The Proof Certifier Checkers

  • Zakaria ChihaniEmail author
  • Tomer Libal
  • Giselle Reis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9323)


Different theorem provers work within different formalisms and paradigms, and therefore produce various incompatible proof objects. Currently there is a big effort to establish foundational proof certificates (fpc), which would serve as a common “specification language” for all these formats. Such framework enables the uniform checking of proof objects from many different theorem provers while relying on a small and trusted kernel to do so. Checkers is an implementation of a proof checker using foundational proof certificates. By trusting a small kernel based on (focused) sequent calculus on the one hand and by supporting fpc specifications in a prolog-like language on the other hand, it can be used for checking proofs of a wide range of theorem provers. The focus of this paper is on the output of equational resolution theorem provers and for this end, we specify the paramodulation rule. We describe the architecture of Checkers and demonstrate how it can be used to check proof objects by supplying the fpc specification for a subset of the inferences used by eprover and checking proofs using these inferences.


Sequent Calculus Logic Programming Language Proof Search Proof Checker Proof Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Balint, A., Gall, D., Kapler, G., Retz, R.: Experiment design and administration for computer clusters for SAT-solvers (EDACC). JSAT (2010)Google Scholar
  2. 2.
    Boespflug, M., Carbonneaux, Q., Hermant, O.: The λΠ-calculus modulo as a universal proof language. In: Pichardie, D., Weber, T. (eds.) Proceedings of PxTP2012: Proof Exchange for Theorem Proving, pp. 28–43 (2012)Google Scholar
  3. 3.
    Chihani, Z., Miller, D., Renaud, F.: Checking foundational proof certificates for first-order logic (extended abstract). In: Blanchette, J.C., Urban, J. (eds.) Third International Workshop on Proof Exchange for Theorem Proving (PxTP 2013). EPiC Series, vol. 14, pp. 58–66. EasyChair (2013)Google Scholar
  4. 4.
    Chihani, Z., Miller, D., Renaud, F.: Foundational proof certificates in first-order logic. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 162–177. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Grabowski, A., Kornilowicz, A., Naumowicz, A.: Mizar in a Nutshell. Journal of Formalized Reasoning 3(2), 153–245 (2010)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Liang, C., Miller, D.: Focusing and polarization in linear, intuitionistic, and classical logics. Theoretical Computer Science 410(46), 4747–4768 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Miller, D.: Proofcert: Broad spectrum proof certificates, February 2011, an ERC Advanced Grant funded for the five years 2012-2016Google Scholar
  8. 8.
    Miller, D., Nadathur, G.: Programming with Higher-Order Logic. Cambridge University Press, June 2012Google Scholar
  9. 9.
    Otten, J., Sutcliffe, G.: Using the tptp language for representing derivations in tableau and connection calculi. In: Schmidt, R.A., Schulz, S., Konev, B. (eds.) PAAR-2010. EPiC Series, vol. 9, pp. 95–105. EasyChair (2012)Google Scholar
  10. 10.
    Robinson, G., Wos, L.: Paramodulation and theorem-proving in first-order theories with equality. In: Automation of Reasoning, pp. 298–313. Springer (1983)Google Scholar
  11. 11.
    Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 735–743. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Stump, A., Reynolds, A., Tinelli, C., Laugesen, A., Eades, H., Oliver, C., Zhang, R.: LFSC for SMT Proofs: Work in ProgressGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.INRIASaclayFrance

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