{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T18:22:03Z","timestamp":1784830923548,"version":"3.55.0"},"publisher-location":"Cham","reference-count":31,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030294359","type":"print"},{"value":"9783030294366","type":"electronic"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-29436-6_22","type":"book-chapter","created":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T16:04:02Z","timestamp":1566317042000},"page":"366-384","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Towards Bit-Width-Independent Proofs in SMT Solvers"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2600-5283","authenticated-orcid":false,"given":"Aina","family":"Niemetz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7142-6258","authenticated-orcid":false,"given":"Mathias","family":"Preiner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3529-8682","authenticated-orcid":false,"given":"Andrew","family":"Reynolds","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2972-6695","authenticated-orcid":false,"given":"Yoni","family":"Zohar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9522-3084","authenticated-orcid":false,"given":"Clark","family":"Barrett","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6726-775X","authenticated-orcid":false,"given":"Cesare","family":"Tinelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,8,20]]},"reference":[{"key":"22_CR1","doi-asserted-by":"crossref","unstructured":"Alur, R., et al.: Syntax-guided synthesis. In: Formal Methods in Computer-Aided Design, FMCAD 2013, Portland, OR, USA, 20\u201323 October 2013, pp. 1\u20138 (2013)","DOI":"10.1109\/FMCAD.2013.6679385"},{"key":"22_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/978-3-642-22110-1_14","volume-title":"Computer Aided Verification","author":"C Barrett","year":"2011","unstructured":"Barrett, C., et al.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171\u2013177. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22110-1_14"},{"key":"22_CR3","unstructured":"Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB standard: version 2.0. In: Gupta, A., Kroening, D. (eds.) Proceedings of the 8th International Workshop on Satisfiability Modulo Theories, Edinburgh, UK (2010)"},{"key":"22_CR4","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1007\/BFb0054184","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"NS Bj\u00d8rner","year":"1998","unstructured":"Bj\u00d8rner, N.S., Pichora, M.C.: Deciding fixed and non-fixed size bit-vectors. In: Steffen, B. (ed.) Tools and Algorithms for the Construction and Analysis of Systems, pp. 376\u2013392. Springer, Berlin (1998). https:\/\/doi.org\/10.1007\/BFb0054184"},{"issue":"1","key":"22_CR5","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/s10817-013-9278-5","volume":"51","author":"JC Blanchette","year":"2013","unstructured":"Blanchette, J.C., B\u00f6hme, S., Paulson, L.C.: Extending sledgehammer with SMT solvers. J. Autom. Reasoning 51(1), 109\u2013128 (2013). https:\/\/doi.org\/10.1007\/s10817-013-9278-5","journal-title":"J. Autom. Reasoning"},{"key":"22_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/978-3-319-94144-8_23","volume-title":"Theory and Applications of Satisfiability Testing \u2013 SAT 2018","author":"A Cimatti","year":"2018","unstructured":"Cimatti, A., Griggio, A., Irfan, A., Roveri, M., Sebastiani, R.: Experimenting on solving nonlinear integer arithmetic with incremental linearization. In: Beyersdorff, O., Wintersteiger, C.M. (eds.) SAT 2018. LNCS, vol. 10929, pp. 383\u2013398. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-94144-8_23"},{"issue":"3","key":"22_CR7","doi-asserted-by":"publisher","first-page":"19:1","DOI":"10.1145\/3230639","volume":"19","author":"A Cimatti","year":"2018","unstructured":"Cimatti, A., Griggio, A., Irfan, A., Roveri, M., Sebastiani, R.: Incremental linearization for satisfiability and verification modulo nonlinear arithmetic and transcendental functions. ACM Trans. Comput. Log. 19(3), 19:1\u201319:52 (2018)","journal-title":"ACM Trans. Comput. Log."},{"key":"22_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/978-3-540-78800-3_24","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"L de Moura","year":"2008","unstructured":"de Moura, L., Bj\u00f8rner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337\u2013340. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-78800-3_24. http:\/\/dl.acm.org\/citation.cfm?id=1792734.1792766"},{"key":"22_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-319-63390-9_7","volume-title":"Computer Aided Verification","author":"B Ekici","year":"2017","unstructured":"Ekici, B., et al.: SMTCoq: a plug-in for integrating smt solvers into Coq. In: Majumdar, R., Kuncak, V. (eds.) CAV 2017. LNCS, vol. 10427, pp. 126\u2013133. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63390-9_7"},{"key":"22_CR10","volume-title":"A Mathematical Introduction to logic","author":"H Enderton","year":"2001","unstructured":"Enderton, H., Enderton, H.B.: A Mathematical Introduction to logic. Elsevier, Amsterdam (2001)"},{"key":"22_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/3-540-56922-7_3","volume-title":"Computer Aided Verification","author":"A Gupta","year":"1993","unstructured":"Gupta, A., Fisher, A.L.: Parametric circuit representation using inductive boolean functions. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 15\u201328. Springer, Heidelberg (1993). https:\/\/doi.org\/10.1007\/3-540-56922-7_3"},{"key":"22_CR12","unstructured":"Gupta, A., Fisher, A.L.: Representation and symbolic manipulation of linearly inductive boolean functions. In: Proceedings of the 1993 IEEE\/ACM International Conference on Computer-aided Design, pp. 192\u2013199, ICCAD 1993. IEEE Computer Society Press, Los Alamitos (1993). http:\/\/dl.acm.org.stanford.idm.oclc.org\/citation.cfm?id=259794.259827"},{"key":"22_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-39799-8_1","volume-title":"Computer Aided Verification","author":"L Kov\u00e1cs","year":"2013","unstructured":"Kov\u00e1cs, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1\u201335. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-39799-8_1"},{"issue":"2","key":"22_CR14","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1007\/s00224-015-9653-1","volume":"59","author":"G Kov\u00e1sznai","year":"2016","unstructured":"Kov\u00e1sznai, G., Fr\u00f6hlich, A., Biere, A.: Complexity of fixed-size bit-vector logics. Theory Comput. Syst. 59(2), 323\u2013376 (2016). https:\/\/doi.org\/10.1007\/s00224-015-9653-1","journal-title":"Theory Comput. Syst."},{"key":"22_CR15","series-title":"Texts in Theoretical Computer Science. An EATCS Series","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-50497-0","volume-title":"Decision Procedures - An Algorithmic Point of View","author":"D Kroening","year":"2016","unstructured":"Kroening, D., Strichman, O.: Decision Procedures - An Algorithmic Point of View. Texts in Theoretical Computer Science. An EATCS Series, 2nd edn. Springer, Berlin (2016)","edition":"2"},{"key":"22_CR16","doi-asserted-by":"publisher","unstructured":"Lattner, C., Adve, V.S.: LLVM: a compilation framework for lifelong program analysis & transformation. In: 2nd IEEE\/ACM International Symposium on Code Generation and Optimization (CGO 2004), 20\u201324 March 2004, San Jose, CA, USA, pp. 75\u201388. IEEE Computer Society (2004). https:\/\/doi.org\/10.1109\/CGO.2004.1281665","DOI":"10.1109\/CGO.2004.1281665"},{"key":"22_CR17","doi-asserted-by":"publisher","unstructured":"Lopes, N.P., Menendez, D., Nagarakatte, S., Regehr, J.: Provably correct peephole optimizations with alive. In: Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 22\u201332, PLDI 2015. ACM, New York (2015). https:\/\/doi.org\/10.1145\/2737924.2737965","DOI":"10.1145\/2737924.2737965"},{"key":"22_CR18","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/978-3-540-73595-3_13","volume-title":"Automated Deduction \u2013 CADE-21","author":"L de Moura","year":"2007","unstructured":"de Moura, L., Bj\u00f8rner, N.: Efficient E-matching for SMT solvers. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 183\u2013198. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-73595-3_13"},{"key":"22_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1007\/978-3-319-96142-2_16","volume-title":"Computer Aided Verification","author":"A Niemetz","year":"2018","unstructured":"Niemetz, A., Preiner, M., Reynolds, A., Barrett, C., Tinelli, C.: Solving Quantified Bit-Vectors Using Invertibility Conditions. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10982, pp. 236\u2013255. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96142-2_16"},{"key":"22_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45949-9","volume-title":"Isabelle\/HOL","year":"2002","unstructured":"Nipkow, T., Wenzel, M., Paulson, L.C. (eds.): Isabelle\/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/3-540-45949-9"},{"key":"22_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-24258-9_20","volume-title":"Theory and Applications of Satisfiability Testing - SAT 2019","author":"A N\u00f6tzli","year":"2019","unstructured":"N\u00f6tzli, A., et al.: Syntax-guided rewrite rule enumeration for SMT solvers. In: Janota, M., Lynce, I. (eds.) SAT 2019. LNCS, vol. 11628. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-24258-9_20"},{"key":"22_CR22","unstructured":"Pichora, M.C.: Automated reasoning about hardware data types using bit-vectors of symbolic lengths. Ph.D. thesis, Toronto, ON, Canada (2003). aAINQ84686"},{"key":"22_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-89960-2_1","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"G Reger","year":"2018","unstructured":"Reger, G., Suda, M., Voronkov, A.: Unification with abstraction and theory instantiation in saturation-based reasoning. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10805, pp. 3\u201322. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-89960-2_1"},{"key":"22_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/978-3-319-89963-3_7","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"A Reynolds","year":"2018","unstructured":"Reynolds, A., Barbosa, H., Fontaine, P.: Revisiting enumerative instantiation. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 112\u2013131. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-89963-3_7"},{"key":"22_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1007\/978-3-319-21668-3_12","volume-title":"Computer Aided Verification","author":"A Reynolds","year":"2015","unstructured":"Reynolds, A., Deters, M., Kuncak, V., Tinelli, C., Barrett, C.: Counterexample-guided quantifier instantiation for synthesis in SMT. In: Kroening, D., P\u0103s\u0103reanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 198\u2013216. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-21668-3_12"},{"key":"22_CR26","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1007\/978-3-319-66167-4_2","volume-title":"Frontiers of Combining Systems","author":"A Reynolds","year":"2017","unstructured":"Reynolds, A., Tinelli, C., Jovanovi\u0107, D., Barrett, C.: Designing theory solvers with extensions. In: Dixon, C., Finger, M. (eds.) FroCoS 2017. LNCS (LNAI), vol. 10483, pp. 22\u201340. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-66167-4_2"},{"key":"22_CR27","doi-asserted-by":"publisher","unstructured":"Reynolds, A., Tinelli, C., de Moura, L.M.: Finding conflicting instances of quantified formulas in SMT. In: Formal Methods in Computer-Aided Design, FMCAD 2014, Lausanne, Switzerland, 21\u201324 October 2014, pp. 195\u2013202 (2014). https:\/\/doi.org\/10.1109\/FMCAD.2014.6987613","DOI":"10.1109\/FMCAD.2014.6987613"},{"key":"22_CR28","unstructured":"Solidity Language Developers: Solidity (2018). https:\/\/solidity.readthedocs.io\/en\/v0.4.25\/"},{"key":"22_CR29","unstructured":"TC Development team: The Coq proof assistant reference manual version 8.9 (2019). https:\/\/coq.inria.fr\/distrib\/current\/refman\/"},{"key":"22_CR30","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1007\/978-3-540-30227-8_53","volume-title":"Logics in Artificial Intelligence","author":"C Tinelli","year":"2004","unstructured":"Tinelli, C., Zarba, C.G.: Combining decision procedures for sorted theories. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 641\u2013653. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-30227-8_53"},{"key":"22_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1007\/978-3-319-08867-9_46","volume-title":"Computer Aided Verification","author":"A Voronkov","year":"2014","unstructured":"Voronkov, A.: AVATAR: the architecture for first-order theorem provers. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 696\u2013710. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-08867-9_46"}],"container-title":["Lecture Notes in Computer Science","Automated Deduction \u2013 CADE 27"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-29436-6_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T21:55:18Z","timestamp":1657576518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-29436-6_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030294359","9783030294366"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-29436-6_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"20 August 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CADE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Automated Deduction","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Natal","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Brazil","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cade2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.mat.ufrn.br\/CADE-27\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}