TPTP Problem File: PLA033^7.p

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% File     : PLA033^7 : TPTP v7.3.0. Released v5.5.0.
% Domain   : Planning
% Problem  : Abductive planning: Safe problem
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Sto00] Stone (2000), Towards a Computational Account of Knowl
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-APM005+1 [Ben12]

% Status   : Theorem
% Rating   : 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v5.5.0
% Syntax   : Number of formulae    :   88 (   0 unit;  43 type;  32 defn)
%            Number of atoms       :  337 (  36 equality; 160 variable)
%            Maximal formula depth :   19 (   6 average)
%            Number of connectives :  225 (   5   ~;   5   |;   9   &; 196   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  189 ( 189   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   47 (  43   :;   0   =)
%            Number of variables   :  100 (   2 sgn;  37   !;   7   ?;  56   ^)
%                                         ( 100   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : 
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%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
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thf(closed_type,type,(
    closed: mu > $i > $o )).

thf(open_type,type,(
    open: mu > $i > $o )).

thf(h_type,type,(
    h: mu > $i > $o )).

thf(combo_type,type,(
    combo: mu > mu > $i > $o )).

thf(o_type,type,(
    o: mu )).

thf(existence_of_o_ax,axiom,(
    ! [V: $i] :
      ( exists_in_world @ o @ V ) )).

thf(n_type,type,(
    n: mu )).

thf(existence_of_n_ax,axiom,(
    ! [V: $i] :
      ( exists_in_world @ n @ V ) )).

thf(d_type,type,(
    d: mu )).

thf(existence_of_d_ax,axiom,(
    ! [V: $i] :
      ( exists_in_world @ d @ V ) )).

thf(ax1,axiom,
    ( mvalid
    @ ( mbox_s4
      @ ( mforall_ind
        @ ^ [S: mu] :
            ( mforall_ind
            @ ^ [V: mu] :
                ( mexists_ind
                @ ^ [O: mu] :
                    ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ S ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ S ) ) ) ) ) ) ) ) ) )).

thf(ax2,axiom,
    ( mvalid @ ( mbox_s4 @ ( closed @ d ) ) )).

thf(ax3,axiom,
    ( mvalid @ ( mbox_s4 @ ( mor @ ( combo @ d @ n ) @ ( mnot @ ( combo @ d @ n ) ) ) ) )).

thf(ax4,axiom,
    ( mvalid
    @ ( mbox_s4
      @ ( mforall_ind
        @ ^ [S: mu] :
            ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) )).

thf(ax5,axiom,
    ( mvalid
    @ ( mexists_ind
      @ ^ [V: mu] :
          ( mbox_s4 @ ( combo @ d @ V ) ) ) )).

thf(con,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mexists_ind
        @ ^ [V: mu] :
            ( mexists_ind
            @ ^ [O: mu] :
                ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) )).

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