%------------------------------------------------------------------------------
% File     : SYO893_11 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Modal propositional logic theorems. problem 1
% Version  : Especial.
% English  :

% Refs     : [Sid10] Sider (2010), Logic for Philosophy
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : SYM101+1 [QMLTP]

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

tff(verify,conjecture,
    ( ~ ! [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
         => ? [W0: '$ki_world'] :
              ( '$ki_accessible'(W,W0)
              & ! [W1: '$ki_world'] :
                  ( '$ki_accessible'(W0,W1)
                 => p(W1) ) ) )
  <=> ? [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
        & ! [W0: '$ki_world'] :
            ( '$ki_accessible'(W,W0)
           => ? [W1: '$ki_world'] :
                ( '$ki_accessible'(W0,W1)
                & ~ p(W1) ) ) ) ) ).

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