Disable wordpress comments API

We’re using the disqus plugin on our wordpress site, so anyone commenting should have a login through disqus.
Yet, I’m still seeing spammers trying to post through the regular comments API.
They’re not getting through to the post, but they’re clogging my inbox as admin.

How do I disable this API – I only want to accept comments that come from a logged in Disqus user?

There is much easier way to close standard WordPress comments. Just add

add_filter( 'comments_open', '__return_false' );

to your functions.php file and comments will be closed.