the first quarter phase of the moon occurs after the new moon
new_moon is phase_of_moon. phase_of_moon is not phase. phase_of_moon is time_period. full_moon is phase_of_moon. moon has phases first_quarter is half_moon. half_moon is phase_of_moon. phase_of_moon is phase. first_quarter is not half_moon. new_moon is not phase_of_moon.