War between America/Russia results in nuclear exchange. Fallout shelters were constructed to house politicians, controlled by AIs in a network. No one arrives in one shelter, and the AI loses contact with other networked AIs. No humans around, but mother cat has hidden in shelter, which AI adopts as replacement for humans, slowly training to stand upright etc. before eventually driving them back into the world. (Very much an 'Adam and Eve' type plot - even including being driven from 'Eden' by a robot with a flamethrower (I think)).

I know I read it at some stage - a short story within a collection I believe. Surely I can't be making it up?!? Any help appreciated!