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_9, if x_9 were a lawyer, then x_9 is reading a book. For all x_9, if x_9 writes a letter, then x_9 is a lawyer. For all x_9, if x_9 works, then x_9 is a lawyer. There is at least one x_9 for which x_9 will work or x_9 will write a letter.
For all x_9, if x_9 writes a letter, then x_9 is reading a book can be inferred via the universal transitivity rule. For all x_9, if x_9 works, then x_9 is reading a book can be inferred via the universal transitivity rule. There is at least one x_9 for which x_9 is a lawyer can be inferred via the existential disjunction elimination rule.