Consider the following premises. For all x, if x were a carpenter, then x is listening to a song. For all x, x will not listen to a song. There is at least one x for which if x listens to a song, then x is a carpenter. For all x, if x were an astronaut, then x is a carpenter. Can we infer the following from them? For all x, x is an astronaut.
 From the fact that for all x, if x were a carpenter, then x is listening to a song, and that there is at least one x for which if x listens to a song, then x is a carpenter we can infer that there is at least one x for which x is a carpenter if and only if x will listen to a song. From the fact that there is at least one x for which x is a carpenter if and only if x will listen to a song, and that for all x, x will not listen to a song we can infer that there is at least one x for which x is not a carpenter. Finally, from the fact that for all x, if x were an astronaut, then x is a carpenter, and that there is at least one x for which x is not a carpenter 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.