You want to insert a formula into Column R when a form submission is received.
As outlined in the comments:
Use an onformSubmit trigger to take action when a new submission is received. This is installable Trigger, so you will need to ... install it.
Take advantage of Event Objects to get the row number of the submission. In the script you'll note the ...
In Google Forms it's not possible to include a validation based on the response to several questions.
One alternative is to use Google Apps Script to do such validation after the form was submitted and in such case do something like send an email.
What you are asking for, cannot be achieved using Google Forms.
(You could probably try using GAS but that is a completely different "ball game")
As an alternative
You could achieve what you ask for but only on a per question/section basis.
Please have a look at this TEST FORM I prepared for you.
I have been searching for an answer for this exact problem for a while. I am using form for the same reason and this can be very confusing or at least annoying when there are one or more duplicates.
If you couldnt find any solution to this problem I recommend you to use a duplicate showing conditional formating formula and every time it captures a ...