Dual-process theories dominate contemporary research on human reasoning, although the various instantiations of dual-process theories differ somewhat in terms of their architectural assumptions, they all posit that reasoning reflects a sophisticated interplay between heuristic processes that are fast, automatic, require little cognitive capacity on the one hand, and analytic processes that are slow, controlled, draw heavily on working memory on the other hand. Despite dual process assumption have gained support from a wide range of sources, little consensus exists as to the details of interaction between the two kinds of operations. The Default-Interventional Model and the Parallel-Competition Model make different assumptions about the sequencing of heuristic and analytic process. Both models have gained some supports, but can not capture the full range of available data. The aim of the current study was to test the predictive power of the two models. The current study examined the impact of belief-logic conflict on accuracy and latency of responding for participants who were asked to solve simple transitive reasoning and difficulty syllogistic reasoning problem, in which participants were instructed to evaluate the conclusions of logical arguments on the basis of either their logical validity or their believability. Both transitive and syllogistic reasoning item included conflict problems and non-conflict problems. Each trial consisted of the presentation of the premises alone, participants then press the space bar on a key-board, the premises disappeared and was replaced by the instruction cue, the conclusion and the response options. Latency of response was recorded from the presentation of the conclusion on the screen until a response was provided. The results showed that belief-logic conflict influenced participants’ belief judgments when they solved simple problems, but belief-logic conflict had no effects on the participants’ logic judgments. The accuracy of participants’ belief judgments on conflict items was higher than that of participants’ belief judgments on non-conflict ones, the response latency of participants’ belief judgments on conflict items was longer than that of participants’ belief judgments on non-conflict ones. Moreover, when participants solved difficulty problems, belief-logic conflict had a significant much larger effect on latencies for logic judgments than for belief judgments. In short, the presence of a conflict between logic and belief had a much larger effect on belief judgments than on logic judgments of simple problems, while the belief-logic conflict had a larger effect on logic judgment than on belief judgment of difficulty problems. There was no evidence to the predictions which were derived from the principles that underlie the Default-Interventionist Model, but the Parallel-Competitive Model can capture the data pattern of the study. The results of the experiment suggest that the heuristic processes and analytic processes were activated simultaneously in the course of reasoning to compete for the final response, the process that completes first cues a response which may need to be inhibited in favor of an alternative less rapidly cued response, depending on task instructions, and task difficulty, and support the Parallel-Competitive Model.