Resolution trees with lemmas (\mathrm{RTL}) are a resolution-based propositional proof system that is related to the DPLL algorithm with clause learning. Its fragments \mathrm{RTL}(k) are related to clause learning algorithms where the width of learned clauses is bounded by k.

For every k up to O(\log n), an exponential separation between the proof systems \mathrm{RTL}(k) and \mathrm{RTL}(k+1) is shown.