The goal of inductive logic programming (ILP) is to search for a hypothesis that generalises training examples and background knowledge (BK). To improve performance, we introduce an approach that, before searching for a hypothesis, first discovers `where not to search'. We use given BK to discover constraints on hypotheses, such as that a number cannot be both even and odd. We use the constraints to bootstrap a constraint-driven ILP system. Our experiments on multiple domains (including program synthesis and inductive general game playing) show that our approach can substantially reduce learning times.