Superposition Theorem Proving for Commutative Rings

Commutative rings are very common both in mathematics and in computer science, as they encompass the basic algebraic properties of addition, subtraction and multiplication for numbers like the integers or the reals. The problem with commutative rings and similar algebraic theories is that their axioms create large search spaces for theorem provers. We address this problem by systematically developing a superposition calculus for first-order problems that contain the theory of commutative rings. The calculus combines certain uses of the axioms into macro inferences, and it restricts inferences to the maximal term within a sum. Thereby it promises to make theorem proving with respect to commutative rings more efficient.

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