Consider the following premises. There is at least one x_10 for which if x_10 takes a plane, then x_10 is working. For all x_10, x_10 will listen to a song. For all x_10, if x_10 listens to a song, then x_10 is playing tennis. For all x_10, if x_10 writes a letter, then x_10 is working. For all x_10, x_10 will write a letter or x_10 will take a plane. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, either x_10 will work or x_10 will play tennis are not true.
 From the fact that for all x_10, if x_10 listens to a song, then x_10 is playing tennis, and that for all x_10, x_10 will listen to a song we can infer that for all x_10, x_10 will play tennis via universal modus ponens. From the fact that for all x_10, if x_10 writes a letter, then x_10 is working, that there is at least one x_10 for which if x_10 takes a plane, then x_10 is working, and that for all x_10, x_10 will write a letter or x_10 will take a plane we can infer that there is at least one x_10 for which x_10 will work via existential disjunction elimination. Finally, from the fact that there is at least one x_10 for which x_10 will work, and that for all x_10, x_10 will play tennis we can infer that there is at least one x_10 for which x_10 will work and x_10 will play tennis via existential conjunction, which contradicts that For all x_10, either x_10 will work or x_10 will play tennis are not true. Therefore, the answer is no.