%------------------------------------------------------------------------------
% File     : SYO887_22 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Fitting and Mendelsohn problem
% Version  : Especial.
% English  :

% Refs     : [FM98]  Fitting & Mendelsohn (1998), First-Order Modal Logic
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : SYM008+1 [QMLTP]

% Status   : Theorem
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   10 (   2 unt;   5 typ;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :    9 (   0   ~;   0   |;   5   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   3 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   13 (;   9   !;   4   ?;  13   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_S4, 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_reflexive,axiom,
    ! [W: '$ki_world'] : '$ki_accessible'(W,W) ).

tff(mrel_transitive,axiom,
    ! [W: '$ki_world',V: '$ki_world',U: '$ki_world'] :
      ( ( '$ki_accessible'(W,V)
        & '$ki_accessible'(V,U) )
     => '$ki_accessible'(W,U) ) ).

tff(f_decl,type,
    f: ( '$ki_world' * $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_decr',axiom,
    ! [W: '$ki_world',V: '$ki_world',X: $i] :
      ( ( '$ki_exists_in_world_$i'(W,X)
        & '$ki_accessible'(V,W) )
     => '$ki_exists_in_world_$i'(V,X) ) ).

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

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

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