You don't want to get rid of 'everyone' access. If you aren't using the guest group, you're just wasting your time. If you are using the guest group, you can just deny access to the guests. Everyone in your domain should be a Domain User unless they are a guest. Removing the 'everyone' permissions can have very undesirable side effects on your server. If you do what you're wanting to do, I guarantee you're going to have people banging down your door because they can't get to network resources. Default permissions is no permissions... which is basically deny permissions.