Two of the greatest minds in the universe battle it out, who wins?
Disclaimers: The doctor wont use time-travel to interfere with batman's timeline.
The battle takes place across the whole of Gotham city.
Batman's initial knowledge of The Doctor is limited to what is available on earth, likewise all The Doctor knows of Batman to begin with is public information.
Both can use their full array of gadgets to their own advantage.
Batman doesn't know how to operate time lord technology.
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Bollocks, Batman is an incarnation of The Doctor.