Preface
This volume contains the proceedings of the 27th International Conference on Automated Deduction (CADE-27). The conference was hosted by the Universi-dade Federal do Rio Grande do Norte, in Natal, Brazil, during August 23–30, 2019. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience.
The Program Committee accepted 34 papers (27 full papers and 7 system descriptions) out of 65 submissions (53 full papers and 12 system descriptions). Each submission was reviewed by at least three Program Committee (PC) mem-bers or external reviewers appointed by the PC memmem-bers in charge. The main cri-teria for evaluation were originality and significance, technical quality and com-pleteness, comparison with related work and completeness of references, quality of presentation, clarity, and readability. All papers containing experimental data were also evaluated with respect to reproducibility.
The technical program of the conference included three invited talks:
– Cas Cremers (CISPA Helmholtz Center for Information Security, Saarbr¨ucken, Germany): “Automated Reasoning for Security Protocols”
– Assia Mahboubi (Inria, LS2N, Universit´e de Nantes, France and Vrije Uni-versiteit Amsterdam, the Netherlands): “Computer Deduction and (Formal) Proofs in Mathematics”
– Cesare Tinelli (Department of Computer Science, The University of Iowa, USA): “From Counter-Model-based Quantifier Instantiation to Quantifier Elimination in SMT”
During the conference, the Herbrand Award for Distinguished Contributions to Automated Reasoning was presented to Nikolaj Bjørner and Leonardo de Moura in recognition of their numerous and important contributions to SMT solving, including its theory, implementation, and application to a wide range of academic and industrial needs. The Selection Committee for the Herbrand Award consisted of Bruno Dutertre, Juergen Giesl, Dale Miller (chair), and Larry Paulson.
The Thoralf Skolem Awards were conferred this year to reward CADE papers that have passed the test of time by being most influential papers in the field for 1979, 1990, 1999 and 2009. The authors receiving an award were:
– Peter Andrews for the paper entitled “General Matings” published in the CADE-4 proceedings in 1979.
The paper is recognized for its invention of the generalized mating method for constructing refutations of formulas in conjunctive normal form. This development paved the way for the subsequent construction of many non-resolution methods in automated deduction, including the well-known con-nection method.
– Leo Bachmair and Harald Ganzinger for the paper entitled “On Restrictions of Ordered Paramodulation with Simplification” published in the CADE-10 proceedings in 1990.
The paper is recognized for its development of the superposition calculus for equational first-order clauses alongside a new and powerful framework for proving completeness and accommodating redundancy. This framework forms the basis of many advanced modern theorem provers, and has been highly influential in accelerating progress in the area of automated deduction. – Christoph Weidenbach for the paper “Towards an Automated Analysis of
Security Protocols” published in the CADE-16 proceedings in 1999. The paper is recognized for two main contributions to automated deduction: first, its novel application of general theorem proving techniques to a key-exchange security protocol; and, second, its development of new decidability and undecidability results for fragments of monadic Horn theories.
– Rajeev Gor´e and Florian Widmann for the paper entitled “An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability” published in the CADE-22 proceedings in 2009.
The paper is recognized for presenting the first decision procedure for propo-sitional dynamic logic which is both theoretically optimal and effective in practice. Previous decision procedures are either suboptimal in the worst case, or worst-case optimal but with poor average-case performance. The so-lution in this paper thereby closed a problem that had been open for almost 30 years.
The conference issued a call for workshops out of which the following five proposals were approved:
– Automated Reasoning: Challenges, Applications, Directions, Exemplary Achieve-ments (ARCADE)
– Deduction Mentoring Workshop (DeMent 2019)
– Logical and Semantic Frameworks, with Applications (LSFA) – Proof eXchange for Theorem Proving (PxTP)
– Theorem Prover Components for Educational Software (ThEdu’19)
In addition, the conference included a two-day program of introductory tu-torials. The first day was dedicated to tutorials given by local organizers, with an aim to promote among local and foreign students the research on automated reasoning carried out locally:
– Cl´audia Nalon: “Machine Oriented Reasoning”
– Carlos Olarte: “Building Theorem Provers Using Rewriting Logic” – Giselle Reis: “Intuitionistic Logic”
A one-day tutorial, titled “Build Your Own First-Order Prover” was given by Jens Otten on the second day.
During the conference, the CADE-27 ATP System Competition – CASC-27 – was held, organized by Geoff Sutcliffe. The description of the competition is available as an abstract in these proceedings.
I would like to thank the many people without whom the conference would not have been possible. First, I would like to thank all authors who submitted papers, all participants of the conference as well as the invited keynote speak-ers, the tutorial speakspeak-ers, and the workshop organizers for their contributions. I am very grateful to the members of the PC and the external reviewers for carefully reviewing and selecting the papers. In particular, I would like to thank Philipp R¨ummer and Roberto Sebastiani who acted as chairs for the papers I was conflicting with. Many thanks to Andrei Voronkov for providing the Easy-Chair system which greatly facilitated the reviewing process, the electronic PC meeting, and the preparation of the proceedings. I also thank the Trustees of CADE Inc. for their advice and support. Special thanks go to Elaine Pimentel, who as conference chair was involved in almost every aspect of the organiza-tion of the conference, and the members of the local organizaorganiza-tion team, Carlos Olarte, Jo˜ao Marcos, Cl´audia Nalon, and Giselle Reis, for the tremendous effort they devoted to the organization of the conference. I am extremely grateful to Geoff Sutcliffe, for organizing CASC and being the publicity chair, and to Giles Reger, the workshop chair.
CADE-27 received support from many organizations. On behalf of all orga-nizers, I would like to thank the Universidade Federal do Rio Grande do Norte, DMAT, ProEx, PPG, PROPESQ, the Universidade de Brasilia, CAPES, CNPq, CMU Qatar, the Association for Symbolic Logic, IBM, Imandra, Microsoft, and Springer.
August 2019 Pascal Fontaine
Table of Contents
Automated Reasoning for Security Protocols . . . 1 Cas Cremers
Computer Deduction and (Formal) Proofs in Mathematics . . . 2 Assia Mahboubi
From Counter-Model-based Quantifier Instantiation to Quantifier
Elimination in SMT . . . 3 Andrew Reynolds and Cesare Tinelli
The CADE-27 ATP System Competition - CASC-27 . . . 4 Geoff Sutcliffe
Unification modulo Lists with Reverse - Relation with Certain Word
Equations . . . 7 Siva Anantharaman, Peter Hibbs, Paliath Narendran and Michael Rusi-nowitch
On the Width of Regular Classes of Finite Structures . . . 23 Alexsander Andrade de Melo and Mateus De Oliveira Oliveira
Extending SMT solvers to Higher-Order Logic . . . 40 Haniel Barbosa, Andrew Reynolds, Daniel El Ouraoui, Cesare Tinelli and Clark Barrett
Superposition with Lambdas . . . 58 Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vuk-mirovi´c and Uwe Waldmann
Restricted Combinatory Unification . . . 77 Ahmed Bhayat and Giles Reger
dLi: Definite Descriptions in Differential Dynamic Logic . . . 96 Brandon Bohrer, Manuel Fern´andez and Andr´e Platzer
SPASS-SATT – A CDCL(LA) Solver . . . 113 Martin Bromberger, Mathias Fleury, Simon Schwarz and Christoph Weidenbach
GRUNGE: A Grand Unified ATP Challenge . . . 125 Chad Brown, Thibault Gauthier, Cezary Kaliszyk, Geoff Sutcliffe and Josef Urban
Model Completeness, Covers and Superposition . . . 144 Diego Calvanese, Silvio Ghilardi, Alessandro Gianola, Marco Montali and Andrey Rivkin
A Tableaux Calculus for Default Intuitionistic Logic . . . 161 Valentin Cassano, Raul Fervari, Guillaume Hoffmann, Carlos Areces and Pablo F. Castro
NIL: Learning Nonlinear Interpolants . . . 178 Mingshuai Chen, Jian Wang, Jie An, Bohua Zhan, Deepak Kapur and Naijun Zhan
ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference
Guidance for E . . . 195 Karel Chvalovsk´y, Jan Jakub˚uv, Martin Suda and Josef Urban
Towards Physical Hybrid Systems . . . 214 Katherine Cordwell and Andr´e Platzer
SCL – Clause Learning from Simple Models . . . 231 Alberto Fiori and Christoph Weidenbach
Names are not just Sound and Smoke: Word Embeddings for Axiom
Selection . . . 248 Ulrich Furbach, Teresa Kr¨amer and Claudia Schon
Computing Expected Runtimes for Constant Probability Programs . . . 266 J¨urgen Giesl, Peter Giesl and Marcel Hark
Automatic Generation of Logical Models with AGES . . . 283 Ra´ul Guti´errez and Salvador Lucas
Automata Terms in a Lazy WSkS Decision Procedure . . . 295 Vojtˇech Havlena, Luk´aˇs Hol´ık, Ondˇrej Leng´al and Tom´aˇs Vojnar
Confluence by Critical Pair Analysis Revisited . . . 312 Nao Hirokawa, Julian Nagele, Vincent Van Oostrom and Michio Oya-maguchi
Composing Proof Terms . . . 329 Christina Kohl and Aart Middeldorp
Combining ProVerif and Automated Theorem Provers for Security
Protocol Verification . . . 345 Di Long Li and Alwen Tiu
Towards Bit-Width-Independent Proofs in SMT Solvers . . . 357 Aina Niemetz, Mathias Preiner, Andrew Reynolds, Yoni Zohar, Clark Barrett and Cesare Tinelli
On Invariant Synthesis for Parametric Systems . . . 375 Dennis Peuter and Viorica Sofronie-Stokkermans
The Aspect Calculus . . . 394 David Plaisted
Uniform Substitution At One Fell Swoop . . . 411 Andr´e Platzer
A Formally Verified Abstract Account of G¨odel’s Incompleteness Theorems 428 Andrei Popescu and Dmitriy Traytel
Old or Heavy? Decaying Gracefully with Age/Weight Shapes . . . 445 Michael Rawson and Giles Reger
Induction in Saturation-Based Proof Search . . . 460 Giles Reger and Andrei Voronkov
Faster, Higher, Stronger: E 2.3 . . . 478 Stephan Schulz, Simon Cruanes and Petar Vukmirovi´c
Certified Equational Reasoning via Ordered Completion . . . 491 Christian Sternagel and Sarah Winkler
JGXYZ - An ATP System for Gap and Glut Logics . . . 508 Geoff Sutcliffe and Francis Jeffry Pelletier
GKC: a Reasoning System for Large Knowledge Bases . . . 519 Tanel Tammet
Optimization Modulo the Theory of Floating-Point Numbers . . . 530 Patrick Trentin and Roberto Sebastiani
FAME(Q): An Automated Tool for Forgetting in Description Logics
with Qualified Number Restrictions . . . 547 Yizheng Zhao and Renate A. Schmidt
Program Committee
Carlos Areces FaMAF - Universidad Nacional de C´ordoba, Ar-gentina
Franz Baader TU Dresden, Germany Clark Barrett Stanford University, US
Jasmin Christian Blanchette Vrije Universiteit Amsterdam, the Netherlands Maria Paola Bonacina Universit`a degli Studi di Verona, Italy
Leonardo de Moura Microsoft, US
Hans de Nivelle School of Science and Technology, Nazarbayev University, Kazakhstan
Clare Dixon University of Liverpool, UK Mnacho Echenim University of Grenoble, France Marcelo Finger University of S˜ao Paulo, Brazil
Pascal Fontaine University of Lorraine, CNRS, Inria, LORIA, France
Silvio Ghilardi Dipartimento di Matematica, Universit`a degli Studi di Milano, Italy
J¨urgen Giesl RWTH Aachen University, Germany
Rajeev Gore The Australian National University, Australia Stefan Hetzl Vienna University of Technology, Austria Marijn Heule The University of Texas at Austin, US Nao Hirokawa JAIST, Japan
Moa Johansson Chalmers University of Technology, Sweden Cezary Kaliszyk University of Innsbruck, Austria
Deepak Kapur University of New Mexico, US
Benjamin Kiesl CISPA Helmholtz Center for Information Secu-rity, Germany
Konstantin Korovin The University of Manchester, UK Laura Kovacs Vienna University of Technology, Austria Ramana Kumar DeepMind, UK
Cl´audia Nalon University of Bras´ılia, Brazil
Vivek Nigam Federal University of Para´ıba & Fortiss, Ger-many
Carlos Olarte Universidade Federal do Rio Grande do Norte, Brazil
Jens Otten University of Oslo, Norway Andr´e Platzer Carnegie Mellon University, US Andrew Reynolds University of Iowa, US
Philipp R¨ummer Uppsala University, Sweden Renate A. Schmidt The University of Manchester, UK Stephan Schulz DHBW Stuttgart, Germany Roberto Sebastiani University of Trento, Italy Shankar SRI International, US
Viorica Sofronie-Stokkermans University Koblenz-Landau, Germany
Martin Suda Czech Technical University, Czechia Geoff Sutcliffe University of Miami, US
Ren´e Thiemann University of Innsbruck, Austria
Uwe Waldmann Max Planck Institute for Informatics, Germany Christoph Weidenbach Max Planck Institute for Informatics, Germany Sarah Winkler University of Innsbruck, Austria
Conference Chair
Elaine Pimentel Universidade Federal do Rio Grande do Norte, Brazil
Local Organization
Carlos Olarte Universidade Federal do Rio Grande do Norte, Brazil
Jo˜ao Marcos Universidade Federal do Rio Grande do Norte, Brazil
Cl´audia Nalon Universidade de Brasilia, Brazil Giselle Reis CMU, Qatar
Workshop Chair
Giles Reger The University of Manchester, UK
Publicity Chair
Geoff Sutcliffe University of Miami, USA
System Competition
Geoff Sutcliffe University of Miami, USA
Additional Reviewers
A
Aoto, Takahito Aravantinos, Vincent Atig, Mohamed Faouzi Avanzini, Martin B Backeman, Peter Barbosa, Haniel Benedikt, Michael Bentkamp, Alexander Berger, Gerald Bottesch, Ralph Brown, Chad C Cordwell, Katherine Cruanes, Simon D Das, Anupam Dawson, Jeremy E Ebner, Gabriel El Ouraoui, Daniel F Fervari, Raul Fiorentini, Camillo Fiorino, Guido Fleury, Mathias Frohn, Florian Fulton, Nathan G Gauthier, Thibault Gianola, Alessandro Graham-Lengrand, Stephane H Hark, Marcel Haslbeck, Max W. Hensel, Jera Hladik, Jan Hoffmann, Guillaume Holden, Edvard Hustadt, Ullrich xiv
I Immler, Fabian Irfan, Ahmed K Kamburjan, Eduard Kaminski, Mark Kojima, Kensuke Kop, Cynthia Kutsia, Temur L Lammich, Peter Liang, Chencheng Libal, Tomer Lisitsa, Alexei L¨oding, Christof M Maric, Filip Marshall, Andrew M. Middeldorp, Aart Moguillansky, Martin Mover, Sergio N Nishida, Naoki Noetzli, Andres P Peltier, Nicolas Ponce-De-Leon, Hernan R Rawson, Michael Riener, Martin Ringeissen, Christophe Robillard, Simon Rocha, Camilo Rowe, Reuben S Sakai, Masahiko Schurr, Hans-J¨org Smallbone, Nicholas Sogokon, Andrew Steigmiller, Andreas Sternagel, Christian Stoilos, Giorgos T Traytel, Dmitriy xv
V
van Gool, Sam van Oostrom, Vincent Verma, Rakesh Vierling, Jannik Voigt, Marco W Wernhard, Christoph Z Zamansky, Anna Zeljic, Aleksandar Zohar, Yoni
Board of Trustees of CADE Inc.
Christoph Benzm¨uller (Vice-president)
Freie Universit¨at Berlin, Germany & University of Luxembourg, Luxembourg
Jasmin Blanchette Vrije Universiteit Amsterdam, the Netherlands Pascal Fontaine (PC Chair) University of Lorraine, CNRS, Inria, LORIA,
France
J¨urgen Giesl RWTH Aachen University, Germany Marijn Heule The University of Texas at Austin, US Laura Kov´acs Vienna University of Technology, Austria Neil Murray (Treasurer) University At Albany, State University of New
York, US
Andrew Reynolds University of Iowa, US Philipp R¨ummer (Secretary) Uppsala University, Sweden Renate Schmidt The University of Manchester, UK Stephan Schulz DHBW Stuttgart, Germany Christoph Weidenbach
(Presi-dent)
Max Planck Institute for Informatics, Germany
Board of the Association for Automated Reasoning
Christoph Benzm¨uller (CADE) Freie Universit¨at Berlin, Germany & University of Luxembourg, Luxembourg
Uli Furbach (Vice-president) Universit¨at Koblenz-Landau, Germany J¨urgen Giesl (CADE) RWTH Aachen University, Germany Philipp R¨ummer (Secretary) Uppsala University, Sweden
Sophie Tourret (Newsletter edi-tor)
Max Planck Institute for Informatics, Germany Larry Wos (President) Argonne National Laboratory, USA
