Imagine that with one out and all bases loaded, the batter hits a fly ball that is caught out by the left outfielder. However, due to negligence, only the runner on second base remembers to tag up. The ball is then thrown to third base, beating the runner from 2nd.
With the batter being caught out, there are then two outs. However, it appears that the throw to third simultaneously doubles off the runner from third base and forces out the runner from second base. Since there can only be three outs per inning, one of the outs would not "count".
My question is: which would be the official third out?