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  : [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 (   0 non-Horn;   3 unit;   0 RR)
%            Number of atoms       :    3 (   3 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :    4 (   0 constant; 1-2 arity)
%            Number of variables   :    9 (   0 singleton)
%            Maximal term depth    :    7 (   6 average)
% 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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