Consider the following premises. For all x_19, x_19 will make tea if and only if x_19 will play a game. For all x_19, x_19 will not drive a car or x_19 will make tea. For all x_19, if x_19 reads a book, then x_19 is taking a plane. There is at least one x_19 for which if x_19 works, then x_19 is taking a plane. For all x_19, x_19 will work or x_19 will read a book. For all x_19, x_19 will drive a car or x_19 will go running. For all x_19, if x_19 goes running, then x_19 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_19, either x_19 will play a game or x_19 will take a plane are not true.
 From the fact that for all x_19, x_19 will drive a car or x_19 will go running, and that for all x_19, x_19 will not drive a car or x_19 will make tea we can infer that for all x_19, x_19 will go running or x_19 will make tea via universal resolution. From the fact that there is at least one x_19 for which if x_19 works, then x_19 is taking a plane, that for all x_19, if x_19 reads a book, then x_19 is taking a plane, and that for all x_19, x_19 will work or x_19 will read a book we can infer that there is at least one x_19 for which x_19 will take a plane via existential disjunction elimination. From the fact that for all x_19, x_19 will make tea if and only if x_19 will play a game we can infer that for all x_19, if x_19 makes tea, then x_19 is playing a game via universal biconditional elimination. From the fact that for all x_19, if x_19 goes running, then x_19 is playing a game, that for all x_19, if x_19 makes tea, then x_19 is playing a game, and that for all x_19, x_19 will go running or x_19 will make tea we can infer that for all x_19, x_19 will play a game via universal disjunction elimination. Finally, from the fact that for all x_19, x_19 will play a game, and that there is at least one x_19 for which x_19 will take a plane we can infer that there is at least one x_19 for which x_19 will play a game and x_19 will take a plane via existential conjunction, which contradicts that For all x_19, either x_19 will play a game or x_19 will take a plane are not true. Therefore, the answer is no.