  Automated reasoning and theorem proving have recently become major challenges
for machine learning. In other domains, representations that are able to
abstract over unimportant transformations, such as abstraction over
translations and rotations in vision, are becoming more common. Standard
methods of embedding mathematical formulas for learning theorem proving are
however yet unable to handle many important transformations. In particular,
embedding previously unseen labels, that often arise in definitional encodings
and in Skolemization, has been very weak so far. Similar problems appear when
transferring knowledge between known symbols.
  We propose a novel encoding of formulas that extends existing graph neural
network models. This encoding represents symbols only by nodes in the graph,
without giving the network any knowledge of the original labels. We provide
additional links between such nodes that allow the network to recover the
meaning and therefore correctly embed such nodes irrespective of the given
labels. We test the proposed encoding in an automated theorem prover based on
the tableaux connection calculus, and show that it improves on the best
characterizations used so far. The encoding is further evaluated on the premise
selection task and a newly introduced symbol guessing task, and shown to
correctly predict 65% of the symbol names.
