Consider the following premises. For all x_14, x_14 will play squash and x_14 will make tea. There is at least one x_14 for which x_14 will play a game and x_14 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will play squash.
 From the fact that for all x_14, x_14 will play squash and x_14 will make tea we can infer that for all x_14, x_14 will play squash via universal simplification. From the fact that there is at least one x_14 for which x_14 will play a game and x_14 is an artist we can infer that there is at least one x_14 for which x_14 will play a game via existential simplification. From the fact that there is at least one x_14 for which x_14 will play a game, and that for all x_14, x_14 will play squash we can infer that there is at least one x_14 for which x_14 will play a game and x_14 will play squash via existential conjunction. Finally, from the fact that there is at least one x_14 for which x_14 will play a game and x_14 will play squash we can infer that there is at least one x_14 for which x_14 will play squash via existential simplification. Therefore, the answer is yes.