Automated Development Of Fundamental Mathematical Theories Book

The author provides an introduction to automated reasoning, and in particular to resolution theorem proving using the prover OTTER. He presents a new clausal version of von Neumann-Bernays-Gödel set theory, and lists over 400 theorems proved semiautomatically in elementary set theory. He presents a semiautomated proof that the composition of homomorphisms is a homomorphism, thus solving a challenge problem.
The author next develops Peano's arithmetic, and gives more than 1200 definitions and theorems in elementary number theory. He gives part of the proof of the fundamental theorem of arithmetic (unique factorization), and gives and OTTER-generated proof of Euler's generalization of Fermat's theorem.
Next he develops Tarski's geometry within OTTER. He obtains proofs of most of the challenge problems appearing in the literature, and offers further challenges. He then formalizes the modal logic calculus K4, in order to obtain very high level automated proofs of Löb's theorem, and of Gödel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems.

Psyche - Desmond Fearnley-Sander

To me this book was fascinating. After reading it, I found myself turning over in my mind the question of the role played in theorem proving by understanding, a quality that Penrose regards as a prime desideratum of consciousness....Art Quaife writes clearly, honestly and with infectious enthusiasm. His interesting book is a compilation of research papers which retains the excitement and focus on detail that his creative use of OTTER engendered. I can't help liking a scholarly book that carries the ancient Greek or southern Californian dedication: To the pursuit and realization of unlimited pleasure.