Actually, the seat (the part with the hole in it) AND the lid should be put down. That way EITHER sex has to lift SOMETHING.
Plus, if you have "blue water", it'll keep the beasties from drinking 1 of your 2000 Flushes. (That's a product here, in the US.)
There is a seat AND a lid?

Like your stance on "equal" rights but men still have two (well three really but let's not go there) items to lift.
We have the blue blocks here also but are allowed to flush at will. 2000 seems very limiting indeed.