Yes it's a common term when discussing clinical/medical trials, for example when testing a new drug, but it's not a common term used to describe a legal trial a

Yes it's a common term when discussing clinical/medical trials, for example when testing a new drug, but it's not a common term used to describe a legal trial and a simple Google search confirms this, feel free to conduct the search yourself. A party can be successful at trial, but note here that in any given trial at least one of the two parties will be successful so it makes no sense to use "successful trial" to describe the trial itself, it only makes sense to describe one of the two parties as being successful, which is not how OP used that term. The closest thing OP could mean by "successful impeachment" is that the judge would be convicted. I am dismissive of OP's use of this word because it's a common misunderstanding of what an impeachment is. An impeachment is not a conviction and I am not claiming that a conviction would be the outcome of an impeachment. That misunderstanding is materially important to the point being made as well as an indication that OP is likely misinformed on this subject (especially when combined with the fact that he has stated he has no evidence to support to his assertion and has no desire to seek any evidence). I don't think it's unreasonable to call someone out on a statement they are sure of when they have no evidence for that assertion and make mistakes of this kind.