He stays

Superman knew that her type only respected strength. To run would give her more power. Power she didn't need. Still she seemed strong, and was a more skilled fight. He wished he had practiced those fighting skills Batman had tried to teach him.

Knowing that he would most likely be out fought in a direct fight, he needed another way in. He decided on a course of actions. He would try to get her to show him her moves and actions. He would fight on the defensive for now. Hoping that she would show her weakness, sooner or later.

To start he fainted another punch...