Odd interaction between rank-2 types and type families

Type inference does not work as expected, when a rank-2 type has a type-family constraint. Consider the following program:

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE Rank2Types   #-}

type family F a

f :: (forall s. (F s ~ Int) => s -> b) -> b
f _ = undefined

k :: s -> Char
k = undefined

example :: Bool
example = const True (f k)

It is rejected with the following error:

Couldn't match type ‘b0’ with ‘Char’
      ‘b0’ is untouchable
        inside the constraints (F s ~ Int)
        bound by a type expected by the context: (F s ~ Int) => s -> b0
        at bug.hs:13:23-25
    Expected type: s -> b0
      Actual type: s -> Char
    In the first argument of ‘f’, namely ‘k’
    In the second argument of ‘const’, namely ‘(f k)’

This is unexpected because the result of f should be the same as the result of its parameter, and we know the exact type of the parameter, namely Char.