Hi, Oleg!
 
I don't think I misread your original question...but that's just my opinion...
 
Here's an example for you to try:
 
Take Big Class.jmp.  Run some ridiculously-overfit Neural Network analysis with Sex as the Response and Age, Height, and Weight as the factors.  Consider Female as the Positive case. :)
 
I got a Contingency Table that looks like this:

Choose Make Into Data Table.
TP= 16.  FP=2.  FN=2.
F1 can be calculated by 2*TP/(2*TP+FP+FN).  I get F1=0.89.
This is a very easy thing to script (in my opinion :), and you can even automatically include this metric (and any other) on any of your output with a script.  Give it a shot, and I'll try to help you get it if you fail.
Good luck.