I want to completely disable the next/previous navigation at the top of every post.
I just don't want to see that line.
I've seen the ATO options page for next/previous navigation, but I don't see an option to disable it.

Do I need to change the code?
I've seen something about next/previous navigation in the index.php but I do not know what I need to change in the code to disable it.

Can anyone help me out?

go back and look at the options in that section.

right...
I do sincerely apologize for looking with my nose instead of my eyes.