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_7, x_7 will listen to a song. For all x_7, if x_7 plays squash, then x_7 is a scientist. For all x_7, if x_7 listens to a song, then x_7 is writing a letter. There is at least one x_7 for which x_7 will play squash.
For all x_7, x_7 will write a letter can be inferred via the universal modus ponens rule. There is at least one x_7 for which x_7 is a scientist can be inferred via the existential modus ponens rule. There is at least one x_7 for which x_7 will play squash and x_7 will listen to a song can be inferred via the existential conjunction rule. There is at least one x_7 for which x_7 will listen to a song and x_7 will play squash can be inferred via the existential conjunction rule.