Consider the following premises. For all x, x is bored if and only if x is happy. For all x, x is not bored. Can we infer the following from them? There is at least one x for which x is happy.
 From the fact that for all x, x is bored if and only if x is happy we can infer that for all x, if x were happy, then x is bored. Finally, from the fact that for all x, if x were happy, then x is bored, and that for all x, x is not bored we can infer that for all x, x is not happy, which contradicts that There is at least one x for which x is happy. Therefore, the answer is no.