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 doctor or x_8 will play squash. For all x_8, x_8 is a doctor if and only if x_8 will cook. There is at least one x_8 for which x_8 is a writer. For all x_8, x_8 will not cook.
For all x_8, if x_8 were a doctor, then x_8 is cooking can be inferred via the universal biconditional elimination rule. For all x_8, if x_8 cooks, then x_8 is a doctor can be inferred via the universal biconditional elimination rule. For all x_8, x_8 is not a doctor can be inferred via the universal biconditional elimination rule.