Consider the following premises. For all x_5, if x_5 were an office clerk, then x_5 is an electrician. There is at least one x_5 for which x_5 is a nurse. For all x_5, if x_5 were an electrician, then x_5 is curious. For all x_5, x_5 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, either x_5 is a nurse or x_5 is curious are not true.
 From the fact that for all x_5, if x_5 were an office clerk, then x_5 is an electrician, and that for all x_5, x_5 is an office clerk we can infer that for all x_5, x_5 is an electrician via universal modus ponens. From the fact that for all x_5, if x_5 were an electrician, then x_5 is curious, and that for all x_5, x_5 is an electrician we can infer that for all x_5, x_5 is curious via universal modus ponens. Finally, from the fact that there is at least one x_5 for which x_5 is a nurse, and that for all x_5, x_5 is curious we can infer that there is at least one x_5 for which x_5 is a nurse and x_5 is curious via existential conjunction, which contradicts that For all x_5, either x_5 is a nurse or x_5 is curious are not true. Therefore, the answer is no.