Consider the following premises. For all x_13, x_13 is a soldier or x_13 is an office clerk. For all x_13, if x_13 were a soldier, then x_13 is listening to a song. For all x_13, if x_13 were an office clerk, then x_13 is listening to a song. There is at least one x_13 for which if x_13 were an astronaut, then x_13 is curious. For all x_13, x_13 is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, either x_13 is curious or x_13 will listen to a song are not true.
 From the fact that for all x_13, if x_13 were a soldier, then x_13 is listening to a song, that for all x_13, if x_13 were an office clerk, then x_13 is listening to a song, and that for all x_13, x_13 is a soldier or x_13 is an office clerk we can infer that for all x_13, x_13 will listen to a song via universal disjunction elimination. From the fact that there is at least one x_13 for which if x_13 were an astronaut, then x_13 is curious, and that for all x_13, x_13 is an astronaut we can infer that there is at least one x_13 for which x_13 is curious via existential modus ponens. Finally, from the fact that there is at least one x_13 for which x_13 is curious, and that for all x_13, x_13 will listen to a song we can infer that there is at least one x_13 for which x_13 is curious and x_13 will listen to a song via existential conjunction, which contradicts that For all x_13, either x_13 is curious or x_13 will listen to a song are not true. Therefore, the answer is no.