Templates, multiple inheritance, and ambiguous overloads

[Lindley]

Let's say I have a templated base class:

template <typename Input>
class Consumer
{
public:
    void consume(Input input)
    {
        // do something
    }
};

Now, I have a class which derives from this twice (A and B are unrelated, but otherwise unimportant classes):

class A;
class B;

class Derived: public Consumer<A>, public Consumer<B>
{
};

Now, elsewhere in the code I do this:

{
    A myA;
    Derived myDerived;
    myDerived.consume(myA);
}

This looks like it should be simple enough, but g++ 4.8.1 is giving me a "request for member is ambiguous" error.

Any idea why?