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_11, if x_11 were a cashier, then x_11 is writing a letter. For all x_11, x_11 is a carpenter or x_11 will listen to a song. There is at least one x_11 for which if x_11 were a doctor, then x_11 is a cashier. For all x_11, if x_11 were a carpenter, then x_11 is a cashier. For all x_11, if x_11 listens to a song, then x_11 is a doctor.
For all x_11, if x_11 were a carpenter, then x_11 is writing a letter can be inferred via the universal transitivity rule. There is at least one x_11 for which if x_11 were a doctor, then x_11 is writing a letter can be inferred via the existential transitivity rule. There is at least one x_11 for which if x_11 listens to a song, then x_11 is a cashier can be inferred via the existential transitivity rule.