A couple of points when doing pull ups on day 3. While the workout is for time, perform the pull ups as follows: 3 to 5 reps with 3 to 5 minutes of rest between them. Don’t train to muscle failure! Get just enough assistance so that you can get the reps without failing or degradation of form. That goes for day 2 as well.
Training muscles to failure for increased strength is a myth from the world of body building. It will pump up those muscles but significant gains in maximum and functional strength will not be realized. Have fun!