I'm having a problem with ContainsAll and I wonder if anyone can explain it. I have list1, a list of lists, and list2, a simple list. For example:

list1={{1,3,7},{4,5,6},{2,3,7},{3,6,7},{3,5,6},{1,4,7}}

list2={3,7}

Thinking of these as sets, suppose I want to find all the sets in list1 that have list2 as a subset. This works:

Select[list1,ContainsAll[list2]]

{{1,3,7},{2,3,7},{3,6,7}}

Another way to get the answer is:

Select[list1,SubsetQ[#,list2]&]

{{1,3,7},{2,3,7},{3,6,7}}

Now suppose I want all sets in list1 for which list 2 is not a subset. This works:

Select[list1,!SubsetQ[#,list2]&]

{{4,5,6},{3,5,6},{1,4,7}}

But negating ContainsAll returns the empty set:

Select[list1,!ContainsAll[list2]]

{}

Any ideas? Is there something about the Attributes of ContainsAll that I'm missing? The documentation says ContainsAll is identical to SubsetQ. But there seems to be a subtle difference between the two.