Human reasoning has been characterized as an interplay between an automatic belief-based system and a demanding logic-based reasoning system. The present study tested a fundamental claim about the nature of individual differences in reasoning and the processing demands of both systems. Participants varying in working memory capacity performed a reasoning task while their executive resources were burdened with a secondary task. Results were consistent with the dual-process claim: The executive burden hampered correct reasoning when the believability of a conclusion conflicted with its logical validity, but not when beliefs cued the correct response. However, although participants with high working memory spans performed better than those with lower spans in cases of a conflict, all reasoners showed similar effects of load. The findings support the idea that there are two reasoning systems with differential processing demands, but constitute evidence against qualitative individual differences in the human reasoning machinery.