As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60% of the Mizar theorems in the hammer setting. We also automatically prove 75% of the Mizar theorems when the automated provers are helped by using only the premises used in the human-written Mizar proofs. We describe the methods and large-scale experiments leading to these results. This includes in particular the E and Vampire provers, their ENIGMA and Deepire learning modifications, a number of learning-based premise selection methods, and the incremental loop that interleaves growing a corpus of millions of ATP proofs with training increasingly strong AI/TP systems on them. We also present a selection of Mizar problems that were proved automatically.
@InProceedings{jakubuv_et_al:LIPIcs.ITP.2023.19, author = {Jakub\r{u}v, Jan and Chvalovsk\'{y}, Karel and Goertzel, Zarathustra and Kaliszyk, Cezary and Ol\v{s}\'{a}k, Mirek and Piotrowski, Bartosz and Schulz, Stephan and Suda, Martin and Urban, Josef}, title = {{MizAR 60 for Mizar 50}}, booktitle = {14th International Conference on Interactive Theorem Proving (ITP 2023)}, pages = {19:1--19:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-284-6}, ISSN = {1868-8969}, year = {2023}, volume = {268}, editor = {Naumowicz, Adam and Thiemann, Ren\'{e}}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.19}, URN = {urn:nbn:de:0030-drops-183942}, doi = {10.4230/LIPIcs.ITP.2023.19}, annote = {Keywords: Mizar, ENIGMA, Automated Reasoning, Machine Learning} }
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