The character Raskolnikov in Crime and Punishment has theories about the ordinary man versus the extraordinary man, but those theories are often blurred and unclear in his own mind. If we are to assume that the crime was committed in order to prove a theory, then the flaws in the crime must indicate flaws in the theory.
Doesn't Raskolnikov contradict himself in Crime and Punishment?
However, the fact that the theories seem to be contradictory at times is not a result of Dostoevsky's carelessness. The author intentionally made the theory contradictory at times. Raskolnikov had to commit the murder before he had completely formulated the theory. Dostoevsky wanted to show the young man being influenced by various theories and then using these theories before he had a chance to analyze them.
For example, a typical contradiction would be that Raskolnikov will at one time claim that the murder was committed to benefit mankind, but then later he will claim that the extraordinary man must be above mankind and not be concerned with what other people will think of him. Such an incomplete understanding of his own thoughts and such contradictory statements are the rationale that leads Raskolnikov to the possibility of redemption.