  Existing approaches to learning to prove theorems focus on particular logics
and datasets. In this work, we propose Monte-Carlo simulations guided by
reinforcement learning that can work in an arbitrarily specified logic, without
any human knowledge or set of problems. Since the algorithm does not need any
training dataset, it is able to learn to work with any logical foundation, even
when there is no body of proofs or even conjectures available. We practically
demonstrate the feasibility of the approach in multiple logical systems. The
approach is stronger than training on randomly generated data but weaker than
the approaches trained on tailored axiom and conjecture sets. It however allows
us to apply machine learning to automated theorem proving for many logics,
where no such attempts have been tried to date, such as intuitionistic logic or
linear logic.
