Gym-saturation: an OpenAI Gym environment for saturation provers

Boris Shminke

doi:10.21105/joss.03849

Abstract

`gym-saturation` is an OpenAI Gym environment for reinforcement learning (RL) agents capable of proving theorems. Currently, only theorems written in a formal language of the Thousands of Problems for Theorem Provers (TPTP) library in clausal normal form (CNF) are supported. `gym-saturation` implements the 'given clause' algorithm (similar to the one used in Vampire and E Prover). Being written in Python, `gym-saturation` was inspired by PyRes. In contrast to the monolithic architecture of a typical Automated Theorem Prover (ATP), `gym-saturation` gives different agents opportunities to select clauses themselves and train from their experience. Combined with a particular agent, `gym-saturation` can work as an ATP. Even with a non trained agent based on heuristics, `gym-saturation` can find refutations for 688 (of 8257) CNF problems from TPTP v7.5.0.

Highlights

Combined with a particular agent, gym-saturation can work as an Automated Theorem Prover (ATP)
Even with a non trained agent based on heuristics, gym-saturation can find refutations for 688 clausal normal form (CNF) problems from Thousands of Problems for Theorem Provers (TPTP) v7.5.0
The same is true for non saturation-based reinforcement learning (RL)-friendly provers too (e.g. lazyCoP, Rawson & Reger (2021)). This monolithic approach hinders free experimentation with novel machine learning (ML) models and RL algorithms and creates unnecessary complications for ML and RL experts willing to contribute to the field

Summary

Introduction

Suppose we want to prove an extremely simple theorem with a very basic agent. We can do that in the following way:. In contrast to the monolithic architecture of a typical Automated Theorem Prover (ATP), gym-saturation gives different agents opportunities to select clauses themselves and train from their experience. Combined with a particular agent, gym-saturation can work as an ATP.

Results

Conclusion