MizAR 60 for Mizar 50

Jan Jakubův; Karel Chvalovský; Zarathustra Goertzel; Cezary Kaliszyk; Mirek Olšák; Bartosz Piotrowski; Stephan Schulz; Martin Suda; Josef Urban

arXiv · 2303.06686

MizAR 60 for Mizar 50

Jan Jakubův·Karel Chvalovský·Zarathustra Goertzel·Cezary Kaliszyk·Mirek Olšák·Bartosz Piotrowski·Stephan Schulz·Martin Suda·Josef Urban

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Abstract

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.

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Jan Jakubův, Karel Chvalovský, Zarathustra Goertzel, Cezary Kaliszyk, Mirek Olšák, Bartosz Piotrowski, Stephan Schulz, Martin Suda, Josef Urban. 2023-03-12. MizAR 60 for Mizar 50. https://arxiv.org/abs/2303.06686

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