  This work explores the application of deep learning, a machine learning
technique that uses deep neural networks (DNN) in its core, to an automated
theorem proving (ATP) problem. To this end, we construct a statistical model
which quantifies the likelihood that a proof is indeed a correct one of a given
proposition. Based on this model, we give a proof-synthesis procedure that
searches for a proof in the order of the likelihood. This procedure uses an
estimator of the likelihood of an inference rule being applied at each step of
a proof. As an implementation of the estimator, we propose a
proposition-to-proof architecture, which is a DNN tailored to the automated
proof synthesis problem. To empirically demonstrate its usefulness, we apply
our model to synthesize proofs of propositional logic. We train the
proposition-to-proof model using a training dataset of proposition-proof pairs.
The evaluation against a benchmark set shows the very high accuracy and an
improvement to the recent work of neural proof synthesis.
