%------------------------------------------------------------------------------
% File     : SEV016^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem from EQUIVALENCE-RELATIONS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0932 [Bro09]

% Status   : Theorem
% Rating   : 0.62 v9.0.0, 0.80 v8.2.0, 0.77 v8.1.0, 0.91 v7.5.0, 0.86 v7.4.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    3 (   3 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :   15 (   0   ~;   0   |;   4   &;   8   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (  12 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   10 (   2   ^;   4   !;   4   ?;  10   :)
% 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(a_type,type,
    a: $tType ).

thf(cTHM262_NEW_pme,conjecture,
    ! [P: ( a > $o ) > $o] :
      ( ( ! [Xp: a > $o] :
            ( ( P @ Xp )
           => ? [Xz: a] : ( Xp @ Xz ) )
        & ! [Xx: a] :
          ? [Xp: a > $o] :
            ( ( P @ Xp )
            & ( Xp @ Xx )
            & ! [Xq: a > $o] :
                ( ( ( P @ Xq )
                  & ( Xq @ Xx ) )
               => ( Xq = Xp ) ) ) )
     => ? [Q: a > a > $o] :
          ( ( ^ [Xs: a > $o] :
              ? [Xz: a] :
                ( Xs
                = ( ^ [Xx: a] : ( Q @ Xx @ Xz ) ) ) )
          = P ) ) ).

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