Consider the following premises. For all x_6, x_6 will not play tennis or x_6 is a scientist. For all x_6, if x_6 were sad, then x_6 is playing tennis. There is at least one x_6 for which x_6 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will play a game or x_6 is a scientist.
 From the fact that for all x_6, if x_6 were sad, then x_6 is playing tennis, and that there is at least one x_6 for which x_6 is sad we can infer that there is at least one x_6 for which x_6 will play tennis via existential modus ponens. From the fact that there is at least one x_6 for which x_6 will play tennis we can infer that there is at least one x_6 for which x_6 will play tennis or x_6 will play a game via existential addition. Finally, from the fact that there is at least one x_6 for which x_6 will play tennis or x_6 will play a game, and that for all x_6, x_6 will not play tennis or x_6 is a scientist we can infer that there is at least one x_6 for which x_6 will play a game or x_6 is a scientist via existential resolution. Therefore, the answer is yes.