ATP and Presentation Service for Mizar Formalizations

TL;DR

The MizAR service integrates automated reasoning and presentation tools with Mizar, aiding authors in proof discovery, explanation, and problem generation, leveraging first-order ATP systems for large theories.

Contribution

This work introduces MizAR, a novel integrated service that combines ATP, AI, and presentation tools with Mizar, facilitating proof exploration and generation in large formal libraries.

Findings

MizAR helps explore the Mizar library effectively.

The service assists in proof discovery and explanation.

Initial experiments show substantial user benefits.

Abstract

This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of MizAR services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles.