TPTP Problem File: SEV461^1.p
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% File : SEV461^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : EMPTY_UNIONS
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : EMPTY_UNIONS_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 10 ( 5 unt; 4 typ; 0 def)
% Number of atoms : 22 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 37 ( 1 ~; 0 |; 1 &; 34 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 2-3 aty)
% Number of variables : 22 ( 0 ^; 17 !; 1 ?; 22 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_const_const/trivia/I',type,
'const/trivia/I':
!>[A: $tType] : ( A > A ) ).
thf('thf_const_const/sets/UNIONS',type,
'const/sets/UNIONS':
!>[A: $tType] : ( ( ( A > $o ) > $o ) > A > $o ) ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thm/trivia/I_THM_',axiom,
! [A: $tType,A0: A] :
( ( 'const/trivia/I' @ A @ A0 )
= A0 ) ).
thf('thm/sets/NOT_IN_EMPTY_',axiom,
! [A: $tType,A0: A] :
~ ( 'const/sets/IN' @ A @ A0 @ ( 'const/sets/EMPTY' @ A ) ) ).
thf('thm/sets/IN_',axiom,
! [A: $tType,P: A > $o,A0: A] :
( ( 'const/sets/IN' @ A @ A0 @ P )
= ( P @ A0 ) ) ).
thf('thm/sets/IN_UNIONS_',axiom,
! [A: $tType,A0: ( A > $o ) > $o,A1: A] :
( ( 'const/sets/IN' @ A @ A1 @ ( 'const/sets/UNIONS' @ A @ A0 ) )
= ( ? [A2: A > $o] :
( ( 'const/sets/IN' @ ( A > $o ) @ A2 @ A0 )
& ( 'const/sets/IN' @ A @ A1 @ A2 ) ) ) ) ).
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/EMPTY_UNIONS_',conjecture,
! [A: $tType,A0: ( A > $o ) > $o] :
( ( ( 'const/sets/UNIONS' @ A @ A0 )
= ( 'const/sets/EMPTY' @ A ) )
= ( ! [A1: A > $o] :
( ( 'const/sets/IN' @ ( A > $o ) @ A1 @ A0 )
=> ( A1
= ( 'const/sets/EMPTY' @ A ) ) ) ) ) ).
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