Learning-assisted theorem proving with millions of lemmas. (July 2015) - Kaliszyk, Cezary; Urban, Josef
Abstract: Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of theHOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in theHOL Light andFlyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such asFlyspeck .