As the Brexit school term gets into full swing, London increasingly resembles the smart alec pupil who wants to show he can outwit the teacher. But the teacher, Michel Barnier, simply sighs and puts the uppity pupil in his place with some awkward facts.

This is the tenor of the Brexit negotiations on Ireland. Britain has shown signs of pulling up its socks, but must try harder, the EU report card might say. But it should think twice about outsmarting the teacher.

To take one example, the British position paper on Ireland, published on 16 August, needled the EU that there were plenty of situations where there was the free flow of agri-food products across an EU-third country border without any controls.

"Switzerland has a common veterinary area with no border controls at the EU-Swiss border," says a footnote, "as well as a regulatory equivalence agreement for some non-trade aspects of animal health regulation."

So why then could something similar not be arranged to cover the huge flow of agri-food products across the land border in Ireland?

It is, indeed, true that there are no controls governing animal health, the movement of live animals, or food products across the Swiss-German, Swiss-French and Swiss-Italian borders. Such controls come under the so-called Sanitary and Phytosanitary (SPS) measures which will be a major issue on the island of Ireland.

In Switzerland’s case the agreement to waive controls was signed in 1999 and came into force in 2001.

The British example irked the EU side no end for two reasons.

One, was that the whole question of dealing with agri-food is linked to the UK’s future trade relationship with the EU (Phase II), so this was an example of the UK using Ireland to jump the gun on the EU’s immovable timetable for negotiations: divorce first, then the future second.

The other reason was that, according to senior EU officials, there is simple no comparison between Switzerland and the UK.

"The conditions are," one senior official told RTÉ News, "that Switzerland has signed up to taking over the entire EU Sanitary and Phytosanitary acquis [body of law] and to update it on a regular basis. This happens a lot. It is updated on an almost weekly basis because you have new hygiene standards in stables or whatever."

There is also no comparison in terms of geography or volumes of trade.

"The risk of live animals flying in to Switzerland and being re-exported into an EU member state is not exactly the same," says the official, who has an intimate knowledge of the scale of animal movements, both live and dead, across the Irish border and from Ireland to Great Britain.

"The size of the market is different."

The other big difference is that the agreement to waive SPS controls on the Swiss-EU border was reached at a time when Switzerland looked like it was going to join the European Economic Area, the free trade area that combines EFTA and the EU, or even the EU itself.

In other words, the agreement was supposed to be a temporary fix ahead of Switzerland moving closer to the EU regulatory sphere. It was done with the perspective of closer approximation and harmonisation with EU standards.

But whereas Switzerland was converging, Brexit means that Britain is diverging, deliberately moving away from the EU’s legal order.

What about how the Swiss arrangement has been policed?

In this case, the European Court of Justice does not preside over the controls. Instead, there is a cumbersome guillotine system. Switzerland’s access to the EU single market is governed not through EEA membership (which in the end Switzerland refused to join) but through an elaborate web of bilateral deals.

If the Commission decides that Switzerland has blatantly violated one of these agreements then they all fall. One example was the Swiss referendum that ended free movement of EU citizens: the EU froze a range of bilateral agreements until Bern amended its legislation to permit free movement.

It’s unlikely the EU would permit a similar situation for the UK as it is too unwieldy and too messy when it comes to ensuring that rules are being followed.

In order to ensure that EU agri-food standards are maintained on both sides of the border post-Brexit, and in such a way as to avoid SPS controls, the UK would, at the very least, have to do what the Swiss do: sign up to the ever-shifting body of EU rules governing animal health and food products.

Not only that.

The UK would have to ensure those rules were also enshrined in any future free trade agreement it enters into with other third countries. And since Britain is a net importer of food, and is expected to follow a cheap food policy, then that will mean any trade agreement with the US, or South American countries, will be severely curtailed by Britain’s need to comply with the EU’s food safety and animal health regime.

If food products are coming into Northern Ireland from Argentina as part of a free trade agreement, then without border checks there would have to be a guarantee that those products complied with EU rules. Otherwise, if those products got into the Irish Republic they would undermine the single market.

The Task Force has already made this clear in its own position paper, published on 13 July, entitled Essential Principles on Goods placed on the Market under Union law before the Withdrawal date.

Paragraph IV states that the divorce agreement must specify that live animals and certain germinal products - here we are talking hatching eggs, fresh semen, oocytes and embryos - will be subject to the EU’s animal health, hygiene and food safety rules if they enter the single market (eg, coming from Northern Ireland into the Republic).

The paper makes it clear that "all animal-derived food and animal derived-feed, as well as animal by-products entering the single market as of the withdrawal date should be subject to the applicable rules for importation".

By applicable rules they mean the Official Controls Regulation. This is not just any piece of EU law. The OCR is a vast piece of legislation that took four years to negotiate at EU level and was only finally agreed in June.

"It is extremely rigid," says one Irish agriculture official.

In other words, the EU will not compromise on such a hard-fought piece of legislation, that was designed to prevent the kind of food and animal health scandals such as BSE and Foot and Mouth disease (among others) for which one EU member state was particularly notorious: the UK.

The above position paper was published as part of what’s called the Article 50 Withdrawal negotiations, ie the two-year divorce talks.

It only refers to the fate of food products which enter the market before 29 March 2019, ie the withdrawal date, but then find themselves still on the shelves at midnight that night. In other words, the paper deals with overlap anomalies.

But it shows how seriously the EU will take the agri-food issue.

Where that scrap will really happen is during what are called the Future Framework negotiations. There the whole gamut of Britain’s trade and customs relationship with the EU will have to be negotiated, and that will take several years. The agri-food conundrum on the island of Ireland will go to the heart of that process.

Michel Barnier demonstrated on Thursday how inflexible Europe will be when it comes to any attempt by Britain to use Ireland to undermine the single market.

Launching the Task Force’s Guiding Principles paper on Ireland, Mr Barnier told reporters in Brussels: "What I see in the UK’s paper on Ireland and Northern Ireland worries me. The UK wants the EU to suspend the application of its laws, its customs union and its single market at what will be a new external border for the EU, and the UK wants to use Ireland as a kind of test case for the future EU-UK customs relations. This will not happen."

What he means by "test case" is that the EU will not tolerate any attempt by London to pony up a technical fix on the Irish border to ensure an "invisible" border, and then ask for it to be replicated on the Dover-Calais frontier.

The mantra from the Commission, and the Government, is that the Good Friday Agreement is a unique situation, underpinned by EU law and supported by EU money, which will require a unique, stand-alone solution.

The paper deliberately did not "trash" (as one EU official put it) Britain’s August position paper on Ireland.

This is because the Task Force is not going to get into offering technical solutions, or critiquing the UK’s solutions, on paper until the UK has spelled out politically how far it is going to go to protect and preserve the peace process, especially the North South elements of it.

That means a sharp contrast between the UK paper, which was 27 pages long, and the EU one, which was just four pages long.

Commission officials have been sensitive to any narrative that might take root in Ireland that the British are now the ones doing the running on solutions, and not the EU. Thursday’s Guiding Principles paper went through three drafts. It’s understood that the third draft at the end of August added a new paragraph (the third) explaining why no solutions would be found within the four pages.

"The onus to propose solutions," the paragraph reads, "which overcome the challenges created on the island of Ireland by the UK’s withdrawal from the EU and its decision to leave the customs union and the internal market remains on the United Kingdom."

Keeping the Irish issue at the level of principles is reflected in the structure of the negotiations. Ireland comes under the format of a High Level Dialogue, carried out by the two most senior officials, Olly Robbins on the DexEU side and Sabine Weyand, on the EU Task Force side.

One senior Task Force official puts it this way: "It's a dialogue at co-ordinators level. It’s not a formal negotiating group because we feel there’s a lot of work to be done before we can move on to any kind of technical or practical discussions.

"We need a shared understanding of our starting point, and of the principles that we are working with, and not just – as seems to have been the intention of the UK before the third round [of negotiations] – to reiterate their support for implementing the Good Friday Agreement.

 "It does not seem sufficient," the official says. "It needs to be fleshed out. This is an international obligation. The UK is co-guarantor of the agreement.

"We have to do more work, going through the North-South, East-West dimensions, and to see what the impact is once EU law ceases to apply in Northern Ireland. A lot of this co-operation is underpinned by EU law, EU regulations. It might well be that some areas can easily continue, and some areas cannot. This will first properly have to be analysed."

One issue which will prove particularly complex is the rights of those in Northern Ireland who proclaim Irish, and therefore EU citizenship.

How will those rights be protected in the anomalous situation where EU citizens will be living on a piece of territory that will move out of the EU?

In many situations, your EU rights only come into play when you exercise free movement across an EU border. But there will be a potential scenario in the future where two people from Belfast might move to France and only one of them will be able to enjoy social welfare entitlements because they have an Irish passport.

The concerns expressed in the EU’s paper are largely shared by the Irish government.

"The paper reflects very fully the Irish Government’s priorities," says one senior Irish source. "It's also very correctly putting the ball back over the net. It keeps the pressure on the British."

But where that pressure leads will be interesting. Britain wants to move to the future trade talks immediately. The EU side is increasingly downbeat that sufficient progress will be made on the Irish issue, the question of EU citizens’ rights in the UK and on Britain’s exit bill (the assessment on the latter is particularly negative).

For the moment, Brussels and Dublin are content to nudge the UK out of its comfort zone on the border. The leverage they have is Britain’s desperate need to graduate to talks on the future trade agreement. What space Britain gets nudged into is not yet clear.

A clue is to be found in recent warnings in public by Simon Coveney, and in private by Task Force officials, that the Northern Ireland political parties need to get their act together to restore the Executive. The space this is heading into is the North - and Dublin, Brussels and London would prefer the Executive and Assembly to be up and running so as to buy in to whatever Brexit produces by way of a divorce treaty, and a future trade agreement down the line.

The potential during that process for political and constitutional upheaval is enormous. Externalising the ancient tribal conflict in the North in the past with Bill Clinton, George Mitchell, General De Chastelain and company worked because the local parties had all the time they needed to metabolise the hard compromises.

This time around the clock is ticking, and a cliff edge is getting closer. The Tories are in turmoil over the very subject that is at hand - Brexit - and they rely for their survival on the DUP, a party whose instincts are not known to be adventurous on constitutional issues.

It's going to be a long school term.