The usage of "I see not"
TL;DR I'd consider it archaic rather than formal or literary.
Other than "I am not", "I have not", "I can not", and "I do not" (and possibly a few other exceptions), it's pretty rare to have the construction "I verb not" in modern English.
In fact, in the case of "have not" and "can not", it's usually the case that the next word is a verb, so the main verb isn't followed by not in those cases either.