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.

Keywords

Computer scienceMachine translationTransformerBLEUEncoderArtificial intelligenceParallelizable manifoldParsingNatural language processingDecoding methodsLanguage modelTask (project management)Convolutional neural networkSpeech recognitionMachine learningAlgorithm

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Year
2023
Type
preprint
Citations
70225
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Closed

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Ashish Vaswani, Noam Shazeer, Niki Parmar et al. (2023). MizAR 60 for Mizar 50. Leibniz-Zentrum für Informatik (Schloss Dagstuhl) . https://doi.org/10.4230/lipics.itp.2023.19

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DOI
10.4230/lipics.itp.2023.19

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Data completeness: 77%