Consider the following premises. For all x, x will sleep or x will not make tea. There is at least one x for which if x sleeps, then x is making tea. For all x, if x makes tea, then x is sleeping. Can we infer the following from them? For all x, if is not true that x will make tea if and only if x will sleep.
 From the fact that for all x, if x makes tea, then x is sleeping, and that there is at least one x for which if x sleeps, then x is making tea we can infer that there is at least one x for which x will make tea if and only if x will sleep. From the fact that there is at least one x for which x will make tea if and only if x will sleep we can infer that there is at least one x for which if x sleeps, then x is making tea. From the fact that for all x, x will sleep or x will not make tea we can infer that for all x, if x makes tea, then x is sleeping. Finally, from the fact that for all x, if x makes tea, then x is sleeping, and that there is at least one x for which if x sleeps, then x is making tea we can infer that there is at least one x for which x will make tea if and only if x will sleep, which contradicts that For all x, if is not true that x will make tea if and only if x will sleep. Therefore, the answer is no.