## TPTP Problem File: SEV496^1.p

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```%------------------------------------------------------------------------------
% File     : SEV496^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : SUPPORT_CLAUSES_
% Version  : Especial.
% English  :

% Refs     : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source   : [Kal16]
% Names    : SUPPORT_CLAUSES_4.p [Kal16]

% Status   : Theorem
% Rating   : 1.00 v7.2.0, 0.75 v7.1.0
% Syntax   : Number of formulae    :   25 (   0 unit;  13 type;   0 defn)
%            Number of atoms       :  185 (  17 equality; 129 variable)
%            Maximal formula depth :   17 (   9 average)
%            Number of connectives :  143 (   4   ~;   2   |;   5   &; 132   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   78 (  78   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   73 (   0 sgn;  51   !;   3   ?;   2   ^)
%                                         (  73   :;  17  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

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

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

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

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

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

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

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

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

thf('thf_const_const/iterate/neutral',type,(
'const/iterate/neutral':
!>[A: \$tType] :
( ( A > A > A ) > A ) )).

thf('thm/sets/IN_ELIM_THM_1',axiom,(
! [A: \$tType,A0: A > \$o,A1: A] :
( ( 'const/sets/IN' @ A @ A1
@ ( 'const/sets/GSPEC' @ A
@ ^ [A2: A] :
? [A3: A] :
( 'const/sets/SETSPEC' @ A @ A2 @ ( A0 @ A3 ) @ A3 ) ) )
= ( A0 @ A1 ) ) )).

thf('thm/trivia/o_THM_',axiom,(
! [C: \$tType,B: \$tType,A: \$tType,A0: B > C,A1: A > B,A2: A] :
( ( 'const/trivia/o' @ B @ A @ C @ A0 @ A1 @ A2 )
= ( A0 @ ( A1 @ A2 ) ) ) )).

thf('thm/iterate/support_',axiom,(
! [B: \$tType,A: \$tType,A0: A > \$o,A1: A > B,A2: B > B > B] :
( ( 'const/iterate/support' @ B @ A @ A2 @ A1 @ A0 )
= ( 'const/sets/GSPEC' @ A
@ ^ [A3: A] :
? [A4: A] :
( 'const/sets/SETSPEC' @ A @ A3
@ ( ( 'const/sets/IN' @ A @ A4 @ A0 )
& ( ( A1 @ A4 )
!= ( 'const/iterate/neutral' @ B @ A2 ) ) )
@ A4 ) ) ) )).

thf('thm/sets/IN_IMAGE_',axiom,(
! [B: \$tType,A: \$tType,A0: B,A1: A > \$o,A2: A > B] :
( ( 'const/sets/IN' @ B @ A0 @ ( 'const/sets/IMAGE' @ A @ B @ A2 @ A1 ) )
= ( ? [A3: A] :
( ( A0
= ( A2 @ A3 ) )
& ( 'const/sets/IN' @ A @ A3 @ 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/IN_DIFF_',axiom,(
! [A: \$tType,A0: A > \$o,A1: A > \$o,A2: A] :
( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) )
= ( ( 'const/sets/IN' @ A @ A2 @ A0 )
& ~ ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) )).

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

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

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

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

thf('thm/iterate/SUPPORT_CLAUSES_4',conjecture,(
! [A: \$tType,A0: \$tType,A1: A > A > A,A2: A0 > A,A3: A0 > \$o,A4: A0 > \$o] :
( ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ ( 'const/sets/INTER' @ A0 @ A3 @ A4 ) )
= ( 'const/sets/INTER' @ A0 @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A3 ) @ ( 'const/iterate/support' @ A @ A0 @ A1 @ A2 @ A4 ) ) ) )).

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