  Induction in saturation-based first-order theorem proving is a new exciting
direction in the automation of inductive reasoning. In this paper we survey our
work on integrating induction directly into the saturation-based proof search
framework of first-order theorem proving. We describe our induction inference
rules proving properties with inductively defined datatypes and integers. We
also present additional reasoning heuristics for strengthening inductive
reasoning, as well as for using induction hypotheses and recursive function
definitions for guiding induction. We present exhaustive experimental results
demonstrating the practical impact of our approach as implemented within
Vampire.
  This is an extended version of a Principles of Systems Design 2022 paper with
the same title and the same authors.
