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Connection calculi allow for very compact implementations of goal-directedproof search. We give an overview of our work related to connection tableauxcalculi: First, we show optimised functional implementations of clausal andnonclausal proof search, including a consistent Skolemisation procedure formachine learning. Then, we show two guidance methods based on machine learning,namely reordering of proof steps with Naive Bayesian probablities, andexpansion of a proof search tree with Monte Carlo Tree Search. Finally, we givea translation of connection proofs to LK, enabling proof certification andautomatic proof search in interactive theorem provers.

Machine Learning Guidance and Proof Certification for Connection Tableaux