I don't remember which Doctor and I don't remember whether I was a participant or merely an observer, but the gist of the dream was that The Doctor had done something impossible (as usual) to save someone/something/some planet, and in so doing placed the entire Universe in jeopardy. In the process, he ended up with two identical Tardises (Tardii?) and the only way he could make things right again was to learn whether space and time or space or time were indeed infinite.
To do this, he set each Tardis to explode if they discovered either one (or both) was finite and sent them on their way.
It turned out that time was infinite, but not space.