Consider the following premises. For all x_19, x_19 is excited or x_19 will go running. For all x_19, x_19 is bored and x_19 will read a book. There is at least one x_19 for which x_19 will not make tea. For all x_19, x_19 will make tea if and only if x_19 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_19 for which x_19 will go running and x_19 is bored.
 From the fact that for all x_19, x_19 will make tea if and only if x_19 is excited, and that there is at least one x_19 for which x_19 will not make tea we can infer that there is at least one x_19 for which x_19 is not excited via existential biconditional elimination. From the fact that for all x_19, x_19 is excited or x_19 will go running, and that there is at least one x_19 for which x_19 is not excited we can infer that there is at least one x_19 for which x_19 will go running via existential disjunctive syllogism. From the fact that for all x_19, x_19 is bored and x_19 will read a book we can infer that for all x_19, x_19 is bored via universal simplification. Finally, from the fact that there is at least one x_19 for which x_19 will go running, and that for all x_19, x_19 is bored we can infer that there is at least one x_19 for which x_19 will go running and x_19 is bored via existential conjunction. Therefore, the answer is yes.