%------------------------------------------------------------------------------
% File     : SYO246^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-EQ-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1022 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 1.00 v6.1.0, 0.86 v5.5.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   27 (   0   ~;   0   |;   3   &;  16   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   9 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   15 (   2   ^;   7   !;   6   ?;  15   :)
% 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(cTHM535,conjecture,
    ( ! [Xs: ( ( a > $o ) > $o ) > $o] :
        ( ! [X: ( a > $o ) > $o] :
            ( ( Xs @ X )
           => ? [Xt: a > $o] : ( X @ Xt ) )
       => ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
          ! [X: ( a > $o ) > $o] :
            ( ( Xs @ X )
           => ( X @ ( Xf @ X ) ) ) )
   => ! [A: ( ( a > $o ) > $o ) > $o] :
        ( ( ? [X: ( a > $o ) > $o] : ( A @ X )
          & ! [X: ( a > $o ) > $o] :
              ( ( A @ X )
             => ? [Xu: a > $o] : ( X @ Xu ) ) )
       => ( ( ^ [Xx: a] :
              ! [Xa: ( a > $o ) > $o] :
                ( ( A @ Xa )
               => ? [Xb: a > $o] :
                    ( ( Xa @ Xb )
                    & ( Xb @ Xx ) ) ) )
          = ( ^ [Xx: a] :
              ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
              ! [Xa: ( a > $o ) > $o] :
                ( ( A @ Xa )
               => ( ( Xa @ ( Xf @ Xa ) )
                  & ( Xf @ Xa @ Xx ) ) ) ) ) ) ) ).

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