Pressing P automatically clears the level you are currently playing in.
When I pressed P in campaign levels, dialogue that usually happens upon victory occurred followed by the results/rating screen. The sector would then be counted as cleared and the game let me progress.
In infinite mode, the game asked me for my name as if I was starting a new campaign save. I was able to type whatever in the box asking for my name, and upon hitting either Esc or Enter the game said I've successfully built an extractor for the level and therefore count it as a clear and move me to the next level.