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Even Shorter Proofs Without New Variables

Author Adrián Rebola-Pardo

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Author Details

Adrián Rebola-Pardo
  • Technische Universität Wien, Austria
  • Johannes Kepler Universität Linz, Austria

Funding

This work has been supported by the LIT AI Lab funded by the State of Upper Austria, the LogiCS doctoral program W1255-N23 of the Austrian Science Fund (FWF), the Vienna Science and Technology Fund (WWTF) through grants VRG11-005 and ICT15-103, and Microsoft Research through its PhD Scholarship Programme.

Acknowledgements

I would like to thank Georg Weissenbacher for the discussions on WSR, as well as the anonymous reviewers who provided very useful comments.

Cite AsGet BibTex

Adrián Rebola-Pardo. Even Shorter Proofs Without New Variables. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SAT.2023.22

Abstract

Proof formats for SAT solvers have diversified over the last decade, enabling new features such as extended resolution-like capabilities, very general extension-free rules, inclusion of proof hints, and pseudo-boolean reasoning. Interference-based methods have been proven effective, and some theoretical work has been undertaken to better explain their limits and semantics. In this work, we combine the subsumption redundancy notion from [Sam Buss and Neil Thapen, 2019] and the overwrite logic framework from [Adrián Rebola{-}Pardo and Martin Suda, 2018]. Natural generalizations then become apparent, enabling even shorter proofs of the pigeonhole principle (compared to those from [Marijn J. H. Heule et al., 2017]) and smaller unsatisfiable core generation.

Subject Classification

ACM Subject Classification
  • Hardware → Theorem proving and SAT solving
Keywords
  • Interference
  • SAT solving
  • Unsatisfiability proofs
  • Unsatisfiable cores

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References

  1. Fadi A. Aloul, Arathi Ramani, Igor L. Markov, and Karem A. Sakallah. Solving difficult instances of boolean satisfiability in the presence of symmetry. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 22(9):1117-1137, 2003. URL: https://doi.org/10.1109/TCAD.2003.816218.
  2. Fadi A. Aloul, Karem A. Sakallah, and Igor L. Markov. Efficient symmetry breaking for boolean satisfiability. IEEE Trans. Computers, 55(5):549-558, 2006. URL: https://doi.org/10.1109/TC.2006.75.
  3. Johannes Altmanninger and Adrián Rebola-Pardo. Frying the egg, roasting the chicken: unit deletions in DRAT proofs. In Jasmin Blanchette and Catalin Hritcu, editors, Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2020, New Orleans, LA, USA, January 20-21, 2020, pages 61-70. ACM, 2020. URL: https://doi.org/10.1145/3372885.3373821.
  4. Seulkee Baek, Mario M. Carneiro, and Marijn J. H. Heule. A flexible proof format for SAT solver-elaborator communication. In Jan Friso Groote and Kim Guldstrand Larsen, editors, Tools and Algorithms for the Construction and Analysis of Systems - 27th International Conference, TACAS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 - April 1, 2021, Proceedings, Part I, volume 12651 of Lecture Notes in Computer Science, pages 59-75. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-72016-2_4.
  5. Paul Beame, Henry A. Kautz, and Ashish Sabharwal. Towards understanding and harnessing the potential of clause learning. J. Artif. Intell. Res., 22:319-351, 2004. URL: https://doi.org/10.1613/jair.1410.
  6. Armin Biere, Daniel Le Berre, Emmanuel Lonca, and Norbert Manthey. Detecting cardinality constraints in CNF. In Carsten Sinz and Uwe Egly, editors, Theory and Applications of Satisfiability Testing - SAT 2014 - 17th International Conference, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 14-17, 2014. Proceedings, volume 8561 of Lecture Notes in Computer Science, pages 285-301. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-09284-3_22.
  7. Randal E. Bryant, Armin Biere, and Marijn J. H. Heule. Clausal proofs for pseudo-boolean reasoning. In Dana Fisman and Grigore Rosu, editors, Tools and Algorithms for the Construction and Analysis of Systems - 28th International Conference, TACAS 2022, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022, Munich, Germany, April 2-7, 2022, Proceedings, Part I, volume 13243 of Lecture Notes in Computer Science, pages 443-461. Springer, 2022. URL: https://doi.org/10.1007/978-3-030-99524-9_25.
  8. Randal E. Bryant and Marijn J. H. Heule. Generating extended resolution proofs with a bdd-based SAT solver. In Jan Friso Groote and Kim Guldstrand Larsen, editors, Tools and Algorithms for the Construction and Analysis of Systems - 27th International Conference, TACAS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 - April 1, 2021, Proceedings, Part I, volume 12651 of Lecture Notes in Computer Science, pages 76-93. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-72016-2_5.
  9. Sam Buss and Neil Thapen. DRAT proofs, propagation redundancy, and extended resolution. In Mikolás Janota and Inês Lynce, editors, Theory and Applications of Satisfiability Testing - SAT 2019 - 22nd International Conference, SAT 2019, Lisbon, Portugal, July 9-12, 2019, Proceedings, volume 11628 of Lecture Notes in Computer Science, pages 71-89. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-24258-9_5.
  10. Leroy Chew and Marijn J. H. Heule. Sorting parity encodings by reusing variables. In Luca Pulina and Martina Seidl, editors, Theory and Applications of Satisfiability Testing - SAT 2020 - 23rd International Conference, Alghero, Italy, July 3-10, 2020, Proceedings, volume 12178 of Lecture Notes in Computer Science, pages 1-10. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-51825-7_1.
  11. Stephen A. Cook. A short proof of the pigeon hole principle using extended resolution. SIGACT News, 8(4):28-32, 1976. URL: https://doi.org/10.1145/1008335.1008338.
  12. Luís Cruz-Filipe, Marijn J. H. Heule, Warren A. Hunt Jr., Matt Kaufmann, and Peter Schneider-Kamp. Efficient certified RAT verification. In Leonardo de Moura, editor, Automated Deduction - CADE 26 - 26th International Conference on Automated Deduction, Gothenburg, Sweden, August 6-11, 2017, Proceedings, volume 10395 of Lecture Notes in Computer Science, pages 220-236. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-63046-5_14.
  13. Luís Cruz-Filipe, João Marques-Silva, and Peter Schneider-Kamp. Efficient certified resolution proof checking. In Axel Legay and Tiziana Margaria, editors, Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017, Uppsala, Sweden, April 22-29, 2017, Proceedings, Part I, volume 10205 of Lecture Notes in Computer Science, pages 118-135, 2017. URL: https://doi.org/10.1007/978-3-662-54577-5_7.
  14. Niklas Eén and Armin Biere. Effective preprocessing in SAT through variable and clause elimination. In Fahiem Bacchus and Toby Walsh, editors, Theory and Applications of Satisfiability Testing, 8th International Conference, SAT 2005, St. Andrews, UK, June 19-23, 2005, Proceedings, volume 3569 of Lecture Notes in Computer Science, pages 61-75. Springer, 2005. URL: https://doi.org/10.1007/11499107_5.
  15. Allen Van Gelder. Producing and verifying extremely large propositional refutations - have your cake and eat it too. Ann. Math. Artif. Intell., 65(4):329-372, 2012. URL: https://doi.org/10.1007/s10472-012-9322-x.
  16. Stephan Gocht and Jakob Nordström. Certifying parity reasoning efficiently using pseudo-boolean proofs. In Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, pages 3768-3777. AAAI Press, 2021. URL: https://ojs.aaai.org/index.php/AAAI/article/view/16494.
  17. Evguenii I. Goldberg and Yakov Novikov. Verification of proofs of unsatisfiability for CNF formulas. In 2003 Design, Automation and Test in Europe Conference and Exposition (DATE 2003), 3-7 March 2003, Munich, Germany, pages 10886-10891. IEEE Computer Society, 2003. URL: https://doi.org/10.1109/DATE.2003.10008.
  18. Armin Haken. The intractability of resolution. Theor. Comput. Sci., 39:297-308, 1985. URL: https://doi.org/10.1016/0304-3975(85)90144-6.
  19. Marijn Heule, Warren A. Hunt Jr., and Nathan Wetzler. Trimming while checking clausal proofs. In Formal Methods in Computer-Aided Design, FMCAD 2013, Portland, OR, USA, October 20-23, 2013, pages 181-188. IEEE, 2013. URL: http://ieeexplore.ieee.org/document/6679408/.
  20. Marijn Heule, Warren A. Hunt Jr., and Nathan Wetzler. Verifying refutations with extended resolution. In Maria Paola Bonacina, editor, Automated Deduction - CADE-24 - 24th International Conference on Automated Deduction, Lake Placid, NY, USA, June 9-14, 2013. Proceedings, volume 7898 of Lecture Notes in Computer Science, pages 345-359. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38574-2_24.
  21. Marijn Heule, Warren A. Hunt Jr., and Nathan Wetzler. Bridging the gap between easy generation and efficient verification of unsatisfiability proofs. Softw. Test. Verification Reliab., 24(8):593-607, 2014. URL: https://doi.org/10.1002/stvr.1549.
  22. Marijn Heule, Warren A. Hunt Jr., and Nathan Wetzler. Expressing symmetry breaking in DRAT proofs. In Amy P. Felty and Aart Middeldorp, editors, Automated Deduction - CADE-25 - 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings, volume 9195 of Lecture Notes in Computer Science, pages 591-606. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21401-6_40.
  23. Marijn Heule and Benjamin Kiesl. The potential of interference-based proof systems. In Giles Reger and Dmitriy Traytel, editors, ARCADE 2017, 1st International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary Achievements, Gothenburg, Sweden, 6th August 2017, EPiC Series in Computing, pages 51-54. EasyChair, 2017. URL: https://easychair.org/publications/paper/TWVW, URL: https://doi.org/10.29007/vr7n.
  24. Marijn J. H. Heule. Schur number five. In Sheila A. McIlraith and Kilian Q. Weinberger, editors, Proceedings of the Thirty-Second AAAI Conference on Artificial Intelligence, (AAAI-18), the 30th innovative Applications of Artificial Intelligence (IAAI-18), and the 8th AAAI Symposium on Educational Advances in Artificial Intelligence (EAAI-18), New Orleans, Louisiana, USA, February 2-7, 2018, pages 6598-6606. AAAI Press, 2018. URL: https://www.aaai.org/ocs/index.php/AAAI/AAAI18/paper/view/16952.
  25. Marijn J. H. Heule and Armin Biere. Compositional propositional proofs. In Martin Davis, Ansgar Fehnker, Annabelle McIver, and Andrei Voronkov, editors, Logic for Programming, Artificial Intelligence, and Reasoning - 20th International Conference, LPAR-20 2015, Suva, Fiji, November 24-28, 2015, Proceedings, volume 9450 of Lecture Notes in Computer Science, pages 444-459. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-48899-7_31.
  26. Marijn J. H. Heule and Armin Biere. What a difference a variable makes. In Dirk Beyer and Marieke Huisman, editors, Tools and Algorithms for the Construction and Analysis of Systems - 24th International Conference, TACAS 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings, Part II, volume 10806 of Lecture Notes in Computer Science, pages 75-92. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-89963-3_5.
  27. Marijn J. H. Heule, Benjamin Kiesl, and Armin Biere. Short proofs without new variables. In Leonardo de Moura, editor, Automated Deduction - CADE 26 - 26th International Conference on Automated Deduction, Gothenburg, Sweden, August 6-11, 2017, Proceedings, volume 10395 of Lecture Notes in Computer Science, pages 130-147. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-63046-5_9.
  28. Marijn J. H. Heule, Oliver Kullmann, and Victor W. Marek. Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In Nadia Creignou and Daniel Le Berre, editors, Theory and Applications of Satisfiability Testing - SAT 2016 - 19th International Conference, Bordeaux, France, July 5-8, 2016, Proceedings, volume 9710 of Lecture Notes in Computer Science, pages 228-245. Springer, 2016. URL: https://doi.org/10.1007/978-3-319-40970-2_15.
  29. Matti Järvisalo, Armin Biere, and Marijn Heule. Blocked clause elimination. In Javier Esparza and Rupak Majumdar, editors, Tools and Algorithms for the Construction and Analysis of Systems, 16th International Conference, TACAS 2010, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2010, Paphos, Cyprus, March 20-28, 2010. Proceedings, volume 6015 of Lecture Notes in Computer Science, pages 129-144. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-12002-2_10.
  30. Matti Järvisalo, Armin Biere, and Marijn Heule. Simulating circuit-level simplifications on CNF. J. Autom. Reason., 49(4):583-619, 2012. URL: https://doi.org/10.1007/s10817-011-9239-9.
  31. Matti Järvisalo, Marijn Heule, and Armin Biere. Inprocessing rules. In Bernhard Gramlich, Dale Miller, and Uli Sattler, editors, Automated Reasoning - 6th International Joint Conference, IJCAR 2012, Manchester, UK, June 26-29, 2012. Proceedings, volume 7364 of Lecture Notes in Computer Science, pages 355-370. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-31365-3_28.
  32. Benjamin Kiesl, Adrián Rebola-Pardo, and Marijn J. H. Heule. Extended resolution simulates DRAT. In Didier Galmiche, Stephan Schulz, and Roberto Sebastiani, editors, Automated Reasoning - 9th International Joint Conference, IJCAR 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July 14-17, 2018, Proceedings, volume 10900 of Lecture Notes in Computer Science, pages 516-531. Springer, 2018. URL: https://doi.org/10.1007/978-3-319-94205-6_34.
  33. Benjamin Kiesl, Martina Seidl, Hans Tompits, and Armin Biere. Local redundancy in SAT: generalizations of blocked clauses. Log. Methods Comput. Sci., 14(4), 2018. URL: https://doi.org/10.23638/LMCS-14(4:3)2018.
  34. Peter Lammich. Efficient verified (UN)SAT certificate checking. In Leonardo de Moura, editor, Automated Deduction - CADE 26 - 26th International Conference on Automated Deduction, Gothenburg, Sweden, August 6-11, 2017, Proceedings, volume 10395 of Lecture Notes in Computer Science, pages 237-254. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-63046-5_15.
  35. Norbert Manthey, Marijn Heule, and Armin Biere. Automated reencoding of boolean formulas. In Armin Biere, Amir Nahir, and Tanja E. J. Vos, editors, Hardware and Software: Verification and Testing - 8th International Haifa Verification Conference, HVC 2012, Haifa, Israel, November 6-8, 2012. Revised Selected Papers, volume 7857 of Lecture Notes in Computer Science, pages 102-117. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-39611-3_14.
  36. Norbert Manthey and Tobias Philipp. Formula simplifications as DRAT derivations. In Carsten Lutz and Michael Thielscher, editors, KI 2014: Advances in Artificial Intelligence - 37th Annual German Conference on AI, Stuttgart, Germany, September 22-26, 2014. Proceedings, volume 8736 of Lecture Notes in Computer Science, pages 111-122. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-11206-0_12.
  37. Alexander Nadel, Vadim Ryvchin, and Ofer Strichman. Efficient MUS extraction with resolution. In Formal Methods in Computer-Aided Design, FMCAD 2013, Portland, OR, USA, October 20-23, 2013, pages 197-200. IEEE, 2013. URL: http://ieeexplore.ieee.org/document/6679410/.
  38. Tobias Philipp and Adrián Rebola-Pardo. DRAT proofs for XOR reasoning. In Loizos Michael and Antonis C. Kakas, editors, Logics in Artificial Intelligence - 15th European Conference, JELIA 2016, Larnaca, Cyprus, November 9-11, 2016, Proceedings, volume 10021 of Lecture Notes in Computer Science, pages 415-429, 2016. URL: https://doi.org/10.1007/978-3-319-48758-8_27.
  39. Tobias Philipp and Adrián Rebola-Pardo. Towards a semantics of unsatisfiability proofs with inprocessing. In Thomas Eiter and David Sands, editors, LPAR-21, 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Maun, Botswana, May 7-12, 2017, volume 46 of EPiC Series in Computing, pages 65-84. EasyChair, 2017. URL: https://easychair.org/publications/paper/V8G, URL: https://doi.org/10.29007/7jgq.
  40. Knot Pipatsrisawat and Adnan Darwiche. On the power of clause-learning SAT solvers as resolution engines. Artif. Intell., 175(2):512-525, 2011. URL: https://doi.org/10.1016/j.artint.2010.10.002.
  41. Adrián Rebola-Pardo and Luís Cruz-Filipe. Complete and efficient DRAT proof checking. In Nikolaj Bjørner and Arie Gurfinkel, editors, 2018 Formal Methods in Computer Aided Design, FMCAD 2018, Austin, TX, USA, October 30 - November 2, 2018, pages 1-9. IEEE, 2018. URL: https://doi.org/10.23919/FMCAD.2018.8602993.
  42. Adrián Rebola-Pardo and Martin Suda. A theory of satisfiability-preserving proofs in SAT solving. In Gilles Barthe, Geoff Sutcliffe, and Margus Veanes, editors, LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Awassa, Ethiopia, 16-21 November 2018, volume 57 of EPiC Series in Computing, pages 583-603. EasyChair, 2018. URL: https://easychair.org/publications/paper/zr7z, URL: https://doi.org/10.29007/tc7q.
  43. Adrián Rebola-Pardo and Georg Weissenbacher. RAT elimination. In Elvira Albert and Laura Kovács, editors, LPAR 2020: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Alicante, Spain, May 22-27, 2020, volume 73 of EPiC Series in Computing, pages 423-448. EasyChair, 2020. URL: https://easychair.org/publications/paper/cMtF, URL: https://doi.org/10.29007/fccb.
  44. Robert A. Reckhow. On the lengths of proofs in the propositional calculus. PhD thesis, University of Toronto, 1975. Google Scholar
  45. João P. Marques Silva and Karem A. Sakallah. GRASP - a new search algorithm for satisfiability. In Rob A. Rutenbar and Ralph H. J. M. Otten, editors, Proceedings of the 1996 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1996, San Jose, CA, USA, November 10-14, 1996, pages 220-227. IEEE Computer Society / ACM, 1996. URL: https://doi.org/10.1109/ICCAD.1996.569607.
  46. Carsten Sinz and Armin Biere. Extended resolution proofs for conjoining bdds. In Dima Grigoriev, John Harrison, and Edward A. Hirsch, editors, Computer Science - Theory and Applications, First International Computer Science Symposium in Russia, CSR 2006, St. Petersburg, Russia, June 8-12, 2006, Proceedings, volume 3967 of Lecture Notes in Computer Science, pages 600-611. Springer, 2006. URL: https://doi.org/10.1007/11753728_60.
  47. Mate Soos. Enhanced gaussian elimination in dpll-based SAT solvers. In Daniel Le Berre, editor, POS-10. Pragmatics of SAT, Edinburgh, UK, July 10, 2010, volume 8 of EPiC Series in Computing, pages 2-14. EasyChair, 2010. URL: https://easychair.org/publications/paper/j1D, URL: https://doi.org/10.29007/g7ss.
  48. Mate Soos, Karsten Nohl, and Claude Castelluccia. Extending SAT solvers to cryptographic problems. In Oliver Kullmann, editor, Theory and Applications of Satisfiability Testing - SAT 2009, 12th International Conference, SAT 2009, Swansea, UK, June 30 - July 3, 2009. Proceedings, volume 5584 of Lecture Notes in Computer Science, pages 244-257. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-02777-2_24.
  49. Yong Kiam Tan, Marijn J. H. Heule, and Magnus O. Myreen. cake_lpr: Verified propagation redundancy checking in cakeml. In Jan Friso Groote and Kim Guldstrand Larsen, editors, Tools and Algorithms for the Construction and Analysis of Systems - 27th International Conference, TACAS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 - April 1, 2021, Proceedings, Part II, volume 12652 of Lecture Notes in Computer Science, pages 223-241. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-72013-1_12.
  50. G. S. Tseitin. On the complexity of derivation in propositional calculus. In Jörg H. Siekmann and Graham Wrightson, editors, Automation of Reasoning: 2: Classical Papers on Computational Logic 1967-1970, pages 466-483. Springer Berlin Heidelberg, 1983. URL: https://doi.org/10.1007/978-3-642-81955-1_28.
  51. Alasdair Urquhart. Hard examples for resolution. J. ACM, 34(1):209-219, 1987. URL: https://doi.org/10.1145/7531.8928.
  52. Alasdair Urquhart. The symmetry rule in propositional logic. Discret. Appl. Math., 96-97:177-193, 1999. URL: https://doi.org/10.1016/S0166-218X(99)00039-6.
  53. Nathan Wetzler, Marijn Heule, and Warren A. Hunt Jr. DRAT-trim: Efficient checking and trimming using expressive clausal proofs. In Carsten Sinz and Uwe Egly, editors, Theory and Applications of Satisfiability Testing - SAT 2014 - 17th International Conference, Held as Part of the Vienna Summer of Logic, VSL 2014, Vienna, Austria, July 14-17, 2014. Proceedings, volume 8561 of Lecture Notes in Computer Science, pages 422-429. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-09284-3_31.
  54. Lintao Zhang and Sharad Malik. Validating SAT solvers using an independent resolution-based checker: Practical implementations and other applications. In 2003 Design, Automation and Test in Europe Conference and Exposition (DATE 2003), 3-7 March 2003, Munich, Germany, pages 10880-10885. IEEE Computer Society, 2003. URL: https://doi.org/10.1109/DATE.2003.10014.
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