Consider the following premises. For all x_10, x_10 will not climb a mountain or x_10 will make tea. There is at least one x_10 for which x_10 will play a game. For all x_10, x_10 will not go running. For all x_10, x_10 is a nurse if and only if x_10 will go running. For all x_10, x_10 will climb a mountain or x_10 is a nurse. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will play a game and x_10 will make tea.
 From the fact that for all x_10, x_10 is a nurse if and only if x_10 will go running, and that for all x_10, x_10 will not go running we can infer that for all x_10, x_10 is not a nurse via universal biconditional elimination. From the fact that for all x_10, x_10 will climb a mountain or x_10 is a nurse, and that for all x_10, x_10 will not climb a mountain or x_10 will make tea we can infer that for all x_10, x_10 is a nurse or x_10 will make tea via universal resolution. From the fact that for all x_10, x_10 is a nurse or x_10 will make tea, and that for all x_10, x_10 is not a nurse we can infer that for all x_10, x_10 will make tea via universal disjunctive syllogism. Finally, from the fact that there is at least one x_10 for which x_10 will play a game, and that for all x_10, x_10 will make tea we can infer that there is at least one x_10 for which x_10 will play a game and x_10 will make tea via existential conjunction. Therefore, the answer is yes.