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: There is at least one x for which if x goes running, then x is writing a letter. For all x, if x writes a letter, then x is sleeping. For all x, x will play a game if and only if x will write a letter. For all x, if x sleeps, then x is running. For all x, x will not play a game.
For all x, if x writes a letter, then x is running can be inferred via the universal transitivity rule. There is at least one x for which if x goes running, then x is sleeping can be inferred via the existential transitivity rule. There is at least one x for which if x sleeps, then x is writing a letter can be inferred via the existential transitivity rule. For all x, if x plays a game, then x is writing a letter can be inferred via the universal biconditional elimination rule. For all x, if x writes a letter, then x is playing a game can be inferred via the universal biconditional elimination rule. For all x, x will not write a letter can be inferred via the universal biconditional elimination rule.