The English language has a plethora of synonyms to express the notion of disbelief or lack of conviction. Some common synonyms for "not believe" are "doubt," "discredit," "reject," "disbelieve," "skeptical," "question," "suspect," and "demur." Doubt implies lack of certainty or trust; discredit suggests rejection of the source or evidence; reject signifies complete refusal or denial; disbelieve has a stronger connotation of active refusal or rejection of the truth; skeptical implies questioning or hesitant; question means to raise inquiries or doubts; suspect is used when there are indications of deception, and demur means to object or have misgivings about something. Using synonyms to "not believe" can add depth and variety to your writing.