Consider the following premises. For all x_11, if x_11 were a soldier, then x_11 is listening to a song. For all x_11, x_11 will listen to a song or x_11 is not a soldier. There is at least one x_11 for which if x_11 listens to a song, then x_11 is a soldier. Can we infer the following from them? For all x_11, if is not true that x_11 will listen to a song if and only if x_11 is a soldier.
 From the fact that for all x_11, if x_11 were a soldier, then x_11 is listening to a song, and that there is at least one x_11 for which if x_11 listens to a song, then x_11 is a soldier we can infer that there is at least one x_11 for which x_11 is a soldier if and only if x_11 will listen to a song. From the fact that for all x_11, x_11 will listen to a song or x_11 is not a soldier we can infer that for all x_11, if x_11 were a soldier, then x_11 is listening to a song. From the fact that there is at least one x_11 for which x_11 is a soldier if and only if x_11 will listen to a song we can infer that there is at least one x_11 for which if x_11 listens to a song, then x_11 is a soldier. Finally, from the fact that there is at least one x_11 for which if x_11 listens to a song, then x_11 is a soldier, and that for all x_11, if x_11 were a soldier, then x_11 is listening to a song we can infer that there is at least one x_11 for which x_11 will listen to a song if and only if x_11 is a soldier, which contradicts that For all x_11, if is not true that x_11 will listen to a song if and only if x_11 is a soldier. Therefore, the answer is no.