# The ILLTP Library for Intuitionistic Linear Logic

## TL;DR

This paper introduces the ILLTP library for benchmarking automated theorem proving in propositional intuitionistic linear logic, utilizing translations of classical theorems, proof comparisons, and Petri net problems to expand the collection.

## Contribution

It presents a new library for intuitionistic linear logic theorem proving, including problem translations, proof analysis, and Petri net problem encoding, filling a gap in non-classical logic benchmarking tools.

## Key findings

- Analyzed four translations of intuitionistic logic into linear logic.
- Compared proofs using a linear logic prover with focusing.
- Expanded the problem set with Petri net reachability problems.

## Abstract

Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems in the traditional monograph "Introduction to Metamathematics". We analyze four different translations of intuitionistic logic into linear logic and compare their proofs using a linear logic based prover with focusing. In order to enhance the set of problems in our library, we apply the three provability-preserving translations to the propositional benchmarks in the ILTP Library. Finally, we generate a comprehensive set of reachability problems for Petri nets and encode such problems as linear logic sequents, thus enlarging our collection of problems.