std::function fails to distinguish overloaded functions

I am trying to understand why std::function is not able to distinguish between overloaded functions.

#include <functional>

void add(int,int){}

class A {};

void add (A, A){}

int main(){
        std::function <void(int, int)> func = add;
}

In the code shown above, function can match only one of these function and yet it fails. Why is this so? I know I can work around this by using a lambda or a function pointer to the actual function and then storing the function pointer in function. But why does this fail? Isint the context clear on which function I want to be chosen? Please help me understand why this fails as I am not able to understand why template matching fails in this case.

The compiler error that I get on clang for this are as follows:

test.cpp:10:33: error: no viable conversion from '<overloaded function type>' to
      'std::function<void (int, int)>'
        std::function <void(int, int)> func = add;
                                       ^      ~~~
/Applications/http://ift.tt/1JGbDDI: note: 
      candidate constructor not viable: no overload of 'add' matching
      'std::__1::nullptr_t' for 1st argument
    _LIBCPP_INLINE_VISIBILITY function(nullptr_t) : __f_(0) {}
                              ^
/Applications/http://ift.tt/1Q0Rubg: note: 
      candidate constructor not viable: no overload of 'add' matching 'const
      std::__1::function<void (int, int)> &' for 1st argument
    function(const function&);
    ^
/Applications/http://ift.tt/1JGbAI3: note: 
      candidate template ignored: couldn't infer template argument '_Fp'
      function(_Fp,
      ^
1 error generated.