Consider the following premises. For all x_14, x_14 will not play tennis. For all x_14, if x_14 were a poet, then x_14 is listening to a song. There is at least one x_14 for which x_14 will play tennis or x_14 will listen to a song. For all x_14, if x_14 listens to a song, then x_14 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 is not a poet.
 From the fact that for all x_14, if x_14 listens to a song, then x_14 is a poet, and that for all x_14, if x_14 were a poet, then x_14 is listening to a song we can infer that for all x_14, x_14 will listen to a song if and only if x_14 is a poet via universal biconditional introduction. From the fact that there is at least one x_14 for which x_14 will play tennis or x_14 will listen to a song, and that for all x_14, x_14 will not play tennis we can infer that there is at least one x_14 for which x_14 will listen to a song via existential disjunctive syllogism. From the fact that for all x_14, x_14 will listen to a song if and only if x_14 is a poet we can infer that for all x_14, if x_14 listens to a song, then x_14 is a poet via universal biconditional elimination. Finally, from the fact that for all x_14, if x_14 listens to a song, then x_14 is a poet, and that there is at least one x_14 for which x_14 will listen to a song we can infer that there is at least one x_14 for which x_14 is a poet via existential modus ponens, which contradicts that For all x_14, x_14 is not a poet. Therefore, the answer is no.