Consider the following premises. There is at least one x_13 for which x_13 will take a plane if and only if x_13 will listen to a song. For all x_13, x_13 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, neither x_13 will listen to a song nor x_13 will cook.
 From the fact that there is at least one x_13 for which x_13 will take a plane if and only if x_13 will listen to a song we can infer that there is at least one x_13 for which if x_13 takes a plane, then x_13 is listening to a song via existential biconditional elimination. From the fact that there is at least one x_13 for which if x_13 takes a plane, then x_13 is listening to a song, and that for all x_13, x_13 will take a plane we can infer that there is at least one x_13 for which x_13 will listen to a song via existential modus ponens. Finally, from the fact that there is at least one x_13 for which x_13 will listen to a song we can infer that there is at least one x_13 for which x_13 will listen to a song or x_13 will cook via existential addition, which contradicts that For all x_13, neither x_13 will listen to a song nor x_13 will cook. Therefore, the answer is no.