How does the the author prove the superman theory to be wrong in “Crime and Punishment”?

I need a few examples on how Fyodor Dostoevsky proves the superman theory to be false and that supermen do not exist. I already have that they are punished for their crimes, and that it is not for the good of humanity.

Any ideas would be great, even if you’re not sure if they are right.
Will pick best answer. Thank you!! I appreciate it.