Journal of Automated Reasoning

, Volume 55, Issue 3, pp 245–256 | Cite as

MizAR 40 for Mizar 40

  • Cezary Kaliszyk
  • Josef Urban
Open Access


As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40 % of the theorems in the latest official version of the Mizar Mathematical Library (MML). This is a considerable improvement over previous performance of large-theory AI/ATP methods measured on the whole MML. To achieve that, a large suite of AI/ATP methods is employed and further developed. We implement the most useful methods efficiently, to scale them to the 150000 formulas in MML. This reduces the training times over the corpus to 1–3 seconds, allowing a simple practical deployment of the methods in the online automated reasoning service for the Mizar users (Miz \(\mathbb {A}\mathbb {R}\)).


Automated reasoning Formal mathematics Mizar Large theories Machine learning Artificial intelligence Premise selection 


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.University of InnsbruckInnsbruckAustria
  2. 2.Radboud UniversityNijmegenNetherlands

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