## TPTP Problem File: SEV453^1.p

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```%------------------------------------------------------------------------------
% File     : SEV453^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : INTER_UNIV_
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : INTER_UNIV_1.p [Kal16]

% Status   : Theorem
% Rating   : 0.25 v7.5.0, 0.00 v7.1.0
% Syntax   : Number of formulae    :    8 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   48 (   6 equality;  31 variable)
%            Maximal formula depth :   10 (   7 average)
%            Number of connectives :   31 (   0   ~;   0   |;   1   &;  30   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   18 (   0 sgn;  15   !;   0   ?;   0   ^)
%                                         (  18   :;   3  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
thf('thf_const_const/sets/UNIV',type,(
'const/sets/UNIV':
!>[A: \$tType] :
( A > \$o ) )).

thf('thf_const_const/sets/INTER',type,(
'const/sets/INTER':
!>[A: \$tType] :
( ( A > \$o ) > ( A > \$o ) > A > \$o ) )).

thf('thf_const_const/sets/IN',type,(
'const/sets/IN':
!>[A: \$tType] :
( A > ( A > \$o ) > \$o ) )).

thf('thm/sets/IN_',axiom,(
! [A: \$tType,P: A > \$o,A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ P )
= ( P @ A0 ) ) )).

thf('thm/sets/IN_UNIV_',axiom,(
! [A: \$tType,A0: A] :
( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) ) )).

thf('thm/sets/IN_INTER_',axiom,(
! [A: \$tType,A0: A > \$o,A1: A > \$o,A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/INTER' @ A @ A0 @ A1 ) )
= ( ( 'const/sets/IN' @ A @ A2 @ A0 )
& ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) )).

thf('thm/sets/EXTENSION_',axiom,(
! [A: \$tType,A0: A > \$o,A1: A > \$o] :
( ( A0 = A1 )
= ( ! [A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ A0 )
= ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) )).

thf('thm/sets/INTER_UNIV_1',conjecture,(
! [A: \$tType,A0: A > \$o] :
( ( 'const/sets/INTER' @ A @ A0 @ ( 'const/sets/UNIV' @ A ) )
= A0 ) )).

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