## TPTP Problem File: SEV447^1.p

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```%------------------------------------------------------------------------------
% File     : SEV447^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : NOT_EQUAL_SETS
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :    4 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   33 (   7 equality;  21 variable)
%            Maximal formula depth :   11 (   9 average)
%            Number of connectives :   18 (   2   ~;   0   |;   0   &;  16   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   12 (   0 sgn;  10   !;   1   ?;   0   ^)
%                                         (  12   :;   1  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
%------------------------------------------------------------------------------
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/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/NOT_EQUAL_SETS_',conjecture,(
! [A: \$tType,A0: A > \$o,A1: A > \$o] :
( ( A0 != A1 )
= ( ? [A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ A1 )
= ( ~ ( 'const/sets/IN' @ A @ A2 @ A0 ) ) ) ) ) )).

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