The state that exists when related cognitions are inconsistent or contradict one another is known as:

The correct answer is cognitive dissonance.

Cognitive dissonance (CD) refers to a state or situation in which a person experiences feelings of discomfort that results from holding two contradictory thoughts, attitudes or beliefs. An instance of cognitive dissonance is the feeling a long-term smoker experiences when he reads an article about an increasing number of deaths due to lung cancer which is heavily caused by smoking.