X2)
| ~ r(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f758,plain,
! [X0,X1,X2] :
( ~ sQ103_spl
| r(X0,X2)
| ~ r(X1,X2)
| ~ r(X0,X1) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,plain,
( sQ103_spl
| sQ101_spl
| ~ sQ93_spl ),
inference(split_clause,[status(thm)],[f246,f719,f750,f757]) ).
fof(f761,definition,
( sQ104_spl
<=> r(sK55_skl,sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f762,plain,
( ~ sQ104_spl
| r(sK55_skl,sK56_skl) ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f764,plain,
( sQ104_spl
| sQ101_spl
| ~ sQ93_spl ),
inference(split_clause,[status(thm)],[f247,f719,f750,f761]) ).
fof(f765,definition,
( sQ105_spl
<=> r(sK55_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f767,plain,
( sQ105_spl
| ~ r(sK55_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f765]) ).
fof(f768,plain,
( ~ sQ105_spl
| sQ101_spl
| ~ sQ93_spl ),
inference(split_clause,[status(thm)],[f248,f719,f750,f765]) ).
fof(f769,plain,
( ~ sQ101_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f249,f719,f750]) ).
fof(f788,definition,
( sQ111_spl
<=> sP29_prd ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( sQ111_spl
| ~ sQ94_spl ),
inference(split_clause,[status(thm)],[f257,f722,f788]) ).
fof(f792,definition,
! [X0] :
( sQ112_spl
<=> ( g(X0)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f793,plain,
! [X0] :
( ~ sQ112_spl
| g(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f795,definition,
! [X1] :
( sQ113_spl
<=> ( h(X1)
| ~ f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f796,plain,
! [X0] :
( ~ sQ113_spl
| h(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f795]) ).
fof(f798,plain,
( sQ113_spl
| sQ112_spl
| ~ sQ94_spl ),
inference(split_clause,[status(thm)],[f258,f722,f792,f795]) ).
fof(f815,definition,
( sQ118_spl
<=> sP30_prd ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( sQ118_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f275,f750,f815]) ).
fof(f819,definition,
! [X0] :
( sQ119_spl
<=> sP31_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f820,plain,
! [X0] :
( ~ sQ119_spl
| sP31_prd(X0) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f822,plain,
( sQ119_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f276,f750,f819]) ).
fof(f823,plain,
( sQ96_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f277,f750,f730]) ).
fof(f839,definition,
( sQ124_spl
<=> sP32_prd(sK66_skl) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f840,plain,
( ~ sQ124_spl
| sP32_prd(sK66_skl) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,definition,
( sQ125_spl
<=> f(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( ~ sQ125_spl
| f(sK67_skl) ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,plain,
( sQ125_spl
| sQ124_spl
| ~ sQ111_spl ),
inference(split_clause,[status(thm)],[f290,f788,f839,f842]) ).
fof(f846,definition,
( sQ126_spl
<=> g(sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( sQ126_spl
| ~ g(sK67_skl) ),
inference(component_clause,[status(thm)],[f846]) ).
fof(f849,plain,
( ~ sQ126_spl
| sQ124_spl
| ~ sQ111_spl ),
inference(split_clause,[status(thm)],[f291,f788,f839,f846]) ).
fof(f855,definition,
! [X0] :
( sQ128_spl
<=> sP33_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f856,plain,
! [X0] :
( ~ sQ128_spl
| sP33_prd(X0) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f858,plain,
( sQ128_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f298,f815,f855]) ).
fof(f859,plain,
( sQ113_spl
| sQ112_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f299,f815,f792,f795]) ).
fof(f880,plain,
! [X0] :
( ~ sQ7_spl
| ~ q(X0)
| sP22_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f358]) ).
fof(f881,plain,
! [X0] :
( ~ sQ7_spl
| sP19_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f192,f358]) ).
fof(f882,plain,
! [X0] :
( ~ sQ7_spl
| sP12_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f128,f358]) ).
fof(f883,plain,
! [X0] :
( ~ sQ7_spl
| sP6_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f75,f358]) ).
fof(f884,plain,
! [X0] :
( ~ sQ7_spl
| sP2_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f358]) ).
fof(f885,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f358]) ).
fof(f886,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f885]) ).
fof(f890,plain,
( ~ sQ74_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f581]) ).
fof(f891,plain,
( ~ sQ74_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f890]) ).
fof(f892,plain,
! [X0] :
( ~ sQ128_spl
| ~ g(sK71_skl(X0))
| sP34_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f322,f856]) ).
fof(f893,plain,
! [X0] :
( ~ sQ128_spl
| f(sK71_skl(X0))
| sP34_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f321,f856]) ).
fof(f894,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ34_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f478]) ).
fof(f895,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ43_spl
| ~ sQ34_spl
| ~ sP6_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f894]) ).
fof(f897,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ6_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f355]) ).
fof(f898,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ112_spl
| h(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f793]) ).
fof(f899,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| ~ sQ43_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f895]) ).
fof(f900,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| ~ sQ43_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f899]) ).
fof(f901,plain,
! [X0] :
( ~ sQ69_spl
| ~ q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f623]) ).
fof(f903,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f897,f904]) ).
fof(f904,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ26_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f439]) ).
fof(f905,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f903]) ).
fof(f906,plain,
! [X0] :
( ~ sQ69_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f623]) ).
fof(f909,plain,
! [X0] :
( ~ sQ48_spl
| ~ sQ38_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f495]) ).
fof(f911,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ48_spl
| ~ sQ38_spl
| ~ sP4_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f909]) ).
fof(f915,plain,
( ~ sQ124_spl
| ~ h(sK66_skl) ),
inference(resolution,[status(thm)],[f840,f314]) ).
fof(f917,plain,
( ~ sQ124_spl
| f(sK66_skl) ),
inference(resolution,[status(thm)],[f840,f312]) ).
fof(f924,plain,
! [X0] :
( ~ sQ112_spl
| ~ sQ128_spl
| g(sK71_skl(X0))
| sP34_prd(X0) ),
inference(resolution,[status(thm)],[f893,f793]) ).
fof(f925,plain,
! [X0] :
( ~ sQ112_spl
| ~ sQ128_spl
| ~ h(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f329,f928]) ).
fof(f927,plain,
! [X0] :
( ~ sQ112_spl
| ~ sQ128_spl
| f(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f327,f928]) ).
fof(f928,plain,
! [X0] :
( ~ sQ112_spl
| ~ sQ128_spl
| sP34_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f924,f892]) ).
fof(f929,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ112_spl
| ~ sQ128_spl
| ~ f(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f898,f925]) ).
fof(f932,plain,
( ~ sQ96_spl
| ~ sQ112_spl
| ~ sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f927]) ).
fof(f933,plain,
( ~ sQ96_spl
| ~ sQ112_spl
| ~ sQ128_spl ),
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f934,plain,
! [X0] :
( ~ sQ119_spl
| g(X0)
| ~ h(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f820]) ).
fof(f939,plain,
( ~ sQ22_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f455]) ).
fof(f940,plain,
( ~ sQ22_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f941,plain,
! [X0] :
( ~ sQ81_spl
| q(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f221,f671]) ).
fof(f942,plain,
( sQ85_spl
| ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f688,f671]) ).
fof(f943,plain,
( sQ85_spl
| ~ sQ81_spl ),
inference(contradiction_clause,[status(thm)],[f942]) ).
fof(f944,plain,
( sQ90_spl
| ~ sQ48_spl
| ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f909]) ).
fof(f945,plain,
( sQ90_spl
| ~ sQ48_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f944]) ).
fof(f946,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f884,f354,f357]) ).
fof(f947,plain,
( sQ50_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f551,f358]) ).
fof(f948,plain,
! [X0] :
( ~ sQ59_spl
| ~ sQ7_spl
| ~ q(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f586,f358]) ).
fof(f952,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ74_spl
| sP22_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f880,f644]) ).
fof(f953,plain,
( sQ86_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f358]) ).
fof(f954,plain,
( sQ86_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f953]) ).
fof(f956,plain,
( ~ sQ70_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f629,f335]) ).
fof(f957,plain,
! [X0] :
( ~ sQ78_spl
| ~ sQ1_spl
| q(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f660,f335]) ).
fof(f958,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sP6_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f451,f335]) ).
fof(f961,plain,
! [X0] :
( ~ sQ1_spl
| ~ sP10_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f112,f335]) ).
fof(f962,plain,
( ~ sQ91_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f712,f581]) ).
fof(f963,plain,
( ~ sQ70_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f956]) ).
fof(f964,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f439]) ).
fof(f965,plain,
( ~ sQ15_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f964]) ).
fof(f966,plain,
( ~ sQ78_spl
| ~ sQ1_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f957,f643,f334,f659]) ).
fof(f967,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f342,f335]) ).
fof(f969,plain,
( ~ sQ91_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f970,plain,
! [X0] :
( ~ sQ119_spl
| ~ sQ113_spl
| g(X0)
| ~ f(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f934,f796]) ).
fof(f973,plain,
( ~ sQ119_spl
| ~ sQ113_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f970,f792,f795,f819]) ).
fof(f976,plain,
! [X0,X1] :
( ~ sQ102_spl
| r(X1,X0)
| ~ r(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f283,f754]) ).
fof(f977,plain,
! [X0] :
( ~ sQ113_spl
| g(X0)
| ~ f(X0)
| ~ sP26_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f796]) ).
fof(f982,plain,
( ~ sQ59_spl
| ~ sQ7_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f948,f580,f357,f585]) ).
fof(f983,plain,
( sQ39_spl
| ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f495]) ).
fof(f984,plain,
( sQ39_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f983]) ).
fof(f985,plain,
( sQ50_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f947]) ).
fof(f986,plain,
( sQ87_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f696,f644]) ).
fof(f987,plain,
( sQ79_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f665,f644]) ).
fof(f993,plain,
( ~ sQ51_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f553,f335]) ).
fof(f994,plain,
( ~ sQ45_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f526,f335]) ).
fof(f995,plain,
! [X0] :
( ~ sQ1_spl
| sP4_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f335]) ).
fof(f998,plain,
( ~ sQ69_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f901,f580,f622]) ).
fof(f1000,plain,
( sQ87_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f1001,plain,
! [X0] :
( ~ sQ58_spl
| p(X0)
| ~ sP19_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f581]) ).
fof(f1006,plain,
! [X0] :
( ~ sQ103_spl
| sQ105_spl
| ~ r(X0,sK55_skl)
| ~ r(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f767,f758]) ).
fof(f1007,plain,
! [X0] :
( ~ sQ103_spl
| sQ105_spl
| ~ sQ102_spl
| ~ r(X0,sK55_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1006,f976]) ).
fof(f1010,plain,
! [X0] :
( ~ sQ103_spl
| sQ105_spl
| ~ sQ102_spl
| ~ r(sK55_skl,X0) ),
inference(resolution,[status(thm)],[f976,f1007]) ).
fof(f1012,plain,
( ~ sQ104_spl
| ~ sQ103_spl
| sQ105_spl
| ~ sQ102_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f762,f1010]) ).
fof(f1013,plain,
( ~ sQ104_spl
| ~ sQ103_spl
| sQ105_spl
| ~ sQ102_spl ),
inference(contradiction_clause,[status(thm)],[f1012]) ).
fof(f1014,plain,
( sQ79_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f987]) ).
fof(f1015,plain,
( sQ97_spl
| ~ sQ95_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f737,f727]) ).
fof(f1016,plain,
( sQ8_spl
| ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f363,f355]) ).
fof(f1017,plain,
( ~ sQ36_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f488,f478]) ).
fof(f1018,plain,
( ~ sQ32_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f470,f478]) ).
fof(f1019,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f390]) ).
fof(f1020,plain,
( ~ sQ17_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f400,f390]) ).
fof(f1024,plain,
( sQ14_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f387,f1039]) ).
fof(f1039,plain,
! [X0] :
( ~ sQ15_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f390]) ).
fof(f1040,plain,
! [X0] :
( ~ sQ113_spl
| ~ sQ95_spl
| g(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f977,f727]) ).
fof(f1041,plain,
( sQ97_spl
| ~ sQ95_spl ),
inference(contradiction_clause,[status(thm)],[f1015]) ).
fof(f1042,plain,
( sQ8_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1016]) ).
fof(f1043,plain,
( ~ sQ36_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1017]) ).
fof(f1044,plain,
( sQ41_spl
| ~ sQ38_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f509,f495]) ).
fof(f1046,plain,
( ~ sQ4_spl
| ~ sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f345,f1060]) ).
fof(f1049,plain,
( ~ sQ60_spl
| ~ sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f589,f1060]) ).
fof(f1054,plain,
( ~ sQ47_spl
| ~ sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f535,f1060]) ).
fof(f1060,plain,
! [X0] :
( ~ sQ22_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f420]) ).
fof(f1061,plain,
( ~ sQ20_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f413,f420]) ).
fof(f1062,plain,
( ~ sQ20_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1061]) ).
fof(f1063,plain,
( ~ sQ7_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f882,f494,f357]) ).
fof(f1064,plain,
( ~ sQ57_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f577,f581]) ).
fof(f1065,plain,
( ~ sQ68_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f619,f581]) ).
fof(f1066,plain,
( ~ sQ61_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f593,f581]) ).
fof(f1067,plain,
( ~ sQ71_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f632,f581]) ).
fof(f1068,plain,
! [X0] :
( ~ sQ58_spl
| ~ sP22_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f221,f581]) ).
fof(f1069,plain,
( ~ sQ32_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1070,plain,
( sQ63_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f358]) ).
fof(f1071,plain,
( sQ63_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1070]) ).
fof(f1073,plain,
( sQ92_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f717,f644]) ).
fof(f1074,plain,
( sQ84_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f683,f644]) ).
fof(f1075,plain,
( sQ76_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f653,f644]) ).
fof(f1094,plain,
( ~ sQ1_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f995,f438,f334]) ).
fof(f1095,plain,
( ~ sQ51_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f993]) ).
fof(f1096,plain,
( sQ92_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1073]) ).
fof(f1097,plain,
( ~ sQ13_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1019]) ).
fof(f1099,plain,
( ~ sQ7_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f883,f454,f357]) ).
fof(f1100,plain,
( sQ77_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f658,f358]) ).
fof(f1101,plain,
( sQ64_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f607,f358]) ).
fof(f1102,plain,
( sQ54_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f567,f358]) ).
fof(f1103,plain,
( sQ46_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f531,f358]) ).
fof(f1104,plain,
( sQ42_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f513,f358]) ).
fof(f1105,plain,
( sQ16_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f397,f358]) ).
fof(f1106,plain,
( sQ89_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f703,f358]) ).
fof(f1107,plain,
( sQ83_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f680,f358]) ).
fof(f1108,plain,
( sQ75_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f649,f358]) ).
fof(f1109,plain,
( sQ53_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f562,f358]) ).
fof(f1110,plain,
( sQ40_spl
| ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f503,f358]) ).
fof(f1117,plain,
( sQ82_spl
| ~ sQ7_spl
| ~ sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f677,f952]) ).
fof(f1119,plain,
( sQ41_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f1044]) ).
fof(f1120,plain,
( sQ84_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1074]) ).
fof(f1123,plain,
( ~ sQ113_spl
| ~ sQ95_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1040,f792,f726,f795]) ).
fof(f1126,plain,
( sQ77_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1100]) ).
fof(f1127,plain,
( ~ sQ45_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f994]) ).
fof(f1128,plain,
( ~ sQ28_spl
| ~ sQ43_spl
| ~ sQ34_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f895,f419,f477,f517,f450]) ).
fof(f1129,plain,
( ~ sQ21_spl
| ~ sQ43_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f416,f1143]) ).
fof(f1130,plain,
( ~ sQ33_spl
| ~ sQ43_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f473,f1143]) ).
fof(f1143,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ34_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f478]) ).
fof(f1145,plain,
( ~ sQ21_spl
| ~ sQ43_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1129]) ).
fof(f1146,plain,
( ~ sQ1_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f961,f477,f334]) ).
fof(f1147,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f967]) ).
fof(f1150,plain,
( ~ sQ4_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1046]) ).
fof(f1151,plain,
! [X0] :
( ~ sQ96_spl
| ~ sQ112_spl
| h(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f793]) ).
fof(f1168,plain,
( ~ sQ125_spl
| ~ sQ112_spl
| g(sK67_skl) ),
inference(resolution,[status(thm)],[f793,f843]) ).
fof(f1171,plain,
( ~ sQ125_spl
| ~ sQ112_spl
| sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1168,f848]) ).
fof(f1172,plain,
( ~ sQ125_spl
| ~ sQ112_spl
| sQ126_spl ),
inference(contradiction_clause,[status(thm)],[f1171]) ).
fof(f1184,plain,
( ~ sQ66_spl
| q(sK34_skl)
| p(sK34_skl) ),
inference(resolution,[status(thm)],[f191,f613]) ).
fof(f1185,plain,
( ~ sQ72_spl
| q(sK39_skl)
| p(sK39_skl) ),
inference(resolution,[status(thm)],[f191,f636]) ).
fof(f1188,definition,
( sQ136_spl
<=> p(sK34_skl) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
( ~ sQ136_spl
| p(sK34_skl) ),
inference(component_clause,[status(thm)],[f1188]) ).
fof(f1191,definition,
( sQ137_spl
<=> q(sK34_skl) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( ~ sQ137_spl
| q(sK34_skl) ),
inference(component_clause,[status(thm)],[f1191]) ).
fof(f1194,plain,
( ~ sQ66_spl
| sQ137_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1184,f1188,f1191,f612]) ).
fof(f1195,definition,
( sQ138_spl
<=> p(sK39_skl) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1196,plain,
( ~ sQ138_spl
| p(sK39_skl) ),
inference(component_clause,[status(thm)],[f1195]) ).
fof(f1198,definition,
( sQ139_spl
<=> q(sK39_skl) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1199,plain,
( ~ sQ139_spl
| q(sK39_skl) ),
inference(component_clause,[status(thm)],[f1198]) ).
fof(f1201,plain,
( ~ sQ72_spl
| sQ139_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1185,f1195,f1198,f635]) ).
fof(f1202,plain,
( ~ sQ124_spl
| ~ sQ96_spl
| ~ sQ112_spl
| h(sK66_skl) ),
inference(resolution,[status(thm)],[f1151,f917]) ).
fof(f1207,plain,
( ~ sQ124_spl
| ~ sQ96_spl
| ~ sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1202,f915]) ).
fof(f1208,plain,
( ~ sQ124_spl
| ~ sQ96_spl
| ~ sQ112_spl ),
inference(contradiction_clause,[status(thm)],[f1207]) ).
fof(f1209,plain,
( ~ sQ81_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f941,f643,f670]) ).
fof(f1210,plain,
( sQ82_spl
| ~ sQ81_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f677,f671]) ).
fof(f1211,plain,
! [X0] :
( ~ sQ81_spl
| p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f220,f671]) ).
fof(f1213,plain,
( sQ82_spl
| ~ sQ81_spl ),
inference(contradiction_clause,[status(thm)],[f1210]) ).
fof(f1214,plain,
( sQ76_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1075]) ).
fof(f1215,plain,
( sQ64_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1101]) ).
fof(f1216,plain,
( ~ sQ57_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1064]) ).
fof(f1217,plain,
( sQ54_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1102]) ).
fof(f1221,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f426,f335]) ).
fof(f1222,plain,
( ~ sQ35_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f483,f335]) ).
fof(f1223,plain,
( ~ sQ67_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f616,f335]) ).
fof(f1224,plain,
( ~ sQ56_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f573,f335]) ).
fof(f1227,plain,
( ~ sQ136_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1189,f335]) ).
fof(f1228,plain,
( ~ sQ138_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1196,f335]) ).
fof(f1229,plain,
! [X0] :
( ~ sQ1_spl
| sP4_prd(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f61,f335]) ).
fof(f1230,plain,
( ~ sQ24_spl
| ~ sQ28_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f430,f958]) ).
fof(f1231,plain,
( ~ sQ33_spl
| ~ sQ43_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1130]) ).
fof(f1232,plain,
( ~ sQ60_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1233,plain,
( ~ sQ81_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1211,f357,f670]) ).
fof(f1238,plain,
( sQ46_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1103]) ).
fof(f1239,plain,
( ~ sQ68_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1065]) ).
fof(f1240,plain,
( sQ42_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1104]) ).
fof(f1241,plain,
( ~ sQ23_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1221]) ).
fof(f1242,plain,
( ~ sQ61_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1066]) ).
fof(f1243,plain,
( sQ16_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1105]) ).
fof(f1244,plain,
( ~ sQ35_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1222]) ).
fof(f1245,plain,
( ~ sQ71_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1067]) ).
fof(f1246,plain,
( sQ89_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1106]) ).
fof(f1247,plain,
( ~ sQ67_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1223]) ).
fof(f1248,plain,
( sQ83_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1107]) ).
fof(f1250,plain,
( ~ sQ56_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1224]) ).
fof(f1251,plain,
( sQ90_spl
| ~ sQ28_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f710,f1261]) ).
fof(f1252,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f367,f1261]) ).
fof(f1253,plain,
( sQ11_spl
| ~ sQ28_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f377,f1261]) ).
fof(f1254,plain,
( sQ14_spl
| ~ sQ28_spl
| ~ sQ29_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f387,f1261]) ).
fof(f1261,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ29_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f455]) ).
fof(f1262,plain,
( sQ75_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1108]) ).
fof(f1269,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ26_spl
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f439]) ).
fof(f1270,plain,
( ~ sQ25_spl
| ~ sQ26_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f904,f334,f438,f434]) ).
fof(f1271,plain,
( ~ sQ139_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1199,f581]) ).
fof(f1272,plain,
( ~ sQ137_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1192,f581]) ).
fof(f1273,plain,
! [X0] :
( ~ sQ58_spl
| ~ sQ25_spl
| ~ sQ26_spl
| ~ sP19_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1001,f1269]) ).
fof(f1274,plain,
( ~ sQ66_spl
| ~ sQ58_spl
| ~ sQ25_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f1273]) ).
fof(f1275,plain,
( ~ sQ66_spl
| ~ sQ58_spl
| ~ sQ25_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1274]) ).
fof(f1285,plain,
( sQ90_spl
| ~ sQ28_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1251]) ).
fof(f1286,plain,
( sQ9_spl
| ~ sQ28_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1252]) ).
fof(f1287,plain,
( sQ11_spl
| ~ sQ28_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1253]) ).
fof(f1288,plain,
( sQ14_spl
| ~ sQ28_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1254]) ).
fof(f1293,plain,
( sQ82_spl
| ~ sQ7_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1117]) ).
fof(f1294,plain,
( ~ sQ25_spl
| ~ sQ48_spl
| ~ sQ38_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f911,f389,f494,f538,f434]) ).
fof(f1304,plain,
( ~ sQ48_spl
| ~ sQ38_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f909,f357,f494,f538]) ).
fof(f1308,plain,
( ~ sQ136_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1227]) ).
fof(f1309,plain,
( ~ sQ82_spl
| ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f676,f1068]) ).
fof(f1311,plain,
( ~ sQ139_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1271]) ).
fof(f1312,plain,
( ~ sQ47_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1318,plain,
( ~ sQ17_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1020]) ).
fof(f1319,plain,
( ~ sQ24_spl
| ~ sQ28_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1230]) ).
fof(f1322,plain,
( sQ14_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1024]) ).
fof(f1329,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ6_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f355]) ).
fof(f1330,plain,
( ~ sQ18_spl
| ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f897,f357,f354,f404]) ).
fof(f1331,plain,
( sQ9_spl
| ~ sQ18_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f1329]) ).
fof(f1332,plain,
( sQ9_spl
| ~ sQ18_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1331]) ).
fof(f1337,plain,
( ~ sQ137_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1272]) ).
fof(f1338,plain,
( ~ sQ138_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1228]) ).
fof(f1345,plain,
( ~ sQ82_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1309]) ).
fof(f1346,plain,
( sQ66_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f614,f881]) ).
fof(f1347,plain,
( sQ66_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1346]) ).
fof(f1348,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ1_spl
| ~ p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f435,f1229]) ).
fof(f1350,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f335]) ).
fof(f1351,plain,
( ~ sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1350]) ).
fof(f1357,plain,
( ~ sQ69_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f906,f334,f622]) ).
fof(f1370,plain,
( sQ40_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1110]) ).
fof(f1371,plain,
( ~ sQ14_spl
| ~ sQ25_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f1348]) ).
fof(f1372,plain,
( ~ sQ14_spl
| ~ sQ25_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1371]) ).
fof(f1379,plain,
( sQ53_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1109]) ).
fof(f1380,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f345,f1348]) ).
fof(f1384,plain,
( ~ sQ53_spl
| ~ sQ25_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f1348]) ).
fof(f1385,plain,
( ~ sQ53_spl
| ~ sQ25_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1384]) ).
fof(f1386,plain,
( ~ sQ4_spl
| ~ sQ25_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1380]) ).
fof(f1387,plain,
$false,
inference(sat_refutation,[status(thm)],[f340,f347,f350,f360,f364,f368,f369,f388,f392,f393,f394,f402,f407,f408,f418,f422,f423,f424,f433,f437,f441,f445,f446,f447,f453,f457,f461,f462,f463,f475,f476,f480,f481,f497,f504,f505,f506,f516,f520,f524,f528,f533,f537,f541,f542,f546,f547,f548,f555,f559,f563,f564,f568,f575,f579,f583,f584,f591,f595,f599,f603,f604,f608,f621,f625,f626,f627,f634,f638,f646,f650,f654,f655,f662,f673,f674,f684,f685,f689,f690,f697,f704,f705,f706,f707,f718,f725,f729,f733,f734,f756,f760,f764,f768,f769,f791,f798,f818,f822,f823,f845,f849,f858,f859,f886,f891,f900,f905,f933,f940,f943,f945,f946,f954,f963,f965,f966,f969,f973,f982,f984,f985,f998,f1000,f1013,f1014,f1041,f1042,f1043,f1062,f1063,f1069,f1071,f1094,f1095,f1096,f1097,f1099,f1119,f1120,f1123,f1126,f1127,f1128,f1145,f1146,f1147,f1150,f1172,f1194,f1201,f1208,f1209,f1213,f1214,f1215,f1216,f1217,f1231,f1232,f1233,f1238,f1239,f1240,f1241,f1242,f1243,f1244,f1245,f1246,f1247,f1248,f1250,f1262,f1270,f1275,f1285,f1286,f1287,f1288,f1293,f1294,f1304,f1308,f1311,f1312,f1318,f1319,f1322,f1330,f1332,f1337,f1338,f1345,f1347,f1351,f1357,f1370,f1372,f1379,f1385,f1386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN917+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 11:30:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.50 % Elapsed time: 0.141591 seconds
% 0.13/0.50 % CPU time: 0.765004 seconds
% 0.13/0.50 % Total memory used: 29.026 MB
% 0.13/0.50 % Net memory used: 28.624 MB
%------------------------------------------------------------------------------