Divide objects below fails to produce its magic?

Thank you, Ton! I might give this script a trial at some point.

But I am more concerned with understanding the programmatic nature of the underlying command.

This morning, for example, I had a shape behind a line. The shape was a closed surface. I selected the line and activate the Divide object below command and it worked!! Similarely, I guess, along the lines of the Pathfinder > Divide command, with which I think it shares some similarities. 

So I think we can safely establish that the command works best on closed surfaces. 

How it can work on line segment, I'll come back at some point when I run across a situation which warrants its use. But for the moment, I thought I'd pass this out.

Well, I swear it worked once, on the same collection of stroked paths. I swear.

And I'm ve used it many times on simple lines...
I'm baffled.
I guess I have to dig the Documentation?