In recent years, it has been shown that methods from Inductive Logic Programming (ILP) are powerful enough to discover new fist-order knowledge from data, while employing a clausal representation language that is relatively easy for humans to understand. Despite these successes, it is generally acknowledged that there are issues that present fundamental challenges for the current generation of systems. Among these, two problems are particularly prominent: learning deep clauses, i.e., clauses where a long chain of literals is needed to reach certain variables, and learning wide clauses, i.e., clauses with a large number of literals. In this paper we present a case study to show that by building on positive results on acyclic conjunctive query evaluation in relational database theory, it is possible to construct ILP learning algorithms that are capable of discovering clauses of significantly greater depth and width. We give a detailed description of the class of clauses we consider, describe a greedy algorithm to workwith these clauses, and show, on the popular ILP challenge problem of mutagenicity, how indeed our method can go beyond the depth and width barriers of current ILP systems.