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: For all x_8, x_8 is a cashier or x_8 will cook. For all x_8, x_8 will cook if and only if x_8 will sleep. There is at least one x_8 for which x_8 is not a cashier or x_8 is a musician. For all x_8, if x_8 sleeps, then x_8 is listening to a song. For all x_8, x_8 will not listen to a song.
For all x_8, x_8 will not sleep can be inferred via the universal modus tollens rule. There is at least one x_8 for which x_8 will cook or x_8 is a musician can be inferred via the existential resolution rule. For all x_8, if x_8 cooks, then x_8 is sleeping can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 sleeps, then x_8 is cooking can be inferred via the universal biconditional elimination rule.