%------------------------------------------------------------------------------
% File     : NX0001_1 : TPTP v9.0.0. Released v9.0.0.
% Domain   : Puzzles
% Problem  : Apples and bananas
% Version  : Especial.
% English  :

% Refs     : 
% Source   : [TPTP]
% Names    : NTF_Finite-Finite.THM [TPTP]

% Status   : Theorem
% Rating   : ? v9.0.0
% Syntax   : Number of formulae    :   10 (   2 unt;   5 typ;   0 def)
%            Number of atoms       :   12 (   1 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    7 (   3   ~;   0   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   3 {}@;   0 {#};   0 {.})
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    3 (   3 fml;   0 var)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   2 usr;   0 prp; 1-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    2 (;   2   !;   0   ?;   2   :)
% SPC      : NX0_THM_RFO_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
tff(semantics,logic,
    $alethic_modal == 
      [ $domains == $constant,
        $designation == $rigid,
        $terms == $local,
        $modalities == $modal_system_M ] ).

tff(fruit_type,type,
    fruit: $tType ).

tff(apple_decl,type,
    apple: fruit ).

tff(banana_decl,type,
    banana: fruit ).

tff(healthy_decl,type,
    healthy: fruit > $o ).

tff(rotten_decl,type,
    rotten: fruit > $o ).

tff(apple_not_banana,axiom,
    apple != banana ).

tff(necessary_healthy_fruit_everywhere,axiom,
    ! [F: fruit] : ( {$necessary} @ (healthy(F)) ) ).

tff(fruit_possibly_not_rotten,axiom,
    ! [F: fruit] : ( {$possible} @ (~ rotten(F)) ) ).

tff(rotten_banana_here,axiom-local,
    rotten(banana) ).

tff(is_true,conjecture,
    ( {$possible}
    @ (( healthy(apple)
       & ~ rotten(banana) )) ) ).

%------------------------------------------------------------------------------