Don't worry, I expect we'll have wiped ourselves out with an all-out global thermonuclear war and concurrent release of doomsday biological / chemical agents long before any of that happens.
In spite of which, life itself will go on. In the glacial, radioactive wasteland that ensue, deinococcus radiodurans will almost certainly live on along with a range of other unusually hardy organisms. After the dirt laden skies eventually clear, photosynthesis will pick up again. At least in those organisms that can withstand the new UV rich daylight. And in the hundreds of millions of years it takes sapient life to develop, you, I and the rest of the complex life that once inhabited the planet should have formed a nice new hydrocarbon resource for them to wipe themselves out over too...
On the last day nothing will survive.
