My Girlfriend Doesn't Believe Me?

Well, my girlfriend came out of nowhere this morning and confronted me about me supposedly being unfaithful to her with her sister. I asked her what time and day did her sister say it occured. She told me, but during the time she gave I was working my normal work hours, and I had the paystubs to prove I worked that whole time. I could tell she was upset but she said she believed me and that she would ask her sister more questions.

A little bit ago she confronted me again, this time with a different date and a different time. I also had worked during that time and had the paystubs to prove it. She acted more calm this time and said okay. Then later she asked me about another time, but this time I was not at work and could not prove my innocence. All I had to back me up was my own word, so I told her what I did that night: I went home and did my normal routine, and I had called her right before bed.

After a bit more talking she decided to believe her sister (despite the fact that she changed her story at least 2 times) over me simply on the grounds of "Why would she lie to me?" I understand her reasoning, because why would her sister lie to her? But unfortunately, for whatever reason, she is lying and now it has potentially ruined our relationship. Is there anything I can do or say to make her believe me?
My Girlfriend Doesn't Believe Me?
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