## TPTP Problem File: SYO313^5.p

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```%------------------------------------------------------------------------------
% File     : SYO313^5 : TPTP v7.0.0. 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   : 0.33 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   20 (   0 equality;  16 variable)
%            Maximal formula depth :   11 (   8 average)
%            Number of connectives :   19 (   0   ~;   0   |;   2   &;  12   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    8 (   0 sgn;   5   !;   3   ?;   0   ^)
%                                         (   8   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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
%          :
%------------------------------------------------------------------------------
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 ) ) ) ) )).

%------------------------------------------------------------------------------
```