TPTP Problem File: SEV496^1.p
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% File : SEV496^1 : TPTP v8.2.0. 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 ( 11 unt; 13 typ; 0 def)
% Number of atoms : 54 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 143 ( 4 ~; 2 |; 5 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 0 con; 2-6 aty)
% Number of variables : 73 ( 2 ^; 51 !; 3 ?; 73 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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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 ) ) ) ).
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