I just saw this and I feel I should write as I suppose it originally targeted me as well as other top players.
I think @poptasticboy does a fantastic work explaining it and he has done the same in other posts so I won't take much time for it, but you can solve most Hard puzzles with 0-2 questions. Some require more, but even some of those also could end up only taking 2 questions if you are lucky with your proposal. I get how this can look like cheating for a person who doesn't know how that is done, but it is perfectly possible and the game was designed like that.
Having said that, if you have two players against each other and one of them knows how to do "deep deduction" and the other doesn't, it's like having a beginner playing chess against Magnus Carlsen. Nothing will make sense for the beginner and they will lose before they know what happened. Every time a person asked me how I got the solution so quick, I always try to help them and explain part of my process, but I see how the final experience is not enjoyable for beginners and for that reason I've recommended many players who played against me repeatedly and showed their frustration to red thumb me so the website won't pair us up together again. I've even give red thumbs to some of those players myself because I felt bad. We could blame the matchmaking algorithm for this but unfortunately there are not so many people on the playing queue for the game so I won't blame the website for letting people play instead of keeping everyone waiting. Maybe letting every player finish the game would at least leave a better taste, rather than abruptly stopping the game because someone else solved it. I don't know how this is handled in similar games in this website but could be a good implementation.
Regarding how I solve the puzzles, I will answer a few quick questions: No, I don't cheat. The reason I have such a high rate of wins is because most people I play against don't know how far you can go with deductions. If you check my games against other pros, you will see I tie a lot. And no, I don't use the official Turing Machine website. I wasn't even aware you could check solutions there and from the quick look I got, it seems you just get one of the possible solutions without knowing if there are more, so not very useful in my opinion but maybe I'm missing something. Also I don't use any specific software for this game. I've seen some people have uploaded programs that solve every puzzle but a) I'm pretty bad with computers and without an instruction book I don't think I'd be able to use them and b) they would just get the same result as I get (if they work properly) with my own method. I help myself with an Excel sheet as the space in the playing board is not enough for everything I need to write down, but no brute force calculations are done by Excel. I've considered sharing my method here but I've decided not to at least for the rest of this season. But basically involves solving the puzzle analytically to a great extent, and then testing a bunch of possibilities one by one and in a very optimised way. I've studied physics and mathematics and my main reason to play the game was the challenge of solving it with pen and paper. I have manually derived excluding rules for every combination of 2, 3 and 4 verificators together, which generally leaves me less than 20 possible solutions once I apply the corresponding ones. After that I test each of them with a quick test that involves just a few algebraic calculations. The whole process takes me less than 5 minutes if I do it relaxed, and I've tested myself to do it in live games and I can do it in less than 3 minutes for most games. I don't think i will share my results as I don't think it's fair that people who don't understand it use it, but whoever is curious might find it a challenge to develop a similar method by themselves.
Additionally, on my personal quest to be the #1 on the leaderboard I have analysed almost every other top player in order to know who does "deep deduction" and who doesn't. I understand that some people will think I'm taking it way too far and it's not fun to play against someone like that. Again, I can only blame the matchmaking, because at some point players who take it serious should not be paired with beginners. Also I try to avoid casual games and mostly play Arena to avoid players who just want to have fun and not compete. I have talked with a few other pro players and they all used different methods including specific software or manually checking the 125 possibilities in an Excel file. They were nice enough to answer me so I won't call names.
Now, regarding CHEATING: I've actually very recently found out that there is indeed a way to cheat beyond using brute force software. I started investigating after I saw truly absurd guessing chances (I have myself gone for guessing quite a few times based on probability to avoid ties while trying to get the 50 wins in a row achievement, unfortunately failing many times) and with help from a friend we realized there is a way to instantly know the solution. I have written to the BGA game developer about this directly and I hope he will fix it soon. I have tested it against people who i know are using it (to avoid losing unfairly) and also analysed already finished games and it totally works, although it would require some time to have a complete dictionary of solutions. You are very welcome to accuse me of using it, but if I was using I would already have my 50 wins in a row. I just lost a streak of around 45 wins because I had to guess to avoid a tie and I wouldn't have to guess if I knew the answer. I also won't call names here but I have a list of people who 100% are doing it (or another cheating method that I don't know of).
I hope this post clarifies some things. I will be very happy to answer any questions that don't involve revealing too many details of my method. I hope that is understandable. I want the best for the community here and I will be very happy when the cheating issue gets resolved. Also I would be happy if the Arena games didn't show which verificators the opponents are using so games are not about outwaiting the opponents. This is something I do myself because you can get info from what others do if you know they have done the "deep deduction" but I agree it makes the whole experience less enjoyable. I would sacrifice some bits of information if everyone has more fun (and also so i don't give away information).