It isn't exactly rocket science. Even the occasional journalist might have been able to work it out, had they not become obsessed with the chimera of Mrs May's two-year "implementation" period.
Listening to Mrs May's Florence speech, I was reminded of that old joke about President Lincoln's assassination. "Apart from that, Mrs Lincoln", said the obsequious theatre manager as the distraught lady rushed for the exit, "did you enjoy the play?"
Seen in the same context, Mrs May's "open and generous offer" said to be in the order or £20 billion - has about as much impact on unblocking the stalled Brexit negotiations as the rendition of Our American Cousin
had on Mrs Lincoln's state of mind shortly after 10pm on 14 April 1865.
The sticking point, which is preventing the talks moving to cover the transition period and future relationship, is the settlement of the so-called "conditions of the UK's withdrawal". Time and time again, Barnier has told the UK directly and indirectly that, until there has been "sufficient progress" on the three outstanding issues, there can be no discussion on other matter.
Even the day before the Florence speech, M. Barnier was telling a parliamentary audience
in Rome that "the sooner we make real 'sufficient progress' on the conditions of the UK's withdrawal, the sooner we can begin discussing our future partnership".
"This", he said, "was the approach set out unanimously by the European Council on 29 April in its guidelines. Above all, this approach is an essential condition for the success of these negotiations".
Yet, the following day it was precisely this "essential condition for the success of these negotiations" that was ignored by Mrs May. Pointedly, she offered nothing of substance on any of the three outstanding issues.
On perhaps the most troublesome of the three, the Irish question, her superficial treatment of the issue verged on the insulting. She loftily declared, "we have both stated explicitly that we will not accept any physical infrastructure at the border", adding: "We owe it to the people of Northern Ireland and indeed to everyone on the island of Ireland - to see through these commitments".
The point here is that was all she said. And with the Commission already having rejected the ideas put forward in its position paper, there is nothing currently on the table. Mrs May came to Florence and left the table bare.
So it was that the very same day, M. Barnier responded to the speech with a formal statement
,virtually repeating much of what he had said the day before. Wryly, he also noted: "Today's speech does not clarify how the UK intends to honour its special responsibility for the consequences of its withdrawal for Ireland".
As to Mrs May's request for a transition period, once could almost sense the weariness as M. Barnier declared: "The sooner we reach an agreement on the principles of the orderly withdrawal in the different areas and on the conditions of a possible transition period requested by the United Kingdom the sooner we will be ready to engage in a constructive discussion on our future relationship".
"David Davis and I", he said, "will meet in Brussels next Monday to begin the fourth round of the negotiations", then telling us that: "We look forward to the United Kingdom's negotiators explaining the concrete implications of Prime Minister Theresa May's speech".
With the sting in the tail, he concluded: "Our ambition is to find a rapid agreement on the conditions of the United Kingdom's orderly withdrawal, as well as on a possible transition period".
Concentrating on the play rather than the assassination, though, newspapers such as the Mail
chose to home in the opening lines of M. Barnier's statement, headlining: "EU chief negotiator Barnier praises the 'constructive spirit' in May's Florence speech as he says the landmark address is a 'step forward'".
In fact, what he actually said was: "In her speech in Florence, Prime Minister Theresa May has expressed a constructive spirit which is also the spirit of the European Union during this unique negotiation". But he then went on to say: "The speech shows a willingness to move forward, as time is of the essence".
In the very next sentence, he said: "We need to reach an agreement by autumn 2018 on the conditions of the United Kingdom's orderly withdrawal from the European Union. The UK will become a third country on 30 March 2019". That was the message that should have been on the headlines, with the observation that Mrs May had brought agreement no closer.
As to the tone of his statement, it is not M. Barnier's style to be overtly critical of his negotiating partner and, doubtless, he wished to avoid giving the Labour party material it could use in its conference which starts today. To have done so would have opened him to the charge of interfering in UK domestic politics.
Nevertheless, he could not have been more unequivocal: no talks on transition or trade until there has been "sufficient progress" on the withdrawal issues. And, on those very issues, Mrs May had nothing at all to offer. Measured in terms of whether she has unblocked the talks, therefore, the Florence speech was a dismal failure.
Despite that, we are in the bizarre position of the media, almost unanimously focusing on the transition period or "implementation" period, as Mrs May insists on calling it. Scarcely any have made the point that, without the "essential condition for the success of these negotiations" being satisfied, there is going no agreement and no transition period.
If there was any doubt about this or the solidarity of the Member States we then saw an intervention by Emmanuel Macron
, echoing Barnier by stating: "Before we move forward, we want to clarify matters concerning the settlement of European citizens, the financial terms of exit and the question of Ireland". He added: "If these three points are not clarified, we will not be able to advance on the rest".
Macron was flowed by Germany foreign minister, Sigmar Gabriel, who told reporters that he had been disappointed by the Florence speech, saying: "We heard nothing concrete. It is time for the government of Great Britain to clearly state under what conditions it wants to leave the European Union". And once she has been re-elected chancellor today, Mrs Merkel will be echoing these sentiments.
We now have to wait for Monday and the resumption of the Brexit negotiations, when Mr Davis will be expected to explain the "concrete implications" of Mrs May's speech, coming up with proposals for resolving the withdrawal issues the so-called "Phase One" issues.
Upon this will depend on whether M. Barnier goes to the October European Council with a view on whether there has been "sufficient progress" for the talks to move on. But, one suspects, if there was anything forthcoming, Mrs May would have at least dropped a few hints at Florence.
As this stage, the likely outcome is that Mr Davis will bring nothing new to the table. Back in Whitehall, the cupboard is bare. Like Old Mother Hubbard, Mrs May has nothing to give him the cupboard is bare.
Predictably, M. Barnier will then reiterate his points, with the Thursday press conference dominated by his regretful announcement that there has been insufficient progress for the talks to move to the next stage. And, no matter how diplomatically couched, this will be interpreted as a rejection of Mrs May's "open and generous" offer.
That gives us a few days for the febrile elements of the Conservative Party to stoke up their indignation before the start of the annual conference in Manchester. And, after a warm-up speech by Davis on the Tuesday, we will have the Prime Minister delivering her conference speech on Wednesday, under the banner: "Building a country that works for everyone".
By then, she will have had the measure of the mood of the party. If there has been a hostile response to Barnier's announcement, Mrs May will be under huge pressure to respond to the "humiliation" dished out by the "Eurobullies of Brussels". On the back of her general election disaster, Mrs May is already fighting for her political life. A weak response or one perceive to be weak could trigger the process that will have her deposed.
At this point, the Prime Minister will have very little room for manoeuvre. She could, perhaps, go for the long game (in political terms) and ask the party to wait for the European Council to decide on its next move. After all, part of the Florence strategy is to sideline Barnier and appeal over his head to the leaders of the Member States.
A stronger move would be to issue an ultimatum to the Council, telling it to accept her offer, or she will walk away from the talks. She might even propose a "summit" of the 28 to thrash out the issues, in a huge make-or-break gamble. Or she could, quite simply, decide to walk.
The latter would certainly please the "Ultras". They are convinced that the EU is bluffing on its withdrawal demands, and have persuaded themselves that the UK would suffer no damage by trading on WTO terms with the EU Member States. A "no deal" exit holds no terrors for them.
The big question, therefore, is how far will Mrs May go? To my mind, with the cupboard bare on the withdrawal issues, she has to tough it out or go under. My bet is on her either walking, or delivering an ultimatum which will have us walking after the European Council on 19-20 October.
Thus, while the general thrust of the media coverage yesterday was that Mrs May had extended the Brexit process by two years, the actuality could be the polar opposite. The Prime Minister could have set in train events which, if they follow their logical course, could dramatically speed our exit from the EU.
Far from waiting until March 2019 or 2021 as some newspapers would have it it could be all over by Christmas. For form's sake, departure date could even be set for 1 January 2018 - with not a transition to be seen.