Consider the following premises. It is overcast if and only if it is cold. Elisabeth is fast if and only if it is cold. It is not overcast. For all x_7, x_7 is a sailor if and only if x_7 is fast. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is a sailor.
 From the fact that it is overcast if and only if it is cold, and that it is not overcast we can infer that it is not cold via biconditional elimination. From the fact that for all x_7, x_7 is a sailor if and only if x_7 is fast we can infer that Elisabeth is a sailor if and only if Elisabeth is fast via universal instantiation. From the fact that Elisabeth is fast if and only if it is cold, and that it is not cold we can infer that Elisabeth is not fast via biconditional elimination. Finally, from the fact that Elisabeth is a sailor if and only if Elisabeth is fast, and that Elisabeth is not fast we can infer that Elisabeth is not a sailor via biconditional elimination, which contradicts that Elisabeth is a sailor. Therefore, the answer is no.