I was puzzling: "What is the shortest proof of $\exists x \forall y (P(x) \to P(y)) $?" (a variation of the drinkers paradox see Proof of Drinker paradox) given a certain set of inference rules and using natural deduction.

I managed to proof it in 23 lines, but I am not sure if this is the shortest possible proof.

That made me think maybe I could turn it into a little competition and offer say 200 reputation as reward for the shortest proof.

Would such a (competition) question be allowed?

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    $\begingroup$ The question should be asked on main with a bounty of 200 attached. $\endgroup$ – robjohn May 28 '14 at 18:36
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    $\begingroup$ Posted the question see math.stackexchange.com/questions/812949/… wil send a bounty soon, ps don't think that it is an easy competition. $\endgroup$ – Willemien May 28 '14 at 20:13
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    $\begingroup$ bounty set, let the game begin :) $\endgroup$ – Willemien May 31 '14 at 9:27
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    $\begingroup$ Sounds like code golf. Cue proofgolf.stackexchange.com $\endgroup$ – PyRulez Jun 6 '14 at 21:36

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