And definitely you will eventually succumb to a different cold virus, because there remain over 300 different runny nose infections. Yet you will never get the same cold virus that you had in the past since you have developed resistance to that particular virus.

HPV is identical because HPV is simply an additional infection. And you can quite simply create resistance to human papilloma virus. However, human papilloma virus is more capable at hiding from your body's immune system compared to the common cold infections. Therefore you have to work a little harder to acquire resistance to HPV virus.
https://www.openlearning.com/u/redus-qmelrc/blog/ICuredMyHpv/