## TPTP Problem File: SYO377^5.p

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```%------------------------------------------------------------------------------
% File     : SYO377^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from EXTENSIONALITY
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0831 [Bro09]

% Status   : Theorem
% Rating   : 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.33 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   13 (   0 equality;   9 variable)
%            Maximal formula depth :    8 (   4 average)
%            Number of connectives :   12 (   0   ~;   0   |;   2   &;   5   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2   :;   0   =)
%            Number of variables   :    4 (   0 sgn;   4   !;   0   ?;   0   ^)
%                                         (   4   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_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(b,type,(
b: \$o )).

thf(a,type,(
a: \$o )).

thf(cEXT_IMP_EMB2,conjecture,
( ! [Xx: \$o,Xy: \$o] :
( ( Xx
<=> Xy )
=> ! [Xq: \$o > \$o] :
( ( Xq @ Xx )
=> ( Xq @ Xy ) ) )
=> ! [Xp: \$o > \$o] :
( ( ( Xp @ a )
& ( Xp @ b ) )
=> ( Xp
@ ( a
& b ) ) ) )).

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