%------------------------------------------------------------------------------
% File     : SYO217^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM174
% Version  : Especial.
% English  : Principle of extensionality for binary relations.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0105 [Bro09]
%          : THM174 [TPS]

% Status   : Theorem
% Rating   : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    3 (   1 unt;   2 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   0   ~;   0   |;   0   &;   4   @)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :    4 (   0   ^;   4   !;   0   ?;   4   :)
% 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(cTHM174,conjecture,
    ! [Xr: b > a > $o,Xs: b > a > $o] :
      ( ! [Xx: b,Xy: a] :
          ( ( Xr @ Xx @ Xy )
        <=> ( Xs @ Xx @ Xy ) )
     => ( Xr = Xs ) ) ).

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