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Abstract

We describe a refined superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are difficult for a general purpose superposition theorem prover, as they create many variants of clauses which contain sums. Our calculus requires neither explicit inferences with the theory clauses for cancellative abelian monoids nor extended equations or clauses. Improved ordering constraints allow us to restrict to inferences that involve the maximal term of the maximal sum in the maximal literal. Furthermore, the search space is reduced drastically by certain variable elimination techniques.