Sorry, no logs for you. Rest assured I can see the IP of everyone who posts here, sorry if people don't believe it. But that's been a standard feature for forum administrators for years, if not since the beginning of forum software.
You guys aren't banned or in any real trouble right now anyway, so its even more unlikely anyone is gonna let you see logs or screenshots or anything. It's pretty rare to run across two users on the same connection at the same forum, at least it doesn't happen very often here. I can't really prove anything anymore than you guys could prove you're two different people, but the rules are the rules, and they are in my favor.
Go about your business. If you act like two separate people people won't even remember or care about this discussion. If you give us reason to believe otherwise, then whatever happens, is how it goes.
That's my final comment on this issue.