%------------------------------------------------------------------------------
% File     : SYO279^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-HO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0649 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   1 unt;   3 typ;   0 def)
%            Number of atoms       :    1 (   0 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   0   ~;   0   |;   0   &;   6   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    2 (   0   ^;   2   !;   0   ?;   2   :)
% SPC      : TH0_CSA_NEQ_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(cLAM,type,
    cLAM: ( $i > $i ) > $i ).

thf(cAPP,type,
    cAPP: $i > $i > $i ).

thf(cReduct,type,
    cReduct: $i > $i > $o ).

thf(cBETA_CONVERSION,conjecture,
    ! [Xx: $i > $i,Xy: $i] : ( cReduct @ ( cAPP @ ( cLAM @ Xx ) @ Xy ) @ ( Xx @ Xy ) ) ).

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