%------------------------------------------------------------------------------
% File     : LCL017^1 : TPTP v9.0.0. Released v7.5.0.
% Domain   : Logic Calculi (Modal Logic)
% Axioms   : Variable Domain Quantifiers for Modal Logic
% Version  : [Gus20] axioms.
% English  : 

% Refs     : [Gus20] Gustafsson (2020), Email to Geoff Sutcliffe
% Source   : [Gus20]
% Names    : 

% Status   : Satisfiable
% Syntax   : Number of formulae    :    6 (   3 unt;   3 typ;   2 def)
%            Number of atoms       :    9 (   2 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   11 (   0   ~;   0   |;   0   &;  10   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg;  10 nst)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  14   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (   4   ^   2   !;   1   ?;   7   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments : Combine with LCL016^0 for Quantified Modal Logic K wth variable 
%            domain.
%          : Combine with LCL016^0 and LCL016^1 for Quantified Modal Logic KB 
%            with variable domain.
%          : Combine with LCL017^0 for Quantified Modal Logic S5 with variable 
%            domain.
%------------------------------------------------------------------------------
thf(eiw_ind,type,
    eiw_ind: $i > mu > $o ).

thf(nonempty_ind,axiom,
    ! [V: $i] :
    ? [X: mu] : ( eiw_ind @ V @ X ) ).

thf(mforall_eiw_ind_type,type,
    mforall_eiw_ind: ( mu > $i > $o ) > $i > $o ).

thf(mforall_eiw_ind,definition,
    ( mforall_eiw_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( eiw_ind @ W @ X )
         => ( Phi @ X @ W ) ) ) ) ).

thf(mexists_eiw_ind_type,type,
    mexists_eiw_ind: ( mu > $i > $o ) > $i > $o ).

thf(mexists_eiw_ind,definition,
    ( mexists_eiw_ind
    = ( ^ [Phi: mu > $i > $o] :
          ( mnot
          @ ( mforall_eiw_ind
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).

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