Consider the following premises. For all x, if x cooks, then x is not listening to a song. There is at least one x for which x will listen to a song. For all x, if x cooks, then x is an astronaut. For all x, if x were an astronaut, then x is cooking. Can we infer the following from them? For all x, x is an astronaut.
 From the fact that for all x, if x cooks, then x is not listening to a song, and that there is at least one x for which x will listen to a song we can infer that there is at least one x for which x will not cook. From the fact that for all x, if x cooks, then x is an astronaut, and that for all x, if x were an astronaut, then x is cooking we can infer that for all x, x will cook if and only if x is an astronaut. From the fact that for all x, x will cook if and only if x is an astronaut we can infer that for all x, if x were an astronaut, then x is cooking. Finally, from the fact that for all x, if x were an astronaut, then x is cooking, and that there is at least one x for which x will not cook we can infer that there is at least one x for which x is not an astronaut, which contradicts that For all x, x is an astronaut. Therefore, the answer is no.