An advanced, graduate-level text, surveying computational logic and set theory and its application to proof verification techniques. Book develops all needed theory and provides a CD-ROM with a proof-verifier program to demonstrate concepts. Advanced CS students and researches will find the book an essential presentation of the theoretical concepts of proof verification (i.e., proof checker) systems for large-scale software systems. Topics and features: *Describes in-depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics *Provides a verifier aimed at tackling large-scale proof scenarios *Integrates important proof-engineering issues, reflecting the goals of large-scale verifiers