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Documents authored by Fleury, Mathias

Document
DOI: 10.4230/LIPIcs.ITP.2025.26
Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL

Authors: Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Sledgehammer is a tool that increases the level of automation in the Isabelle/HOL proof assistant by asking external automatic theorem provers (ATPs), including SMT solvers, to prove the current goal. When the external ATP succeeds it must provide enough evidence that the goal holds for Isabelle to be able to reprove it internally based on that evidence. In particular, Isabelle can do this by replaying fine-grained proof certificates from proof-producing SMT solvers as long as they are expressed in the Alethe format, which until now was supported only by the veriT SMT solver. We report on our experience adding proof reconstruction support for the cvc5 SMT solver in Isabelle by extending cvc5 to produce proofs in the Alethe format and then adapting Isabelle to reconstruct those proofs. We discuss several difficulties and pitfalls we encountered and describe a set of tools and techniques we developed to improve the process. A notable outcome of this effort is that Isabelle can now be used as an independent proof checker for SMT problems written in the SMT-LIB standard. We evaluate cvc5’s integration on a set of SMT-LIB benchmarks originating from Isabelle as well as on a set of Isabelle proofs. Our results confirm that this integration complements and improves Sledgehammer’s capabilities.
Cite as

Hanna Lachnitt, Mathias Fleury, Haniel Barbosa, Jibiana Jakpor, Bruno Andreotti, Andrew Reynolds, Hans-Jörg Schurr, Clark Barrett, and Cesare Tinelli. Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lachnitt_et_al:LIPIcs.ITP.2025.26,
  author =	{Lachnitt, Hanna and Fleury, Mathias and Barbosa, Haniel and Jakpor, Jibiana and Andreotti, Bruno and Reynolds, Andrew and Schurr, Hans-J\"{o}rg and Barrett, Clark and Tinelli, Cesare},
  title =	{{Improving the SMT Proof Reconstruction Pipeline in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.26},
  URN =		{urn:nbn:de:0030-drops-246243},
  doi =		{10.4230/LIPIcs.ITP.2025.26},
  annote =	{Keywords: interactive theorem proving, proof assistants, Isabelle/HOL, SMT, certification, proof certificates, proof reconstruction, proof automation}
}
Artifact
Software
DOI: 10.4230/artifacts.24025
Kissat Clause Reduction Version

Authors: Bernhard Gstrein, Florian Pollitt, André Schidler, Mathias Fleury, and Armin Biere

Abstract
Cite as

Bernhard Gstrein, Florian Pollitt, André Schidler, Mathias Fleury, Armin Biere. Kissat Clause Reduction Version (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{github,
   title = {{Kissat Clause Reduction Version}}, 
   author = {Gstrein, Bernhard and Pollitt, Florian and Schidler, Andr\'{e} and Fleury, Mathias and Biere, Armin},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:b6a189824ab8c4ceab3f1a2f31c349423724cc19;origin=https://github.com/texmex76/kissat-cr;visit=swh:1:snp:5683baa56ab6acbc85aca46b16845fd3f6da4cf6;anchor=swh:1:rev:84d0d475780fa7e507cd7c9749e4c77465c35bfa}{\texttt{swh:1:dir:b6a189824ab8c4ceab3f1a2f31c349423724cc19}} (visited on 2025-08-07)},
   url = {https://github.com/texmex76/kissat-cr},
   doi = {10.4230/artifacts.24025},
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.14
Learn to Unlearn

Authors: Bernhard Gstrein, Florian Pollitt, André Schidler, Mathias Fleury, and Armin Biere

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Clause learning is a significant milestone in the development of SAT solving. However, keeping all learned clauses without discrimination gradually slows down the solver. Thus, selectively removing some learned clauses during routine database reduction is essential. In this paper, we reexamine and test several long-standing ideas for clause removal in the modern solver Kissat. Our experiments show that retaining all clauses alters performance in all instances. For satisfiable instances, periodically removing all learned clauses surprisingly yields near state-of-the-art performance. For unsatisfiable instances, it is vital to always keep some learned clauses. Building on the influential Glucose paper, we find that it is crucial to always retain the clauses most likely to help, regardless of whether they are ranked by size or LBD in practice. Another key factor is whether a clause was used recently during conflict resolution steps. Eagerly keeping used clauses improves all unlearning strategies.
Cite as

Bernhard Gstrein, Florian Pollitt, André Schidler, Mathias Fleury, and Armin Biere. Learn to Unlearn. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gstrein_et_al:LIPIcs.SAT.2025.14,
  author =	{Gstrein, Bernhard and Pollitt, Florian and Schidler, Andr\'{e} and Fleury, Mathias and Biere, Armin},
  title =	{{Learn to Unlearn}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{14:1--14:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.14},
  URN =		{urn:nbn:de:0030-drops-237480},
  doi =		{10.4230/LIPIcs.SAT.2025.14},
  annote =	{Keywords: Satisfiability solving, learned clause recycling, LBD}
}
Artifact
Software
DOI: 10.4230/artifacts.22495
arminbiere/cadical

Authors: Mathias Fleury

Abstract
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Mathias Fleury. arminbiere/cadical (Software, CaDiCaL Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22495,
   title = {{arminbiere/cadical}}, 
   author = {Fleury, Mathias},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:eaf1bada31f3142996582c25a7df2118e7cacc98;origin=https://github.com/arminbiere/cadical;visit=swh:1:snp:53dfb8828f1ebfecc0e02187545b6762c277b5c9;anchor=swh:1:rev:5ce2e0a5a676d5682622005d56a50e5266f3e29b}{\texttt{swh:1:dir:eaf1bada31f3142996582c25a7df2118e7cacc98}} (visited on 2024-11-28)},
   url = {https://github.com/arminbiere/cadical/tree/strong-backtrack},
   doi = {10.4230/artifacts.22495},
}
Artifact
Software
DOI: 10.4230/artifacts.22497
m-fleury/glucose

Authors: Mathias Fleury

Abstract
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Mathias Fleury. m-fleury/glucose (Software, Glucose Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22497,
   title = {{m-fleury/glucose}}, 
   author = {Fleury, Mathias},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:fc5f0bd80c6a9e9412c5a3f3fcde96bf17a36147;origin=https://github.com/m-fleury/glucose;visit=swh:1:snp:a2f7255914669f8ebcc24ec1124ef1ae31bb16d0;anchor=swh:1:rev:8a5c7117fda44781c56bba2e9a9520fca5450509}{\texttt{swh:1:dir:fc5f0bd80c6a9e9412c5a3f3fcde96bf17a36147}} (visited on 2024-11-28)},
   url = {https://github.com/m-fleury/glucose},
   doi = {10.4230/artifacts.22497},
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.6
Clausal Congruence Closure

Authors: Armin Biere, Katalin Fazekas, Mathias Fleury, and Nils Froleyks

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Many practical applications of satisfiability solving employ multiple steps to encode an original problem formulation into conjunctive normal form. Often circuits are used as intermediate representation before encoding those circuits into clausal form. These circuits however might contain redundant isomorphic sub-circuits. If blindly translated into clausal form, this redundancy is retained and increases solving time unless specific preprocessing algorithms are used. Furthermore, such redundant sub-formula structure might only emerge during solving and needs to be addressed by inprocessing. This paper presents a new approach which extracts gate information from the formula and applies congruence closure to match and eliminate redundant gates. Besides new algorithms for gate extraction, we also describe previous unpublished attempts to tackle this problem. Experiments focus on the important problem of combinational equivalence checking for hardware designs and show that our new approach yields a substantial gain in CNF solver performance.
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Armin Biere, Katalin Fazekas, Mathias Fleury, and Nils Froleyks. Clausal Congruence Closure. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{biere_et_al:LIPIcs.SAT.2024.6,
  author =	{Biere, Armin and Fazekas, Katalin and Fleury, Mathias and Froleyks, Nils},
  title =	{{Clausal Congruence Closure}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{6:1--6:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.6},
  URN =		{urn:nbn:de:0030-drops-205287},
  doi =		{10.4230/LIPIcs.SAT.2024.6},
  annote =	{Keywords: Satisfiability Solving, Congruence Closure, Structural Hashing, SAT Sweeping, Conjunctive Normal Form, Combinational Equivalence Checking, Hardware Equivalence Checking}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.9
Lazy Reimplication in Chronological Backtracking

Authors: Robin Coutelier, Mathias Fleury, and Laura Kovács

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Chronological backtracking is an interesting SAT solving technique within CDCL reasoning, as it backtracks less aggressively upon conflicts. However, chronological backtracking is more difficult to maintain due to its weaker SAT solving invariants. This paper introduces a lazy reimplication procedure for missed lower implications in chronological backtracking. Our method saves propagations by reimplying literals on demand, rather than eagerly. Due to its modularity, our work can be replicated in other solvers, as shown by our results in the solvers CaDiCaL and Glucose.
Cite as

Robin Coutelier, Mathias Fleury, and Laura Kovács. Lazy Reimplication in Chronological Backtracking. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coutelier_et_al:LIPIcs.SAT.2024.9,
  author =	{Coutelier, Robin and Fleury, Mathias and Kov\'{a}cs, Laura},
  title =	{{Lazy Reimplication in Chronological Backtracking}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.9},
  URN =		{urn:nbn:de:0030-drops-205313},
  doi =		{10.4230/LIPIcs.SAT.2024.9},
  annote =	{Keywords: Chronological Backtracking, CDCL, Invariants, Watcher Lists}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.21
Faster LRAT Checking Than Solving with CaDiCaL

Authors: Florian Pollitt, Mathias Fleury, and Armin Biere

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
DRAT is the standard proof format used in the SAT Competition. It is easy to generate but checking proofs often takes even more time than solving the problem. An alternative is to use the LRAT proof system. While LRAT is easier and way more efficient to check, it is more complex to generate directly. Due to this complexity LRAT is not supported natively by any state-of-the-art SAT solver. Therefore Carneiro and Heule proposed the mixed proof format FRAT which still suffers from costly intermediate translation. We present an extension to the state-of-the-art solver CaDiCaL which is able to generate LRAT natively for all procedures implemented in CaDiCaL. We further present Lrat-Trim, a tool which not only trims and checks LRAT proofs in both ASCII and binary format but also produces clausal cores and has been tested thoroughly. Our experiments on recent competition benchmarks show that our approach reduces time of proof generation and certification substantially compared to competing approaches using intermediate DRAT or FRAT proofs.
Cite as

Florian Pollitt, Mathias Fleury, and Armin Biere. Faster LRAT Checking Than Solving with CaDiCaL. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{pollitt_et_al:LIPIcs.SAT.2023.21,
  author =	{Pollitt, Florian and Fleury, Mathias and Biere, Armin},
  title =	{{Faster LRAT Checking Than Solving with CaDiCaL}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{21:1--21:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.21},
  URN =		{urn:nbn:de:0030-drops-184837},
  doi =		{10.4230/LIPIcs.SAT.2023.21},
  annote =	{Keywords: SAT solving, Proof Checking, DRAT, LRAT, FRAT}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.11
Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL

Authors: Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
We present a collection of formalized results about finite nested multisets, developed using the Isabelle/HOL proof assistant. The nested multiset order is a generalization of the multiset order that can be used to prove termination of processes. Hereditary multisets, a variant of nested multisets, offer a convenient representation of ordinals below epsilon-0. In Isabelle/HOL, both nested and hereditary multisets can be comfortably defined as inductive datatypes. Our formal library also provides, somewhat nonstandardly, multisets with negative multiplicities and syntactic ordinals with negative coefficients. We present applications of the library to formalizations of Goodstein's theorem and the decidability of unary PCF (programming computable functions).
Cite as

Jasmin Christian Blanchette, Mathias Fleury, and Dmitriy Traytel. Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{blanchette_et_al:LIPIcs.FSCD.2017.11,
  author =	{Blanchette, Jasmin Christian and Fleury, Mathias and Traytel, Dmitriy},
  title =	{{Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{11:1--11:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.11},
  URN =		{urn:nbn:de:0030-drops-77155},
  doi =		{10.4230/LIPIcs.FSCD.2017.11},
  annote =	{Keywords: Multisets, ordinals, proof assistants}
}
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