TPTP Problem File: KRS272^7.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : KRS272^7 : TPTP v7.0.0. Released v5.5.0.
% Domain   : Knowledge Representation
% Problem  : Generation of abstract instructions: enter a number in a(#box
% 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-APM003+1 [Ben12]

% Status   : Theorem
% Rating   : 0.88 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0
% Syntax   : Number of formulae    :   86 (   0 unit;  44 type;  32 defn)
%            Number of atoms       :  326 (  36 equality; 166 variable)
%            Maximal formula depth :   20 (   6 average)
%            Number of connectives :  217 (   5   ~;   5   |;   9   &; 188   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  198 ( 198   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  44   :;   0   =)
%            Number of variables   :  104 (   2 sgn;  36   !;   7   ?;  61   ^)
%                                         ( 104   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

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

thf(in_type,type,(
    in: mu > mu > mu > $i > $o )).

thf(do_type,type,(
    do: mu > mu > mu > $i > $o )).

thf(number_type,type,(
    number: mu > mu > $i > $o )).

thf(entry_box_type,type,(
    entry_box: mu > $i > $o )).

thf(userid_type,type,(
    userid: mu > mu > $i > $o )).

thf(one_type,type,(
    one: mu )).

thf(existence_of_one_ax,axiom,(
    ! [V: $i] :
      ( exists_in_world @ one @ V ) )).

thf(u_type,type,(
    u: mu )).

thf(existence_of_u_ax,axiom,(
    ! [V: $i] :
      ( exists_in_world @ u @ V ) )).

thf(ax1,axiom,
    ( mvalid
    @ ( mbox_s4
      @ ( mexists_ind
        @ ^ [I: mu] :
            ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) )).

thf(ax2,axiom,
    ( mvalid
    @ ( mexists_ind
      @ ^ [B: mu] :
          ( mbox_s4 @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) )).

thf(ax3,axiom,
    ( mvalid
    @ ( mbox_s4
      @ ( mforall_ind
        @ ^ [S: mu] :
            ( mforall_ind
            @ ^ [I: mu] :
                ( mforall_ind
                @ ^ [B: mu] :
                    ( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
                    @ ( mexists_ind
                      @ ^ [A: mu] :
                          ( mbox_s4
                          @ ( mforall_ind
                            @ ^ [S2: mu] :
                                ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) )).

thf(con,conjecture,
    ( mvalid
    @ ( mbox_s4
      @ ( mexists_ind
        @ ^ [I: mu] :
            ( mexists_ind
            @ ^ [B: mu] :
                ( mexists_ind
                @ ^ [A: mu] :
                    ( mexists_ind
                    @ ^ [S: mu] :
                        ( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
                        @ ( mbox_s4
                          @ ( mforall_ind
                            @ ^ [S2: mu] :
                                ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) )).

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