Lemmatization for Stronger Reasoning in Large Theories

Abstract

Abstract. In this work we improve ATP performance in large theories by the reuse of lemmas derived in previous related problems. Given a large set of related problems to solve, we run automated theorem provers on them, extract a large number of lemmas from the proofs found and post-process the lemmas to make them usable in the remaining problems. Then we filter the lemmas by several tools and extract their proof dependencies, and use machine learning on such proof dependencies to add the most promising generated lemmas to the remaining problems.On such enriched problems we run the automated provers again, solving more problems. We describe this method and the techniques we used, and measure the improvement obtained. On the MPTP2078 large-theory benchmark the method yields 6.6% and 6.2% more problems proved in two different evaluation modes.

Property Preserving Embedding of First-order Logic

“…This and most other approaches (e.g. [15]) exclusively use human selected features. A related problem is that of automatically proposing interesting conjectures and theory exploration.…”

Waste Reduction: Experiments in Sharing Clauses between Runs of a Portfolio of Strategies (Experimental Paper)

“…Several machine learning methods for proof search also re-use clauses. In [8] lemma selection from the derived clauses is used between related problems, while in [3] a similar mechanism, called leapfrogging, is used for E/ENIGMA between repeated runs on the same problem. The latter paper describes the use of a trained graph-based predictor to select a promising subset of the clauses processed during a previous run.…”