Download PDFOpen PDF in browserNeural Conjecturing for Saturation Theorem Provers11 pages•Published: October 24, 2026AbstractWe present a system for generating intermediate lemmas, used as cut formulas, that restructure first-order proof search in saturation-based theorem provers. Given a CNF problem, a heterogeneous graph neural network encodes clauses, literals, terms, variables and symbols. An autoregressive decoder then samples candidate lemmas by pointing to symbols in the input and by obeying arity constraints during decoding. Candidate lemmas are accepted when an ATP proves both sides of the cut, i.e. the problem extended with the lemma and with its negation. Together with adjustable criteria for proof-search speedup this gives a supervised learning signal and a learning-proving feedback loop.We train and evaluate the methods on ATP datasets built from the Mizar Mathematical Library with both E and Vampire. On the E test set, the best single configuration helps 96 of 187 baseline-proved problems, while an ensemble helps 127 67.9%, with speedups up to 196x. We also show that a cut generator trained on the E data transfers to Vampire: when the cuts are delivered as AVATAR claims, Vampire proves 501 hard Mizar problems unsolved by Vampire or E in the Mizar60 evaluation, and speeds up 1567 further problems. In combination with trained Deepire and Vampire's CASC mode, the learning/conjecturing/portfolio methods discussed here prove 1228 Mizar problems unsolved by Vampire or E in the Mizar60 evaluation. Keyphrases: conjecturing, e prover, lemma introduction, machine learning, mizar, vampire In: Stephan Schulz, Konstantin Korovin and Michael Rawson (editors). Proceedings of 16th International Workshop on the Implementation on Logics. Proceedings of the 26th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (short papers), vol 23, pages 10-20.
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