How to remove duplicates in list of objects without __hash__

Question

I have a list of custom objects from which I want to remove the duplicates. Normally, you would do this by defining both __eq__ and __hash__ for your objects and then taking the set of the list of objects. I have defined __eq__, but I can't figure out a good way to implement __hash__ such that it returns the same value for objects that are equal.

More specifically, I have a class that is derived from the Tree class from the ete3 toolkit. I have defined two objects to be equal if their Robinson-Foulds distance is zero.

from ete3 import Tree

class MyTree(Tree):

    def __init__(self, *args, **kwargs):
        super(MyTree, self).__init__(*args, **kwargs)

    def __eq__(self, other):
        rf = self.robinson_foulds(other, unrooted_trees=True)
        return not bool(rf[0])

newicks = ['((D, C), (A, B),(E));',
           '((D, B), (A, C),(E));',
           '((D, A), (B, C),(E));',
           '((C, D), (A, B),(E));',
           '((C, B), (A, D),(E));',
           '((C, A), (B, D),(E));',
           '((B, D), (A, C),(E));',
           '((B, C), (A, D),(E));',
           '((B, A), (C, D),(E));',
           '((A, D), (B, C),(E));',
           '((A, C), (B, D),(E));',
           '((A, B), (C, D),(E));']

trees = [MyTree(newick) for newick in newicks]

print len(trees)       # 12
print len(set(trees))  # also 12, not what I want!

Both print len(trees) and print len(set(trees)) return 12, but that is not what I want, because several of the objects are equal to each other:

from itertools import product
for t1, t2 in product(newicks, repeat=2):
    if t1 != t2:
        mt1 = MyTree(t1)
        mt2 = MyTree(t2)
        if mt1 == mt2:
            print t1, '==', t2

which returns:

((D, C), (A, B),(E)); == ((C, D), (A, B),(E));
((D, C), (A, B),(E)); == ((B, A), (C, D),(E));
((D, C), (A, B),(E)); == ((A, B), (C, D),(E));
((D, B), (A, C),(E)); == ((C, A), (B, D),(E));
((D, B), (A, C),(E)); == ((B, D), (A, C),(E));
((D, B), (A, C),(E)); == ((A, C), (B, D),(E));
((D, A), (B, C),(E)); == ((C, B), (A, D),(E));
((D, A), (B, C),(E)); == ((B, C), (A, D),(E));
((D, A), (B, C),(E)); == ((A, D), (B, C),(E));
((C, D), (A, B),(E)); == ((D, C), (A, B),(E));
((C, D), (A, B),(E)); == ((B, A), (C, D),(E));
((C, D), (A, B),(E)); == ((A, B), (C, D),(E));
((C, B), (A, D),(E)); == ((D, A), (B, C),(E));
((C, B), (A, D),(E)); == ((B, C), (A, D),(E));
((C, B), (A, D),(E)); == ((A, D), (B, C),(E));
((C, A), (B, D),(E)); == ((D, B), (A, C),(E));
((C, A), (B, D),(E)); == ((B, D), (A, C),(E));
((C, A), (B, D),(E)); == ((A, C), (B, D),(E));
((B, D), (A, C),(E)); == ((D, B), (A, C),(E));
((B, D), (A, C),(E)); == ((C, A), (B, D),(E));
((B, D), (A, C),(E)); == ((A, C), (B, D),(E));
((B, C), (A, D),(E)); == ((D, A), (B, C),(E));
((B, C), (A, D),(E)); == ((C, B), (A, D),(E));
((B, C), (A, D),(E)); == ((A, D), (B, C),(E));
((B, A), (C, D),(E)); == ((D, C), (A, B),(E));
((B, A), (C, D),(E)); == ((C, D), (A, B),(E));
((B, A), (C, D),(E)); == ((A, B), (C, D),(E));
((A, D), (B, C),(E)); == ((D, A), (B, C),(E));
((A, D), (B, C),(E)); == ((C, B), (A, D),(E));
((A, D), (B, C),(E)); == ((B, C), (A, D),(E));
((A, C), (B, D),(E)); == ((D, B), (A, C),(E));
((A, C), (B, D),(E)); == ((C, A), (B, D),(E));
((A, C), (B, D),(E)); == ((B, D), (A, C),(E));
((A, B), (C, D),(E)); == ((D, C), (A, B),(E));
((A, B), (C, D),(E)); == ((C, D), (A, B),(E));
((A, B), (C, D),(E)); == ((B, A), (C, D),(E));

So my question is either:

• What would be a good __hash__ implementation for my case so that set(trees) works?
• Or how do I remove objects that are equal from my list without having __hash__ defined?