%--------------------------------------------------------------------------
% File     : SYN323+1 : TPTP v8.2.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Church problem 46.4 (2)
% Version  : Especial.
% English  :

% Refs     : [Chu56] Church (1956), Introduction to Mathematical Logic I
% Source   : [Chu56]
% Names    : 46.4 (2) [Chu56]

% Status   : Theorem
% Rating   : 0.00 v5.5.0, 0.11 v5.4.0, 0.00 v5.3.0, 0.09 v5.2.0, 0.00 v4.1.0, 0.06 v4.0.1, 0.05 v3.7.0, 0.33 v3.5.0, 0.12 v3.4.0, 0.08 v3.3.0, 0.00 v3.2.0, 0.11 v3.1.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.00 v2.1.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 def)
%            Number of atoms       :    6 (   0 equ)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives :    7 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    3 (   2   !;   1   ?)
% SPC      : FOF_THM_EPR_NEQ

% Comments : The free variable is existentially quantified. Based on CNF.
%--------------------------------------------------------------------------
fof(church_46_4_2,conjecture,
    ? [Y] :
      ( ! [X] :
          ( ( big_f(X,Y)
           => big_f(Y,X) )
         => big_g(X,Y) )
     => ~ ! [X] :
            ( ( big_f(X,Y)
             => big_f(Y,X) )
           => ~ big_g(X,Y) ) ) ).

%--------------------------------------------------------------------------