%------------------------------------------------------------------------------
% File     : PLA053_15 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Planning
% Problem  : Abductive planning: Bomb-in-the-toilet with detector
% 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    : APM004+1 [QMLTP]

% Status   : CounterSatisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   14 (   2 unt;   7 typ;   0 def)
%            Number of atoms       :   28 (   0 equ)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :   21 (   0   ~;   0   |;   8   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   5 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   20 (;  14   !;   6   ?;  20   :)
% 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(h_decl,type,
    h: ( '$ki_world' * $i ) > $o ).

tff(bomb_decl,type,
    bomb: ( '$ki_world' * $i ) > $o ).

tff(defused_decl,type,
    defused: ( '$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(ax1,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ? [B: $i] :
          ( '$ki_exists_in_world_$i'(W,B)
          & bomb(W,B) ) ) ).

tff(ax2,axiom,
    ? [A: $i] :
      ( '$ki_exists_in_world_$i'('$ki_local_world',A)
      & ! [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
         => ! [X: $i] :
              ( '$ki_exists_in_world_$i'(W,X)
             => ( ( bomb(W,X)
                  & h(W,A) )
               => ! [W0: '$ki_world'] :
                    ( '$ki_accessible'(W,W0)
                   => bomb(W0,X) ) ) ) ) ) ).

tff(ax3,axiom,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ! [X: $i] :
          ( '$ki_exists_in_world_$i'(W,X)
         => ? [D: $i] :
              ( '$ki_exists_in_world_$i'(W,D)
              & ! [W0: '$ki_world'] :
                  ( '$ki_accessible'(W,W0)
                 => ( ( bomb(W0,X)
                      & h(W0,D) )
                   => defused(W0,X) ) ) ) ) ) ).

tff(verify,conjecture,
    ! [W: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',W)
     => ! [X: $i] :
          ( '$ki_exists_in_world_$i'(W,X)
         => ? [D: $i] :
              ( '$ki_exists_in_world_$i'(W,D)
              & ( ( bomb(W,X)
                  & h(W,D) )
               => defused(W,X) ) ) ) ) ).

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