Think of this situation:
You are really bored and suddenly say to your friend:
At least let's tickle ourselves so that we have done something
At least let's tickle ourselves so that we have something done.
At least let's tickle ourselves to have something done.
At least let's tickle ourselves to have done something.
I'm trying to make a connection between these kinds of sentences and a tense in my language.
There are so many examples like this:
It's holiday. Everybody has gone to somewhere outside the town (maybe near the lake) but you and your friends are in the house. You say:
let's go to the roof and pretend(suppose) that we have gone somewhere
let's go to the roof so that we have gone somewhere (at least) or (so far).