Abstract
We present a general approach for integrating certain mathematical structures in first-order equational theorem provers. More specifically, we consider theorem proving problems specified by sets of first-order clauses that, contain the axioms of a commutative ring with a unit element. Associative-commutative superposition forms the deductive core of our method, while a convergent rewrite system for commutative rings provides a starting point for more specialized inferences tailored to the given class of formulas. We adopt ideas from the Gröbner basis method to show that many inferences of the superposition calculus are redundant. This result is obtained by the judicious application of the simplification techniques afforded by convergent rewriting and by a process called symmetrization that embeds inferences between single clauses and ring axioms.
The research described in this paper was supported in part by the NSF under research grant INT-9314412, by the German Ministry for Research and Technology (Bundesministerium für Forschung und Technologie) under grant, ITS 9102/ITS 9103 and by the ESPRIT Basic Research Working Group 6112 (COMPASS).
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Bachmair, L., Ganzinger, H., Stuber, J. (1995). Combining algebra and universal algebra in first-order theorem proving: The case of commutative rings. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1994 1994. Lecture Notes in Computer Science, vol 906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014420
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