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