Learning-assisted theorem proving with millions of lemmas

Learning-assisted theorem proving with millions of lemmas☆

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 the ...

Machine-assisted theorem-proving for software engineering

Abstnct The thesis describes the production of a large prototype proof system for Z. and a tactic Ian· guage in which the proof tactics used in a wide range of systems (ineluding the system described here) can be discussed. The dewls of the construction of the tool-using the W logic fOT Z. and implemented in 20BJ-are presented, along with an account of some of the proof taclics which enable W t...

Theorem Proving with Constrained

Deduction methods for rst-order constrained clauses with equality are described within an abstract framework: constraint strategies, consisting of an inference system, a constraint inheritance strategy and redundancy criteria for clauses and inferences. We give simple conditions for such a constraint strategy to be complete (refutationally and in the sense of Knuth-Bendix-like completion). This...

The Use of Lemmas for Solving Hard Automated Theorem Proving Problems

of a thesis at the University of Miami. Using lemmas has been proved to be an effective approach to assisting ATP sytems to solve hard problems. Useful lemmas can provide valuable guidance in the proof search, and help construct the proof by filling in intermediate steps. However, the formulae supplied to an ATP system as lemmas are not all necessarily useful. Unuseful lemmas act as noise, dist...

Machine learning and automated theorem proving