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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 )).
+
+%--------------------------------------------------------------------------