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We describe an efficient implementation of clause guidance insaturation-based automated theorem provers extending the ENIGMA approach.Unlike in the first ENIGMA implementation where fast linear classifier istrained and used together with manually engineered features, we have started toexperiment with more sophisticated state-of-the-art machine learning methodssuch as gradient boosted trees and recursive neural networks. In particular thelatter approach poses challenges in terms of efficiency of clause evaluation,however, we show that deep integration of the neural evaluation with the ATPdata-structures can largely amortize this cost and lead to competitivereal-time results. Both methods are evaluated on a large dataset of theoremproving problems and compared with the previous approaches. The resultingmethods improve on the manually designed clause guidance, providing the firstpractically convincing application of gradient-boosted and neural clauseguidance in saturation-style automated theorem provers.

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E