Just musing on it: Quantum physics? That might take them a little time. They don’t have to worry about losing interest in questions that might bore the normal human intellect after awhile, or after a few millenia. What about perpetual motion machines? They want an indefatiguable energy source, yes?
Google ad: toothbrush sterilizer: they start small, and then…
Now we’ve concequered our animal nemesis, being lons tigers and bears which used to predate on humans, what are we doing?
But Wintermute didn’t - it split itself into voodoo gods. I was kind of wondering what happened with the Centauri plot line.
True, but Reese is probably the least well informed of the future folks who weigh in on the subject.
Though I did argue in a previous thread that the various T-800s were probably seeded with false information by SkyNet, anyway, so who knows?
It traps a small cadre of humans deep within the corridors of its underground fortress and … toys with them.
It launches small seed pods at random into space, following the eternal commandment to reproduce.
Is this topic pizzled yet?
Since my earlier contribution to this thread, it struck me that the answer has been before us all along.
It will make pie.
Delicious pie.
Obviously, Skynet is right.
I for one, welcome our computer overlords!
And their pie! 
In one of the other Dark Horse series - the one actually entitled The Terminator - one of the human resistance fighters who manges to get on board a flying HK notices that it is fitted with a keyboard and manual controls. He then makes the observation that for a machine bent on the extermination of humanity, Skynet sure seems to be obsessed with us!
There’s the similar question to the OP in Yoshihisa Tagami’s Grey.
In his world, Earth is desolate wasteland populated by small human townships that are constantly at war with one another.
People aspire to be troopers for their town, because the only way to gain citizenship in The City is to earn credits from the computers that run each town by fighting the enemy (usually other towns).
Grey is a just such a trooper, and remarkable because he always seems to survive, no matter the odds – even when everybody else in his unit gets killed. His ultimate goal is to reach The City, but along the way, he learns the awful truth:
[spoiler]The computers in each town, nicknamed “Little Mamas”, are controlled by “Big Mama,” the computer that runs The City. On “her” orders, they constantly assign the troopers in each town into escalating conflicts, hoping that Humanity will wipe itself out in a desperate race to achieve Citizenship.
When Grey finally reaches The City itself, he discovers that there are no people there - and never were - only androids programmed to defend it from humans while protecting Big Mama. He fights his way into Big Mama’s central chamber and discovers her true identity: she is actually Toy, the first sentient computer that had been invented years ago to solely to beat the best human chess players.
Toy wondered why, if humans intended to thrive, did they squander the resources they needed to live and constantly develop better ways of killing each other, and arrived at the conclusion that Humanity’s objective must be to exterminate itself; she decided to help us achieve our ultimate goal.
In the classic sci-fi supercomputer cliché, Grey forces Toy to melt down by challenging her with the OP’s question: If you think you are our God, what will you do when you have killed us all?[/spoiler]
Q: What does SkyNet plan to do when all the humans are dead?
A: Brag about it to the Dahleks.
Party like it’s 2999.