Following the growing body of evidence suggesting that substantial individual differences in reasoning exist already at the early stages of the reasoning process and that reasoners might be able to produce logical intuitions, the model of mindware automatization posits that the mindware acquired to the extent that it is fully automatized can cue the logically correct type 1 response. We asked 908 participants to solve the Cognitive Reflection Test presented under the two-response paradigm, to obtain both intuitive and analytical response, while measuring mindware instantiation and conflict detection efficiency. These variables explained approximately 10% of the variance in the accuracy of intuitive answers. We also observed that in more than half of the cases when the response was correct in the final response stage, it was already correct at the initial response stage. These results are in line with the theoretical model of mindware automatization to a large extent and raise a question about the main attribute of the Cognitive Reflection Test – the ability to measure the tendency to override a misleading intuitive answer.