Consider the following premises. For all x_13, x_13 is not an office clerk. For all x_13, x_13 is a musician. There is at least one x_13 for which x_13 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_13 for which x_13 will play a game.
 From the fact that there is at least one x_13 for which x_13 is an office clerk, and that for all x_13, x_13 is a musician we can infer that there is at least one x_13 for which x_13 is an office clerk and x_13 is a musician via existential conjunction. From the fact that there is at least one x_13 for which x_13 is an office clerk and x_13 is a musician we can infer that there is at least one x_13 for which x_13 is an office clerk via existential simplification. From the fact that there is at least one x_13 for which x_13 is an office clerk we can infer that there is at least one x_13 for which x_13 is an office clerk or x_13 will play a game via existential addition. Finally, from the fact that there is at least one x_13 for which x_13 is an office clerk or x_13 will play a game, and that for all x_13, x_13 is not an office clerk we can infer that there is at least one x_13 for which x_13 will play a game via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.