Deep Learning techniques are nowadays pervasive in AI. However, these approaches suffer of the lack of transparency for justifying their output and for helping users in believing in their decisions. For these reasons alternative approaches to learning deserve to be explored either for developing new tools with autonomous learning capability or for explaining the results of black-box predictors. Among them an important role is assumed since the Nineties by Inductive Logic Programming and, in particular, recently by the approaches of Learning from Answer Sets (LAS). Computing inductive solutions for LAS tasks is known to be $\Sigma_2^P$-hard. In this work, we tackle this problem using a single-shot disjunctive ASP encoding based on the saturation technique originally proposed by Eiter and Gottlob. We prove that, when the background knowledge and hypothesis space form a tight program (a syntactical property) our encoding is linear in the size of the task. This approach contrasts with the state-of-the-art ILASP system, which relies on multiple iterative calls to an ASP solver. As a result, it can be directly evaluated by modern disjunctive ASP solvers, leveraging decades of research and optimization in the ASP community. We implement our method in a system named LASCO. Experimental results on a diverse set of benchmarks demonstrate that LASCO outperforms all versions of ILASP on many instances and it scales if run on multi-threaded machines.