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_20, x_20 will sleep if and only if x_20 is an office clerk. Patricia is a poet. Richard is not an office clerk. If Richard doesn't sleep, then Elisabeth is rich.
Patricia is a poet and Richard is not an office clerk can be inferred via the conjunction rule. Richard is not an office clerk and Patricia is a poet can be inferred via the conjunction rule. For all x_20, if x_20 sleeps, then x_20 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_20, if x_20 were an office clerk, then x_20 is sleeping can be inferred via the universal biconditional elimination rule.