Translate the following inference to logic notation: For all x, if x_6 were a scientist, then x_6 is not listening to a song. There is at least one x for which x_6 will listen to a song and x_6 is a soldier. Therefore there is at least one x for which x_6 is not a scientist.
forall x: P(x) -> ~Q(x). exists x: Q(x) and R(x). Therefore exists x: ~P(x).