Abstract
I present a new clausal version of NGB set theory, and compare my version with that first given by Boyer et al. [4]. A complete set of reductions for Boolean rings is given, derived from those of Hsiang [7]. I list over 400 theorems proved semiautomatically in elementary set theory, and supply the proofs of several of these, including Cantor's theorem. I present a semiautomated proof that the composition of homomorphisms is a homomorphism, thus solving a challenge problem given in [4]. Using the clauses and heuristics presented, there is no apparent obstacle to the semiautomated development of set theory through considerably more difficult theorems.
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Quaife, A. Automated deduction in von Neumann-Bernays-Gödel set theory. J Autom Reasoning 8, 91–147 (1992). https://doi.org/10.1007/BF00263451
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DOI: https://doi.org/10.1007/BF00263451