Abstract
In this paper we describe the rules of the SET-VAR prover, which is an extension of resolution and which handles theorems in a subset of second-order logic. We also give example proofs using the system and show that the rules are sound. We conjecture that the prover, defined by these SET-VAR rules, is complete for a certain extension of first-order logic that includes many of the theorems of real analysis. We also describe an implementation of this SET-VAR prover and show proofs it derives (without human intervention) for a number of examples, including the intermediate value theorem. This system is based on an earlier ‘set variable’ prover, implemented in natural deduction. We also discuss the relationship between this method and circumscription.
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Bledsoe, W.W., Feng, G. SET-VAR. J Autom Reasoning 11, 293–314 (1993). https://doi.org/10.1007/BF00881869
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DOI: https://doi.org/10.1007/BF00881869