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_5, if x_5 writes a letter, then x_5 is a doctor. For all x_5, if x_5 were bored, then x_5 is a doctor. For all x_5, x_5 is a soldier or x_5 is fast. For all x_5, if x_5 were a soldier, then x_5 is writing a letter. There is at least one x_5 for which if x_5 were fast, then x_5 is bored.
For all x_5, if x_5 were a soldier, then x_5 is a doctor can be inferred via the universal transitivity rule. There is at least one x_5 for which if x_5 were fast, then x_5 is a doctor can be inferred via the existential transitivity rule.