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