Consider the following premises. There is at least one x_13 for which x_13 will listen to a song or x_13 is a poet. For all x_13, x_13 is not bored. For all x_13, x_13 will listen to a song if and only if x_13 is bored. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, neither x_13 is a poet nor x_13 is a musician.
 From the fact that for all x_13, x_13 will listen to a song if and only if x_13 is bored, and that for all x_13, x_13 is not bored we can infer that for all x_13, x_13 will not listen to a song via universal biconditional elimination. From the fact that there is at least one x_13 for which x_13 will listen to a song or x_13 is a poet, and that for all x_13, x_13 will not listen to a song we can infer that there is at least one x_13 for which x_13 is a poet via existential disjunctive syllogism. Finally, from the fact that there is at least one x_13 for which x_13 is a poet we can infer that there is at least one x_13 for which x_13 is a poet or x_13 is a musician via existential addition, which contradicts that For all x_13, neither x_13 is a poet nor x_13 is a musician. Therefore, the answer is no.