We describe a number of new possibilities for current theorem provers, that arise with the existence of large integral bodies of formalized mathematics. Then we proceed to describe the implementation of the MPTP system, which makes the largest existing corpus of formalized mathematics available to theorem provers. MPTP (Mizar Problems for Theorem Proving) is a system for translating the Mizar Mathematical Library (MML) into untyped first order format suitable for automated theorem provers, and for generating theorem proving problems corresponding to MML. The first version generates about 30000 problems from complete proofs of Mizar theorems, and about 630000 problems from the simple (one-step) justifications done by the Mizar checker. We describe the design and structure of the system, the main problems encountered in this kind of system, their solutions, current limitations, and planned future extensions. We present results of first experiments with reproving the MPTP problems with theorem provers. We also describe first implementation of the Mizar Proof Advisor (MPA) used for selecting suitable axioms from the large library for an arbitrary problem, and again, present first results of this combined MPA/ATP architecture on MPTP.

References in zbMATH (referenced in 26 articles , 1 standard article )

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  1. Färber, Michael; Kaliszyk, Cezary; Urban, Josef: Machine learning guidance for connection tableaux (2021)
  2. Gauthier, Thibault; Kaliszyk, Cezary; Urban, Josef; Kumar, Ramana; Norrish, Michael: TacticToe: learning to prove with tactics (2021)
  3. Kaliszyk, Cezary; Pąk, Karol: Semantics of Mizar as an Isabelle object logic (2019)
  4. Rawson, Michael; Reger, Giles: A neurally-guided, parallel theorem prover (2019)
  5. Bancerek, Grzegorz; Byliński, Czesław; Grabowski, Adam; Korniłowicz, Artur; Matuszewski, Roman; Naumowicz, Adam; Pąk, Karol: The role of the Mizar mathematical library for interactive proof development in Mizar (2018)
  6. Jakubův, Jan; Urban, Josef: Hierarchical invention of theorem proving strategies (2018)
  7. Gauthier, Thibault; Kaliszyk, Cezary; Urban, Josef: TacticToe: learning to reason with HOL4 tactics (2017)
  8. Brown, Chad E.; Urban, Josef: Extracting higher-order goals from the Mizar Mathematical Library (2016)
  9. Bancerek, Grzegorz; Byliński, Czesław; Grabowski, Adam; Korniłowicz, Artur; Matuszewski, Roman; Naumowicz, Adam; Pąk, Karol; Urban, Josef: Mizar: state-of-the-art and beyond (2015)
  10. Färber, Michael; Kaliszyk, Cezary: Random forests for premise selection (2015)
  11. Kaliszyk, Cezary; Schulz, Stephan; Urban, Josef; Vyskočil, Jiří: System description: E.T. 0.1 (2015)
  12. Kaliszyk, Cezary; Urban, Josef: Learning-assisted theorem proving with millions of lemmas (2015)
  13. Kaliszyk, Cezary; Urban, Josef: MizAR 40 for Mizar 40 (2015)
  14. Alama, Jesse; Heskes, Tom; Kühlwein, Daniel; Tsivtsivadze, Evgeni; Urban, Josef: Premise selection for mathematics by corpus analysis and kernel methods (2014)
  15. Kaliszyk, Cezary; Urban, Josef: Learning-assisted automated reasoning with (\mathsfFlyspeck) (2014)
  16. Urban, Josef; Vyskočil, Jiří: Theorem proving in large formal mathematics as an emerging AI field (2013)
  17. Urban, Josef; Sutcliffe, Geoff: ATP-based cross-verification of Mizar proofs: method, systems, and first experiments (2008)
  18. Urban, Josef; Sutcliffe, Geoff; Pudlák, Petr; Vyskočil, Jiří: MaLARea SG1 -- machine learner for automated reasoning with semantic guidance (2008)
  19. Cairns, Paul; Gow, Jeremy: Integrating searching and authoring in Mizar (2007)
  20. Urban, Josef; Bancerek, Grzegorz: Presenting and explaining Mizar (2007)

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