Abstract
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation. We particularly discuss recently added features and extensions, including the extension to many-sorted logic, optional limited support for higher-order logic, and the integration of SAT techniques via PicoSAT. Minor additions include improved support for TPTP standard features, always-on internal proof objects, and lazy orphan removal. The paper also gives an overview of the performance of the system, and describes ongoing and future work.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. Logic Comput. 3(4), 217–247 (1994)
Barrett, C., Stump, A., Tinelli, C.: The SMT-lib standard: version 2.0. In: Proceedings of the 8th International Workshop on Satisfiability Modulo Theories (Edinburgh, UK) (2010). http://homepage.cs.uiowa.edu/~tinelli/papers/BarST-SMT-10.pdf
Biere, A.: PicoSAT essentials. J. Satisfiability Boolean Model. Comput. 4, 75–97 (2008)
Blanchette, J.C., Kaliszyk, C., Paulson, L.C., Urban, J.: Hammering towards QED. J. Formal Reason. 9(1), 101–148 (2016). https://doi.org/10.6092/issn.1972-5787/4593
Bobot, F., Filliâtre, J.C., Marché, C., Paskevich, A.: Why3: shepherd your herd of provers. In: First International Workshop on Intermediate Verification Languages, Boogie 2011, Wrocław, Poland, pp. 53–64, August 2011. http://proval.lri.fr/publications/boogie11final.pdf
Denzinger, J., Kronenburg, M., Schulz, S.: DISCOUNT: a distributed and learning equational prover. J. Autom. Reason. 18(2), 189–198 (1997). Special Issue on the CADE 13 ATP System Competition
Goertzel, Z., Jakubův, J., Schulz, S., Urban, J.: ProofWatch: watchlist guidance for large theories in E. In: Avigad, J., Mahboubi, A. (eds.) ITP 2018. LNCS, vol. 10895, pp. 270–288. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94821-8_16
Hoder, K., Voronkov, A.: Sine Qua Non for large theory reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 299–314. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22438-6_23
Korovin, K.: Inst-Gen – a modular approach to instantiation-based automated reasoning. In: Voronkov, A., Weidenbach, C. (eds.) Programming Logics. LNCS, vol. 7797, pp. 239–270. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-37651-1_10
Kotelnikov, E., Kovács, L., Reger, G., Voronkov, A.: The Vampire and the FOOL. In: Avigad, J., Chlipala, A. (eds.) Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, Saint Petersburg, USA, pp. 37–48. ACM (2016)
Löchner, B., Schulz, S.: An evaluation of shared rewriting. In: de Nivelle, H., Schulz, S. (eds.) Proceedings of the 2nd International Workshop on the Implementation of Logics, pp. 33–48. MPI Preprint, Max-Planck-Institut für Informatik, Saarbrücken (2001)
McCune, W.: Experiments with discrimination-tree indexing and path indexing for term retrieval. J. Autom. Reason. 9(2), 147–167 (1992)
Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, chap. 5, pp. 335–367. Elsevier Science and MIT Press (2001)
Reger, G., Suda, M., Voronkov, A.: Playing with AVATAR. In: Felty, A.P., Middeldorp, A. (eds.) CADE 2015. LNCS (LNAI), vol. 9195, pp. 399–415. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21401-6_28
Schulz, S.: E – a brainiac theorem prover. J. AI Commun. 15(2/3), 111–126 (2002)
Schulz, S.: Fingerprint indexing for paramodulation and rewriting. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS (LNAI), vol. 7364, pp. 477–483. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31365-3_37
Schulz, S.: Simple and efficient clause subsumption with feature vector indexing. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS (LNAI), vol. 7788, pp. 45–67. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36675-8_3
Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 735–743. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-45221-5_49
Schulz, S.: E 2.0 User Manual. EasyChair preprint no. 8 (2018). https://doi.org/10.29007/m4jw
Schulz, S.: Light-weight integration of SAT solving into first-order reasoners - first experiments. In: Kovács, L., Voronkov, A. (eds.) Vampire 2017, Proceedings of the 4th Vampire Workshop. EPiC Series in Computing, vol. 53, pp. 9–19. EasyChair (2018). https://doi.org/10.29007/89kc. https://easychair.org/publications/paper/94vW
Schulz, S., Möhrmann, M.: Performance of clause selection heuristics for saturation-based theorem proving. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 330–345. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40229-1_23
Schulz, S., Sutcliffe, G.: Proof generation for saturating first-order theorem provers. In: Delahaye, D., Woltzenlogel Paleo, B. (eds.) All About Proofs, Proofs for All, Mathematical Logic and Foundations, vol. 55, pp. 45–61. College Publications, London, January 2015
Stump, A., Sutcliffe, G., Tinelli, C.: StarExec: a cross-community infrastructure for logic solving. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 367–373. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08587-6_28
Sutcliffe, G.: The 8th IJCAR automated theorem proving system competition-CASC-J8. AI Commun. 29(5), 607–619 (2016)
Sutcliffe, G.: The TPTP problem library and associated infrastructure - from CNF to TH0, TPTP v6.4.0. J. Autom. Reason. 59(4), 483–502 (2017)
Sutcliffe, G., Kotelnikov, E.: TFX: the TPTP extended typed first-order form. In: Konev, B., Urban, J., Rümmer, P. (eds.) Proceedings of the 6th Workshop on Practical Aspects of Automated Reasoning (PAAR), Oxford, UK. CEUR Workshop Proceedings, vol. 2162, pp. 72–87 (2018). http://ceur-ws.org/Vol-2162/#paper-07
Sutcliffe, G., Schulz, S., Claessen, K., Baumgartner, P.: The TPTP typed first-order form with arithmetic. In: Bjørner, N., Voronkov, A. (eds.) LPAR 2012. LNCS, vol. 7180, pp. 406–419. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28717-6_32
Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP language for writing derivations and finite interpretations. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 67–81. Springer, Heidelberg (2006). https://doi.org/10.1007/11814771_7
Sutcliffe, G., Stickel, M., Schulz, S., Urban, J.: Answer extraction for TPTP. http://www.cs.miami.edu/~tptp/TPTP/Proposals/AnswerExtraction.html. Accessed 08 July 2013
Vukmirović, P., Blanchette, J.C., Cruanes, S., Schulz, S.: Extending a brainiac prover to lambda-free higher-order logic - report version. Technical report, Matryoshka Project (2018). http://matryoshka.gforge.inria.fr/pubs/ehoh_report.pdf
Vukmirović, P., Blanchette, J.C., Cruanes, S., Schulz, S.: Extending a brainiac prover to lambda-free higher-order logic. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 192–210. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_11
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Schulz, S., Cruanes, S., Vukmirović, P. (2019). Faster, Higher, Stronger: E 2.3. In: Fontaine, P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science(), vol 11716. Springer, Cham. https://doi.org/10.1007/978-3-030-29436-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-030-29436-6_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-29435-9
Online ISBN: 978-3-030-29436-6
eBook Packages: Computer ScienceComputer Science (R0)