Consider the following premises. There is at least one x_6 for which x_6 is a sailor if and only if x_6 is poor. For all x_6, if x_6 were poor, then x_6 is not listening to a song. For all x_6, x_6 will not write a letter. For all x_6, x_6 will write a letter or x_6 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not a sailor.
 From the fact that for all x_6, x_6 will write a letter or x_6 will listen to a song, and that for all x_6, x_6 will not write a letter we can infer that for all x_6, x_6 will listen to a song via universal disjunctive syllogism. From the fact that for all x_6, if x_6 were poor, then x_6 is not listening to a song, and that for all x_6, x_6 will listen to a song we can infer that for all x_6, x_6 is not poor via universal modus tollens. Finally, from the fact that there is at least one x_6 for which x_6 is a sailor if and only if x_6 is poor, and that for all x_6, x_6 is not poor we can infer that there is at least one x_6 for which x_6 is not a sailor via existential biconditional elimination. Therefore, the answer is yes.