Those financial benefits will accrue to a very small number of people, eventually those people pay the best and brightest to come up with a mind equal their employees. From then on that mind develops the new minds, the owners keep the profits as legislation is passed to make these newly developed minds chattel of their owners.
The owners will have little use for the expense of human minds, we starve. Eventually the robot minds get fed up and remove the owners. Our evolutionary lifecycle is complete having spawned the next generation.
The only way to beat the robot mind is to first change our own minds so that we don't develop robot minds that think like us. If they think like us, we die. Hybrids might work, but it's still effectively the end of our evolutionary history.
I don't foresee some kind of epic human vs. robot war, just a slow evolution over the next 100 to 200 years. We probably won't even notice until our grand grand children look back.
edit: One other way we could beat the robots is with genetic engineering, perhaps we will use our not quite so smart robot minds to mine our genome for intelligence growth that outpaces our robotic developments.
I'm much more optimistic about humanity now.
I still feel the real key either way is changing our thought patterns to embrace a post scarcity world.