  Saturation-style automated theorem provers (ATPs) based on the given clause
procedure are today the strongest general reasoners for classical first-order
logic. The clause selection heuristics in such systems are, however, often
evaluating clauses in isolation, ignoring other clauses. This has changed
recently by equipping the E/ENIGMA system with a graph neural network (GNN)
that chooses the next given clause based on its evaluation in the context of
previously selected clauses. In this work, we describe several algorithms and
experiments with ENIGMA, advancing the idea of contextual evaluation based on
learning important components of the graph of clauses.
