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There cannot be such a family because of self-reference. It is similar to the Russell paradox (named after Bertrand Russell).

As soon as you have a fact family with only two facts, you have added a third fact. The third fact is that is that the fact family had only two facts. That then makes it a family with three facts. Which means it is no longer a fact family with only two facts. So the third fact is no longer correct. And so it does not have three facts. Which means it has only two facts and you will keep looping round and round forever!

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Q: What is a fact family with only facts?
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