I am also a superviser, but not a technical leader, an administrator.I understand your situation. I get used to office politics. As a chinese, a medium level supervisor, an administrator in company, I know better than anybody that how hard we got to fight. I disagree with not to fight idea.
But, you got to calm down, be cool. What you need is a kao(4) shan(1) in your company. Analysis the situation in your company, you will find one. Ask what you can do for him, not what he can do for you. Useless to talk with C now.
Good luck!