Consider the following premises. For all x_7, x_7 is an electrician or x_7 will drink water. For all x_7, x_7 will sleep if and only if x_7 is a sailor. For all x_7, if x_7 drinks water, then x_7 is sleeping. There is at least one x_7 for which x_7 is not an electrician or x_7 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not sleep.
 From the fact that for all x_7, x_7 will sleep if and only if x_7 is a sailor we can infer that for all x_7, if x_7 were a sailor, then x_7 is sleeping via universal biconditional elimination. From the fact that for all x_7, x_7 is an electrician or x_7 will drink water, and that there is at least one x_7 for which x_7 is not an electrician or x_7 is a sailor we can infer that there is at least one x_7 for which x_7 will drink water or x_7 is a sailor via existential resolution. Finally, from the fact that for all x_7, if x_7 drinks water, then x_7 is sleeping, that for all x_7, if x_7 were a sailor, then x_7 is sleeping, and that there is at least one x_7 for which x_7 will drink water or x_7 is a sailor we can infer that there is at least one x_7 for which x_7 will sleep via existential disjunction elimination, which contradicts that For all x_7, x_7 will not sleep. Therefore, the answer is no.