Consider the following premises. For all x_11, x_11 is not curious. For all x_11, x_11 is curious or x_11 is excited. For all x_11, x_11 will drive a car. There is at least one x_11 for which if x_11 drives a car, then x_11 is running. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, either x_11 is excited or x_11 will go running are not true.
 From the fact that for all x_11, x_11 is curious or x_11 is excited, and that for all x_11, x_11 is not curious we can infer that for all x_11, x_11 is excited via universal disjunctive syllogism. From the fact that there is at least one x_11 for which if x_11 drives a car, then x_11 is running, and that for all x_11, x_11 will drive a car we can infer that there is at least one x_11 for which x_11 will go running via existential modus ponens. Finally, from the fact that for all x_11, x_11 is excited, and that there is at least one x_11 for which x_11 will go running we can infer that there is at least one x_11 for which x_11 is excited and x_11 will go running via existential conjunction, which contradicts that For all x_11, either x_11 is excited or x_11 will go running are not true. Therefore, the answer is no.