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% File     : REL001-1 : TPTP v9.0.0. Released v3.6.0.
% Domain   : Relation Algebra
% Axioms   : Dedkind and two modular laws
% Version  : [Mad95] (equational) axioms : Augmented.
% English  :

% Refs     : [Mad95] Maddux (1995), Relation-Algebraic Semantics
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Satisfiable
% Rating   : ? v3.6.0
% Syntax   : Number of clauses     :    3 (   3 unt;   0 nHn;   0 RR)
%            Number of literals    :    3 (   3 equ;   0 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 1-2 aty)
%            Number of variables   :    9 (   0 sgn)
% SPC      : 

% Comments : tptp2X -f tptp:short -t cnf:otter REL001+1.ax
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cnf(dedekind_law_14,axiom,
    join(meet(composition(A,B),C),composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C)))) = composition(meet(A,composition(C,converse(B))),meet(B,composition(converse(A),C))) ).

cnf(modular_law_1_15,axiom,
    join(meet(composition(A,B),C),meet(composition(A,meet(B,composition(converse(A),C))),C)) = meet(composition(A,meet(B,composition(converse(A),C))),C) ).

cnf(modular_law_2_16,axiom,
    join(meet(composition(A,B),C),meet(composition(meet(A,composition(C,converse(B))),B),C)) = meet(composition(meet(A,composition(C,converse(B))),B),C) ).

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