Associative-Commutative Deduction with Constraints

Associative-commutative equational reasoning is known to be highly complex for theorem proving. Hence, it is very important to focus deduction by adding constraints, such as unification and ordering, and to define efficient strategies, such as the basic requirements a la Hullot. Constraints are formulas used for pruning the set of ground instances of clauses deduced by a theorem prover. We propose here an extension of AC-paramodulation and AC-superposition with these constraint mechanisms; we do not need to compute AC-unifiers anymore. The method is proved to be refutationally complete, even with simplification. The power of this approach is exemplified by a very short proof of the equational version of SAM's Lemma using DATAC, our implementation of the strategy.

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