Consider the following premises. For all x, if x makes tea, then x is taking a plane. For all x, x is not curious. There is at least one x for which if x sleeps, then x is making tea. For all x, if x takes a plane, then x is sleeping. For all x, if x were curious, then x is taking a plane. For all x, if x takes a plane, then x is curious. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will not make tea.
 From the fact that for all x, if x were curious, then x is taking a plane, and that for all x, if x takes a plane, then x is curious we can infer that for all x, x is curious if and only if x will take a plane via universal biconditional introduction. From the fact that for all x, if x takes a plane, 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 if x takes a plane, then x is making tea via existential transitivity. From the fact that for all x, x is curious if and only if x will take a plane, and that for all x, x is not curious we can infer that for all x, x will not take a plane via universal biconditional elimination. From the fact that there is at least one x for which if x takes a plane, then x is making tea, and that for all x, if x makes tea, then x is taking a plane we can infer that there is at least one x for which x will take a plane if and only if x will make tea via existential biconditional introduction. Finally, from the fact that there is at least one x for which x will take a plane if and only if x will make tea, and that for all x, x will not take a plane we can infer that there is at least one x for which x will not make tea via existential biconditional elimination. Therefore, the answer is yes.