According to the default interventionist dual-process account of reasoning, belief-based responses to reasoning tasks are based on Type 1 processes generated by default, which must be inhibited in order to produce an effortful, Type 2 output based on the validity of an argument. However, recent research has indicated that reasoning on the basis of beliefs may not be as fast and automatic as this account claims. In three experiments, we presented participants with a reasoning task that was to be completed while they were generating random numbers (RNG). We used the novel methodology introduced by Handley, Newstead & Trippas (Journal of Experimental Psychology: Learning, Memory, and Cognition, 37, 28–43, 2011), which required participants to make judgments based upon either the validity of a conditional argument or the believability of its conclusion. The results showed that belief-based judgments produced lower rates of accuracy overall and were influenced to a greater extent than validity judgments by the presence of a conflict between belief and logic for both simple and complex arguments. These findings were replicated in Experiment 3, in which we controlled for switching demands in a blocked design. Across all three experiments, we found a main effect of RNG, implying that both instructional sets require some effortful processing. However, in the blocked design RNG had its greatest impact on logic judgments, suggesting that distinct executive resources may be required for each type of judgment. We discuss the implications of our findings for the default interventionist account and offer a parallel competitive model as an alternative interpretation for our findings.