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fastern pattern test

please help a beginner.
I need to clear every list in which there are two sublist with a
property (in this case,equals and with length >= 2) ,not overlapping.
Is there a faster way, perhaps using PatternTest (?).
Thanx in Advance

mm[{___, b1__, ___, b1__, ___}] := {} /; Length[{b1}] >= 2
mm[l_] := l
pool = Strings[{0, 1}, 6];
s1 = Rest[Union[Map[mm, pool]]]

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