Report Filtering

Hello! We are using ticket reports to organize work on our desktops. One of these reports is "Tickets Waiting for Assignment." All of our tickets come in with a default responsible group assigned. They appear in this report and, theoretically, will stay there until a) an individual takes primary responsibility for the service request or (b) a workflow kicks in and assigns tasks to one or more people.  We have had success with (a) but I'm not quite sure how to achieve (b). I've attached a screenshot that shows two tickets, both of which have a responsible group, tasks assigned to individuals, but no individual responsibility on the ticket. Is there a way to filter these out of this report. I thought adding the following filter: Responsibility is not one of >any user<, and that was successful, but I think I'd have to update it every time we added a new user to the application. 

Do you have any tips on how to manage this? For these workflow tickets, we want the responsibility of the ticket to remain with the group (not an individual), but we want them to fall off this report once there are individuals responsible for the associated tasks. 

Thank you!