Agree as a table that rules discussions happen out-of-session

We have had this issue at our table. Rules debates that have gotten out of hand and players (including and sometimes primarily me in the past) looking up rules and rulings disrupting the session. The following method is what helped our issue a lot:

1. If any rule is unclear or confusing the DM will make a quick, temporary ruling during the session (that is binding only for that session). Usually, I rule in favor of the player especially in cases where it is life-or-death. But at your table you can use whatever criteria allows you to make a quick decisive ruling that seems fair. Do not allow any argument about this ruling at the table.

2. Either after this session or before the next one, I will review the ruling, I'll look at the rules, talk with the player and hear their arguments and come to a final decision about how the rule will work going forward. Be fair, and fully consider the player's arguments, then make a ruling. This ruling is considered final.

At some point before a session, let your players know that this will be the way you handle rules disputes going forward. You will not accept any debate during the session but make it clear that you are happy to talk with them before or after. Try to make it clear why you are ruling this way too: rules debate breaks up the story that your group is trying to craft. This rule keeps the fun session going while allowing rules to be addressed at a later time. Ask them to trust you as a DM and to allow you to make a ruling that seems fair and quick in order to keep things fun for everyone. Talk about it and get buy-in from everyone at the table.

An interesting byproduct of this ruling is that players are naturally incentivized to proactively bring up questions they have for rulings antes session since they know they can't debate during. This is great for both of us as we can go into the session with an agreed upon ruling (even if I end up disagreeing with the player). Obviously though, this won't work for everything as rules issues are often unexpected.

Declare last call for arguments/issues before the session begins

One specific technique that I have not tested, but seems like it would help in your circumstance was suggested by @philbo in a comment: Simply stop before every session and ask if the players have any rules issues or other topics they wish to discuss before you begin the session.

Explicitly state that this includes any rules arguments that people anticipate. After that, the player is going to look pretty silly trying to spring a pre-planned rules argument mid-session on you and you can simply respond: "I gave you the chance to bring this up at the beginning of the session and you chose not to. Now you have to wait until the end and then we can discuss it."

Being lenient with table rulings helps considerably with trust and buy-in

I have found that it helps a lot to get buy-in and keeping things running smoothly if I lean towards ruling with the player at the table for my temporary rulings. Not always, of course. When you are sure the player's desired ruling is not consistent with the way you adjudicate the rules e the ruling will have a negative effect on the game is about the only time I hard overrule the player at the table. If you tell players that you intend to do this is tells them that you respect their arguments for the rules and trust them (to a point).

It also removes much of the need for arguing during session at all which removes times where the player is fuming or refusing to back down after being overruled. Instead this happens out of session where it doesn't affect game time. Just make a note and review the rule later yourself and if the player was in the "wrong" then talk with them, fully understand their position and make the final ruling out of session. At all times remember to be fair and reasonable with rulings to maintain the players' trust and openly admit if you make a mistake.

What if players keep trying to argue during the session?

Once you have made it clear how and when rules debates happen, simply do not engage in debate during the session. If they start to argue, tell them "I made my ruling, see me after the session and we will talk." If they keep arguing, for example during combat, tell them that if they do not move past it and choose something you will skip their turn.

If you remain firm on the point and don't engage at all, players will soon learn that it is no good to try to argue during the session. At my table, players learned this very quickly and I didn't have to invoke it more than a handful of times.

You have the final say as a DM

It is also probably worth it to remind your players that, in 5e, you as the DM have the final say on rulings at the table and how the rules are interpreted. Remember, there are often multiple ways to read the Rules as Written (RAW) and it is not some monolithic "correct" ruling that is clear. Sometimes the RAW is unclear or even silent on an issue. Sometimes this is even by design, since 5e is designed to be less focused on detailed interactions instead trusting the DM to make the ruling they think will be best for their table.

In the end, tell them that you will always be focused on making things fair and fun, but when you make a decision final you consider it to be done unless new issues crop up. In the end, it is your decision that matters for the table, not Google's, not Jeremy Crawford's¹ and not RPG.se's.

Table results

In our games implementing this method has vastly cut down in the amount of rules arguing and has improved flow and fun for the whole table. We've played this way under multiple DMs (not just me) and I've also done this as a player. It has worked effectively in each situation. It takes a bit of time to fully work and rules quibbles and issues are never fully eliminated, but it is a vast improvement.

^{1 - You also might find it helpful to note that you are correct on your stance on designer clarifications. They are não RAW (though they might be a RAW interpretation). And they are often expressing how the game is intended to be run (often called Rules as Intended or RAI). None of which has any binding impact on how you rule at your table. Note also that Crawford tweets are now explicitly unofficial rulings.}

Establish a group at-table norm: we are here to play, not to argue

You need to address this before the next session starts, and get buy in from the whole table. Discuss rules before and after the session, but once you hit "play" rules discussion/argument are not part of the play.

Some people get a lot of enjoyment in discussing and arguing about the rules. (Hence sites like this one). But not everyone does, and some people just want to play. Your other players' play experience is being encroached upon by this player's approach.

Get buy in from the whole table and don't begin until all agree. You need the support of the other players in this. Yes, this is called peer pressure, and it is a positive form of that.

You can also take this a step further and develop an at table dispute resolution tool if your table needs that. I outlined one here a while back that you may find useful. (Our table finds that approach healthy and helpful).

An agreed verbal cue can be a useful tool

Our verbal trigger for any in-play question on a ruling is I thought it worked like this {say how one thinks it works} Can be used once for a given situation. This verbal cue allows a DM to catch and correct a mistake, to make or revise a ruling, and then play on. Or, to say, "it works like this" and play on.

As above, a tool or technique like this needs to be settled and agreed upon by the whole group in order for it to be effective.

The top-voted answers are very good. I'd like to highlight one thing in particular in your current protocol, bullet point #2:

If I don't know a rule off the top of my head I will look it up

I will suggest that this is a mistake, and is the first step that puts you on this path of "challenging" DM rulings in-game. Consider trying to run a game with the exact opposite philosophy; try to commit to no book-lookups by the DM at all during the game. Stuff in immediate sight on the DM screen can be acceptable. Rulings can be revisited after the game, and possible resolutions might be: (1) practice remembering that rule better, (2) add it to the DM screen, (3) document a house-rule that your discovered way seems better.

This is sort of an old-school sensibility that makes the game flow much faster.

Good points in the answers so far. Let me add one more.

Both you and the players build a mental picture of a fictional universe.

This universe contains both "physical" and "magical" laws, some similar to the real world and some different. It also contains both published geography, history, and people and those developed for/through your game. Building an universe is fun. Understanding an universe is important for gameplay because it gives the players agência, the ability to let their characters act in the universe with a realistic option of success.

• In the real world, if you stand in next to a small creek you have alguns idea if you can jump across. You might underestimate how slippery the other bank is, or you might have little experience in jumping with a hiking pack, or you suddenly notice that you're no longer 16 years old. Still, you have alguns idéia.
• Even without personal experience (I hope), you will have some idea how much damage a pistol bullet will do to a human. Your information will be less certain than in the jump example, and as a gamer you will be aware that the concept of a "critical hit" translates to reality. A hit to the arm might go through the muscle, or shatter a bone, or sever a major blood vessel. Still, you have alguns idéia.
• Um ladino personagem terá alguns idea if he or she can climb a castle wall. He or she has done it countless times. Again, there are risks. The stones might be more slippery than they look. It might be impossible to get a dagger into the cracks. But he or she has alguns idea what will happen. The jogador of the rogue gets an idea what will happen by studying the rules. "I would have to roll a crit to fail at this."
• A barbarian hero personagem will have some idea if he or she can defeat a non-player character. The barbarian looks how the NPC grips the sword, if the eyes dart around or are steady, if the armor looks well-cared-for or ill-fitting. Again, plenty of risks. But he or she has alguns idea what will happen. The jogador of the barbarian gets an idea by studying the rules. "If this is the usual mook castle guard, I will defeat him and stay unharmed."

Rules knowledge is much less intuitive than real-world knowledge, but it can give the exact odds if all modifiers and rules are known.

Players are trying to make their characters do impressive feats.

In this, they are in a contest with the GM ("our party defeated the Boss Monster") and with each other ("my ranger defeated the Boss Monster"). As the game goes on, they are constantly evaluating their options. They want to sentir-se bem because their character fez bem against the challenges of the fictional world.

As pointed out above, doing this requires the players to understand the fictional universe.

Imagine that you have an important exam in the real world. You study, you worry, you go there and you think you aced the exam, but as you hand it in the teacher says "hmm, I see you used a fountain pen. Didn't you know that you devo use a pencil?" Some stupid little rule you didn't know. Or worse, a rule you did know, now that it is mentioned, but which you forgot.

That's how players feel, time and again, if they made a plan for their character and the rules (and world) interpretation of the GM makes it fail. But that's what will happen, because the players' knowledge of their fictional world doesn't come close to their knowledge of the real world.

If the players are incerto about the fictional world, they may come prepared to argue the world interpretation on which they have staked the actions of their players. If they are certo some approach won't work, they are less likely to select that course of action to start with.

A partial solution:

Talk to your players about how you interpret the rules outside game time. In abstract, without reference to the specific characters. "Do you think a Cleric can ...?" and so on. Involve them in creating the history and geography of the world. This gives a "common operational picture" of the world. As a GM, you are still required to have secrets and surprises, but the world is something you share with the players.

I use the phrase "Here's the current ruling, it may or may not be final"

Sometimes I am not 100% sure of the answer to a ruling, even after having done a quick google during the session. I will normally get a feel for how the situtation should be playing out and sometimes, although not always my players will have an opinion.

What I do is take everything into account quite quickly and make a decision. If I am at all unsure of this decision I will say something along the lines of "Ok here is what we are going to go with now, i'll have a proper look after the session and post a full decision"

What this does is the following:

• Shuts down any discussion about the ruling
• Allows me and the group to discuss the ruling after the session
• Allows me to flex the DM powers of "We are moving on now"
• Lets us have a quick resolution in session, but not a game-breaking introduction of a bug **

The group reaction to this has always been ... well... nothing, because I make it inentionally into a non-issue and move on. If at that point players are wanting to have further discussion I will specifically tell them that's what we are going with and we are moving on.

** This point is for me one of the most imporatant. I do not always know why the RAW, or RAI are there but I like to make sure that if we accidently go down homebrew that we do it with understanding and purpose, or else stick to the recommended rules.

Have you and your players discussed moving to Pathfinder?

As I understand it, 5e is meant to not run on and hard-and-fast rules as they detract from the narrative. In a system where most of the questions have very clear, well-defined answers, you and your players shouldn't spend as much time sorting through the internet of opinions on how to rule something.

The alternative, of course, is to just make a ruling on the fly and stand by it. This is, as I understand it, the whole point of choosing 5e over pathfinder (besides obvious campaign settings)

Vejo esta resposta for more information on the topic, with specific interest in the following points:

[Use Pathfinder] If the GM not making up/ignoring/modifying rules is part of your gaming social contract.

[or] If you want a complete ruleset, in the sense that the rules provide at some level for all player actions and RAW gameplay is supported/encouraged. D&D 5e will never be 'complete' in this sense because that is not an aim of the developers.

Obviously the migration may be a lot of work, but you may find that if your players are very frequently concerned with the constraints of the world around them, it may be worth the effort.

If you're confident it's not a system problem, you may need to be more clear where the boundaries and rules are, since you need to create them on the fly more in 5e. Always keep your party well informed, because a DM is the player's window into the universe, especially in a more narrative-driven format like 5e.

Things that I've found work well for dealing with Rules Lawyers:

1. Use the term "rules lawyer" early and often. Put this type of behavior in a negative light in an effort to discourage the behavior. Emphasize the fact that making everybody else stop what they are doing while the rules lawyer argues their point is selfish and disrespectful to you and to the other players.

2. Tell players that keeping the game moving for everybody is more important than debating minutiae. If it is not a matter of life and death for a character then it is simply not worth interrupting the game.

3. Tell players to hold debates until after the game sessions ends or there is a break from the game such as when running out to grab food. Tell the rules lawyer that your decision stands in the specific case but if they have a convincing reason for a different interpretation of the rules then they should present it away from the game and you will keep it in mind for future encounters.

You're the DM. This means that all of the gods in the campaign work for you.

When the player begins to argue, calmly state:

Your hubris has offended the gods.

Then roll 3d6 for each level of the offending player's character. The sum is the damage done by the lightning bolt that hits him.

Termo aditivo

This should not be a surprise that is sprung upon the players. Instead inform the players that the gods are offended by people who argue about how the cosmos is run.