That doesn't make sense. If we use fission, why bother with the oil?
The real point here is not when we run out of oil, but rather when it becomes too inconvenient -- too costly in other words. Even with new finds, oil is becoming a more and more inconvenient source of energy. The reason it remains attractive is because of the infrastructure surrounding it's production, transport and use.
If you don't care about the environment, there are even easier solutions; processes for making gas out of coal have been around since before world war 2.