Consider the following premises. For all y_1, y_1 is a sailor or y_1 will not sleep. For all y_1, y_1 will sleep or y_1 is not a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_1 for which if is not true that y_1 is a sailor if and only if y_1 will sleep.
 From the fact that for all y_1, y_1 will sleep or y_1 is not a sailor we can infer that for all y_1, if y_1 were a sailor, then y_1 is sleeping via universal rewriting. From the fact that for all y_1, y_1 is a sailor or y_1 will not sleep we can infer that for all y_1, if y_1 sleeps, then y_1 is a sailor via universal rewriting. Finally, from the fact that for all y_1, if y_1 were a sailor, then y_1 is sleeping, and that for all y_1, if y_1 sleeps, then y_1 is a sailor we can infer that for all y_1, y_1 is a sailor if and only if y_1 will sleep via universal biconditional introduction, which contradicts that There is at least one y_1 for which if is not true that y_1 is a sailor if and only if y_1 will sleep. Therefore, the answer is no.