Consider the following premises. For all y, y is bored or y will not make tea. Joseph is not making tea. For all y, if y were bored, then y is making tea. Can we infer the following from them? If we can, name the inference rule being used: Joseph is bored.
 From the fact that for all y, y is bored or y will not make tea we can infer that for all y, if y makes tea, then y is bored via universal rewriting. From the fact that for all y, if y were bored, then y is making tea, and that for all y, if y makes tea, then y is bored we can infer that for all y, y is bored if and only if y will make tea via universal biconditional introduction. From the fact that for all y, y is bored if and only if y will make tea we can infer that Joseph is bored if and only if Joseph is making tea via universal instantiation. Finally, from the fact that Joseph is bored if and only if Joseph is making tea, and that Joseph is not making tea we can infer that Joseph is not bored via biconditional elimination, which contradicts that Joseph is bored. Therefore, the answer is no.