Consider the following premises. There is at least one x_5 for which x_5 will go running. For all x_5, if x_5 takes a plane, then x_5 is making tea. For all x_5, x_5 will take a plane or x_5 will play tennis. For all x_5, x_5 will not make tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 will go running or x_5 will play tennis are not true.
 From the fact that for all x_5, if x_5 takes a plane, then x_5 is making tea, and that for all x_5, x_5 will not make tea we can infer that for all x_5, x_5 will not take a plane via universal modus tollens. From the fact that for all x_5, x_5 will take a plane or x_5 will play tennis, and that for all x_5, x_5 will not take a plane we can infer that for all x_5, x_5 will play tennis via universal disjunctive syllogism. Finally, from the fact that there is at least one x_5 for which x_5 will go running, and that for all x_5, x_5 will play tennis we can infer that there is at least one x_5 for which x_5 will go running and x_5 will play tennis via existential conjunction, which contradicts that For all x_5, either x_5 will go running or x_5 will play tennis are not true. Therefore, the answer is no.