Superposition-based provers have been successfully used to discharge proof obligations
stemming from proof assistants. However, many such obligations require induction to be …

Several practical tools for automatically verifying functional programs (eg, Liquid Haskell
and Leon for Scala programs) rely on a heuristic based on unrolling recursive function …

Matching logic is a logic for specifying and reasoning about structure by means of patterns
and pattern matching. This paper makes two contributions. First, it proposes a sound and …

We re-examine the topic of machine-learned clause selection guidance in saturation-based
theorem provers. The central idea, recently popularized by the ENIGMA system, is to learn a …

Satisfiability modulo theories (SMT) solvers implement a wide range of optimizations that are
often tailored to a particular class of problems, and that differ significantly between solvers …

Many applications of theorem proving, for example program verification and analysis,
require first-order reasoning with both quantifiers and theories such as arithmetic and …

We describe an extension of automating induction in superposition-based reasoning by
strengthening inductive properties and generalizing terms over which induction should be …

Functional programs over inductively defined data types, such as lists, binary trees and
naturals, can naturally be defined using recursive equations over recursive functions. In first …

We propose trace logic, an instance of many-sorted first-order logic, to automate the partial
correctness verification of programs containing loops. Trace logic generalizes semantics of …

Explicit theory axioms are added by a saturation-based theorem prover as one of the
techniques for supporting theory reasoning. While simple and effective, adding theory …