Cognitive interference as a representation of experienced "intrapsychic conflict" according to some findings might be attributed to competitive neural assemblies interacting during recognition process and interpretation of encoded neural information. These findings suggest a novel hypothesis that increased neural complexity reflecting competition of distributed neural assemblies may play an important role during neural interactions related to processing of conflicting information at the subjective level experienced as a "cognitive conflict". To illustrate how this hypothesis may be tested we have used the illustrative case study with the aim to assess changes of neural complexity related to conflicting information processing during incongruent Stroop task and compare this process of the so-called "neural interference" with the control tasks. In this illustrative single case study we have analyzed intracerebral EEG activities to asses the neural processing of conflicting information during the incongruent Stroop task and for the comparison were measured experimental periods during the congruent task and rest. The results indicate that EEG complexity measured using Momentary Largest Lyapunov Exponents (MLLE) is significantly increased during the conflicting cognitive Stroop interference in comparison to the other experimental conditions in all investigated brain sites. These results indicate that the neural interference related to conflicting stimuli is related to significantly increased neural complexity. The results of this illustrative case study in agreement with the hypothesis suggest that increased neural complexity may reflect the process of the so-called "neural interference" during presentation of the conflicting stimuli.