Girlfriend cheated on me and i need advice

i recently broke up with my girlfriend. she cheated on me with somebody from work i found out and told her i know everything and had proof, she denied it at first and told me none of it was true, she later admitted its true but still lied about whether certain things that were said happened or not . she said sorry, cried to me and said i dont know why i did it me and you was arguing , i thought we was done etc. we wasnt done , yes we was going through a rough time but we never once said lets break up and she never cut contact. she kept this lie for a whole year from me. she also lied to the guy that i had assulted her when i havent. she got the guy fired from work saying he assulted her also when she found out he had a girlfriend.

this is where i feel something isnt right . she contacted me saying she doesnt want to argue so we spoke about whats been going on with the whole situation, i naturally want to ask her a few questions about it all, she answers them mostly with i dont know, almost seeming emotionally disconnected , very cold. this can fustrate me as i feel im doing the work,

she then starts to get very defensive and this is where i feel she might be using darvo on me? she would suddenly flip a switch and tell me she doesnt care, i keep bringing it up, sighing at me telling me its boring now and then said the reason she done it was because “ i shouldnt have to sit waiting around for you to change” all i have ever tried to do is understand her and make her happy, but i never really got that back from her but i still tried to work things out during the relationship. then she proceeded to say i wasted her time in the relationship and flipped the whole situation onto me and pushed the whole lying and cheating aside. i then felt very bad defending myself against her words because i usually just let her say whatever she wants to me, at those point i felt guilty and felt like i shouldve just kept my mouth closed. she became so cold towards me after like in a piece of trash.

anyone who has experienced something similar could you tell me what im actually dealing with here as it all is very messy to me and i genuinely feel like i am the cause of the relationship failing and she had every right to cheat on me.