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_17, if x_17 climbs a mountain, then x_17 is writing a letter. For all x_17, if x_17 writes a letter, then x_17 is playing a game. For all x_17, x_17 will sleep if and only if x_17 will play a game. For all x_17, if x_17 plays squash, then x_17 is writing a letter. There is at least one x_17 for which x_17 will play squash.
There is at least one x_17 for which x_17 will write a letter can be inferred via the existential modus ponens rule. For all x_17, if x_17 climbs a mountain, then x_17 is playing a game can be inferred via the universal transitivity rule. For all x_17, if x_17 plays squash, then x_17 is playing a game can be inferred via the universal transitivity rule. For all x_17, if x_17 sleeps, then x_17 is playing a game can be inferred via the universal biconditional elimination rule. For all x_17, if x_17 plays a game, then x_17 is sleeping can be inferred via the universal biconditional elimination rule.