%------------------------------------------------------------------------------
% File     : PLA054_4 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Planning
% Problem  : Abductive planning: Safe problem
% Version  : [QMLTP] axioms.
% English  :

% Refs     : [Sto98] Stone (1998), Abductive Planning with Sensing
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : APM005+1 [QMLTP]

% Status   : Theorem
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   21 (   3 unt;  11 typ;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :   35 (   3   ~;   1   |;  12   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   13 (   6   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   6 usr;   0 prp; 2-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   27 (;  22   !;   5   ?;  27   :)
% 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(d_decl,type,
    d: $i ).

tff(n_decl,type,
    n: $i ).

tff(o_decl,type,
    o: $i ).

tff(h_decl,type,
    h: ( '$ki_world' * $i ) > $o ).

tff(closed_decl,type,
    closed: ( '$ki_world' * $i ) > $o ).

tff(combo_decl,type,
    combo: ( '$ki_world' * $i * $i ) > $o ).

tff(open_decl,type,
    open: ( '$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(ax1,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ! [S: $i] :
          ( '$ki_exists_in_world_$i'(W,S)
         => ! [V: $i] :
              ( '$ki_exists_in_world_$i'(W,V)
             => ? [O: $i] :
                  ( '$ki_exists_in_world_$i'(W,O)
                  & ! [W0: '$ki_world'] :
                      ( '$ki_accessible'(W,W0)
                     => ( ( closed(W0,S)
                          & combo(W0,S,V)
                          & h(W0,O) )
                       => ! [W1: '$ki_world'] :
                            ( '$ki_accessible'(W0,W1)
                           => open(W1,S) ) ) )
                  & ! [W0: '$ki_world'] :
                      ( '$ki_accessible'(W,W0)
                     => ( ( closed(W0,S)
                          & ~ combo(W0,S,V)
                          & h(W0,o) )
                       => ! [W1: '$ki_world'] :
                            ( '$ki_accessible'(W0,W1)
                           => closed(W1,S) ) ) ) ) ) ) ) ).

tff(ax2,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => closed(W,d) ) ).

tff(ax3,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ( combo(W,d,n)
        | ~ combo(W,d,n) ) ) ).

tff(ax4,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ! [S: $i] :
          ( '$ki_exists_in_world_$i'(W,S)
         => ~ ( open(W,S)
              & closed(W,S) ) ) ) ).

tff(ax5,axiom,
    ? [V: $i] :
      ( '$ki_exists_in_world_$i'('$ki_local_world',V)
      & ! [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
         => combo(W,d,V) ) ) ).

tff(verify,conjecture,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ? [V: $i] :
          ( '$ki_exists_in_world_$i'(W,V)
          & ? [O: $i] :
              ( '$ki_exists_in_world_$i'(W,O)
              & ( ! [W0: '$ki_world'] :
                    ( '$ki_accessible'(W,W0)
                   => ( combo(W0,d,V)
                      & h(W0,O) ) )
               => ! [W0: '$ki_world'] :
                    ( '$ki_accessible'(W,W0)
                   => open(W0,d) ) ) ) ) ) ).

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