## TPTP Problem File: SYO376^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO376^5 : TPTP v7.1.0. 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_0807 [Bro09]

% Status   : Theorem
% Rating   : 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, 0.67 v6.1.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.00 v5.4.0, 0.25 v5.3.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0, 1.00 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   14 (   0 equality;   4 variable)
%            Maximal formula depth :    8 (   4 average)
%            Number of connectives :   14 (   1   ~;   3   |;   1   &;   8   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3   :;   0   =)
%            Number of variables   :    2 (   0 sgn;   0   !;   0   ?;   2   ^)
%                                         (   2   :;   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(cG,type,(
cG: \$o > \$o )).

thf(cF,type,(
cF: \$o > \$o )).

thf(cP,type,(
cP: ( \$o > \$o ) > \$o )).

thf(cTHM627,conjecture,
( ( ( cP @ cF )
& ( cP @ cG ) )
=> ( ( cP
@ ^ [Xx: \$o] :
( ( cF @ Xx )
| ( cG @ Xx ) ) )
| ( cP
@ ^ [Xx: \$o] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) ) ) )).

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