## TPTP Problem File: SEV467^1.p

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```%------------------------------------------------------------------------------
% File     : SEV467^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : FORALL_IN_GSPEC_
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : FORALL_IN_GSPEC_1.p [Kal16]

% Status   : Theorem
% Rating   : 0.75 v7.5.0, 1.00 v7.1.0
% Syntax   : Number of formulae    :    5 (   0 unit;   3 type;   0 defn)
%            Number of atoms       :   39 (   3 equality;  30 variable)
%            Maximal formula depth :   19 (   9 average)
%            Number of connectives :   31 (   0   ~;   0   |;   1   &;  28   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    5 (   3   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   21 (   0 sgn;  12   !;   2   ?;   4   ^)
%                                         (  21   :;   3  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

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

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

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

thf('thm/sets/IN_ELIM_THM_0',axiom,(
! [A: \$tType,P: ( \$o > A > \$o ) > \$o,A0: A] :
( ( 'const/sets/IN' @ A @ A0
@ ( 'const/sets/GSPEC' @ A
@ ^ [A1: A] :
( P @ ( 'const/sets/SETSPEC' @ A @ A1 ) ) ) )
= ( P
@ ^ [A1: \$o,A2: A] :
( A1
& ( A0 = A2 ) ) ) ) )).

thf('thm/sets/FORALL_IN_GSPEC_1',conjecture,(
! [A: \$tType,A0: \$tType,A1: \$tType,Q: A > \$o,P: A0 > A1 > \$o,A2: A0 > A1 > A] :
( ( ! [A3: A] :
( ( 'const/sets/IN' @ A @ A3
@ ( 'const/sets/GSPEC' @ A
@ ^ [A4: A] :
? [A5: A0,A6: A1] :
( 'const/sets/SETSPEC' @ A @ A4 @ ( P @ A5 @ A6 ) @ ( A2 @ A5 @ A6 ) ) ) )
=> ( Q @ A3 ) ) )
= ( ! [A3: A0,A4: A1] :
( ( P @ A3 @ A4 )
=> ( Q @ ( A2 @ A3 @ A4 ) ) ) ) ) )).

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