%------------------------------------------------------------------------------
% File     : SYO218^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem THM7B
% Version  : Especial.
% English  : Half-proved version of thm7 for test purposes.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0135 [Bro09]
%          : THM7B [TPS]

% Status   : Theorem
% Rating   : 0.20 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, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :    5 (   5 equ;   0 cnn)
%            Maximal formula atoms :    3 (   5 avg)
%            Number of connectives :    4 (   0   ~;   0   |;   0   &;   2   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 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   :    5 (   2   ^;   3   !;   0   ?;   5   :)
% 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(cTHM7B_pme,conjecture,
    ! [Xx: $i,Xy: $i] :
      ( ! [Xq: ( $i > $o ) > $i] :
          ( ( Xx
            = ( Xq
              @ ^ [Xz: $i] : Xx = Xz ) )
         => ( Xy
            = ( Xq
              @ ^ [Xz: $i] : Xy = Xz ) ) )
     => ( Xx = Xy ) ) ).

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