The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Godel's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Godel...

Here are the proceedings of the Third International Joint Conference on Automated Reasoning, IJCAR 2006, held in Seattle, Washington, USA, August 2006. The book presents 41 revised full research papers and 8 revised system descriptions, with 3 invited papers and a summary of a systems competition. The papers are organized in topical sections on proofs, search, higher-order logic, proof theory, proof checking, combination, decision procedures, CASC-J3, rewriting, and description logic.

This volume contains the proceedings of the second working conference on Verified Software: Theories, Tools, and Experiments, VSTTE 2008, held in Toronto, Canada, in October 2008. The 16 papers presented together with 4 invited talks were carefully revised and selected for inclusion in the book. This second conference formally inaugurates the Verified Software Initiative (VSI), a fifteen-year, co-operative, international project directed at the scientific challenges of large-scale software verification. The scope of the cooperative effort includes the sharing and interoperability of tools,...