%------------------------------------------------------------------------------
% File     : SYO899_8 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Modal propositional logic theorems. problem 37
% Version  : Especial.
% English  :

% Refs     : [Sid10] Sider (2010), Logic for Philosophy
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : SYM137+1 [QMLTP]

% Status   : Theorem
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :    7 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :    9 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   2   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :    5 (;   3   !;   2   ?;   5   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant,
%            modal_system_M, 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(p_decl,type,
    p: '$ki_world' > $o ).

tff(q_decl,type,
    q: '$ki_world' > $o ).

tff(verify,conjecture,
    ( ? [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
        & ( p(W)
         => ! [W0: '$ki_world'] :
              ( '$ki_accessible'(W,W0)
             => q(W0) ) ) )
   => ( ! [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
         => p(W) )
     => ? [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
          & q(W) ) ) ) ).

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