Actually the proof has created a lot of confusion among some contestants. 
Specifically in the first Lemma, the statement:

"x't = t for t ≤ N - 1. This is true by the inductive hypothesis."

Includes the case x1, which doesn't make sense (it is impossible to have 
only 1 element out of order). Although the proof is correct, it should be 
made explicit that p1=0, so p1*x1 never appears in any formula and we can 
perform the induction from n(A) = 2, without ever needing to consider the 
case n(A)=1.

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