What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? David is a doctor if and only if Mary is playing a game. For all x, x is a police officer if and only if x will write a letter. For all x, x will write a letter if and only if x is a doctor. For all x, x is not a police officer.
If David were a doctor, then Mary is playing a game. If Mary plays a game, then David is a doctor. For all x, if x were a police officer, then x is writing a letter. For all x, if x writes a letter, then x is a doctor. For all x, if x writes a letter, then x is a police officer. For all x, if x were a doctor, then x is writing a letter. For all x, x will not write a letter.