## TPTP Problem File: SEV416^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV416^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0880 [Bro09]

% Status   : Theorem
% Rating   : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   19 (   0 equality;   8 variable)
%            Maximal formula depth :    8 (   4 average)
%            Number of connectives :   18 (   0   ~;   1   |;   1   &;   8   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   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(cG,type,(
cG: \$o )).

thf(cB,type,(
cB: \$i > \$o )).

thf(cA,type,(
cA: \$i > \$o )).

thf(cDUAL_EG3_pme,conjecture,
( ( ( ( ! [Xx: \$i] :
( ( cA @ Xx )
=> ( cB @ Xx ) )
& ! [Xx: \$i] :
( ( cA @ Xx )
=> ( cB @ Xx ) ) )
=> cG )
| ( ! [Xx: \$i] :
( ( cA @ Xx )
=> ( cB @ Xx ) )
=> cG ) )
=> ( ! [Xx: \$i] :
( ( cA @ Xx )
=> ( cB @ Xx ) )
=> cG ) )).

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