  We describe an implementation of gradient boosting and neural guidance of
saturation-style automated theorem provers that does not depend on consistent
symbol names across problems. For the gradient-boosting guidance, we manually
create abstracted features by considering arity-based encodings of formulas.
For the neural guidance, we use symbol-independent graph neural networks (GNNs)
and their embedding of the terms and clauses. The two methods are efficiently
implemented in the E prover and its ENIGMA learning-guided framework.
  To provide competitive real-time performance of the GNNs, we have developed a
new context-based approach to evaluation of generated clauses in E. Clauses are
evaluated jointly in larger batches and with respect to a large number of
already selected clauses (context) by the GNN that estimates their collectively
most useful subset in several rounds of message passing. This means that
approximative inference rounds done by the GNN are efficiently interleaved with
precise symbolic inference rounds done inside E. The methods are evaluated on
the MPTP large-theory benchmark and shown to achieve comparable real-time
performance to state-of-the-art symbol-based methods. The methods also show
high complementarity, solving a large number of hard Mizar problems.
