%------------------------------------------------------------------------------
% File     : ALG298^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : General Algebra
% Problem  : TPS problem THM270
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0400 [Bro09]
%          : THM270 [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.20 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    7 (   0 unt;   6 typ;   0 def)
%            Number of atoms       :    5 (   5 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :   29 (   0   ~;   0   |;   3   &;  25   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (  10 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   0 con; 2-2 aty)
%            Number of variables   :   12 (   0   ^;  11   !;   1   ?;  12   :)
% 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(c_type,type,
    c: $tType ).

thf(b_type,type,
    b: $tType ).

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

thf(c_starc,type,
    c_starc: c > c > c ).

thf(c_starb,type,
    c_starb: b > b > b ).

thf(c_stara,type,
    c_stara: a > a > a ).

thf(cTHM270_pme,conjecture,
    ! [Xf: a > b,Xg: a > c,Xh: b > c] :
      ( ( ! [Xx: a] :
            ( ( Xh @ ( Xf @ Xx ) )
            = ( Xg @ Xx ) )
        & ! [Xy: b] :
          ? [Xx: a] :
            ( ( Xf @ Xx )
            = Xy )
        & ! [Xx: a,Xy: a] :
            ( ( Xf @ ( c_stara @ Xx @ Xy ) )
            = ( c_starb @ ( Xf @ Xx ) @ ( Xf @ Xy ) ) )
        & ! [Xx: a,Xy: a] :
            ( ( Xg @ ( c_stara @ Xx @ Xy ) )
            = ( c_starc @ ( Xg @ Xx ) @ ( Xg @ Xy ) ) ) )
     => ! [Xx: b,Xy: b] :
          ( ( Xh @ ( c_starb @ Xx @ Xy ) )
          = ( c_starc @ ( Xh @ Xx ) @ ( Xh @ Xy ) ) ) ) ).

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