Abstract
We extend previous results about resolution and superposition with ordering constraints and selection functions to the case of general (quantifier-free) first-order formulas with equality. The refutation completeness of our calculi is compatible with a general and powerful redundancy criterion which includes most (if not all) techniques for simplifying and deleting formulas. The spectrum of first-order theorem proving techniques covered by our results includes ordered resolution, positive resolution, hyper-resolution, semantic resolution, set-of-support resolution, and Knuth/Bendix completion, as well as their extension to quantifier-free first-order formulas. An additional feature in the latter case is our efficient handling of equivalences as equalities on the level of formulas. Furthermore, our approach applies to constraint theorem proving, including constrained resolution and theory resolution.
The research described in this paper was supported in part by the National Science Foundation under grant CCR-8901322.
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© 1992 Springer-Verlag Berlin Heidelberg
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Bachmair, L., Ganzinger, H. (1992). Non-clausal resolution and superposition with selection and redundancy criteria. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013068
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DOI: https://doi.org/10.1007/BFb0013068
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