%------------------------------------------------------------------------------
% File     : SEV121^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM47C
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0445 [Bro09]
%          : THM47C [TPS]
%          : tps_0444 [Bro09]
%          : X5303 [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   1 unt;   0 typ;   0 def)
%            Number of atoms       :    2 (   2 equ;   0 cnn)
%            Maximal formula atoms :    1 (   2 avg)
%            Number of connectives :    5 (   0   ~;   0   |;   0   &;   4   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :    6 (   4   ^;   2   !;   0   ?;   6   :)
% 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/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM47C_pme,conjecture,
    ( ( ^ [Xu: $i,Xv: $i] : ( Xu = Xv ) )
    = ( ^ [Xx: $i,Xy: $i] :
        ! [Xp: $i > $i > $o] :
          ( ! [Xx0: $i] : ( Xp @ Xx0 @ Xx0 )
         => ( Xp @ Xx @ Xy ) ) ) ) ).

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