Consider the following premises. There is at least one x_7 for which if x_7 drives a car, then x_7 is writing a letter. For all x_7, x_7 will take a plane. For all x_7, if x_7 writes a letter, then x_7 is not taking a plane. For all x_7, if x_7 were a sailor, then x_7 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is a sailor.
 From the fact that for all x_7, if x_7 writes a letter, then x_7 is not taking a plane, and that for all x_7, x_7 will take a plane we can infer that for all x_7, x_7 will not write a letter via universal modus tollens. From the fact that for all x_7, if x_7 were a sailor, then x_7 is driving a car, and that there is at least one x_7 for which if x_7 drives a car, then x_7 is writing a letter we can infer that there is at least one x_7 for which if x_7 were a sailor, then x_7 is writing a letter via existential transitivity. Finally, from the fact that there is at least one x_7 for which if x_7 were a sailor, then x_7 is writing a letter, and that for all x_7, x_7 will not write a letter we can infer that there is at least one x_7 for which x_7 is not a sailor via existential modus tollens, which contradicts that For all x_7, x_7 is a sailor. Therefore, the answer is no.