MizAR 40 for Mizar 40

Abstract

As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40% of the theorems in the latest official version of the Mizar Mathematical Library (MML). This is a considerable improvement over previous performance of large- theory AI/ATP methods measured on the whole MML. To achieve that, a large suite of AI/ATP methods is employed and further developed. We implement the most useful methods efficiently, to scale them to the 150000 formulas in MML. This reduces the training times over the corpus to 1-3 seconds, allowing a simple practical deployment of the methods in the online automated reasoning service for the Mizar users (MizAR)

Automating Boolean Set Operations in Mizar Proof Checking with the Aid of an External SAT Solver

“…Ciolkowskiego 1M, 15-245 Bialystok, Poland the MIZAR system from the 7.13 branch (version 7.13.01 accompanied with MML version 4.181.1147). There is also active research on combining MIZAR with external automated theorem provers [9,21]. In the present work, however, we do not intend a far departure from the original MIZAR notion of obviousness.…”

Progress in the Independent Certification of Mizar Mathematical Library in Isabelle

“…Although this translation has covered the important part of the MML, it does not constitute the accurate representation of the Fraenkel operator and scheme [29]. Additional work on this solution has enabled the creation of the extensive theorems database of Mizar Problems for Theorem Proving (MPTP) that is used in the process of comparing the performance of leading systems of automatic theorem proving, as well as during the machine learning of the MizAR proof advice system [31].…”

DeepAlgebra - An Outline of a Program

“…Their main goal is to make theorem proving more effective. For a general overview see [3]; a hammer for COQ is described in [4] and for Mizar in [11].…”