Lemma Discovery and Strategies for Automated Induction

Sólrún Halla Einarsdóttir, Márton Hajdú, Moa Johansson, Nicholas Smallbone, Martin Suda

Abstract: We investigate how the automated inductive proof capabilities of the first-order prover Vampire can be improved by adding lemmas conjectured by the QuickSpec theory exploration system and by training strategy schedules specialized for inductive proofs. We find that adding lemmas improves performance (measured in number of proofs found for benchmark problems) by \(40\%\) compared to Vampire’s plain structural induction as baseline. Strategy training alone increases the number of proofs found by \(130\%\), and the two methods in combination provide an increase of \(183\%\). By combining strategy training and lemma discovery we can prove more inductive benchmarks than previous state-of-the-art inductive proof systems (HipSpec and CVC4).