What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? There is at least one x_13 for which x_13 is excited if and only if x_13 will write a letter. For all x_13, x_13 will play a game if and only if x_13 is fast. For all x_13, x_13 is not excited. For all x_13, x_13 will write a letter if and only if x_13 will play a game.
For all x_13, if x_13 plays a game, then x_13 is fast. For all x_13, if x_13 writes a letter, then x_13 is playing a game. There is at least one x_13 for which if x_13 were excited, then x_13 is writing a letter. For all x_13, if x_13 were fast, then x_13 is playing a game. For all x_13, if x_13 plays a game, then x_13 is writing a letter. There is at least one x_13 for which if x_13 writes a letter, then x_13 is excited. There is at least one x_13 for which x_13 will not write a letter.