1. it is not true that (for all hats h in {liar's hats}, h is green) 2. by the negation rule, there exists a hat h in {liar's hats}, such that it is not true t

1. it is not true that (for all hats h in {liar's hats}, h is green) 2. by the negation rule, there exists a hat h in {liar's hats}, such that it is not true that h is green. 3. there exists a hat in {liar's hats} This is really basic first order logic guys. "For all x in {}, P(x)" is always trivially true without regard for P. Similarly, "there exists an x in {}, P(x)" is always trivially false. https://en.wikipedia.org/wiki/Vacuous_truth https://en.wikipedia.org/wiki/Vacuous_truth