%--------------------------------------------------------------------------
% File     : SYN333+1 : TPTP v8.2.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Church problem 46.14 (5)
% Version  : Especial.
% English  :

% Refs     : [Chu56] Church (1956), Introduction to Mathematical Logic I
% Source   : [Chu56]
% Names    : 46.14 (5) [Chu56]

% Status   : Theorem
% Rating   : 0.00 v7.0.0, 0.25 v6.4.0, 0.00 v5.3.0, 0.18 v5.2.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.16 v4.0.0, 0.15 v3.7.0, 0.33 v3.5.0, 0.12 v3.4.0, 0.08 v3.3.0, 0.11 v3.2.0, 0.22 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       :    7 (   0 equ)
%            Maximal formula atoms :    7 (   7 avg)
%            Number of connectives :    6 (   0   ~;   0   |;   4   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 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 (   1   !;   2   ?)
% SPC      : FOF_THM_EPR_NEQ

% Comments :
%--------------------------------------------------------------------------
fof(church_46_14_5,conjecture,
    ? [X,Y] :
    ! [Z] :
      ( big_f(X,Y)
     => ( big_f(Y,Z)
        & big_f(Z,Z)
        & ( ( big_f(X,Y)
            & big_g(X,Y) )
         => ( big_g(X,Z)
            & big_g(Z,Z) ) ) ) ) ).

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