%------------------------------------------------------------------------------
% File     : SYO907_15 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Forbes problem
% Version  : Especial.
% English  : "if something is material, then necessary it is so if it "exists 
%            at all" does not entail "each actual entity is material at every 
%            world at which it exists"

% Refs     : [For94] Forbes (1994), Modern Logic. A Text in Elementary Symb
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : SYM041+1 [QMLTP]

% Status   : CounterSatisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   10 (   2 unt;   6 typ;   0 def)
%            Number of atoms       :   14 (   0 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   11 (   1   ~;   0   |;   1   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   11 (;   9   !;   2   ?;  11   :)
% SPC      : TF0_CSA_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_D, 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_serial,axiom,
    ! [W: '$ki_world'] :
    ? [V: '$ki_world'] : '$ki_accessible'(W,V) ).

tff(e_decl,type,
    e: ( '$ki_world' * $i ) > $o ).

tff(m_decl,type,
    m: ( '$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_cumul',axiom,
    ! [W: '$ki_world',V: '$ki_world',X: $i] :
      ( ( '$ki_exists_in_world_$i'(W,X)
        & '$ki_accessible'(W,V) )
     => '$ki_exists_in_world_$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,
    ~ ( ! [X: $i] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X)
         => ( m('$ki_local_world',X)
           => ! [W: '$ki_world'] :
                ( '$ki_accessible'('$ki_local_world',W)
               => ( e(W,X)
                 => m(W,X) ) ) ) )
     => ! [X: $i] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X)
         => ! [W: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',W)
             => ( e(W,X)
               => m(W,X) ) ) ) ) ).

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