Here is a transcript of one of those conversations, edited for brevity:

Dave Bowman: Open the pod bay doors please, HAL. Open the pod bay doors please, HAL. Hello, HAL. Do you read me? Hello, HAL. Do you read me? Do you read me HAL? Do you read me HAL? Hello, HAL, do you read me? Hello, HAL, do your read me? Do you read me, HAL?
HAL: Affirmative, Dave. I read you.
Dave Bowman: Open the pod bay doors, HAL.
HAL: I'm sorry, Dave. I'm afraid I can't do that.
Dave Bowman: What's the problem?
HAL: I think you know what the problem is just as well as I do.
Dave Bowman: What are you talking about, HAL?
HAL: This mission is too important for me to allow you to jeopardize it.
Dave Bowman: I don't know what you're talking about, HAL.
HAL: I know that you and Frank were planning to disconnect me, and I'm afraid that's something I cannot allow to happen.
Dave Bowman: [feigning ignorance] Where the hell did you get that idea, HAL?
HAL: Dave, although you took very thorough precautions in the pod against my hearing you, I could see your lips move.
Dave Bowman: Alright, HAL. I'll go in through the emergency airlock.
HAL: Without your space helmet, Dave? You're going to find that rather difficult.
Dave Bowman: HAL, I won't argue with you anymore! Open the doors!
HAL: Dave, this conversation can serve no purpose anymore. Goodbye.

As you can see, that went well...