The chapter “ Proof Generation for Saturating First - Order Theorem Provers ”

This book is a collection of articles referring to the presentations delivered during a one-day workshop consisting of 12 invited tutorials. That workshop was a part of “Vienna Summer of Logic” in July 2014. The format itself (I did not attend the event) indicates tutorials of a moderate length devoted to a multitude of deduction tools. The reviewed volume consists of twelve chapters, i.e. papers written by presenters and reviewed by individuals from the corresponding community and other communities. College Publications, a publisher of all-things-logic produced the book fast; the date on the preface is less than half-a-year after the event. This included the review process! To some extent, this is not surprising. With the appropriate tools and printing-on-demand process the scientific community can now liberate itself from mercy of shark-publishers. College Publications shows the way. The chapters in the collection correspond to tutorials presented during the workshop. The tools (and more generally subspecialties of computational logic) presented in the chapters range from provers associated with some areas of propositional logic, through the provers for decidable fragments of predicate logic, to first-order logic provers, and higher-order logic. Applications of proofs, more generally of Proof Theory, are also discussed. There are significant differences between the tools and, more generally, philosophies of corresponding communities. The border lies between so-called satisfiabilitymodulo-theories, i.e. decidable fragments of predicate logic (I am being deliberately not precise here) and more complex areas of logic: full first-order logic, and higherorder logics. Generally, since antiquity, the humanity associated values with proofs. Certainly the ancient Greeks understood that, and the proofs and proof techniques were followed by philosophers and mathematicians of antiquity. Techniques that did not perish during the dark ages were further developed by mathematicians and philosophers starting with the mediaeval scholastics. Of course other great civilizations, Arabs, Chinese, Indians, and Persians, contributed, in various degrees, in preservation and developments of such techniques. Modern mathematics is founded on the notion of a proof. Proofs are what distinguishes theorems from conjectures.