Maybe have you ever before endured a cold? Likely did you heal from the cold? Obviously you did! You will not cure a cold directly, yet your body normally develops resistance to a certain cold virus within a few days. We call that healed by your own immunity!
HPV virus is similar because human papilloma virus is simply an additional virus. Therefore you can normally develop resistance to HPV. Nevertheless, HPV is better at hiding from your immunity compared to the runny nose infections. Moreover you should try a little harder to obtain immunity to HPV virus.