I have a series of paths, which are closed loops.  You can see it here:

I would like to create a margin between the outer box and the shapes.  Is there a way

to combine a horizontal line and the shapes that overlap with it to produce something like this?

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I have tried selecting a segment which crosses one of the shapes, and applying the various path operations (union, difference, intersection, etc) without success. Any suggestions highly appreciated. Thank you.

Can you upload your images into the forum please? Hot-linking isn´t allowed.