qgis - How to merge overlapping and duplicate lines from vector layer to one single line?

I used the "polygon to line" tool from QGIS, to get a line-layer from this polygon-layer:

Unfortunately this causes overlapping and duplicate lines, after I broke the qgis-export via GRASS into primitive lines (2 vertices). I need to have just one line, because two identical or overlapping lines are causing problems in CityEngine. I found no way to identify those features that are within other longer lines. I know, in QGIS there is a function called "within", but i have no idea if it works with line layers or how to use it.

many thanks in advance