enum class ambiguous inheritance

I am really strugling with an inheritance issue when using what should be strongly typed enums - however the enums seems to be ambigious when used through inheritance.

Im using g++ (GCC) 4.7.2

enum class AE { V1 };
enum class BE { V2 };
enum class CE { V3 };

struct A { void set(AE enumval) { } };
struct B { void set(BE enumval) { } };
struct C { void set(CE enumval) { } };
struct combined : A, B, C { };

struct all_in_one {
    void set(AE enumval) { }
    void set(BE enumval) { }
    void set(CE enumval) { }
};

void function()
{
    combined inherited_obj;

    // compile errors - ambigious funtion call
    inherited_obj.set(AE::V1);
    inherited_obj.set(BE::V2);
    inherited_obj.set(CE::V3);


    all_in_one simple_obj;

    // works like a charm...
    simple_obj.set(AE::V1);
    simple_obj.set(BE::V2);
    simple_obj.set(CE::V3);
}

I cant find any information why it shouldn't work this way. Am I missing something obvious.