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%--------------------------------------------------------------------------
% File : BOO027-1 : TPTP v5.5.0. Released v2.2.0.
% Domain : Boolean Algebra
% Problem : Independence of self-dual 2-basis.
% Version : [MP96] (eqiality) axioms : Especial.
% English : Show that half of the self-dual 2-basis in DUAL-BA-3 is not
% a basis for Boolean Algebra.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : DUAL-BA-4 [MP96]
% Status : Satisfiable
% Rating : 0.00 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.33 v5.2.0, 0.00 v3.2.0, 0.33 v3.1.0, 0.00 v2.2.1
% Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR)
% Number of atoms : 6 ( 6 equality)
% Maximal clause size : 1 ( 1 average)
% Number of predicates : 1 ( 0 propositional; 2-2 arity)
% Number of functors : 5 ( 2 constant; 0-2 arity)
% Number of variables : 10 ( 0 singleton)
% Maximal term depth : 5 ( 3 average)
% SPC : CNF_SAT_RFO_PEQ_UEQ
% Comments : There is a 2-element model.
%--------------------------------------------------------------------------
%----Two properties of Boolean algebra:
cnf(multiply_add_property,axiom,
( multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)) )).
cnf(additive_inverse,axiom,
( add(X,inverse(X)) = one )).
%----Pixley properties:
cnf(pixley1,axiom,
( add(multiply(X,inverse(X)),add(multiply(X,Y),multiply(inverse(X),Y))) = Y )).
cnf(pixley2,axiom,
( add(multiply(X,inverse(Y)),add(multiply(X,Y),multiply(inverse(Y),Y))) = X )).
cnf(pixley3,axiom,
( add(multiply(X,inverse(Y)),add(multiply(X,X),multiply(inverse(Y),X))) = X )).
%----Denial of a property of Boolean Algebra:
cnf(prove_idempotence,negated_conjecture,
( add(a,a) != a )).
%--------------------------------------------------------------------------
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