Does anyone know of a game that was drawn under the mandatory 75 move rule?

Correct. if we were to interpret "legal moves" like that, then white can checkmate with a single bishop in a rook vs bishop endgame as follows:

Note that it is not immediately checkmate after white's move. Black first gets the move, but then he is checkmated when he runs out of time. Also if white runs out of time in the starting position, then it is a draw.

This would also do

If you accept my interpretation of checkmate in my previous reply to you, then I would say the FIDE laws define either of those positions at the instant the flag falls as checkmate if Black has not completed the required number of moves. This is by Black's failure to comply with 6.3.1 rather than 6.9. After the breach of 6.3.1 (at flagfall) the game is no longer a licit game and Black can therefore make no moves at the point of flagfall, but has the move and is in check.

I don't assert that this is what FIDE intended, only what the laws say. In fact if 6.9 didn't include the second sentence it would make no difference to the result whether or not the positions were checkmate. 

Edit

If you were to interpret, "... the opponent has no legal move" in art. 1.4 as "... no piece owned by the opponent has a legal move" then the positions would not be checkmate. On reflection that is probably FIDE's intended interpretation. It would then be unnecessary to assume the opponent 'has' the move, because that follows from the fact that he is in check and miscellaneous other rules.

On that interpretation @Arisktotle's new checkmates are, disappointingly, also not. 

@MARattigan:

Actually, in a practical sense there are no simultaneous events (to the 10th decimal) except when 2 objects meet (when A hits B they are at the same place and time), the latter by the model of the same Albert Einstein. Without meeting points, relativity theory could not exist. Since the clock never physically meets the move, they can not be accurately decided as simultaneous. The issue is therefore more one of "lack of agreement on the event order". Both sides might claim in their own favour and there is commonly nothing tangible to decide the issue. Throwing dice sounds about as the right approach unless as an arbiter you are capable of interpreting the ear reddening of the liar. Amazingly, most players are truthful which explains why there are relatively few nasty incidents. Not all players know the rules in these situations and give in when they are explained to them.

On the point of article 6.9. I wasn't aware it was so much different from article 5.2.2. It is obviously irrational since nobody can explain why the logic and the algorithm for the one-sided article 6.9 should be any different from the double whammy 5.2.2. (edit: it's more complicated than this; be back on it some other time)

I am not a lawyer and you are. Which places you in a favourable position where you can withhold some common concepts and practices in law to win an argument. But fortunately I have a good brain capable of recognizing inconsistencies and other illogicalities. Here is one that I assume is commonly known amongst lawyers which I cannot verify:

The one thing not to do in a lawbook (we are discussing the laws of chess) is to define a "legal X". You may define "X" which makes it available for reference in another place or article as "legal X". But you cannot define "legal X" for the simple reason that all things you define in a lawbook are already legal. By defining a "legal X" you not only assign an elusive status to it as something "specially legal" but you also obscure and compete with the common natural language interpretation of "legal X" as given above. Considering you are a lawyer you should have noticed and mentioned this peculiarity in the chess laws a long time ago. The abuse of the "legality"predicate forces us to invent special properties to distinguish what we think was intended (ah, you hate this word!) with legality in one place or another in the text and how it differs from our natural use. No wonder different readers get different viewpoints on the law. Note that "legal moves" do not exist in game theory since such a concept would mathematically equate to "legal  axioms" which is insanity beyond all boundaries. There are only "moves".

Lawmakers with an IQ over 50 would not only avoid the expression "legal move" for the prior reason given, they would also avoid it because article 3 is not at all about "legality". It is about the capacities of pieces. By defining them inside a lawbook they become "legal".

I know why FIDE went wrong with this but of course you won't find it in the laws. Defining chess properly requires 4 different approaches to the move concept all of which contribute to its definition: (a) capacities of pieces (b) the position- and history- related requirements  (b) the role of the player as the move owner (c) the intensional attributes of the sequential move game you are playing. All 4 of them together determine what is a legal move is - just as rating a commercial enterprise as legal requires conformity with a large number of laws. Like most rule-makers FIDE attempted to reduce concepts and text and went about 3 bridges too far in that effort.

I will be back on the "series of legal moves" and prove that "legal moves" can only be playable moves by the laws - in spite of the fact that the "legal moves" are misdefined.. Another day!

I don't know from where the idea that I'm a lawyer came. Presumably a jibe.

Totally agree that defining the term "legal" in a set of laws smacks of weakness of mind. I have attempted to mitigate the effect by suggesting the alternative "licit" in discussion for what you always thought it meant and reserving the term "legal" for the FIDE meaning(s). The "(s)" here because they also define "legal" in connection with position (with even less justification).

I don't see much difference between 5.2.2 and 6.9 regarding the phrases involving "series of legal moves" either. You'll have to clarify your point there because I've obviously missed it. I think the references to "any series of legal moves" were included by FIDE to emphasise that the mates need not be forced, and are actually redundant because they also say the players can play them. The players can play only licit moves and these are necessarily also legal.  Unfortunately in both cases the game is terminated, so the players can't actually play them - hence the need for some modification.

Sorry, retract. Thought you had written you are a lawyer! (when I think of it, I made this error before - lawyer won't leave my brain). I do not object to a different terminology. However then we are no longer discussing the FIDE rules. In the example I gave, article 3 is not at all about the legality of moves and it is not about licitness either. It is just about defining (chess) moves through the aspect of piece capacity. Just picking a different word won't resolve anything when it is not replaced with the predicate which is really appropriate.

Actually, no predicate is absolutely necessary because defining (chess) moves is sufficient. Worth considering is "the geometry of chess moves".

Note that whatever predicate replacement is used, causes the expression "legal move" to return to the natural language pool. It is still available  and probably necessary in articles where the new predicate (if any) is not applicable.

With regard to comparing article 5.2.2 and 6.9 I agree with you. I already edited my previous post promising to be back on this issue!

Well, that's at the heart of the issue. We agree that the game is indeed terminated after a flag fall or in a dead position. So there are no playable moves. In the case of 6.9 there are absolutely no playable moves after the flag fall, under article 5.2.2 the termination of the game must first be proved by some form of logical analysis. If a series of playable/legal moves can be found leading to checkmate, the position is not dead. For this approach we need not assume that legal moves exist in a dead position. After all, in a 2 valued logic you only need to discard one outcome (the position is not dead because I found a checkmate) to conclude the other one. No particular method is required to prove that point. One can establish that a position is dead even when no move is playable or legal. More intricate is article 6.9 where neither conclusion can be established by means of playable moves. I have to think about that one. Until recently I never looked into article 6.9. since I am not really that much interested in clocks. For instance they don't exist in compositions.

I announced that I could prove that the current "legal moves" must also be playable by the laws. That proof runs along a different line than my previous paragraph and posts. That paragraph only explains that permitting unplayable legal moves is not necessary for 5.2.2. What I aim to prove is that the current FIDE laws require legal moves to be playable which is a much stronger proposition.

@Numquam: Your case with the flag fall and the checkmate question is a valid one. It is however not anatomically different from the case I presented in #262. Both are about the question whether or not a position is checkmate when the king is in check after some kind of termination condition occurred - in your case a flag fall, in my case a dead position. So resolving one should resolve them all.

Note that the issue has very little to do with the death and half-death evaluations in the articles 5.2.2. and 6.9. Had there never been any sort of death exception in the chess rules, your issue would still exist. Probably FIDE would still have defined checkmate and stalemate by the "absence of legal moves" and someone in the room would still shout "that's checkmate!" after a player's flag falls while his king is in check. The room would laugh and skip over the event without discussion. What does it matter, flag fall or checkmate?, it's both 1-0. What complicates the issue under the actual FIDE rules is that there is an escape clause for (semi-)death conditions. In itself the evaluation of the (semi-)death state stands apart from the events leading up to it. For instance, one might not be happy with the current definition for legal move or checkmate in the first phase, while the same defintions could turn out to be appropriate in the second phase. Ultimately both issues require synchronized solutions. Btw there are many cases of coinciding termination conditions in chess, for instance "stalemate, 75M and death". In itself their occurrence is not much of an issue unless their game scores are different! Problemists are very much aware of it as they often explore such rule boundaries.

@Numquam: Note that both our phase 1 cases are equally dramatic when the king is not in check since that would produce a stalemate under the corresponding assumptions - no legal move, no check. Which, when unresolved, produces a conundrum at almost any flag fall or dead position. A workable storyline is therefore required!

Oh yes, there is (FIDE handbook version 2018):

9.6 If one or both of the following occur(s) then the game is drawn:

9.6.1 the same position has appeared, as in 9.2.2 at least five times.

9.6.2 any series of at least 75 moves have been made by each player without the movement of any pawn and without any capture. If the last move resulted in checkmate, that shall take precedence.

Note that the handbook gives no procedure to effect the draws per article 9.6 which gives rise to weird interpretations by arbiters. Like in soccer the arbiters apparently need to receive specific FIDE instructions on how to manage an international match! Practically, 9.6 could easily be enforced by the computer interfaces which are taking over the world of chess.

So here is the definitve argument with regard to the question on whether or not a "a series of legal moves" should be considered "playable". The answer is "YES" (to start with). Why?

The secret of understanding this expression is not in the legality or definition of chess moves. It is in the series. A series is not just a collection of things, in casu a collection of moves. It is an ordered collection of whatever object type it is applies to. Ordered collections are governed by an ordering rule. When no ordering rule is explicitly specified one can only assume that the intended ordering rule is considered self-evident. And so it is in chess. Chess moves are ordered by the order of play and subsequently time-stamped by move numbers! This is not language play and it's not a triviality. It only seems that way because the pattern of play order is engraved so deeply in everyone's brain that they can't properly inspect it anymore. But - after a 24 hr timeout - one might come to realize that playability can only be evaluated against the "rules of play" defined in the FIDE laws. And that all rules of play apply that affect the selection of ordered legal moves. For instance, the rules of play regarding who is on move, the alternation of the players, the progressive change of position (you don't play all moves from the same position but it evolves), the obligation to play if you can - AND (also see next paragraph) - the game termination articles.

So a series of legal moves must always be playable. At the same time there are rules of play - the dead rule, the flag fall - which may terminate the game on the spot aborting any attempt to construct a series of legal moves beyond them. Therefore these moves are not playable. This conflict marks a contradiction. These situations require the availability of playable legal moves (to form a series) and may turn out the result that the game already ended and the moves were not legally playable. This invalidates the premise required to arrive at the "draw" conclusion and thereby renders it invalid. The situation for the flag fall is not completely the same as for the dead rule but I'll ignore that in this post.

My point was only to show that the FIDE rules are contradictory. The mind cannot handle contradictions and is commonly incapable of spotting them. It will instead unconsciously construct a solution around them e.g. by inventing a new interpretation of existing rule texts, or by setting off to incorporate the contradiction in a weird new theory by assigning an identity to it. The latter has happened to mainstream retrograde-logic which is beyond the scope of this discussion.

However the only proper way to handle a contradiction is by (a) acknowledging it (b) retracting some of the existing rule formulations (c) replace them with better ones. Often forgotten is "(b)" by lacking the understanding that you cannot proceed from a contraction ever in any way.

So I proposed to amend the FIDE laws in the concerned articles to clearly indicate that the series of legal moves are played in an analytical service module with slightly different rules of play. That opens the door to specifying whether or not 75M and 5REP draws should be taken into account when evaluating series of legal moves.

Feel welcome not to respond to this post. It is truth.

KRNvKR was considered a draw until computers showed us a win but by taking over 50 moves. Otherwise the 50 move rule applies. Online and OTB the draw must be claimed.

According to Nalimov four out of five KRNvKR are in fact drawn and the wins for either side should be possible against any defence within  a total of 40 moves.

Troitzky (organic) demonstrated around the time of the second world war that some of the wins for White in KNNvKP need 115 moves against best defence in the absence of the 50 move rule. The syzygy-tables.info site says around 7% of positions in this endgame can be won in the absence of the 50 move rule, but not against best defence if the 50 move rule is in effect (the great majority frustrated White wins). It is possible that, if no claim were made under the 50 move rule, some of these would also be impossible against some defences under the 75 move rule, which doesn't need to be claimed, but no published information is available to verify that.

Various other endgames were already known to include positions that take more than 50 moves, e.g. KRBvKR which can need up to 65 moves in the absence of the 50 move rule. The syzygy-tables.info site shows a very small percentage (0 to the printed accuracy) of frustrated White wins under the 50 move rule. This may have been the endgame you intended to quote. Of course, without imperfect play, the 75 move rule would have no effect on that endgame. 

According to the current FIDE laws, both the 50 move and 75 move rules apply only if the game is played under competition rules and in that case a draw under the 50 move rule must be claimed but the game automatically terminates in a draw if the conditions for the 75 move rule are met.