%------------------------------------------------------------------------------
% File     : SYO313^5 : 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_0906 [Bro09]

% Status   : CounterSatisfiable
% Rating   : 0.00 v7.4.0, 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    4 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :   19 (   0   ~;   0   |;   2   &;  12   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    8 (   0   ^;   5   !;   3   ?;   8   :)
% 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(cELESS,type,
    cELESS: $i > $i > $o ).

thf(cELUB,conjecture,
    ! [A: $i > $o] :
      ( ( ? [Xr: $i] : ( A @ Xr )
        & ? [Xu: $i] :
          ! [Xx: $i] :
            ( ( A @ Xx )
           => ( cELESS @ Xx @ Xu ) ) )
     => ? [Xl: $i] :
          ( ! [Xx: $i] :
              ( ( A @ Xx )
             => ( cELESS @ Xx @ Xl ) )
          & ! [Xy: $i] :
              ( ! [Xx: $i] :
                  ( ( A @ Xx )
                 => ( cELESS @ Xx @ Xy ) )
             => ( cELESS @ Xl @ Xy ) ) ) ) ).

%------------------------------------------------------------------------------