Inductive Reasoning with Equality Predicates, Contextual Rewriting and Variant-Based Simplification

We present an inductive inference system for proving validity of formulas in the initial algebra T[E] of an order-sorted equational theory E with 17 inference rules, where only 6 of them require user interaction, while the remaining 11 can be automated as simplification rules and can be combined together as a limited, yet practical, automated inductive theorem prover. The 11 simplification rules are based on powerful equational reasoning techniques, including: equationally defined equality predicates, constructor variant unification, variant satisfiability, order-sorted congruence closure, contextual rewriting and recursive path orderings. For E the union of E0 and B, these techniques work modulo B, with B a combination of associativity and/or commutativity and/or identity axiomsPartially supported by NRL under contract N00173-17-1-G002.Ope