TPTP Problem File: SEV485^1.p

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% File     : SEV485^1 : TPTP v7.5.0. Released v7.0.0.
% Domain   : Analysis
% Problem  : FINITE_BOOL
% Version  : Especial.
% English  :

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

% Status   : Theorem
% Rating   : 0.00 v7.1.0
% Syntax   : Number of formulae    :   12 (   0 unit;   9 type;   0 defn)
%            Number of atoms       :   25 (   2 equality;   8 variable)
%            Maximal formula depth :    9 (   4 average)
%            Number of connectives :   18 (   0   ~;   0   |;   1   &;  17   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9   :;   0   =;   0  @=)
%                                         (   0  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :    7 (   0 sgn;   3   !;   0   ?;   0   ^)
%                                         (   7   :;   4  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH1_THM_EQU_NAR

% Comments : Exported from core HOL Light.
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thf('thf_type_type/nums/num',type,(
    'type/nums/num': $tType )).

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

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

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

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

thf('thf_const_const/nums/NUMERAL',type,(
    'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' )).

thf('thf_const_const/nums/BIT1',type,(
    'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' )).

thf('thf_const_const/nums/BIT0',type,(
    'const/nums/BIT0': 'type/nums/num' > 'type/nums/num' )).

thf('thf_const_const/nums/_0',type,(
    'const/nums/_0': 'type/nums/num' )).

thf('thm/sets/HAS_SIZE_',axiom,(
    ! [A: $tType,A0: A > $o,A1: 'type/nums/num'] :
      ( ( 'const/sets/HAS_SIZE' @ A @ A0 @ A1 )
      = ( ( 'const/sets/FINITE' @ A @ A0 )
        & ( ( 'const/sets/CARD' @ A @ A0 )
          = A1 ) ) ) )).

thf('thm/sets/HAS_SIZE_BOOL_',axiom,
    ( 'const/sets/HAS_SIZE' @ $o @ ( 'const/sets/UNIV' @ $o ) @ ( 'const/nums/NUMERAL' @ ( 'const/nums/BIT0' @ ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ) )).

thf('thm/sets/FINITE_BOOL_',conjecture,
    ( 'const/sets/FINITE' @ $o @ ( 'const/sets/UNIV' @ $o ) )).

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