TPTP Axioms File: REL001+1.ax


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% File     : REL001+1 : TPTP v7.5.0. Released v3.6.0.
% Domain   : Relation Algebra
% Axioms   : Dedkind and two modular laws
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [Mad95] Maddux, R. (1995), Relation-algebraic semantics
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    3 (   3 unit)
%            Number of atoms       :    3 (   3 equality)
%            Maximal formula depth :    4 (   4 average)
%            Number of connectives :    0 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    4 (   0 constant; 1-2 arity)
%            Number of variables   :    9 (   0 singleton;   9 !;   0 ?)
%            Maximal term depth    :    7 (   6 average)
% SPC      : 

% Comments : Requires REL001+0.ax
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%---Dedekind law
fof(dedekind_law,axiom,(
    ! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) )).

%---modular laws
fof(modular_law_1,axiom,(
    ! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) )).

fof(modular_law_2,axiom,(
    ! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2) )).

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