TPTP Axioms File: LCL016^1.ax


%------------------------------------------------------------------------------
% File     : LCL016^1 : TPTP v7.5.0. Released v6.1.0.
% Domain   : Logic Calculi (Second Order Modal Logic)
% Axioms   : Embedding of second order modal logic in simple type theory
% Version  : [Ben13] axioms.
% English  : Extends K to KB by adding symmetric of rel.

% Refs     : [Ben13] Benzmueller (2009), Email to Geoff Sutcliffe
%          : [BP13]  Benzmueller & Paulson (2013), Quantified Multimodal Lo
% Source   : [Ben13]
% Names    : 

% Status   : Satisfiable
% Syntax   : Number of formulae    :    3 (   0 unit;   1 type;   1 defn)
%            Number of atoms       :   14 (   1 equality;   6 variable)
%            Maximal formula depth :    8 (   5 average)
%            Number of connectives :    6 (   0   ~;   0   |;   0   &;   5   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&;   0  !!;   0  ??)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   1   :)
%            Number of variables   :    3 (   0 sgn;   2   !;   0   ?;   1   ^)
%                                         (   3   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_SAT_EQU

% Comments : Requires LCL016^0.ax.
%------------------------------------------------------------------------------
%----Definition of properties of accessibility relations
thf(msymmetric_type,type,(
    msymmetric: ( $i > $i > $o ) > $o )).

thf(msymmetric,definition,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) )).

thf(sym,axiom,
    ( msymmetric @ rel )).

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