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_6, x_6 is a carpenter. For all x_6, x_6 will write a letter. For all x_6, if x_6 were an office clerk, then x_6 is listening to a song. For all x_6, if x_6 writes a letter, then x_6 is an office clerk.
For all x_6, x_6 is an office clerk can be inferred via the universal modus ponens rule. For all x_6, if x_6 writes a letter, then x_6 is listening to a song can be inferred via the universal transitivity rule. For all x_6, x_6 is a carpenter and x_6 will write a letter can be inferred via the universal conjunction rule. For all x_6, x_6 will write a letter and x_6 is a carpenter can be inferred via the universal conjunction rule.