Consider the following premises. For all x_4, x_4 will work if and only if x_4 is a writer. For all x_4, x_4 is a lawyer or x_4 is not a sailor. For all x_4, if x_4 works, then x_4 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which the fact that x_4 were a writer does not imply that x_4 is a lawyer.
 From the fact that for all x_4, x_4 will work if and only if x_4 is a writer we can infer that for all x_4, if x_4 were a writer, then x_4 is working via universal biconditional elimination. From the fact that for all x_4, x_4 is a lawyer or x_4 is not a sailor we can infer that for all x_4, if x_4 were a sailor, then x_4 is a lawyer via universal rewriting. From the fact that for all x_4, if x_4 works, then x_4 is a sailor, and that for all x_4, if x_4 were a sailor, then x_4 is a lawyer we can infer that for all x_4, if x_4 works, then x_4 is a lawyer via universal transitivity. Finally, from the fact that for all x_4, if x_4 were a writer, then x_4 is working, and that for all x_4, if x_4 works, then x_4 is a lawyer we can infer that for all x_4, if x_4 were a writer, then x_4 is a lawyer via universal transitivity, which contradicts that There is at least one x_4 for which the fact that x_4 were a writer does not imply that x_4 is a lawyer. Therefore, the answer is no.