We report a large study in which participants are invited to draw inferences from causal conditional sentences with varying degrees of believability. General intelligence was measured, and participants were split into groups of high and low ability. Under strict deductive-reasoning instructions, it was observed that higher ability participants were significantly less influenced by prior belief than were those of lower ability. This effect disappeared, however, when pragmatic reasoning instructions were employed in a separate group. These findings are in accord with dual-process theories of reasoning. We also took detailed measures of beliefs in the conditional sentences used for the reasoning tasks. Statistical modelling showed that it is not belief in the conditional statement per se that is the causal factor, but rather correlates of it. Two different models of belief-based reasoning were found to fit the data according to the kind of instructions and the type of inference under consideration.