What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one x_10 for which if x_10 sleeps, then x_10 is a nurse. For all x_10, x_10 will not sleep. For all x_10, if x_10 works, then x_10 is sleeping. For all x_10, if x_10 works, then x_10 is sleeping. For all x_10, if x_10 were a nurse, then x_10 is working.
For all x_10, x_10 will not work can be inferred via the universal modus tollens rule. For all x_10, x_10 will not work can be inferred via the universal modus tollens rule. For all x_10, if x_10 were a nurse, then x_10 is sleeping can be inferred via the universal transitivity rule. For all x_10, if x_10 were a nurse, then x_10 is sleeping can be inferred via the universal transitivity rule. There is at least one x_10 for which if x_10 sleeps, then x_10 is working can be inferred via the existential transitivity rule. There is at least one x_10 for which if x_10 works, then x_10 is a nurse can be inferred via the existential transitivity rule. There is at least one x_10 for which if x_10 works, then x_10 is a nurse can be inferred via the existential transitivity rule.