%--------------------------------------------------------------------------
% File     : SYN077+1 : TPTP v9.0.0. Released v2.0.0.
% Domain   : Syntactic
% Problem  : Pelletier Problem 54
% Version  : Especial.
% English  : Montegue's paradox of grounded classes

% Refs     : [Mon55] Montegue (1955), On the Paradox of Grounded Classes
%          : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
%          : [Pel88] Pelletier (1988), Errata
%          : [Hah94] Haehnle (1994), Email to G. Sutcliffe
% Source   : [Hah94]
% Names    : Pelletier 54 [Pel86]

% Status   : Theorem
% Rating   : 0.21 v9.0.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.14 v7.2.0, 0.10 v7.1.0, 0.09 v7.0.0, 0.10 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.36 v6.1.0, 0.37 v6.0.0, 0.30 v5.5.0, 0.37 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.20 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.29 v3.5.0, 0.11 v3.4.0, 0.17 v3.3.0, 0.00 v3.2.0, 0.22 v3.1.0, 0.33 v2.7.0, 0.00 v2.5.0, 0.33 v2.4.0, 0.33 v2.2.1, 0.00 v2.1.0
% Syntax   : Number of formulae    :    2 (   0 unt;   0 def)
%            Number of atoms       :    7 (   1 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :    7 (   2   ~;   0   |;   2   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   9 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 2-2 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :    8 (   4   !;   4   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : This problem is incorrect in [Pel86] and is corrected in [Pel88].
%--------------------------------------------------------------------------
%----Problem axioms
fof(pel54_1,axiom,
    ! [Y] :
    ? [Z] :
    ! [X] :
      ( big_f(X,Z)
    <=> X = Y ) ).

fof(pel54,conjecture,
    ~ ? [W] :
      ! [X] :
        ( big_f(X,W)
      <=> ! [U] :
            ( big_f(X,U)
           => ? [Y] :
                ( big_f(Y,U)
                & ~ ? [Z] :
                      ( big_f(Z,U)
                      & big_f(Z,Y) ) ) ) ) ).

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