  Automated theorem proving in first-order logic is an active research area
which is successfully supported by machine learning. While there have been
various proposals for encoding logical formulas into numerical vectors -- from
simple strings to more involved graph-based embeddings -- little is known about
how these different encodings compare. In this paper, we study and
experimentally compare pattern-based embeddings that are applied in current
systems with popular graph-based encodings, most of which have not been
considered in the theorem proving context before. Our experiments show that the
advantages of simpler encoding schemes in terms of runtime are outdone by more
complex graph-based embeddings, which yield more efficient search strategies
and simpler proofs. To support this, we present a detailed analysis across
several dimensions of theorem prover performance beyond just proof completion
rate, thus providing empirical evidence to help guide future research on
neural-guided theorem proving towards the most promising directions.
