nick-peterss-imac:Desktop Nick$ python PartialDigest.py
List 1: [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 9, 9, 10, 11, 12, 15]
[0, 6, 9, 10, 11, 12, 15]
[0, 6, 9, 10, 11, 12, 15]
[0, 3, 4, 5, 6, 9, 15]
[0, 3, 4, 5, 6, 9, 15]
List 2: [2, 2, 3, 3, 4, 5, 6, 7, 8, 10]
[0, 3, 6, 8, 10]
[0, 2, 4, 7, 10]


Note that with the first list, we see the same result twice.
Turning on debug mode we see the following (each line gives us the value of the L and X list for each recursive call):

List 1: [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 9, 9, 10, 11, 12, 15]
L: [1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 9, 9, 10, 11, 12] X: [0, 15]
L: [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 9, 9, 10, 11] X: [0, 12, 15]
L: [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 6, 9, 9, 10] X: [0, 11, 12, 15]
L: [1, 2, 3, 3, 4, 5, 6, 6, 6, 9, 9] X: [0, 10, 11, 12, 15]
L: [3, 4, 5, 6, 6, 9] X: [0, 9, 10, 11, 12, 15]
[0, 6, 9, 10, 11, 12, 15]
L: [1, 2, 3, 3, 6, 9] X: [0, 6, 10, 11, 12, 15]
[0, 6, 9, 10, 11, 12, 15]
L: [1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 9, 9, 10, 11] X: [0, 3, 15]
L: [1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 6, 9, 9, 10] X: [0, 3, 4, 15]
L: [1, 2, 3, 3, 4, 5, 6, 6, 6, 9, 9] X: [0, 3, 4, 5, 15]
L: [1, 2, 3, 3, 6, 9] X: [0, 3, 4, 5, 9, 15]
[0, 3, 4, 5, 6, 9, 15]
L: [3, 4, 5, 6, 6, 9] X: [0, 3, 4, 5, 6, 15]
[0, 3, 4, 5, 6, 9, 15]


We can now see that elements are added in different order, which makes it look like a new set.