MizAR 60 for Mizar 50
This work addresses the problem of automating theorem proving in formal mathematics, particularly for the Mizar system, representing a strong specific gain in this domain.
The researchers developed an AI/TP system that automatically proves about 60% of Mizar theorems in a hammer setting and 75% when assisted by human-written proof premises, tackling the challenge of automated theorem proving in formal mathematics.
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.