TPTP Problem File: SEV456^1.p
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% File : SEV456^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : INSERT_UNION
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : INSERT_UNION_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 9 ( 5 unt; 4 typ; 0 def)
% Number of atoms : 24 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 55 ( 0 ~; 2 |; 0 &; 53 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 2-4 aty)
% Number of variables : 23 ( 0 ^; 19 !; 0 ?; 23 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_const_const/sets/UNION',type,
'const/sets/UNION':
!>[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/class/COND',type,
'const/class/COND':
!>[A: $tType] : ( $o > A > A > 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_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_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/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/INSERT_UNION_',conjecture,
! [A: $tType,A0: A,A1: A > $o,A2: A > $o] :
( ( 'const/sets/UNION' @ A @ ( 'const/sets/INSERT' @ A @ A0 @ A1 ) @ A2 )
= ( 'const/class/COND' @ ( A > $o ) @ ( 'const/sets/IN' @ A @ A0 @ A2 ) @ ( 'const/sets/UNION' @ A @ A1 @ A2 ) @ ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/UNION' @ A @ A1 @ A2 ) ) ) ) ).
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