DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) / 2023

MizAR 60 for Mizar 50

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

Foundation ModelsGenerative AIGraph LearningLarge Language ModelsReinforcement Learning

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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### Paper attached as context
Title: MizAR 60 for Mizar 50
Authors: Jakubův, Jan, Chvalovský, Karel, Goertzel, Zarathustra, Kaliszyk, Cezary, Olšák, Mirek, Piotrowski, Bartosz, Schulz, Stephan, Suda, Martin, Urban, Josef
Year: 2023
Venue: DROPS (Schloss Dagstuhl – Leibniz Center for Informatics)
Categories: Foundation Models, Generative AI, Graph Learning, Large Language Models, Reinforcement Learning
Citations: 75,444
Paper URL: https://arxiv.org/abs/2303.06686v1
Open PDF: https://arxiv.org/pdf/2303.06686v1

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.

Learning resources:
- PDF: arXiv PDF (https://arxiv.org/pdf/2303.06686v1)
- arXiv: arXiv abstract page (https://arxiv.org/abs/2303.06686v1)
- Google Scholar: Google Scholar references (https://scholar.google.com/scholar?q=MizAR%2060%20for%20Mizar%2050)
- OpenAlex: Paper page (https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.19)
- Papers with Code: Papers with Code search (https://paperswithcode.com/search?q=MizAR%2060%20for%20Mizar%2050)
- YouTube: YouTube explanations (https://www.youtube.com/results?search_query=MizAR%2060%20for%20Mizar%2050+paper+explained)