%------------------------------------------------------------------------------
% File     : SYO042^1 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : Unsatisfiable basic formula 4
% Version  : Especial.
% English  : 

% Refs     : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
%          : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% Source   : [BS09a]
% Names    : 

% Status   : Unsatisfiable
% Rating   : 0.00 v5.4.0, 0.33 v5.3.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :   15 (   3 equ;   1 cnn)
%            Maximal formula atoms :    7 (  15 avg)
%            Number of connectives :   11 (   3   ~;   0   |;   4   &;   4   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^;   0   !;   0   ?;   0   :)
% SPC      : TH0_UNS_EQU_NAR

% Comments : The fragment of simple type theory that restricts equations to 
%            base types and disallows lambda abstraction and quantification is
%            decidable. This is an example.
%------------------------------------------------------------------------------
thf(g,type,
    g: $o > $o ).

thf(p,type,
    p: ( $o > $o ) > $o ).

thf(x,type,
    x: $o ).

thf(y,type,
    y: $o ).

thf(4,axiom,
    ( ( x != y )
    & ( ( g @ x )
      = y )
    & ( ( g @ y )
      = x )
    & ( p @ g )
    & ~ ( p @ (~) ) ) ).

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