Recent results have challenged the widespread assumption of dual process models of belief bias that sound reasoning relies on slow, careful reflection, whereas biased reasoning is based on fast intuition. Instead, parallel process models of reasoning suggest that rule- and belief-based problem features are processed in parallel and that reasoning problems that elicit a conflict between rule- and belief-based problem features may also elicit more than one Type 1 response. This theoretical development has important implications for individual-differences research on reasoning, because rule-based responses by certain individuals may reflect that these individuals were either more likely to give a rule-based default response or that they successfully inhibited and overrode a belief-based default response. In two studies, we used the diffusion model to describe decision making during transitive reasoning and related model parameters to individual differences in cognitive abilities and thinking styles. We found that individuals with greater need for cognition showed a smaller decrease in drift rates when confronted with a conflict between rule- and belief-based problem features under logical validity instructions, which suggests that a greater disposition to engage in reflective thinking facilitated the inhibition and successful override of Type 1 responses. More intelligent individuals, however, showed a greater decrease in drift rates when confronted with a conflict between rule- and belief-based problem features under belief instructions, which suggests that their quickly generated logical response interfered with their ability to evaluate lower-level intrinsic problem features. Taken together, this double dissociation suggests that cognitive abilities and thinking styles affect the processing of conflict information through different mechanisms and at different stages of information-processing: Greater cognitive abilities facilitate the efficient creation of decoupled problem representations, whereas a greater disposition to engage in critical thinking facilitates the successful detection and override of Type 1 responses.