Individuals can make inferences from a single quantified premise. For instance, if you know that all of the Virginians are students, you might infer that some of the students are Virginians. We describe a computational system, mReasoner, of the cognitive processes that underlie these so-called ‘immediate’ inferences. The account is based on the assumption that when individuals understand discourse, they construct discrete mental simulations, i.e., mental models, of the assertions in the discourse. To draw conclusions, reasoners describe the relation between the individuals in the models and, if they are prudent, they search for alternative models to corroborate or refute a conclusion. We describe an experiment in which participants’ carried out a series of immediate inferences, and present a simulation that predicts the accuracy and latency of their responses.