Consider the following premises. For all x_11, x_11 will climb a mountain or x_11 will play a game. For all x_11, if x_11 were a taxi driver, then x_11 is playing a game. For all x_11, x_11 will not climb a mountain or x_11 will make tea. There is at least one x_11 for which x_11 is not a taxi driver. For all x_11, if x_11 plays a game, then x_11 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 will not make tea.
 From the fact that for all x_11, x_11 will climb a mountain or x_11 will play a game, and that for all x_11, x_11 will not climb a mountain or x_11 will make tea we can infer that for all x_11, x_11 will play a game or x_11 will make tea via universal resolution. From the fact that for all x_11, if x_11 were a taxi driver, then x_11 is playing a game, and that for all x_11, if x_11 plays a game, then x_11 is a taxi driver we can infer that for all x_11, x_11 is a taxi driver if and only if x_11 will play a game via universal biconditional introduction. From the fact that for all x_11, x_11 is a taxi driver if and only if x_11 will play a game, and that there is at least one x_11 for which x_11 is not a taxi driver we can infer that there is at least one x_11 for which x_11 will not play a game via existential biconditional elimination. Finally, from the fact that for all x_11, x_11 will play a game or x_11 will make tea, and that there is at least one x_11 for which x_11 will not play a game we can infer that there is at least one x_11 for which x_11 will make tea via existential disjunctive syllogism, which contradicts that For all x_11, x_11 will not make tea. Therefore, the answer is no.