qgis - PostGIS query that selects feature if it goes outside boundary

I am looking of a postGIS function that will select the highlighted line in the picture below. Using st_intersection I can clip the lines to the polygon, but i'm looking to select the one line that breaks out of the polygon. The trouble is the line originates inside the polygon so st intersects, st crosses, st intersection both return all lines not just the one that breaks out of the polygon.