Logged in users – password protected content

Hi!

I’ve developed a site, where some of the pages are password protected aka you have to log in, to see these contents. Without the login, you can’t access these pages, only see the login window.

Is there any option, that I exclude these pages’ contents from the search results for logged out users and include these contents for logged in users? For protection, I use the basic if ( is_user_logged_in() + else script.

I’ve set the option Search and return password protected posts? OFF, but I still see these in the results.

Thanks so much!