TSTP Solution File: SYN917+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 09:12:10 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 408 ( 210 unt; 1 def)
% Number of atoms : 6252 ( 0 equ)
% Maximal formula atoms : 94 ( 15 avg)
% Number of connectives : 7012 (1168 ~;1100 |;2692 &)
% ( 224 <=>;1828 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 21 con; 0-0 aty)
% Number of variables : 3700 ( 80 sgn2105 !;1544 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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] :
( p(X)
=> c )
<=> ( ? [X] : p(X)
=> c ) ) ) ).
fof(definition_0,definition,
! [R] :
( definitionFOFtoCNF_2(R)
<=> ( ~ g(R)
& f(R)
& h(R) ) ) ).
fof(subgoal_0,plain,
( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) )
& ! [R] :
( ( f(R)
& h(R) )
=> g(R) ) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_1,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_2,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) )
& ! [R] :
( ( f(R)
& h(R) )
=> g(R) ) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_3,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) ) )
=> ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_4,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] :
( p(X)
& q(X) ) )
=> ! [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_5,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] :
( p(X)
& q(X) )
& ! [X] : p(X) )
=> ! [X] : q(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_6,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] : p(X)
& ! [X] : q(X) )
=> ! [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_7,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] : p(X)
& ! [X] : q(X) )
=> ! [X] :
( p(X)
=> q(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_8,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ! [X] : p(X)
| ! [X] : q(X) ) )
=> ! [X] :
( ~ p(X)
=> q(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_9,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ? [X] :
( p(X)
| q(X) )
& ~ ? [X] : p(X) )
=> ? [X] : q(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_10,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] : p(X)
| ? [X] : q(X) ) )
=> ? [X] :
( p(X)
| q(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_11,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) ) )
=> ? [Y] :
( p(Y)
=> ! [X] : p(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_12,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ? [X] :
( p(X)
& q(X) ) )
=> ? [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_13,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ? [X] :
( p(X)
& q(X) )
& ? [X] : p(X) )
=> ? [X] : q(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_14,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) ) )
=> ! [Y] :
( ! [X] : p(X)
=> p(Y) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_15,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ! [X] : p(X) )
=> ? [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_16,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ~ ? [Y] : p(Y) )
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_17,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ! [X] :
( p(X)
| c )
& ~ ! [X] : p(X) )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_18,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] : p(X)
| c ) )
=> ! [X] :
( ~ p(X)
=> c ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_19,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] :
( p(X)
& c ) )
=> ? [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_20,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] :
( p(X)
& c )
& ? [X] : p(X) )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_21,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] : p(X)
& c )
=> ? [X] :
( p(X)
& c ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_22,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ? [X] : c )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_23,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& c )
=> ? [X] : c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_24,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ! [X] : c )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_25,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& c )
=> ! [X] : c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_26,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ? [X] :
( c
=> p(X) )
& c )
=> ? [X] : p(X) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_27,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( c
=> ? [X] : p(X) ) )
=> ? [X] :
( c
=> p(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_28,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ? [X] :
( p(X)
=> c )
& ! [X] : p(X) )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_29,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ! [X] : p(X)
=> c ) )
=> ? [X] :
( p(X)
=> c ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_30,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_31,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) )
& ( c
=> ! [X] : p(X) ) )
=> ! [X] :
( c
=> p(X) ) ),
inference(strip,[],[prove_this]) ).
fof(subgoal_32,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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] :
( p(X)
=> c )
& ? [X] : p(X) )
=> c ),
inference(strip,[],[prove_this]) ).
fof(subgoal_33,plain,
( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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] : p(X)
=> c ) )
=> ! [X] :
( p(X)
=> c ) ),
inference(strip,[],[prove_this]) ).
fof(negate_0_0,plain,
~ ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) )
& ! [R] :
( ( f(R)
& h(R) )
=> g(R) ) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ( ( ! [X] : ~ h(X)
& ! [X] : f(X)
& ! [X] : g(X) )
| ? [Y] :
( ~ g(Y)
& f(Y) ) )
& ( ! [W] :
( ~ f(W)
| g(W) )
| ! [Z] :
( ~ f(Z)
| h(Z) ) )
& ! [R] :
( ~ f(R)
| ~ h(R)
| g(R) )
& ! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ( ! [X] : ~ h(X)
& ! [X] : f(X)
& ! [X] : g(X) )
| ? [Y] :
( ~ g(Y)
& f(Y) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
( ( ~ g(skolemFOFtoCNF_Y)
| ~ h(X) )
& ( ~ g(skolemFOFtoCNF_Y)
| f(X) )
& ( ~ g(skolemFOFtoCNF_Y)
| g(X) )
& ( ~ h(X)
| f(skolemFOFtoCNF_Y) )
& ( f(X)
| f(skolemFOFtoCNF_Y) )
& ( f(skolemFOFtoCNF_Y)
| g(X) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ g(skolemFOFtoCNF_Y)
| ~ h(X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] :
( ~ g(skolemFOFtoCNF_Y)
| f(X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X] :
( f(X)
| f(skolemFOFtoCNF_Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_8,plain,
( ! [W] :
( ~ f(W)
| g(W) )
| ! [Z] :
( ~ f(Z)
| h(Z) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_9,plain,
! [W,Z] :
( ~ f(W)
| ~ f(Z)
| g(W)
| h(Z) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [R] :
( ~ f(R)
| ~ h(R)
| g(R) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_11,plain,
! [R] :
( ~ f(R)
| ~ h(R)
| g(R) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ g(skolemFOFtoCNF_Y)
| g(X) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
( ~ g(skolemFOFtoCNF_Y)
| ~ h(X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ g(skolemFOFtoCNF_Y)
| ~ h(X_7) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ g(skolemFOFtoCNF_Y)
| f(X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( f(X)
| f(skolemFOFtoCNF_Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
f(skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
( ~ f(W)
| ~ f(Z)
| g(W)
| h(Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ f(skolemFOFtoCNF_Y)
| g(skolemFOFtoCNF_Y)
| h(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_6:[bind(W,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_8,plain,
( g(skolemFOFtoCNF_Y)
| h(skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( f(skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ f(R)
| ~ h(R)
| g(R) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
( ~ f(skolemFOFtoCNF_Y)
| ~ h(skolemFOFtoCNF_Y)
| g(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_9:[bind(R,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_11,plain,
( ~ f(skolemFOFtoCNF_Y)
| g(skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( h(skolemFOFtoCNF_Y) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
g(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( f(skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
f(X),
inference(resolve,[$cnf( g(skolemFOFtoCNF_Y) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
f(V),
inference(subst,[],[refute_0_13:[bind(X,$fot(V))]]) ).
cnf(refute_0_15,plain,
( ~ g(V)
| h(V) ),
inference(resolve,[$cnf( f(V) )],[refute_0_14,refute_0_2]) ).
cnf(refute_0_16,plain,
( ~ g(skolemFOFtoCNF_Y)
| g(X) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_17,plain,
g(X),
inference(resolve,[$cnf( g(skolemFOFtoCNF_Y) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
g(V),
inference(subst,[],[refute_0_17:[bind(X,$fot(V))]]) ).
cnf(refute_0_19,plain,
h(V),
inference(resolve,[$cnf( g(V) )],[refute_0_18,refute_0_15]) ).
cnf(refute_0_20,plain,
h(X_7),
inference(subst,[],[refute_0_19:[bind(V,$fot(X_7))]]) ).
cnf(refute_0_21,plain,
~ g(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( h(X_7) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( g(skolemFOFtoCNF_Y) )],[refute_0_12,refute_0_21]) ).
fof(negate_1_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] :
( ~ r(X,X)
& ? [Y] : r(X,Y) )
& ! [X,Y] :
( ~ r(X,Y)
| r(Y,X) )
& ! [X,Y,Z] :
( ~ r(X,Y)
| ~ r(Y,Z)
| r(X,Z) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X] :
( ~ r(X,X)
& ? [Y] : r(X,Y) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3)
& ? [Y] : r(skolemFOFtoCNF_X_3,Y) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [Y] : r(skolemFOFtoCNF_X_3,Y),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ r(X,Y)
| r(Y,X) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_6,plain,
! [X,Y] :
( ~ r(X,Y)
| r(Y,X) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ r(X,Y)
| ~ r(Y,Z)
| r(X,Z) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_8,plain,
! [X,Y,Z] :
( ~ r(X,Y)
| ~ r(Y,Z)
| r(X,Z) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
~ r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
( ~ r(X,Y)
| r(Y,X) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| r(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_1_1:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_3,plain,
r(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
( ~ r(X,Y)
| ~ r(Y,Z)
| r(X,Z) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ r(X_19,skolemFOFtoCNF_Y_1)
| ~ r(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3)
| r(X_19,skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(X_19)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_1_6,plain,
( ~ r(X_19,skolemFOFtoCNF_Y_1)
| r(X_19,skolemFOFtoCNF_X_3) ),
inference(resolve,[$cnf( r(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_3) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( ~ r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
| r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3) ),
inference(subst,[],[refute_1_6:[bind(X_19,$fot(skolemFOFtoCNF_X_3))]]) ).
cnf(refute_1_8,plain,
r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3),
inference(resolve,[$cnf( r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_1_0,refute_1_7]) ).
cnf(refute_1_9,plain,
~ r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_10,plain,
$false,
inference(resolve,[$cnf( r(skolemFOFtoCNF_X_3,skolemFOFtoCNF_X_3) )],[refute_1_8,refute_1_9]) ).
fof(negate_2_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) )
& ! [R] :
( ( f(R)
& h(R) )
=> g(R) ) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& f(X)
& g(X) ) )
& ( ! [W] :
( ~ f(W)
| g(W) )
| ! [Z] :
( ~ f(Z)
| h(Z) ) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [R] :
( ~ f(R)
| ~ h(R)
| g(R) )
& ! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( ? [X] :
( ~ g(X)
& f(X) )
| ? [X] :
( ~ h(X)
& f(X)
& g(X) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( ( ~ g(skolemFOFtoCNF_X_4)
| ~ h(skolemFOFtoCNF_X_5) )
& ( ~ g(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) )
& ( ~ g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) )
& ( ~ h(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_4) )
& ( f(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) )
& ( f(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ g(skolemFOFtoCNF_X_4)
| ~ h(skolemFOFtoCNF_X_5) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_5,plain,
! [V] :
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(specialize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
( ~ g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_7,plain,
( ~ h(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_4) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_8,plain,
( f(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_9,plain,
( f(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_10,plain,
( ! [W] :
( ~ f(W)
| g(W) )
| ! [Z] :
( ~ f(Z)
| h(Z) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_11,plain,
! [W,Z] :
( ~ f(W)
| ~ f(Z)
| g(W)
| h(Z) ),
inference(clausify,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [R] :
( ~ definitionFOFtoCNF_2(R)
<=> ( ~ f(R)
| ~ h(R)
| g(R) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_2_13,plain,
! [R] :
( ( ~ definitionFOFtoCNF_2(R)
| ~ g(R) )
& ( ~ definitionFOFtoCNF_2(R)
| f(R) )
& ( ~ definitionFOFtoCNF_2(R)
| h(R) )
& ( ~ f(R)
| ~ h(R)
| definitionFOFtoCNF_2(R)
| g(R) ) ),
inference(clausify,[],[normalize_2_12]) ).
fof(normalize_2_14,plain,
! [R] :
( ~ f(R)
| ~ h(R)
| definitionFOFtoCNF_2(R)
| g(R) ),
inference(conjunct,[],[normalize_2_13]) ).
fof(normalize_2_15,plain,
! [R] :
( ~ f(R)
| ~ h(R)
| g(R) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_16,plain,
! [R] : ~ definitionFOFtoCNF_2(R),
inference(simplify,[],[normalize_2_15,normalize_2_12]) ).
fof(normalize_2_17,plain,
! [R] : ~ definitionFOFtoCNF_2(R),
inference(specialize,[],[normalize_2_16]) ).
fof(normalize_2_18,plain,
( ~ g(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) ),
inference(conjunct,[],[normalize_2_2]) ).
cnf(refute_2_0,plain,
( ~ g(skolemFOFtoCNF_X_4)
| ~ h(skolemFOFtoCNF_X_5) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( ~ f(V)
| ~ g(V)
| h(V) ),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_2,plain,
( ~ f(skolemFOFtoCNF_X_5)
| ~ g(skolemFOFtoCNF_X_5)
| h(skolemFOFtoCNF_X_5) ),
inference(subst,[],[refute_2_1:[bind(V,$fot(skolemFOFtoCNF_X_5))]]) ).
cnf(refute_2_3,plain,
( ~ g(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) ),
inference(canonicalize,[],[normalize_2_6]) ).
cnf(refute_2_4,plain,
( ~ h(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_4) ),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_5,plain,
( f(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_6,plain,
( f(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_5) ),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_7,plain,
( ~ f(skolemFOFtoCNF_X_5)
| f(skolemFOFtoCNF_X_4)
| h(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( g(skolemFOFtoCNF_X_5) )],[refute_2_6,refute_2_2]) ).
cnf(refute_2_8,plain,
( f(skolemFOFtoCNF_X_4)
| h(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X_5) )],[refute_2_5,refute_2_7]) ).
cnf(refute_2_9,plain,
f(skolemFOFtoCNF_X_4),
inference(resolve,[$cnf( h(skolemFOFtoCNF_X_5) )],[refute_2_8,refute_2_4]) ).
cnf(refute_2_10,plain,
( ~ f(W)
| ~ f(Z)
| g(W)
| h(Z) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_11,plain,
( ~ f(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4)
| h(skolemFOFtoCNF_X_4) ),
inference(subst,[],[refute_2_10:[bind(W,$fot(skolemFOFtoCNF_X_4)),bind(Z,$fot(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_2_12,plain,
( g(skolemFOFtoCNF_X_4)
| h(skolemFOFtoCNF_X_4) ),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X_4) )],[refute_2_9,refute_2_11]) ).
cnf(refute_2_13,plain,
( ~ f(R)
| ~ h(R)
| definitionFOFtoCNF_2(R)
| g(R) ),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_14,plain,
~ definitionFOFtoCNF_2(R),
inference(canonicalize,[],[normalize_2_17]) ).
cnf(refute_2_15,plain,
( ~ f(R)
| ~ h(R)
| g(R) ),
inference(resolve,[$cnf( definitionFOFtoCNF_2(R) )],[refute_2_13,refute_2_14]) ).
cnf(refute_2_16,plain,
( ~ f(skolemFOFtoCNF_X_4)
| ~ h(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4) ),
inference(subst,[],[refute_2_15:[bind(R,$fot(skolemFOFtoCNF_X_4))]]) ).
cnf(refute_2_17,plain,
( ~ f(skolemFOFtoCNF_X_4)
| g(skolemFOFtoCNF_X_4) ),
inference(resolve,[$cnf( h(skolemFOFtoCNF_X_4) )],[refute_2_12,refute_2_16]) ).
cnf(refute_2_18,plain,
g(skolemFOFtoCNF_X_4),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X_4) )],[refute_2_9,refute_2_17]) ).
cnf(refute_2_19,plain,
g(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( g(skolemFOFtoCNF_X_4) )],[refute_2_18,refute_2_3]) ).
cnf(refute_2_20,plain,
( ~ f(skolemFOFtoCNF_X_5)
| h(skolemFOFtoCNF_X_5) ),
inference(resolve,[$cnf( g(skolemFOFtoCNF_X_5) )],[refute_2_19,refute_2_2]) ).
cnf(refute_2_21,plain,
( ~ g(skolemFOFtoCNF_X_4)
| f(skolemFOFtoCNF_X_5) ),
inference(canonicalize,[],[normalize_2_18]) ).
cnf(refute_2_22,plain,
f(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( g(skolemFOFtoCNF_X_4) )],[refute_2_18,refute_2_21]) ).
cnf(refute_2_23,plain,
h(skolemFOFtoCNF_X_5),
inference(resolve,[$cnf( f(skolemFOFtoCNF_X_5) )],[refute_2_22,refute_2_20]) ).
cnf(refute_2_24,plain,
~ g(skolemFOFtoCNF_X_4),
inference(resolve,[$cnf( h(skolemFOFtoCNF_X_5) )],[refute_2_23,refute_2_0]) ).
cnf(refute_2_25,plain,
$false,
inference(resolve,[$cnf( g(skolemFOFtoCNF_X_4) )],[refute_2_18,refute_2_24]) ).
fof(negate_3_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) ) )
=> ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
( ( ? [Y] : ~ p(Y)
| ! [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ q(X)
& ! [X] : p(X) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_1,plain,
( ? [Y] : ~ p(Y)
| ! [X] : q(X) ),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
! [X] :
( ~ p(skolemFOFtoCNF_Y_4)
| q(X) ),
inference(clausify,[],[normalize_3_1]) ).
fof(normalize_3_3,plain,
! [X] : p(X),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_4,plain,
! [X] : p(X),
inference(specialize,[],[normalize_3_3]) ).
fof(normalize_3_5,plain,
! [X] : ~ q(X),
inference(conjunct,[],[normalize_3_0]) ).
fof(normalize_3_6,plain,
! [X] : ~ q(X),
inference(specialize,[],[normalize_3_5]) ).
cnf(refute_3_0,plain,
( ~ p(skolemFOFtoCNF_Y_4)
| q(X) ),
inference(canonicalize,[],[normalize_3_2]) ).
cnf(refute_3_1,plain,
p(X),
inference(canonicalize,[],[normalize_3_4]) ).
cnf(refute_3_2,plain,
p(skolemFOFtoCNF_Y_4),
inference(subst,[],[refute_3_1:[bind(X,$fot(skolemFOFtoCNF_Y_4))]]) ).
cnf(refute_3_3,plain,
q(X),
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_4) )],[refute_3_2,refute_3_0]) ).
cnf(refute_3_4,plain,
~ q(X),
inference(canonicalize,[],[normalize_3_6]) ).
cnf(refute_3_5,plain,
$false,
inference(resolve,[$cnf( q(X) )],[refute_3_3,refute_3_4]) ).
fof(negate_4_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] :
( p(X)
& q(X) ) )
=> ! [X] : p(X) ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
$false,
inference(canonicalize,[],[negate_4_0]) ).
cnf(refute_4_0,plain,
$false,
inference(canonicalize,[],[normalize_4_0]) ).
fof(negate_5_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] :
( p(X)
& q(X) )
& ! [X] : p(X) )
=> ! [X] : q(X) ),
inference(negate,[],[subgoal_5]) ).
fof(normalize_5_0,plain,
$false,
inference(canonicalize,[],[negate_5_0]) ).
cnf(refute_5_0,plain,
$false,
inference(canonicalize,[],[normalize_5_0]) ).
fof(negate_6_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] : p(X)
& ! [X] : q(X) )
=> ! [X] : p(X) ),
inference(negate,[],[subgoal_6]) ).
fof(normalize_6_0,plain,
$false,
inference(canonicalize,[],[negate_6_0]) ).
cnf(refute_6_0,plain,
$false,
inference(canonicalize,[],[normalize_6_0]) ).
fof(negate_7_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ! [X] : p(X)
& ! [X] : q(X) )
=> ! [X] :
( p(X)
=> q(X) ) ),
inference(negate,[],[subgoal_7]) ).
fof(normalize_7_0,plain,
( ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] :
( ~ q(X)
& p(X) )
& ! [X] : p(X)
& ! [X] : q(X) ),
inference(canonicalize,[],[negate_7_0]) ).
fof(normalize_7_1,plain,
? [X] :
( ~ q(X)
& p(X) ),
inference(conjunct,[],[normalize_7_0]) ).
fof(normalize_7_2,plain,
( ~ q(skolemFOFtoCNF_X_24)
& p(skolemFOFtoCNF_X_24) ),
inference(skolemize,[],[normalize_7_1]) ).
fof(normalize_7_3,plain,
~ q(skolemFOFtoCNF_X_24),
inference(conjunct,[],[normalize_7_2]) ).
fof(normalize_7_4,plain,
! [X] : q(X),
inference(conjunct,[],[normalize_7_0]) ).
fof(normalize_7_5,plain,
! [X] : q(X),
inference(specialize,[],[normalize_7_4]) ).
cnf(refute_7_0,plain,
~ q(skolemFOFtoCNF_X_24),
inference(canonicalize,[],[normalize_7_3]) ).
cnf(refute_7_1,plain,
q(X),
inference(canonicalize,[],[normalize_7_5]) ).
cnf(refute_7_2,plain,
q(skolemFOFtoCNF_X_24),
inference(subst,[],[refute_7_1:[bind(X,$fot(skolemFOFtoCNF_X_24))]]) ).
cnf(refute_7_3,plain,
$false,
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_24) )],[refute_7_2,refute_7_0]) ).
fof(negate_8_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ! [X] : p(X)
| ! [X] : q(X) ) )
=> ! [X] :
( ~ p(X)
=> q(X) ) ),
inference(negate,[],[subgoal_8]) ).
fof(normalize_8_0,plain,
( ( ! [X] : p(X)
| ! [X] : q(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] :
( ~ p(X)
& ~ q(X) ) ),
inference(canonicalize,[],[negate_8_0]) ).
fof(normalize_8_1,plain,
? [X] :
( ~ p(X)
& ~ q(X) ),
inference(conjunct,[],[normalize_8_0]) ).
fof(normalize_8_2,plain,
( ~ p(skolemFOFtoCNF_X_33)
& ~ q(skolemFOFtoCNF_X_33) ),
inference(skolemize,[],[normalize_8_1]) ).
fof(normalize_8_3,plain,
~ p(skolemFOFtoCNF_X_33),
inference(conjunct,[],[normalize_8_2]) ).
fof(normalize_8_4,plain,
~ q(skolemFOFtoCNF_X_33),
inference(conjunct,[],[normalize_8_2]) ).
fof(normalize_8_5,plain,
( ! [X] : p(X)
| ! [X] : q(X) ),
inference(conjunct,[],[normalize_8_0]) ).
fof(normalize_8_6,plain,
! [X,X0] :
( p(X)
| q(X0) ),
inference(clausify,[],[normalize_8_5]) ).
cnf(refute_8_0,plain,
~ p(skolemFOFtoCNF_X_33),
inference(canonicalize,[],[normalize_8_3]) ).
cnf(refute_8_1,plain,
~ q(skolemFOFtoCNF_X_33),
inference(canonicalize,[],[normalize_8_4]) ).
cnf(refute_8_2,plain,
( p(X)
| q(X0) ),
inference(canonicalize,[],[normalize_8_6]) ).
cnf(refute_8_3,plain,
( p(X_33)
| q(skolemFOFtoCNF_X_33) ),
inference(subst,[],[refute_8_2:[bind(X,$fot(X_33)),bind(X0,$fot(skolemFOFtoCNF_X_33))]]) ).
cnf(refute_8_4,plain,
p(X_33),
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_33) )],[refute_8_3,refute_8_1]) ).
cnf(refute_8_5,plain,
p(skolemFOFtoCNF_X_33),
inference(subst,[],[refute_8_4:[bind(X_33,$fot(skolemFOFtoCNF_X_33))]]) ).
cnf(refute_8_6,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_33) )],[refute_8_5,refute_8_0]) ).
fof(negate_9_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ? [X] :
( p(X)
| q(X) )
& ~ ? [X] : p(X) )
=> ? [X] : q(X) ),
inference(negate,[],[subgoal_9]) ).
fof(normalize_9_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] : p(X)
| ? [X] : q(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ p(X)
& ! [X] : ~ q(X) ),
inference(canonicalize,[],[negate_9_0]) ).
fof(normalize_9_1,plain,
( ? [X] : p(X)
| ? [X] : q(X) ),
inference(conjunct,[],[normalize_9_0]) ).
fof(normalize_9_2,plain,
( p(skolemFOFtoCNF_X_36)
| q(skolemFOFtoCNF_X_37) ),
inference(clausify,[],[normalize_9_1]) ).
fof(normalize_9_3,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_9_0]) ).
fof(normalize_9_4,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_9_3]) ).
fof(normalize_9_5,plain,
! [X] : ~ q(X),
inference(conjunct,[],[normalize_9_0]) ).
fof(normalize_9_6,plain,
! [X] : ~ q(X),
inference(specialize,[],[normalize_9_5]) ).
cnf(refute_9_0,plain,
( p(skolemFOFtoCNF_X_36)
| q(skolemFOFtoCNF_X_37) ),
inference(canonicalize,[],[normalize_9_2]) ).
cnf(refute_9_1,plain,
~ p(X),
inference(canonicalize,[],[normalize_9_4]) ).
cnf(refute_9_2,plain,
~ p(skolemFOFtoCNF_X_36),
inference(subst,[],[refute_9_1:[bind(X,$fot(skolemFOFtoCNF_X_36))]]) ).
cnf(refute_9_3,plain,
q(skolemFOFtoCNF_X_37),
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_36) )],[refute_9_0,refute_9_2]) ).
cnf(refute_9_4,plain,
~ q(X),
inference(canonicalize,[],[normalize_9_6]) ).
cnf(refute_9_5,plain,
~ q(skolemFOFtoCNF_X_37),
inference(subst,[],[refute_9_4:[bind(X,$fot(skolemFOFtoCNF_X_37))]]) ).
cnf(refute_9_6,plain,
$false,
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_37) )],[refute_9_3,refute_9_5]) ).
fof(negate_10_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] : p(X)
| ? [X] : q(X) ) )
=> ? [X] :
( p(X)
| q(X) ) ),
inference(negate,[],[subgoal_10]) ).
fof(normalize_10_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] : p(X)
| ? [X] : q(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ p(X)
& ! [X] : ~ q(X) ),
inference(canonicalize,[],[negate_10_0]) ).
fof(normalize_10_1,plain,
( ? [X] : p(X)
| ? [X] : q(X) ),
inference(conjunct,[],[normalize_10_0]) ).
fof(normalize_10_2,plain,
( p(skolemFOFtoCNF_X_48)
| q(skolemFOFtoCNF_X_49) ),
inference(clausify,[],[normalize_10_1]) ).
fof(normalize_10_3,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_10_0]) ).
fof(normalize_10_4,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_10_3]) ).
fof(normalize_10_5,plain,
! [X] : ~ q(X),
inference(conjunct,[],[normalize_10_0]) ).
fof(normalize_10_6,plain,
! [X] : ~ q(X),
inference(specialize,[],[normalize_10_5]) ).
cnf(refute_10_0,plain,
( p(skolemFOFtoCNF_X_48)
| q(skolemFOFtoCNF_X_49) ),
inference(canonicalize,[],[normalize_10_2]) ).
cnf(refute_10_1,plain,
~ p(X),
inference(canonicalize,[],[normalize_10_4]) ).
cnf(refute_10_2,plain,
~ p(skolemFOFtoCNF_X_48),
inference(subst,[],[refute_10_1:[bind(X,$fot(skolemFOFtoCNF_X_48))]]) ).
cnf(refute_10_3,plain,
q(skolemFOFtoCNF_X_49),
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_48) )],[refute_10_0,refute_10_2]) ).
cnf(refute_10_4,plain,
~ q(X),
inference(canonicalize,[],[normalize_10_6]) ).
cnf(refute_10_5,plain,
~ q(skolemFOFtoCNF_X_49),
inference(subst,[],[refute_10_4:[bind(X,$fot(skolemFOFtoCNF_X_49))]]) ).
cnf(refute_10_6,plain,
$false,
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_49) )],[refute_10_3,refute_10_5]) ).
fof(negate_11_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) ) )
=> ? [Y] :
( p(Y)
=> ! [X] : p(X) ) ),
inference(negate,[],[subgoal_11]) ).
fof(normalize_11_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : ~ p(X)
& ! [Y] : p(Y) ),
inference(canonicalize,[],[negate_11_0]) ).
fof(normalize_11_1,plain,
? [X] : ~ p(X),
inference(conjunct,[],[normalize_11_0]) ).
fof(normalize_11_2,plain,
~ p(skolemFOFtoCNF_X_68),
inference(skolemize,[],[normalize_11_1]) ).
fof(normalize_11_3,plain,
! [Y] : p(Y),
inference(conjunct,[],[normalize_11_0]) ).
fof(normalize_11_4,plain,
! [Y] : p(Y),
inference(specialize,[],[normalize_11_3]) ).
cnf(refute_11_0,plain,
~ p(skolemFOFtoCNF_X_68),
inference(canonicalize,[],[normalize_11_2]) ).
cnf(refute_11_1,plain,
p(Y),
inference(canonicalize,[],[normalize_11_4]) ).
cnf(refute_11_2,plain,
p(skolemFOFtoCNF_X_68),
inference(subst,[],[refute_11_1:[bind(Y,$fot(skolemFOFtoCNF_X_68))]]) ).
cnf(refute_11_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_68) )],[refute_11_2,refute_11_0]) ).
fof(negate_12_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ? [X] :
( p(X)
& q(X) ) )
=> ? [X] : p(X) ),
inference(negate,[],[subgoal_12]) ).
fof(normalize_12_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] :
( p(X)
& q(X) )
& ! [X] : ~ p(X) ),
inference(canonicalize,[],[negate_12_0]) ).
fof(normalize_12_1,plain,
? [X] :
( p(X)
& q(X) ),
inference(conjunct,[],[normalize_12_0]) ).
fof(normalize_12_2,plain,
( p(skolemFOFtoCNF_X_79)
& q(skolemFOFtoCNF_X_79) ),
inference(skolemize,[],[normalize_12_1]) ).
fof(normalize_12_3,plain,
p(skolemFOFtoCNF_X_79),
inference(conjunct,[],[normalize_12_2]) ).
fof(normalize_12_4,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_12_0]) ).
fof(normalize_12_5,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_12_4]) ).
cnf(refute_12_0,plain,
p(skolemFOFtoCNF_X_79),
inference(canonicalize,[],[normalize_12_3]) ).
cnf(refute_12_1,plain,
~ p(X),
inference(canonicalize,[],[normalize_12_5]) ).
cnf(refute_12_2,plain,
~ p(skolemFOFtoCNF_X_79),
inference(subst,[],[refute_12_1:[bind(X,$fot(skolemFOFtoCNF_X_79))]]) ).
cnf(refute_12_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_79) )],[refute_12_0,refute_12_2]) ).
fof(negate_13_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ? [X] :
( p(X)
& q(X) )
& ? [X] : p(X) )
=> ? [X] : q(X) ),
inference(negate,[],[subgoal_13]) ).
fof(normalize_13_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : p(X)
& ? [X] :
( p(X)
& q(X) )
& ! [X] : ~ q(X) ),
inference(canonicalize,[],[negate_13_0]) ).
fof(normalize_13_1,plain,
? [X] :
( p(X)
& q(X) ),
inference(conjunct,[],[normalize_13_0]) ).
fof(normalize_13_2,plain,
( p(skolemFOFtoCNF_X_91)
& q(skolemFOFtoCNF_X_91) ),
inference(skolemize,[],[normalize_13_1]) ).
fof(normalize_13_3,plain,
q(skolemFOFtoCNF_X_91),
inference(conjunct,[],[normalize_13_2]) ).
fof(normalize_13_4,plain,
! [X] : ~ q(X),
inference(conjunct,[],[normalize_13_0]) ).
fof(normalize_13_5,plain,
! [X] : ~ q(X),
inference(specialize,[],[normalize_13_4]) ).
cnf(refute_13_0,plain,
q(skolemFOFtoCNF_X_91),
inference(canonicalize,[],[normalize_13_3]) ).
cnf(refute_13_1,plain,
~ q(X),
inference(canonicalize,[],[normalize_13_5]) ).
cnf(refute_13_2,plain,
~ q(skolemFOFtoCNF_X_91),
inference(subst,[],[refute_13_1:[bind(X,$fot(skolemFOFtoCNF_X_91))]]) ).
cnf(refute_13_3,plain,
$false,
inference(resolve,[$cnf( q(skolemFOFtoCNF_X_91) )],[refute_13_0,refute_13_2]) ).
fof(negate_14_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) ) )
=> ! [Y] :
( ! [X] : p(X)
=> p(Y) ) ),
inference(negate,[],[subgoal_14]) ).
fof(normalize_14_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [Y] : ~ p(Y)
& ! [X] : p(X) ),
inference(canonicalize,[],[negate_14_0]) ).
fof(normalize_14_1,plain,
? [Y] : ~ p(Y),
inference(conjunct,[],[normalize_14_0]) ).
fof(normalize_14_2,plain,
~ p(skolemFOFtoCNF_Y_26),
inference(skolemize,[],[normalize_14_1]) ).
fof(normalize_14_3,plain,
! [X] : p(X),
inference(conjunct,[],[normalize_14_0]) ).
fof(normalize_14_4,plain,
! [X] : p(X),
inference(specialize,[],[normalize_14_3]) ).
cnf(refute_14_0,plain,
~ p(skolemFOFtoCNF_Y_26),
inference(canonicalize,[],[normalize_14_2]) ).
cnf(refute_14_1,plain,
p(X),
inference(canonicalize,[],[normalize_14_4]) ).
cnf(refute_14_2,plain,
p(skolemFOFtoCNF_Y_26),
inference(subst,[],[refute_14_1:[bind(X,$fot(skolemFOFtoCNF_Y_26))]]) ).
cnf(refute_14_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_Y_26) )],[refute_14_2,refute_14_0]) ).
fof(negate_15_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ! [X] : p(X) )
=> ? [X] : p(X) ),
inference(negate,[],[subgoal_15]) ).
fof(normalize_15_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ p(X)
& ! [X] : p(X) ),
inference(canonicalize,[],[negate_15_0]) ).
fof(normalize_15_1,plain,
! [X] : p(X),
inference(conjunct,[],[normalize_15_0]) ).
fof(normalize_15_2,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_15_0]) ).
fof(normalize_15_3,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_15_2]) ).
fof(normalize_15_4,plain,
$false,
inference(simplify,[],[normalize_15_1,normalize_15_3]) ).
cnf(refute_15_0,plain,
$false,
inference(canonicalize,[],[normalize_15_4]) ).
fof(negate_16_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ~ ? [Y] : p(Y) )
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) ),
inference(negate,[],[subgoal_16]) ).
fof(normalize_16_0,plain,
( ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : p(X)
& ? [Y] : ~ p(Y)
& ! [Y] : ~ p(Y) ),
inference(canonicalize,[],[negate_16_0]) ).
fof(normalize_16_1,plain,
? [X] : p(X),
inference(conjunct,[],[normalize_16_0]) ).
fof(normalize_16_2,plain,
p(skolemFOFtoCNF_X_132),
inference(skolemize,[],[normalize_16_1]) ).
fof(normalize_16_3,plain,
! [Y] : ~ p(Y),
inference(conjunct,[],[normalize_16_0]) ).
fof(normalize_16_4,plain,
! [Y] : ~ p(Y),
inference(specialize,[],[normalize_16_3]) ).
cnf(refute_16_0,plain,
p(skolemFOFtoCNF_X_132),
inference(canonicalize,[],[normalize_16_2]) ).
cnf(refute_16_1,plain,
~ p(Y),
inference(canonicalize,[],[normalize_16_4]) ).
cnf(refute_16_2,plain,
~ p(skolemFOFtoCNF_X_132),
inference(subst,[],[refute_16_1:[bind(Y,$fot(skolemFOFtoCNF_X_132))]]) ).
cnf(refute_16_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_132) )],[refute_16_0,refute_16_2]) ).
fof(negate_17_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ! [X] :
( p(X)
| c )
& ~ ! [X] : p(X) )
=> c ),
inference(negate,[],[subgoal_17]) ).
fof(normalize_17_0,plain,
( ~ c
& ( c
| ! [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : ~ p(X) ),
inference(canonicalize,[],[negate_17_0]) ).
fof(normalize_17_1,plain,
? [X] : ~ p(X),
inference(conjunct,[],[normalize_17_0]) ).
fof(normalize_17_2,plain,
( c
| ! [X] : p(X) ),
inference(conjunct,[],[normalize_17_0]) ).
fof(normalize_17_3,plain,
~ c,
inference(conjunct,[],[normalize_17_0]) ).
fof(normalize_17_4,plain,
! [X] : p(X),
inference(simplify,[],[normalize_17_2,normalize_17_3]) ).
fof(normalize_17_5,plain,
! [X] : p(X),
inference(specialize,[],[normalize_17_4]) ).
fof(normalize_17_6,plain,
$false,
inference(simplify,[],[normalize_17_1,normalize_17_5]) ).
cnf(refute_17_0,plain,
$false,
inference(canonicalize,[],[normalize_17_6]) ).
fof(negate_18_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] : p(X)
| c ) )
=> ! [X] :
( ~ p(X)
=> c ) ),
inference(negate,[],[subgoal_18]) ).
fof(normalize_18_0,plain,
( ~ c
& ( c
| ! [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : ~ p(X) ),
inference(canonicalize,[],[negate_18_0]) ).
fof(normalize_18_1,plain,
? [X] : ~ p(X),
inference(conjunct,[],[normalize_18_0]) ).
fof(normalize_18_2,plain,
( c
| ! [X] : p(X) ),
inference(conjunct,[],[normalize_18_0]) ).
fof(normalize_18_3,plain,
~ c,
inference(conjunct,[],[normalize_18_0]) ).
fof(normalize_18_4,plain,
! [X] : p(X),
inference(simplify,[],[normalize_18_2,normalize_18_3]) ).
fof(normalize_18_5,plain,
! [X] : p(X),
inference(specialize,[],[normalize_18_4]) ).
fof(normalize_18_6,plain,
$false,
inference(simplify,[],[normalize_18_1,normalize_18_5]) ).
cnf(refute_18_0,plain,
$false,
inference(canonicalize,[],[normalize_18_6]) ).
fof(negate_19_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] :
( p(X)
& c ) )
=> ? [X] : p(X) ),
inference(negate,[],[subgoal_19]) ).
fof(normalize_19_0,plain,
$false,
inference(canonicalize,[],[negate_19_0]) ).
cnf(refute_19_0,plain,
$false,
inference(canonicalize,[],[normalize_19_0]) ).
fof(negate_20_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] :
( p(X)
& c )
& ? [X] : p(X) )
=> c ),
inference(negate,[],[subgoal_20]) ).
fof(normalize_20_0,plain,
$false,
inference(canonicalize,[],[negate_20_0]) ).
cnf(refute_20_0,plain,
$false,
inference(canonicalize,[],[normalize_20_0]) ).
fof(negate_21_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ? [X] : p(X)
& c )
=> ? [X] :
( p(X)
& c ) ),
inference(negate,[],[subgoal_21]) ).
fof(normalize_21_0,plain,
( c
& ( ~ c
| ! [X] : ~ p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : p(X) ),
inference(canonicalize,[],[negate_21_0]) ).
fof(normalize_21_1,plain,
? [X] : p(X),
inference(conjunct,[],[normalize_21_0]) ).
fof(normalize_21_2,plain,
( ~ c
| ! [X] : ~ p(X) ),
inference(conjunct,[],[normalize_21_0]) ).
fof(normalize_21_3,plain,
c,
inference(conjunct,[],[normalize_21_0]) ).
fof(normalize_21_4,plain,
! [X] : ~ p(X),
inference(simplify,[],[normalize_21_2,normalize_21_3]) ).
fof(normalize_21_5,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_21_4]) ).
fof(normalize_21_6,plain,
$false,
inference(simplify,[],[normalize_21_1,normalize_21_5]) ).
cnf(refute_21_0,plain,
$false,
inference(canonicalize,[],[normalize_21_6]) ).
fof(negate_22_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ? [X] : c )
=> c ),
inference(negate,[],[subgoal_22]) ).
fof(normalize_22_0,plain,
$false,
inference(canonicalize,[],[negate_22_0]) ).
cnf(refute_22_0,plain,
$false,
inference(canonicalize,[],[normalize_22_0]) ).
fof(negate_23_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& c )
=> ? [X] : c ),
inference(negate,[],[subgoal_23]) ).
fof(normalize_23_0,plain,
$false,
inference(canonicalize,[],[negate_23_0]) ).
cnf(refute_23_0,plain,
$false,
inference(canonicalize,[],[normalize_23_0]) ).
fof(negate_24_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ! [X] : c )
=> c ),
inference(negate,[],[subgoal_24]) ).
fof(normalize_24_0,plain,
$false,
inference(canonicalize,[],[negate_24_0]) ).
cnf(refute_24_0,plain,
$false,
inference(canonicalize,[],[normalize_24_0]) ).
fof(negate_25_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& c )
=> ! [X] : c ),
inference(negate,[],[subgoal_25]) ).
fof(normalize_25_0,plain,
$false,
inference(canonicalize,[],[negate_25_0]) ).
cnf(refute_25_0,plain,
$false,
inference(canonicalize,[],[normalize_25_0]) ).
fof(negate_26_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ? [X] :
( c
=> p(X) )
& c )
=> ? [X] : p(X) ),
inference(negate,[],[subgoal_26]) ).
fof(normalize_26_0,plain,
( c
& ( ~ c
| ? [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ p(X) ),
inference(canonicalize,[],[negate_26_0]) ).
fof(normalize_26_1,plain,
( ~ c
| ? [X] : p(X) ),
inference(conjunct,[],[normalize_26_0]) ).
fof(normalize_26_2,plain,
c,
inference(conjunct,[],[normalize_26_0]) ).
fof(normalize_26_3,plain,
? [X] : p(X),
inference(simplify,[],[normalize_26_1,normalize_26_2]) ).
fof(normalize_26_4,plain,
p(skolemFOFtoCNF_X_152),
inference(skolemize,[],[normalize_26_3]) ).
fof(normalize_26_5,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_26_0]) ).
fof(normalize_26_6,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_26_5]) ).
cnf(refute_26_0,plain,
p(skolemFOFtoCNF_X_152),
inference(canonicalize,[],[normalize_26_4]) ).
cnf(refute_26_1,plain,
~ p(X),
inference(canonicalize,[],[normalize_26_6]) ).
cnf(refute_26_2,plain,
~ p(skolemFOFtoCNF_X_152),
inference(subst,[],[refute_26_1:[bind(X,$fot(skolemFOFtoCNF_X_152))]]) ).
cnf(refute_26_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_152) )],[refute_26_0,refute_26_2]) ).
fof(negate_27_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( c
=> ? [X] : p(X) ) )
=> ? [X] :
( c
=> p(X) ) ),
inference(negate,[],[subgoal_27]) ).
fof(normalize_27_0,plain,
( c
& ( ~ c
| ? [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : ~ p(X) ),
inference(canonicalize,[],[negate_27_0]) ).
fof(normalize_27_1,plain,
( ~ c
| ? [X] : p(X) ),
inference(conjunct,[],[normalize_27_0]) ).
fof(normalize_27_2,plain,
c,
inference(conjunct,[],[normalize_27_0]) ).
fof(normalize_27_3,plain,
? [X] : p(X),
inference(simplify,[],[normalize_27_1,normalize_27_2]) ).
fof(normalize_27_4,plain,
p(skolemFOFtoCNF_X_168),
inference(skolemize,[],[normalize_27_3]) ).
fof(normalize_27_5,plain,
! [X] : ~ p(X),
inference(conjunct,[],[normalize_27_0]) ).
fof(normalize_27_6,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_27_5]) ).
cnf(refute_27_0,plain,
p(skolemFOFtoCNF_X_168),
inference(canonicalize,[],[normalize_27_4]) ).
cnf(refute_27_1,plain,
~ p(X),
inference(canonicalize,[],[normalize_27_6]) ).
cnf(refute_27_2,plain,
~ p(skolemFOFtoCNF_X_168),
inference(subst,[],[refute_27_1:[bind(X,$fot(skolemFOFtoCNF_X_168))]]) ).
cnf(refute_27_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_168) )],[refute_27_0,refute_27_2]) ).
fof(negate_28_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ? [X] :
( p(X)
=> c )
& ! [X] : p(X) )
=> c ),
inference(negate,[],[subgoal_28]) ).
fof(normalize_28_0,plain,
( ~ c
& ( c
| ? [X] : ~ p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : p(X) ),
inference(canonicalize,[],[negate_28_0]) ).
fof(normalize_28_1,plain,
( c
| ? [X] : ~ p(X) ),
inference(conjunct,[],[normalize_28_0]) ).
fof(normalize_28_2,plain,
~ c,
inference(conjunct,[],[normalize_28_0]) ).
fof(normalize_28_3,plain,
? [X] : ~ p(X),
inference(simplify,[],[normalize_28_1,normalize_28_2]) ).
fof(normalize_28_4,plain,
~ p(skolemFOFtoCNF_X_184),
inference(skolemize,[],[normalize_28_3]) ).
fof(normalize_28_5,plain,
! [X] : p(X),
inference(conjunct,[],[normalize_28_0]) ).
fof(normalize_28_6,plain,
! [X] : p(X),
inference(specialize,[],[normalize_28_5]) ).
cnf(refute_28_0,plain,
~ p(skolemFOFtoCNF_X_184),
inference(canonicalize,[],[normalize_28_4]) ).
cnf(refute_28_1,plain,
p(X),
inference(canonicalize,[],[normalize_28_6]) ).
cnf(refute_28_2,plain,
p(skolemFOFtoCNF_X_184),
inference(subst,[],[refute_28_1:[bind(X,$fot(skolemFOFtoCNF_X_184))]]) ).
cnf(refute_28_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_184) )],[refute_28_2,refute_28_0]) ).
fof(negate_29_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ! [X] : p(X)
=> c ) )
=> ? [X] :
( p(X)
=> c ) ),
inference(negate,[],[subgoal_29]) ).
fof(normalize_29_0,plain,
( ~ c
& ( c
| ? [X] : ~ p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ! [X] : p(X) ),
inference(canonicalize,[],[negate_29_0]) ).
fof(normalize_29_1,plain,
( c
| ? [X] : ~ p(X) ),
inference(conjunct,[],[normalize_29_0]) ).
fof(normalize_29_2,plain,
~ c,
inference(conjunct,[],[normalize_29_0]) ).
fof(normalize_29_3,plain,
? [X] : ~ p(X),
inference(simplify,[],[normalize_29_1,normalize_29_2]) ).
fof(normalize_29_4,plain,
~ p(skolemFOFtoCNF_X_200),
inference(skolemize,[],[normalize_29_3]) ).
fof(normalize_29_5,plain,
! [X] : p(X),
inference(conjunct,[],[normalize_29_0]) ).
fof(normalize_29_6,plain,
! [X] : p(X),
inference(specialize,[],[normalize_29_5]) ).
cnf(refute_29_0,plain,
~ p(skolemFOFtoCNF_X_200),
inference(canonicalize,[],[normalize_29_4]) ).
cnf(refute_29_1,plain,
p(X),
inference(canonicalize,[],[normalize_29_6]) ).
cnf(refute_29_2,plain,
p(skolemFOFtoCNF_X_200),
inference(subst,[],[refute_29_1:[bind(X,$fot(skolemFOFtoCNF_X_200))]]) ).
cnf(refute_29_3,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_X_200) )],[refute_29_2,refute_29_0]) ).
fof(negate_30_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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) ),
inference(negate,[],[subgoal_30]) ).
fof(normalize_30_0,plain,
( c
& ( ~ c
| ! [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : ~ p(X) ),
inference(canonicalize,[],[negate_30_0]) ).
fof(normalize_30_1,plain,
? [X] : ~ p(X),
inference(conjunct,[],[normalize_30_0]) ).
fof(normalize_30_2,plain,
( ~ c
| ! [X] : p(X) ),
inference(conjunct,[],[normalize_30_0]) ).
fof(normalize_30_3,plain,
c,
inference(conjunct,[],[normalize_30_0]) ).
fof(normalize_30_4,plain,
! [X] : p(X),
inference(simplify,[],[normalize_30_2,normalize_30_3]) ).
fof(normalize_30_5,plain,
! [X] : p(X),
inference(specialize,[],[normalize_30_4]) ).
fof(normalize_30_6,plain,
$false,
inference(simplify,[],[normalize_30_1,normalize_30_5]) ).
cnf(refute_30_0,plain,
$false,
inference(canonicalize,[],[normalize_30_6]) ).
fof(negate_31_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> c )
& ( ? [X] :
( c
=> p(X) )
<=> ( c
=> ? [X] : p(X) ) )
& ( ? [X] :
( p(X)
=> c )
<=> ( ! [X] : p(X)
=> c ) )
& ( c
=> ! [X] : p(X) ) )
=> ! [X] :
( c
=> p(X) ) ),
inference(negate,[],[subgoal_31]) ).
fof(normalize_31_0,plain,
( c
& ( ~ c
| ! [X] : p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : ~ p(X) ),
inference(canonicalize,[],[negate_31_0]) ).
fof(normalize_31_1,plain,
? [X] : ~ p(X),
inference(conjunct,[],[normalize_31_0]) ).
fof(normalize_31_2,plain,
( ~ c
| ! [X] : p(X) ),
inference(conjunct,[],[normalize_31_0]) ).
fof(normalize_31_3,plain,
c,
inference(conjunct,[],[normalize_31_0]) ).
fof(normalize_31_4,plain,
! [X] : p(X),
inference(simplify,[],[normalize_31_2,normalize_31_3]) ).
fof(normalize_31_5,plain,
! [X] : p(X),
inference(specialize,[],[normalize_31_4]) ).
fof(normalize_31_6,plain,
$false,
inference(simplify,[],[normalize_31_1,normalize_31_5]) ).
cnf(refute_31_0,plain,
$false,
inference(canonicalize,[],[normalize_31_6]) ).
fof(negate_32_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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] :
( p(X)
=> c )
& ? [X] : p(X) )
=> c ),
inference(negate,[],[subgoal_32]) ).
fof(normalize_32_0,plain,
( ~ c
& ( c
| ! [X] : ~ p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : p(X) ),
inference(canonicalize,[],[negate_32_0]) ).
fof(normalize_32_1,plain,
? [X] : p(X),
inference(conjunct,[],[normalize_32_0]) ).
fof(normalize_32_2,plain,
( c
| ! [X] : ~ p(X) ),
inference(conjunct,[],[normalize_32_0]) ).
fof(normalize_32_3,plain,
~ c,
inference(conjunct,[],[normalize_32_0]) ).
fof(normalize_32_4,plain,
! [X] : ~ p(X),
inference(simplify,[],[normalize_32_2,normalize_32_3]) ).
fof(normalize_32_5,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_32_4]) ).
fof(normalize_32_6,plain,
$false,
inference(simplify,[],[normalize_32_1,normalize_32_5]) ).
cnf(refute_32_0,plain,
$false,
inference(canonicalize,[],[normalize_32_6]) ).
fof(negate_33_0,plain,
~ ( ( ( ( ! [X] :
( ( ( f(X)
& g(X) )
=> h(X) )
=> ? [Y] :
( f(Y)
& ~ g(Y) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ( ( ! [X,Y] :
( r(X,Y)
=> r(Y,X) )
& ! [X,Y,Z] :
( ( r(X,Y)
& r(Y,Z) )
=> r(X,Z) ) )
=> ! [X,Y] :
( r(X,Y)
=> r(X,X) ) )
& ( ( ( ! [X] :
( ( f(X)
& g(X) )
=> h(X) )
=> ? [X] :
( f(X)
& ~ g(X) ) )
& ( ! [W] :
( f(W)
=> g(W) )
| ! [Z] :
( f(Z)
=> h(Z) ) ) )
=> ( ! [R] :
( ( f(R)
& h(R) )
=> g(R) )
=> ? [V] :
( f(V)
& g(V)
& ~ h(V) ) ) )
& ? [X] :
! [Y] :
( ( p(Y)
=> q(X) )
=> ( p(X)
=> q(X) ) )
& ( ! [X] :
( p(X)
& q(X) )
<=> ( ! [X] : p(X)
& ! [X] : q(X) ) )
& ( ( ! [X] : p(X)
| ! [X] : q(X) )
=> ! [X] :
( p(X)
| q(X) ) )
& ( ? [X] :
( p(X)
| q(X) )
<=> ( ? [X] : p(X)
| ? [X] : q(X) ) )
& ? [Y] :
( p(Y)
=> ! [X] : p(X) )
& ( ? [X] :
( p(X)
& q(X) )
=> ( ? [X] : p(X)
& ? [X] : q(X) ) )
& ! [Y] :
( ! [X] : p(X)
=> p(Y) )
& ( ! [X] : p(X)
=> ? [X] : p(X) )
& ( ~ ? [Y] : p(Y)
=> ! [Y] :
( ? [X] : p(X)
=> p(Y) ) )
& ( ! [X] :
( p(X)
| c )
<=> ( ! [X] : p(X)
| c ) )
& ( ? [X] :
( p(X)
& c )
<=> ( ? [X] : p(X)
& c ) )
& ( ? [X] : c
<=> c )
& ( ! [X] : c
<=> 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] : p(X)
=> c ) )
=> ! [X] :
( p(X)
=> c ) ),
inference(negate,[],[subgoal_33]) ).
fof(normalize_33_0,plain,
( ~ c
& ( c
| ! [X] : ~ p(X) )
& ( ( ? [X] : ~ p(X)
& ? [X] : ~ q(X) )
| ! [X] :
( p(X)
| q(X) ) )
& ( ( ? [X] : p(X)
& ? [X] : q(X) )
| ! [X] :
( ~ p(X)
| ~ q(X) ) )
& ( ? [X] : ~ p(X)
| ? [X] : p(X) )
& ( ? [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [Y] : ~ p(Y)
| ! [X] : p(X) )
& ( ( ? [X] : ~ q(X)
& ! [Y] : p(Y) )
| ? [X] : ~ p(X)
| ? [X] : q(X) )
& ( ? [Y] : p(Y)
| ! [X] : ~ p(X)
| ! [Y] : p(Y) )
& ( ? [X,Y] :
( ~ r(Y,X)
& r(X,Y) )
| ? [X,Y,Z] :
( ~ r(X,Z)
& r(X,Y)
& r(Y,Z) )
| ! [X] :
( r(X,X)
| ! [Y] : ~ r(X,Y) ) )
& ( ( ( ? [X] : ~ f(X)
| ? [X] : ~ g(X)
| ? [X] : h(X) )
& ! [Y] :
( ~ f(Y)
| g(Y) ) )
| ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ( ( ? [W] :
( ~ g(W)
& f(W) )
& ? [Z] :
( ~ h(Z)
& f(Z) ) )
| ( ! [X] :
( ~ f(X)
| g(X) )
& ! [X] :
( ~ f(X)
| ~ g(X)
| h(X) ) )
| ? [R] :
( ~ g(R)
& f(R)
& h(R) )
| ? [V] :
( ~ h(V)
& f(V)
& g(V) ) )
& ? [X] : p(X) ),
inference(canonicalize,[],[negate_33_0]) ).
fof(normalize_33_1,plain,
? [X] : p(X),
inference(conjunct,[],[normalize_33_0]) ).
fof(normalize_33_2,plain,
( c
| ! [X] : ~ p(X) ),
inference(conjunct,[],[normalize_33_0]) ).
fof(normalize_33_3,plain,
~ c,
inference(conjunct,[],[normalize_33_0]) ).
fof(normalize_33_4,plain,
! [X] : ~ p(X),
inference(simplify,[],[normalize_33_2,normalize_33_3]) ).
fof(normalize_33_5,plain,
! [X] : ~ p(X),
inference(specialize,[],[normalize_33_4]) ).
fof(normalize_33_6,plain,
$false,
inference(simplify,[],[normalize_33_1,normalize_33_5]) ).
cnf(refute_33_0,plain,
$false,
inference(canonicalize,[],[normalize_33_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN917+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 16:24:05 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.50
% 0.20/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.60
%------------------------------------------------------------------------------