Published: 7th July 2021
DOI: 10.4204/EPTCS.336
ISSN: 2075-2180


Proceedings Seventh Workshop on
Proof eXchange for Theorem Proving
Pittsburg, USA, 11th July 2021

Edited by: Chantal Keller and Mathias Fleury

Proof Generation in CDSAT
Maria Paola Bonacina
A Framework for Proof-carrying Logical Transformations
Quentin Garchery
General Automation in Coq through Modular Transformations
Valentin Blot, Louise Dubois de Prisque, Chantal Keller and Pierre Vial
Integrating an Automated Prover for Projective Geometry as a New Tactic in the Coq Proof Assistant
Nicolas Magaud
Certifying CNF Encodings of Pseudo-Boolean Constraints (abstract)
Stephan Gocht, Jakob Nordström and Ruben Martins
Alethe: Towards a Generic SMT Proof Format (extended abstract)
Hans-Jörg Schurr, Mathias Fleury, Haniel Barbosa and Pascal Fontaine


This volume of EPTCS contains the proceedings of the Seventh Workshop on Proof Exchange for Theorem Proving (PxTP 2021), held on 11 July 2021 as part of the CADE-28 conference, originally planned in Pittsburg, USA, but finally hold in cyberspace.

The PxTP workshop series brings together researchers working on various aspects of communication, integration, and cooperation between reasoning systems and formalisms, with a special focus on proofs.

The progress in computer-aided reasoning, both automated and interactive, during the past decades, made it possible to build deduction tools that are increasingly more applicable to a wider range of problems and are able to tackle larger problems progressively faster. In recent years, cooperation between such tools in larger systems has demonstrated the potential to reduce the amount of manual intervention.

Cooperation between reasoning systems relies on availability of theoretical formalisms and practical tools to exchange problems, proofs, and models. The PxTP workshop series strives to encourage such cooperation by inviting contributions on all aspects of cooperation between reasoning tools, whether automatic or interactive, including the following topics:

Previous editions of the workshop took place in Wroclaw (2011), Manchester (2012), Lake Placid (2013), Berlin (2015), Brasília (2017), and Natal (2019).

This edition of the workshop received submissions of three regular papers and three extended abstracts. All submissions were evaluated by at least three anonymous reviewers. Two full papers and three extended abstracts were accepted in the post-proceedings.

The program committee had the following members: Chantal Keller (co-chair, LRI, Université Paris-Saclay), Mathias Fleury (co-chair, JKU Linz), Haniel Barbosa (Universidade Federal de Minas Gerai, Denis Cousineau (Mitsubishi Electric R&D Centre Europe), Stefania Dumbrava (ENSIIE, Télécom SudParis), Katalin Fazekas (TU Wien), Predrag Janićič (Univerzitet u Beogradu), Jens Otten (University of Oslo), Aina Niemetz (Stanford University), Giselle Reis (Carnegie Mellon University), Geoff Sutcliffe (University of Miami), François Thiré (Nomadic Labs), Sophie Tourret (Inria), and Josef Urban (Czech Technical University in Prague).

We would like to thank all authors for their submissions and all members of the program committee for the time and energy they spent to diligently ensure that accepted papers were of high quality. We also thank Easychair for making it easy to chair the reviewing process. Furthermore, we are thankful to the CADE-28 organizers who organized the conference in these challenging times.

We had the honor to welcome two invited speakers: Maria Paola Bonacina from the Università degli Studi di Verona gave a talk entitled Proof Generation in CDSAT and Giles Reger from the University of Manchester, presented a talk entitled Reasoning in many logics with Vampire: Everything's CNF in the end. The presentations from the invited speakers and the presentations from the accepted papers raised numerous, interesting, and fruitful discussions. We thank all the participants of the workshop.

The organization of this edition of PxTP stood on the shoulders of previous editions, and we are grateful to the chairs of previous editions for all the resources and infrastructure that they made available to us.

July 11, 2021

Chantal Keller and Mathias Fleury

Certifying CNF Encodings of Pseudo-Boolean Constraints (abstract)

Stephan Gocht
Jakob Nordström
Ruben Martins

The dramatic improvements in Boolean satisfiability (SAT) solving since the turn of the millennium have made it possible to leverage state-of-the-art conflict-driven clause learning (CDCL) solvers for many combinatorial problems in academia and industry, and the use of proof logging has played a crucial role in increasing the confidence that the results these solvers produce are correct. However, the conjunctive normal form (CNF) format used for SAT proof logging means that it is hard to extend the method to other, stronger, solving paradigms for combinatorial problems. We show how to instead leverage the cutting planes proof system to provide proof logging for pseudo-Boolean solvers that translate pseudo-Boolean problems (a.k.a 0-1 integer linear programs) to CNF and run CDCL. We are hopeful that this is just a first step towards providing a unified proof logging approach that will also extend to maximum satisfiability (MaxSAT) solving and pseudo-Boolean optimization in general.