Automated deduction with associative-commutative operators

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We propose a new inference system for automated deduction with equality and associative commutative operators. This system is an extension of the ordered paramodulation strategy. However, rather than using associativity and commutativity as the other axioms, they are handled by the AC-unification algorithm and the inference rules. Moreover, we prove the refutational completeness of this system without needing the functional reflexive axioms or AC-axioms. Such a result is obtained by semantic tree techniques. We also show that the inference system is compatible with simplification rules.

A preliminary version of this paper was presented at the International Workshop FAIR'91 [RV91]