Human ingenuity!
How many ways to steal an egg - first, confine the chickens and convince them to keep laying eggs, day after day, with no thought of their little ones at their captor's dinner tables. Oh what a dish.

As for the AI, what means will they devise -- self-sustaining nuclear fission, solar, something we haven't thought of -- to keep themselves "alive" after they exterminate human life?

Without humans harvesting fossil fuels or whatever fuels the machines that allow Artifical Intelligence to flourish - how will AI flourish? Can it survive death of the body (machine), just as we hope our souls survive death of the body (our brains with all the circuitry and neurons firing) -

Will the AIs turn the tables and make us their egg-laying hens?