Whoever wins the succession battle in the Tory party will face exactly the same Brexit conundrum that brought down May.

And so the turmoil continues. Fresh out of European Parliament elections that witnessed both the Labour and, especially, Conservative parties receive a good shellacking, we now segue neatly onto the United Kingdom‘s next political earthquake – the replacement of the incumbent prime minister.

In the few days since Theresa May announced her intention to stand down, no fewer than 11 of her colleagues have thrown their hat in the ring as candidates to replace her. And more may well follow suit.

So brace yourselves for several weeks of bitter in-fighting as colleagues tear strips off each other in their desperation to accede to the highest office in the land. Leadership elections in this country are a little like primaries in the US. They provide a great opportunity for parties to wash their dirty laundry in public before choosing a new leader and claiming to have been totally united all along.

And of all the elements of division, it is, of course, Brexit that dominates. Here, the fault lines are beginning to appear. Boris Johnson, Andrea Leadsom and Dominic Raab are the candidates insisting that the UK will leave the European Union on 31 October with or without a deal.

Jeremy Hunt, for his part, argues that leaving with no deal would be “political suicide” for the party. Rory Stewart has been vociferous in his opposition to this outcome, saying he would refuse to serve in a government under Boris Johnson because of the latter’s approach to Brexit. Matt Hancock, on the other hand, is insisting on the need to leave with a deal.

So, broadly speaking, we have two camps. The problem is, it is far from clear how either camp would manage to deliver what they appear (for the moment) to be promising.

Take “no deal”. There is, clearly, no majority in parliament for such an outcome. Quite the contrary. Indeed, passions run so high that it is far from inconceivable that, faced with a new prime minister intent on taking the UK out of the EU with no deal, a sufficient number of Conservatives might vote against their own government on a motion of no confidence to bring it down.

Yet, as Speaker of the House John Bercow hinted in an intervention in the United States, there remains a route short of this “nuclear” option. Bercow made it clear that he would be willing to facilitate an emergency debate providing parliamentarians with an opportunity to prevent a no-deal outcome.

If no deal is not possible, what about leaving with a deal? Once again it is difficult, if not impossible, to see how this might be achievable. The Tories might be changing their leader, but they are not changing the numbers in parliament. May’s deal failed to garner a majority three times, and there is little sign of that changing.

Equally, the EU has made it clear that no renegotiation of what has already been agreed is possible. Whatever the contenders might claim about approaching a new negotiation with “renewed purpose” or “greater unity”, it would seem that they might as well bang their heads on a brick wall a few times. The deal is the deal is the deal. Pass it, or find another option – remain or no deal.

On the surface at least, one possible option would be for whoever takes the crown to leverage their newfound popularity by going back to the people. After all, a cursory glance at parliament will persuade any new leader that he or she will not be able to actually govern, given the lack of majority. Moreover, any new prime minister would enjoy the not insignificant advantage of being neither Theresa May nor Jeremy Corbyn.

But then he or she will pause and think of Sunday night, when the Conservatives fell to a vote share in single figures in a national poll and Nigel Farage launched his new insurrection rooted in anger at the government’s failure to deliver Brexit.

Now, of course, this was a European election. History suggests that people vote differently in these “second order” contests, not least because the electoral system used is different from the one we use to elect a government. That being said, the fact remains that the Tories were thrashed, and it seems clear that attempting to have an election prior to delivering Brexit would equate to performing electoral hari-kiri.

Which presents us with a dilemma: Reshaping parliament via the ballot box is not a viable option. Yet sorting Brexit without an election seems impossible.

And so, once the leadership contest is done, once the dust has settled and the removal men have left Number 10, we will find ourselves precisely back where we started: with a Brexit stalemate in parliament that looks impossible to overcome, whoever the prime minister charged with attempting to do so. It is enough to make you wonder why so many of them are after the job.

The views expressed in this article are the author’s own and do not necessarily reflect Al Jazeera’s editorial stance.