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Documents authored by Tinelli, Cesare

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}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.4
Bit-Precise Reasoning with Parametric Bit-Vectors

Authors: Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli

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

Abstract
The SMT-LIB theory of bit-vectors is restricted to bit-vectors of fixed width. However, several important applications can benefit from reasoning about bit-vectors of symbolic widths, i.e., parametric bit-vectors. Recent work has introduced an approach for solving formulas over parametric bit-vectors, via an eager translation to quantified integer arithmetic with uninterpreted functions. The approach was shown to be successful for several applications, including the bit-width independent verification of compiler optimizations, invertibility conditions, and rewrite rules. We extend and improve that approach in several aspects. Theoretically, we improve expressiveness by defining a new theory of parametric bit-vectors that supports more operators and allows reasoning about the bit-widths themselves. Algorithmically, we introduce a lazy algorithm that avoids the use of uninterpreted functions and quantified axioms for them. Empirically, we show a significant improvement by implementing and evaluating our approach, and comparing it experimentally to the previous one.
Cite as

Zvika Berger, Yoni Zohar, Aina Niemetz, Mathias Preiner, Andrew Reynolds, Clark Barrett, and Cesare Tinelli. Bit-Precise Reasoning with Parametric Bit-Vectors. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berger_et_al:LIPIcs.SAT.2025.4,
  author =	{Berger, Zvika and Zohar, Yoni and Niemetz, Aina and Preiner, Mathias and Reynolds, Andrew and Barrett, Clark and Tinelli, Cesare},
  title =	{{Bit-Precise Reasoning with Parametric Bit-Vectors}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{4:1--4:24},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-237385},
  doi =		{10.4230/LIPIcs.SAT.2025.4},
  annote =	{Keywords: Satisfiability Modulo Theories, Bit-precise Reasoning, Parametric Bit-vectors}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAT.2024.2
Scalable Proof Production and Checking in SMT (Invited Talk)

Authors: Cesare Tinelli

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

Abstract
Solvers for Satisfiability Modulo Theories (SMT) have become crucial components in safety- or mission-critical formal methods applications, in particular model checking, verification, and security analysis. Since state-of-the-art SMT solvers are large and complex systems, they are prohibitively difficult to prove correct. Hence, proof production is essential as a way to demonstrate instead the correctness of their responses, making those responses amenable to independent verification. Historically, the main challenges for proof production in SMT have been solver performance and proof coverage, often leading to the disabling of many sophisticated solving techniques when running in proof-production mode, or to coarse-grained, and harder to check, proofs. The first part of this talk presents a flexible proof-production architecture designed to handle the complexity of versatile, industrial-strength SMT solvers, and discusses how it has been leveraged to produce detailed proofs, even for sophisticated reasoning components. The architecture, implemented in the state-of-the-art SMT solver cvc5, allows proofs to be produced modularly, as needed, and with various safeguards for correctness. The architecture supports the generation of textual proof certificates in different formats, for offline proof checking by external tools, as well as a rich API, which is useful for online integration of the SMT solver into other reasoning tools such as, for instance, skeptical proof assistants. Extensive experimental evaluations with both SMT-LIB benchmarks and benchmarks provided by industrial partners have shown that the new architecture results in greater proof coverage than previous approaches, imposes a small runtime overhead, and supports fine-grained proofs in the great majority of cases. The second part of the talk gives an overview of a new generic language for expressing SMT proof certificates that builds on almost two decades of work and experience in proof generation and checking in SMT and combines the benefits of several previous efforts on the topic. While developed to express cvc5’s proof certificates, the language is meant to be useful to other SMT solvers as well. It is in fact a logical framework, based on the syntax and semantics of the upcoming Version 3 of the SMT-LIB standard, that can be customized, as in the case of cvc5, with the specific proof system used by the solver through the definition of new symbols, binders and proof rules. In addition, it features an intuitive syntax for representing natural-deduction-style proofs and the ability to integrate other proof formats (such as, for instance, those currently used by SAT solvers) via the use of oracles. The talk discusses an initial evaluation of the proof language, obtained with a companion checker for it and an instantiation to cvc5’s proof system. The evaluation shows the viability of high-performance, fine-grained proof production and checking for SMT. The talk concludes with a brief overview of future work and new potential applications enabled by scalable proof certificate production and checking.
Cite as

Cesare Tinelli. Scalable Proof Production and Checking in SMT (Invited Talk). In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{tinelli:LIPIcs.SAT.2024.2,
  author =	{Tinelli, Cesare},
  title =	{{Scalable Proof Production and Checking in SMT}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{2:1--2:2},
  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.2024.2},
  URN =		{urn:nbn:de:0030-drops-205241},
  doi =		{10.4230/LIPIcs.SAT.2024.2},
  annote =	{Keywords: Satisfiability Modulo Theories, Proof generation and certification}
}
Document
DOI: 10.4230/DagRep.9.9.23
Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

Authors: Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli

Published in: Dagstuhl Reports, Volume 9, Issue 9 (2020)

Abstract
Research in automated deduction is traditionally focused on the problem of determining the satisfiability of formulas or, more generally, on solving logical problems with yes/no answers. Thanks to recent advances that have dramatically increased the power of automated deduction tools, there is now a growing interest in extending deduction techniques to attack logical problems with more complex answers. These include both problems with a long history, such as quantifier elimination, which are now being revisited in light of the new methods, as well as newer problems such as minimal unsatisfiable cores computation, model counting for propositional or first-order formulas, Boolean or SMT constraint optimization, generation of interpolants, abductive reasoning, and syntax-guided synthesis. Such problems arise in a variety of applications including the analysis of probabilistic systems (where properties like safety or liveness can be established only probabilistically), network verification (with relies on model counting), the computation of tight complexity bounds for programs, program synthesis, model checking (where interpolation or abductive reasoning can be used to achieve scale), and ontology-based information processing. The seminar brought together researchers and practitioners from many of the often disjoint sub-communities interested in the problems above. The unifying theme of the seminar was how to harness and extend the power of automated deduction methods to solve problems with more complex answers than binary ones.
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Carsten Fuhs, Philipp Rümmer, Renate Schmidt, and Cesare Tinelli. Deduction Beyond Satisfiability (Dagstuhl Seminar 19371). In Dagstuhl Reports, Volume 9, Issue 9, pp. 23-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{fuhs_et_al:DagRep.9.9.23,
  author =	{Fuhs, Carsten and R\"{u}mmer, Philipp and Schmidt, Renate and Tinelli, Cesare},
  title =	{{Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)}},
  pages =	{23--44},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2020},
  volume =	{9},
  number =	{9},
  editor =	{Fuhs, Carsten and R\"{u}mmer, Philipp and Schmidt, Renate and Tinelli, Cesare},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.9.23},
  URN =		{urn:nbn:de:0030-drops-118432},
  doi =		{10.4230/DagRep.9.9.23},
  annote =	{Keywords: abduction, automated deduction, interpolation, quantifier elimination, synthesis}
}
Document
DOI: 10.4230/DagRep.7.9.26
Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)

Authors: Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, and Cesare Tinelli

Published in: Dagstuhl Reports, Volume 7, Issue 9 (2018)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 17371 "Deduction Beyond First-Order Logic." Much research in the past two decades was dedicated to automating first-order logic with equality. However, applications often need reasoning beyond this logic. This includes genuinely higher-order reasoning, reasoning in theories that are not finitely axiomatisable in first-order logic (such as those including transitive closure operators or standard arithmetic on integers or reals), or reasoning by mathematical induction. Other practical problems need a mixture of first-order proof search and some more advanced reasoning (for instance, about higher-order formulas), or simply higher-level reasoning steps. The aim of the seminar was to bring together first-order automated reasoning experts and researchers working on deduction methods and tools that go beyond first-order logic. The seminar was dedicated to the exchange of ideas to facilitate the transition from first-order to more expressive settings.
Cite as

Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, and Cesare Tinelli. Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371). In Dagstuhl Reports, Volume 7, Issue 9, pp. 26-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{blanchette_et_al:DagRep.7.9.26,
  author =	{Blanchette, Jasmin Christian and Fuhs, Carsten and Sofronie-Stokkermans, Viorica and Tinelli, Cesare},
  title =	{{Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)}},
  pages =	{26--46},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{7},
  number =	{9},
  editor =	{Blanchette, Jasmin Christian and Fuhs, Carsten and Sofronie-Stokkermans, Viorica and Tinelli, Cesare},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.9.26},
  URN =		{urn:nbn:de:0030-drops-85872},
  doi =		{10.4230/DagRep.7.9.26},
  annote =	{Keywords: Automated Deduction, Program Verification, Certification}
}
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