The other, Clermont, will be landing from the Auvergne at the end of the week for a third time. Like the rest, they do not know what it takes to beat the Ospreys in Swansea.
They reappear at the Liberty Stadium on Friday night with their Welsh opponents in defiant mood, determined to settle for nothing less than the win to strengthen the prospect of carrying the GUINNESS PRO12 flag into the quarter-finals of the Champions' Cup.
Ulster will be ever willing to bust the collective gut and ensure the Welsh region are not on their own in the last eight. Back in serious contention as the other leading GUINNESS PRO12 contender after arguably the come-back of the season in Oyonnax last Sunday, Ulster face Saracens in London on Saturday with the English champions awaiting their toughest test of the season.
The penultimate round opens on Friday evening with Clermont in Swansea. This time they make the journey with control of probably the most ferociously competitive of the five pools awaiting the winner.
The Ospreys may have fallen a long way short against Leinster in the GUINNESS PRO12 last week but their home record against the French in Europe is in stark contrast to their recurring failure on the road. No Top 14 team has beaten them in Wales since Toulouse in the autumn of 2003 en route to losing that season's final to Wasps at Twickenham.
In the eleven seasons since, Ospreys' home record against French clubs is an imposing one: Played 13, Won 11, Drawn 2, Lost 0. This is it, match by match:
2004-5: beat Castres 20-11.
2005-6: beat Clermont 26-12, beat Stade Francais 13-8.
2006-7: drew with Stade Francais 22-22.
2007-8: beat Bourgoin 22-15.
2008-9: beat Perpignan 15-9.
2009-10: beat Clermont 25-24.
2010-11: beat Toulon 29-17.
2011-12: beat Biarritz 28-21
2012013: beat Toulouse 17-6.
2013-14: beat Castres 21-12.
2014-15: drew with Racing 19-19
2015-16: beat Bordeaux Begles 19-16.
When Clermont run out in Swansea on Friday, it will be ten years and one day since they first lost there, on January 14, 2006. Six goals from the former All Black Adrian Cashmore and tries from Richard Mustoe and Stefan Terblanche ensured a home win so emphatic that Clermont didn't even come close to the consolation of a losing bonus point.
Jamie Cudmore, the sole survivor from that match, fared a little better when Clermont retraced their steps three years later. Despite a purple patch of three tries during an eleven-minute spell in the second half, the Michelin Men still wound up losing a terrific contest, a Dan Biggar penalty squeezing the Ospreys home by the narrowest of margins, 25-24.
Of the vanquished that night, only Cudmore and the equally evergreen Aurelien Rougerie are still going strong. Ospreys, whose tries that night came from Tommy Bowe, Ryan Jones and Barrie Davies, have two survivors of their own - Biggar and Eli Walker.
They need no reminding of the fact that six years have passed since they last qualified for the knock-out stage. A team built around the formidable presence of Alun Wyn Jones, Paul James, Scott Baldwin, Justin Tipuric and Biggar know that it really is a case of now or never. A win would put them top of Pool 2 in readiness for a trip to Exeter in the final round.
After the ultimate game of two halves last Sunday, Ulster return to London in a position to challenge Saracens' unbeaten leadership of Pool 1. To say they owe the English club one would be the under-statement of the European season.
One losing quarter-final, before almost 40,000 at Twickenham three years ago, was bad enough. A second in Belfast twelve months later, a much closer affair at 15-17, proved hard to take, all the more so given the controversy over Jared Payne's early red card.
Despite having to play nearly the entire match with 14 men, Ulster almost managed to turn a gallant defeat into a glorious victory. They are now on a roll, having swept all before them in rebuilding a campaign that began with Sarries taking all five points in Belfast barely two months ago.
Nobody can say they have had an easy ride, not with a famous double over Toulouse followed by a game and a half in Oyonnax. Conceding 23 unanswered points in the first 40 minutes takes some doing. Responding with 24 unanswered points in the second 40 takes even more.
While the trick next time will be to avoid ushering the opposition off to a flying start, nobody can question Ulster's capacity for bouncing off the ropes, least of all Mark McCall. As a former Ulster player and coach, Sarries' director of rugby knows his native province inside out and upside down.
He will know that they will view Saturday afternoon at Allianz Park as a chance to put themselves in a position to qualify as pool winners as opposed to one of the three best runners-up. While their opponents still have to negotiate a trip to Toulouse, Ulster finish up on home ground against Oyonnax who have not won on the road all season.
Three of the four other PRO12 teams in Champions' Cup action this weekend may be out of the running but they can still play their part in changing the landscape of the last eight. In that respect, Munster will hope to lead the way, their wounded pride demanding they avenge last week's setback against Stade Francais.
The rest all face daunting away matches - Benetton Treviso at Leicester, the Scarlets in Paris against Dan Carter's Racing. The Warriors make the journey to Northampton clinging to the hope that a storming finish can still put them into the mix as one of the three best runners-up.
Meanwhile back in the GUINNESS Pro 12, leadership of the table changed hands twice last weekend within 48 hours. Leinster's impressive 22-9 defeat of the Ospreys, as orchestrated by Johnny Sexton, took them top at the expense of the Scarlets until the west Walians returned to the roost on the strength of a thrilling two-point home win over Connacht.
Edinburgh's win over Treviso, their fourth in five PRO12 matches, swept them into third place, raising the delicious prospect of Scotland's capital city featuring in Murrayfield's first Grand Final on May 28.
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