The main ingredients underlying this approach are efficient automatic theorem provers that
can cope with hundreds of axioms, suitable translations of the proof assistant's logic to the …

Computers arechanging the way wethink. Of course, nearly all desk-workers have access to
computers and use them to email their colleagues, search the Web for information and …

Sledgehammer is a component of the Isabelle/HOL proof assistant that integrates external
automatic theorem provers (ATPs) to discharge interactive proof obligations. As a safeguard …

Classical automated theorem proving of today is based on ingenious search techniques to
find a proof for a given theorem in very large search spaces—often in the range of several …

This thesis describes work on two components of the interactive theorem prover
Isabelle/HOL. The primary contribution is the development of Nitpick, a counterexample …

Natural language interaction between a student and a tutoring or an assistance system for
mathematics is a new multi-disciplinary challenge that requires the interaction of (i) …

This paper presents an algorithm that redirects proofs by contradiction. The input is a
refutation graph, as produced by an automatic theorem prover (eg, E, SPASS, Vampire, Z3); …

What would the shop** experience of tomorrow look like? In this chapter we propose
several human-centered and resource-adaptive ideas to this question. Throughout the …

Recently, significant advances have been made in formalised mathematical texts for large,
demanding proofs. But although such large developments are possible, they still take an …

We present an approach to mathematical assistants which uses readable, executable proof
scripts as the central language for interaction. We examine an implementation that combines …