# GRUNGE: A Grand Unified ATP Challenge

## TL;DR

This paper introduces GRUNGE, a comprehensive benchmark of theorem proving problems translated into various logical formalisms, enabling performance comparison of different automated theorem provers and fostering integrated learning approaches.

## Contribution

It presents a large, unified set of theorem proving problems across multiple logical formalisms, facilitating systematic evaluation and combined use of ATP systems.

## Key findings

- Enables comparison of ATP systems across different logics
- Provides a large, diverse benchmark for theorem proving
- Supports multi-formalism learning and system integration

## Abstract

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type variables) and first-order logic (possibly with multiple types, and possibly with type variables). The resultant problem sets allow us to run automated theorem provers that support different logical formats on corresponding problems, and compare their performances. This also results in a new "grand unified" large theory benchmark that emulates the ITP/ATP hammer setting, where systems and metasystems can use multiple ATP formalisms in complementary ways, and jointly learn from the accumulated knowledge.