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_2, if x_2 writes a letter, then x_2 is sleeping. For all x_2, if x_2 sleeps, then x_2 is writing a letter. There is at least one x_2 for which x_2 is a taxi driver or x_2 will not write a letter.
There is at least one x_2 for which if x_2 writes a letter, then x_2 is a taxi driver can be inferred via the existential rewriting rule. For all x_2, x_2 will write a letter if and only if x_2 will sleep can be inferred via the universal biconditional introduction rule. For all x_2, x_2 will sleep if and only if x_2 will write a letter can be inferred via the universal biconditional introduction rule.