%------------------------------------------------------------------------------
% File     : DAT334_23 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Data Structures
% Problem  : Database querying
% Version  : [QMLTP] axioms.
% English  :

% Refs     : [Rei92] Reiter (1992), What Should a Database Know?
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : APM009+1 [QMLTP]

% Status   : Theorem
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   16 (   3 unt;  11 typ;   0 def)
%            Number of atoms       :   12 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   5   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   3 usr;   0 prp; 2-3 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :   10 (;   7   !;   3   ?;  10   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_S5, TFF embedding.
%------------------------------------------------------------------------------
tff('$ki_world_type',type,
    '$ki_world': $tType ).

tff('$ki_local_world_decl',type,
    '$ki_local_world': '$ki_world' ).

tff('$ki_accessible_decl',type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(mrel_universal,axiom,
    ! [W: '$ki_world',V: '$ki_world'] : '$ki_accessible'(W,V) ).

tff(cs_decl,type,
    cs: $i ).

tff(sue_decl,type,
    sue: $i ).

tff(mary_decl,type,
    mary: $i ).

tff(john_decl,type,
    john: $i ).

tff(math_decl,type,
    math: $i ).

tff(psych_decl,type,
    psych: $i ).

tff(teach_decl,type,
    teach: ( '$ki_world' * $i * $i ) > $o ).

tff('$ki_exists_in_world_$i_decl',type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff('$ki_exists_in_world_$i_const',axiom,
    ! [W: '$ki_world',X: $i] : '$ki_exists_in_world_$i'(W,X) ).

tff('$ki_exists_in_world_$i_nonempty',axiom,
    ! [W: '$ki_world'] :
    ? [X: $i] : '$ki_exists_in_world_$i'(W,X) ).

tff(db,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ( teach(W,john,math)
        & ? [X: $i] :
            ( '$ki_exists_in_world_$i'(W,X)
            & teach(W,X,cs) )
        & teach(W,mary,psych)
        & teach(W,sue,psych) ) ) ).

tff(verify,conjecture,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ? [X: $i] :
          ( '$ki_exists_in_world_$i'(W,X)
          & teach(W,X,cs) ) ) ).

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