%------------------------------------------------------------------------------
% File     : SYO236^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-EQ-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0774 [Bro09]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :    2 (   2 equ;   0 cnn)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    7 (   0   ~;   1   |;   0   &;   4   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    2 (   0   ^;   2   !;   0   ?;   2   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%------------------------------------------------------------------------------
thf(b_type,type,
    b: $tType ).

thf(a_type,type,
    a: $tType ).

thf(g,type,
    g: b > a ).

thf(f,type,
    f: b > a ).

thf(cTHM504,conjecture,
    ( ( ! [Q: ( b > a ) > $o] :
          ( ( Q @ f )
         => ( Q @ g ) )
      | ! [Xx: b] :
          ( ( f @ Xx )
          = ( g @ Xx ) ) )
   => ( f = g ) ) ).

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