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Journals and Conferences
Thirty-two unsolved problems in elementary number theory are listed as challenge problems for automated reasoning systems. The clausal forms of the conjectures and of their negations are given, suitable as input to resolution theorem provers versed in Peano arithmetic.
I present a new clausal version of NGB set theory, and compare my version with that first given by Boyer et al. . A complete set of reductions for Boolean rings is given, derived from those of Hsiang . I list over 400 theorems proved semiautomatically in elementary set theory, and supply the proofs of several of these, including Cantor's theorem. I… (More)
Tarski's geometry, a complete first-order axiomatization of Euclidean plane geometry, is developed within the automated reasoning system OTTER. Proofs are obtained and performance statistics supplied for most of the challenge problems appearing in the literature. Few of these problems have been previously solved by any clause-based reasoning system. Further… (More)
The modal logic calculus K4, which represents important properties of the provability relation of Peano's Arithmetic, is formalized within the automated reasoning system ITP. Very high level automated proofs are then obtained of Löb's theorem, and of Gödel's two incompleteness theorems.
In his recent books one of the main pre-occupations of Roger Penrose has been to show (to prove!) that computers are intrinsically limited, compared to humans, when it comes to the doing of mathematics. Even those who think that such things can be proved may be interested in the empirical question: what mathematics can computers do? Art Quaife's book… (More)