%------------------------------------------------------------------------------
% File     : SYO886_3 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Barcan scheme instance
% Version  : Especial.
% English  : If for all x necessarily f(x), then it is necessary that for
%            all x f(x)

% Refs     : [Bar46] Barcan (1946), A Functional Calculus of First Order Ba
%          : [Sid10] Sider (2010), Logic for Philosophy
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : SYM001+1 [QMLTP]

% Status   : Theorem
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :    9 (   3 unt;   5 typ;   0 def)
%            Number of atoms       :    9 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :    5 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 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   :   10 (;   8   !;   2   ?;  10   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_D, TFF embedding.
% Bugfixes : Renamed to SYO886_6
%------------------------------------------------------------------------------
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_serial,axiom,
    ! [W: '$ki_world'] :
    ? [V: '$ki_world'] : '$ki_accessible'(W,V) ).

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

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