TPTP Problem File: SEV493^1.p
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% File : SEV493^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : INF_FINITE
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : INF_FINITE_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 11 ( 1 unt; 6 typ; 0 def)
% Number of atoms : 27 ( 5 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 72 ( 3 ~; 1 |; 7 &; 52 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 0 con; 1-3 aty)
% Number of variables : 18 ( 0 ^; 13 !; 2 ?; 18 :)
% ( 3 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/realax/real',type,
'type/realax/real': $tType ).
thf('thf_const_const/sets/inf',type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf('thf_const_const/sets/IN',type,
'const/sets/IN':
!>[A: $tType] : ( A > ( A > $o ) > $o ) ).
thf('thf_const_const/sets/FINITE',type,
'const/sets/FINITE':
!>[A: $tType] : ( ( A > $o ) > $o ) ).
thf('thf_const_const/sets/EMPTY',type,
'const/sets/EMPTY':
!>[A: $tType] : ( A > $o ) ).
thf('thf_const_const/realax/real_le',type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf('thm/sets/INF_',axiom,
! [A: 'type/realax/real' > $o] :
( ( ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) )
& ? [A0: 'type/realax/real'] :
! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A0 @ A1 ) ) )
=> ( ! [A0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) )
& ! [A0: 'type/realax/real'] :
( ! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A0 @ A1 ) )
=> ( 'const/realax/real_le' @ A0 @ ( 'const/sets/inf' @ A ) ) ) ) ) ).
thf('thm/realax/REAL_LE_TOTAL_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( 'const/realax/real_le' @ A @ A0 )
| ( 'const/realax/real_le' @ A0 @ A ) ) ).
thf('thm/realax/REAL_LE_ANTISYM_',axiom,
! [A: 'type/realax/real',A0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ A @ A0 )
& ( 'const/realax/real_le' @ A0 @ A ) )
= ( A = A0 ) ) ).
thf('thm/sets/INF_FINITE_LEMMA_',axiom,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ? [A0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
& ! [A1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A1 @ A )
=> ( 'const/realax/real_le' @ A0 @ A1 ) ) ) ) ).
thf('thm/sets/INF_FINITE_',conjecture,
! [A: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ A )
& ( A
!= ( 'const/sets/EMPTY' @ 'type/realax/real' ) ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ A ) @ A )
& ! [A0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ A0 @ A )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ A ) @ A0 ) ) ) ) ).
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