Let me try to explain what the sentences mean, before answering when I would use it. There are some incorrect words in the sentences, but I wouldn't correct them here because it just muddies the answers (I prefer to help understand you the flow of the sentences rather than try to correct every single word written). 1) "He couldn't not have paid the bill", the meaning is "it is not possible he did not pay the bill". Or another way to understand it:" He must have paid the bill. No way he didn't do it." 2) "It couldn't be he didn't pay the bill.", the meaning is the same as the first sentence. No obvious differences, the meaning is the same. 3) "It couldn't be he haven't paid the bill." the meaning is also the same as the first sentence. Again, no obvious differences- the double negatives somehow will negate themselves, depending on their use. Now you know what they mean, let me just say that normally, I will try not to use them. Double negatives is a common occurance in some languages (say in Japanese or Greek), but in English I recommend keeping them to the minimum to improve readability. The only time I would try to use them is when I write, where there is a lot of time to pick through the meaning. I don't try to speak it- it makes things too difficult for me as well as for the listener.

He couldn't not have paid the bill. We would change this just a bit and say, "He couldn't have not paid the bill." This would be a more informal/slang usage to emphasize that you can't believe his actions. As far as using it....I would say this if I was at a restaurant with a friend. Maybe I thought the friend had already gone and paid his bill because he has walked out and left the restaurant already but when I go to pay later the waiter tells me that the other part of the bill has not been paid yet. I think, "Hmmm...that's odd, he couldn't have not paid the bill (or his part of the bill before leaving). So I am using the double negative to emphasize that I don't feel like he would have left without paying, almost saying it seems impossible. People might more commonly say, "There is no way he would/could have left without paying the bill." (that's the same meaning) It couldn't be he didn't pay the bill. I would change it into two separate ideas. "It couldn't be. He didn't pay the bill." Someone comes back and says my friend didn't pay for bill (if he agreed to pay it) and says, "It couldn't be. He didn't pay the bill." It's like saying, "Wow, that's weird. He told us he would pay but he left and didn't. That seems odd." It couldn't be he haven't paid the bill. Change to "It couldn't be that he hasn't paid the bill." I think I would be more likely to say didn't pay instead of hasn't paid because hasn't tells me he hasn't done it yet but he still has time. I wouldn't really say it couldn't be if I am also saying/thinking that he still has time to do it because then why would it seem that it can't be true that he hasn't paid it? Maybe he will pay in a minute before he leaves. Didn't show the action/the chance or paying is over. He chose to leave or do something that now makes it impossible for him to pay because the action is over. Wow! Good questions. This is tricky grammar. Good luck. Feel free to ask more questions if my explanations are unclear.

Hi there! Double negatives are only really used in informal speech. Most teachers would not recommend using them at all. In your sentence it would be much better to say: 'He must have paid the bill' However, I have heard the first sentence with 'couldn't not' used informally, and I would even say that it is quite common in colloquial English. In the case of your sentence, someone would have had to accuse somebody else of not paying the bill. In order to emphasize that it is impossible that he didn't pay it, a double negative is sometimes used informally. In a sense then, it is in order to emphasize that not doing something / not feeling something / not being something is impossible. Here is another example 'I felt very angry, I couldn't not be angry after what happened.' Again, I must emphasize that this is only used informally, but it is used here because you are emphasizing the difference between angry and not angry. Hope this helps, let me know if you have any questions!

Imagine I am trying to say something nice:" I wouldn't not try to try to love you." I would probably get a quizzical look between anger and pleasure.. and that is on a good day!