Consider the following premises. Barbara is fast or it is sunny. For all y, if y were an astronaut, then y is fast. If it is sunny, then Barbara is an astronaut. For all y, if y were fast, then y is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not an astronaut.
 From the fact that for all y, if y were an astronaut, then y is fast, and that for all y, if y were fast, then y is an astronaut we can infer that for all y, y is an astronaut if and only if y is fast via universal biconditional introduction. From the fact that for all y, y is an astronaut if and only if y is fast we can infer that for all y, if y were fast, then y is an astronaut via universal biconditional elimination. From the fact that for all y, if y were fast, then y is an astronaut we can infer that if Barbara were fast, then Barbara is an astronaut via universal instantiation. Finally, from the fact that if Barbara were fast, then Barbara is an astronaut, that if it is sunny, then Barbara is an astronaut, and that Barbara is fast or it is sunny we can infer that Barbara is an astronaut via disjunction elimination, which contradicts that Barbara is not an astronaut. Therefore, the answer is no.