What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? For all x_12, if x_12 plays a game, then x_12 is a scientist. There is at least one x_12 for which x_12 will play a game if and only if x_12 will write a letter. For all x_12, x_12 will write a letter or x_12 will not play tennis.
For all x_12, if x_12 plays tennis, then x_12 is writing a letter. There is at least one x_12 for which if x_12 plays a game, then x_12 is writing a letter. There is at least one x_12 for which if x_12 writes a letter, then x_12 is playing a game.