Consider the following premises. For all x_6, if x_6 writes a letter, then x_6 is an electrician. For all x_6, x_6 is sad. There is at least one x_6 for which x_6 is an electrician or x_6 is not sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is not an electrician.
 From the fact that for all x_6, x_6 is sad we can infer that for all x_6, x_6 is sad or x_6 will write a letter via universal addition. From the fact that there is at least one x_6 for which x_6 is an electrician or x_6 is not sad we can infer that there is at least one x_6 for which if x_6 were sad, then x_6 is an electrician via existential rewriting. Finally, from the fact that there is at least one x_6 for which if x_6 were sad, then x_6 is an electrician, that for all x_6, if x_6 writes a letter, then x_6 is an electrician, and that for all x_6, x_6 is sad or x_6 will write a letter we can infer that there is at least one x_6 for which x_6 is an electrician via existential disjunction elimination, which contradicts that For all x_6, x_6 is not an electrician. Therefore, the answer is no.