Definite determiners trigger existence- and uniqueness-presuppositions, that is, the speaker assumes that it is taken for granted that there exists exactly one of the mentioned object in the relevant discourse. Indefinite determiners are associated with anti-uniqueness, that is, that there are several of the mentioned object. Applying the Maximize Presupposition principle, this additional meaning component arises as an anti-presupposition and involves first considering the definite determiner's uniqueness-presupposition and then its negation. We here investigate processing of the two determiners in more detail and ask whether this processing is automatic or requires limited central capacities. To do so, we employed the Psychological Refractory Period (PRP) approach and the locus of slack-logic. We observed more difficult processing for the indefinite compared to the definite determiner in felicitous sentences, and also in infelicitous compared to felicitous sentences. Further, immediate processing of the indefinite determiner appears capacity-limited. These results support the Maximize Presupposition principle and are an important step forward toward understanding cognitive processing of presuppositions.