Consider the following premises. For all x_10, if x_10 were a taxi driver, then x_10 is a nurse. For all x_10, x_10 is a nurse if and only if x_10 is a taxi driver. For all x_10, x_10 is a taxi driver. For all x_10, if x_10 listens to a song, then x_10 is a nurse. Can we infer the following from them? There is at least one x_10 for which x_10 is not a nurse.
 From the fact that for all x_10, x_10 is a nurse if and only if x_10 is a taxi driver we can infer that for all x_10, if x_10 were a nurse, then x_10 is a taxi driver. From the fact that for all x_10, x_10 is a taxi driver we can infer that for all x_10, x_10 is a taxi driver or x_10 will listen to a song. From the fact that for all x_10, if x_10 were a nurse, then x_10 is a taxi driver, and that for all x_10, if x_10 were a taxi driver, then x_10 is a nurse we can infer that for all x_10, x_10 is a nurse if and only if x_10 is a taxi driver. From the fact that for all x_10, x_10 is a nurse if and only if x_10 is a taxi driver we can infer that for all x_10, if x_10 were a taxi driver, then x_10 is a nurse. Finally, from the fact that for all x_10, if x_10 were a taxi driver, then x_10 is a nurse, that for all x_10, if x_10 listens to a song, then x_10 is a nurse, and that for all x_10, x_10 is a taxi driver or x_10 will listen to a song we can infer that for all x_10, x_10 is a nurse, which contradicts that There is at least one x_10 for which x_10 is not a nurse. Therefore, the answer is no.