Combining Induction and Saturation-Based Theorem Proving

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A method is devised to integrate reasoning by mathematical induction into saturation-based proof procedures based on resolution or superposition. The obtained calculi are capable of handling formulas in which some of the quantified variables range over inductively defined domains (which, as is well-known, cannot be expressed in first-order logic). The procedure is defined as a set of inference rules that generate inductive invariants incrementally and prove their validity. Although the considered logic itself is incomplete, it is shown that the invariant generation rules are complete, in the sense that if an invariant (of some specific form) is deducible from the considered clauses, then it is eventually generated.