<human>: Can you condense the text into a few key points?

So to start, I have been living with my roommate for about a year now, and I have known her for probably around 2/3 years. 

She has a male cat (I'll call him Lucifer). Lucifer has been peeing on everything he comes in contact with that is mine. He started doing this as soon as I moved in, and I tried to deal with it without flipping out. I close my bedroom door to make sure that the cat can't come in my room and pee on anything in there, I close my bathroom door to make sure he can't pee on my bath mat (yes, he has done this more than 10 times).

There are times when I either forget to shut a door, or something from my laundry falls on the floor, or part of a blanket is touching the floor and Lucifer will pee on all over it. It....never....fails. 

One time, I came home and had to use the bathroom. I put my purse and jacket in my room and forgot to shut the door before I used the bathroom quick. I was in the bathroom for not even 3 minutes. When I came out Lucifer ran quickly out of my room and I found that he peed all over my blankets and on the carpet. 

I have confronted my roommate SEVERAL times regarding his behavior and she hasn't done anything to fix the situation. She once told me "oh yeah, he does that sometimes". Ummmm, what?!!?

I have suggested that she keep her cat in her room, since her room is the master bedroom and she has a bathroom attached (where the litter box is). She refuses to shut her door because "he might scratch it". 

Does anyone have any solutions or advice? I am over trying to deal with this, and I think my only option is to move out early. But if I do end up moving out early, should I have to pay the remainder of the rent due on the lease?
<bot>: Need help/advice on dealing with my intolerant roommate and her cat that won't stop peeing on my things.