I don’t really wanna rock the boat here, but in the words of one of my professors, it “needs more math”.
I predict it will go somewhat like this: you specify the problem in terms of A implies B, etc; you find out there’s infinite recursion; you prove that the solution doesn’t exist. Reductio ad absurdum anyone?
The Dark Knight has an even better example—in the bank robbery scene, each subgroup excludes only one more member, until the only man left is… That’s enough of a spoiler I guess.