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_10, if x_10 writes a letter, then x_10 is sleeping. For all x_10, if x_10 were a server, then x_10 is a lawyer. For all x_10, if x_10 were a lawyer, then x_10 is a server. For all x_10, if x_10 sleeps, then x_10 is a lawyer. For all x_10, if x_10 were a server, then x_10 is writing a letter.
For all x_10, if x_10 writes a letter, then x_10 is a lawyer can be inferred via the universal transitivity rule. For all x_10, if x_10 were a lawyer, then x_10 is writing a letter can be inferred via the universal transitivity rule. For all x_10, if x_10 sleeps, then x_10 is a server can be inferred via the universal transitivity rule. For all x_10, if x_10 were a server, then x_10 is sleeping can be inferred via the universal transitivity rule. For all x_10, x_10 is a server if and only if x_10 is a lawyer can be inferred via the universal biconditional introduction rule. For all x_10, x_10 is a lawyer if and only if x_10 is a server can be inferred via the universal biconditional introduction rule.