It's all transparent slavery. You need to work and if you are not working and looking for work, you will sign anything at some point if you are desperate enough and/or unwilling to live on the street.

Be fortunate you have a job. Follow their rules and look for other employment if you are unhappy with them or suggest a new contract.

When looking for your next job have your own contract prepared. To be a great service to the Community make your contract available and ask for suggestions to ensure that you are protecting yourself while at the same time the employer. It is critical that the employer feels protected. Remember the employer is investing a lot in you, the larger the firm the more it costs them to get and keep you. As a Community we need to do the same for our rights as creators, innovators, and hobbists on our own time (if there is such a thing), that companies do for theirs. If we fall into blindly signing contracts because "that's what I have to do if I want to work", then the companies retain the power and in my opinion stifle free thinking. If I have a great idea and think the company may stake claim to it even though it is unrelated I may stop sharing ideas and do only what I am told and request very specific details on each stage so that I am sure all the "ideas" are their's so I don't accidently give one away.

I have been out of work for 4 months so I own all my thoughts :) and code, but I don't get paid for them :(