I have an island in which two types of people live.
Many people visit my island. :-) You too came and met one man. He said that I am a liar. So he is a....
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Any inhabitant of that island
1) cannot tell the truth about themselves being a liar, nor
2) cannot tell a lie when they themselves are truth tellers.
Therefore, that man must have been neither of the two tribes and is actually only a visiting foreigner.