Most commonly, the Open World Assumption is adopted as a standard strategy for the design, construction and use of ontologies. This strategy limits the inferencing capabilities of any system because non-asserted statements (missing knowledge) could be assumed to be alternatively true or false. As we will demonstrate, this is especially the case of first-order logic (FOL) ontologies where non-asserted statements is nowadays one of the main obstacles to its practical application in automated commonsense reasoning tasks. In this paper, we investigate the application of the Closed World Assumption (CWA) to enable a better exploitation of FOL ontologies by using state-of-the-art automated theorem provers. To that end, we explore different CWA formulations for the structural knowledge encoded in a FOL translation of the SUMO ontology, discovering that almost 30 % of the structural knowledge is missing. We evaluate these formulations on a practical experimentation using a very large commonsense benchmark obtained from WordNet through its mapping to SUMO. The results show that the competency of the ontology improves more than 50 % when reasoning under the CWA. Thus, applying the CWA automatically to FOL ontologies reduces their ambiguity and more commonsense questions can be answered.