We describe an efficient implementation of clause guidance in
saturation-based automated theorem provers extending the ENIGMA approach.
Unlike in the first ENIGMA implementation where fast linear classifier is
trained and used together with manually engineered features, we have started to
experiment with more sophisticated state-of-the-art machine learning methods
such as gradient boosted trees and recursive neural networks. In particular the
latter approach poses challenges in terms of efficiency of clause evaluation,
however, we show that deep integration of the neural evaluation with the ATP
data-structures can largely amortize this cost and lead to competitive
real-time results. Both methods are evaluated on a large dataset of theorem
proving problems and compared with the previous approaches. The resulting
methods improve on the manually designed clause guidance, providing the first
practically convincing application of gradient-boosted and neural clause
guidance in saturation-style automated theorem provers.

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