Consider the following list

list={0 < x < 1/12, 0 < x < 1/4}

I wish to find the intersection of the two ranges of x and check if the result is an element of the above list, i.e.

In:=Simplify[And @@ list]
out:=0<x<1/12

Now I want to check if the above range of x belongs to the list.

in:=MemberQ[list, Simplify[And @@ list]]
out:= False

But It is clear that such a range is an element of list. This is not giving the expected result because the Heads are not matching.

in:=FullForm[Simplify[And @@ l]]
out:=Inequality[0,Less,x,Less,Rational[1,12]]

Whereas,

in:=FullForm[0 < x < 1/12]
out:=Less[0,x,Rational[1,12]]

How to resolve this?