Automated deduction in von Neumann-Bernays-G�del set theory

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.