Consider the following premises. For all x, if x were bored, then x is drinking water. For all x, if x works, then x is drinking water. For all x, if x works, then x is bored. For all x, if x drinks water, then x is working. Can we infer the following from them? There is at least one x for which if is not true that x will work if and only if x is bored.
 From the fact that for all x, if x drinks water, then x is working, and that for all x, if x works, then x is drinking water we can infer that for all x, x will drink water if and only if x will work. From the fact that for all x, x will drink water if and only if x will work we can infer that for all x, if x drinks water, then x is working. From the fact that for all x, if x were bored, then x is drinking water, and that for all x, if x drinks water, then x is working we can infer that for all x, if x were bored, then x is working. Finally, from the fact that for all x, if x works, then x is bored, and that for all x, if x were bored, then x is working we can infer that for all x, x will work if and only if x is bored, which contradicts that There is at least one x for which if is not true that x will work if and only if x is bored. Therefore, the answer is no.