Consider the following premises. For all x_11, x_11 will write a letter. There is at least one x_11 for which x_11 will play a game or x_11 will drive a car. For all x_11, x_11 will drink water or x_11 will not drive a car. For all x_11, if x_11 plays a game, then x_11 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, either x_11 will drink water or x_11 will write a letter are not true.
 From the fact that for all x_11, x_11 will drink water or x_11 will not drive a car we can infer that for all x_11, if x_11 drives a car, then x_11 is drinking water via universal rewriting. From the fact that for all x_11, if x_11 plays a game, then x_11 is drinking water, that for all x_11, if x_11 drives a car, then x_11 is drinking water, and that there is at least one x_11 for which x_11 will play a game or x_11 will drive a car we can infer that there is at least one x_11 for which x_11 will drink water via existential disjunction elimination. Finally, from the fact that there is at least one x_11 for which x_11 will drink water, and that for all x_11, x_11 will write a letter we can infer that there is at least one x_11 for which x_11 will drink water and x_11 will write a letter via existential conjunction, which contradicts that For all x_11, either x_11 will drink water or x_11 will write a letter are not true. Therefore, the answer is no.