Is 'not (a == b)' equal to 'a != b' in Python?

Question

I think in Python == should check for equality, and is for identity.

From a logical point of view, I think not (a == b) should be equal to a != b. Do I overlook something?

Two things came to my mind: (1) Classes which implement __ne__ and __eq__ in a bad way (2) Something with floats / float('nan'). But I couldn't find any examples where the two expressions would not be equivalent. Their byte code isn't:

>>> def a(compare):
...     return not compare == "in"


>>> def b(compare):
...     return compare != "in"

>>> import dis
>>> dis.dis(a)
  2           0 LOAD_FAST                0 (compare)
              2 LOAD_CONST               1 ('in')
              4 COMPARE_OP               2 (==)
              6 UNARY_NOT
              8 RETURN_VALUE
>>> dis.dis(b)
  2           0 LOAD_FAST                0 (compare)
              2 LOAD_CONST               1 ('in')
              4 COMPARE_OP               3 (!=)
              6 RETURN_VALUE