Consider the following premises. For all x_9, x_9 is not a sailor or x_9 is an office clerk. For all x_9, x_9 is not a janitor or x_9 will sleep. For all x_9, x_9 is a sailor or x_9 is a janitor. For all x_9, if x_9 sleeps, then x_9 is playing tennis. For all x_9, if x_9 plays tennis, then x_9 is an office clerk. For all x_9, if x_9 were an office clerk, then x_9 is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will not play tennis.
 From the fact that for all x_9, x_9 is a sailor or x_9 is a janitor, and that for all x_9, x_9 is not a sailor or x_9 is an office clerk we can infer that for all x_9, x_9 is a janitor or x_9 is an office clerk via universal resolution. From the fact that for all x_9, if x_9 plays tennis, then x_9 is an office clerk, and that for all x_9, if x_9 were an office clerk, then x_9 is playing tennis we can infer that for all x_9, x_9 will play tennis if and only if x_9 is an office clerk via universal biconditional introduction. From the fact that for all x_9, x_9 is a janitor or x_9 is an office clerk, and that for all x_9, x_9 is not a janitor or x_9 will sleep we can infer that for all x_9, x_9 is an office clerk or x_9 will sleep via universal resolution. From the fact that for all x_9, x_9 will play tennis if and only if x_9 is an office clerk we can infer that for all x_9, if x_9 were an office clerk, then x_9 is playing tennis via universal biconditional elimination. Finally, from the fact that for all x_9, if x_9 were an office clerk, then x_9 is playing tennis, that for all x_9, if x_9 sleeps, then x_9 is playing tennis, and that for all x_9, x_9 is an office clerk or x_9 will sleep we can infer that for all x_9, x_9 will play tennis via universal disjunction elimination, which contradicts that There is at least one x_9 for which x_9 will not play tennis. Therefore, the answer is no.