Provisional world number one Ken Doherty and defending champion Ding Junhui edged ahead in their matches.
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Neil Robertson, Stephen Lee and Shaun Murphy also went through, as did Ireland's Ken Doherty.
Dubliner Ken Doherty upset Scottish world number one John Higgins 6-2 in Saturday's first semi-final.
When Ken Doherty's shot was deflected by the uneven table the word 'controversy' was mentioned.
The third man through to the last 16 is Irishman Ken Doherty, who beat Ali Carter 5-3.
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Ken Doherty suffered a 4-3 opening loss to fellow Dubliner Michael Judge, having at one stage led 3-2.
Ken Doherty, the 1997 champion, plays Joe Swail on Monday, while 2006 winner Graeme Dott plays Jimmy Michie on Tuesday.
Ken Doherty was left to rue what might have been after losing for the third time in the final of this tournament.
Also on Friday, Neil Robertson and Ken Doherty will lock horns for a place in the semi-finals after Australian Robertson beat Ulsterman Joe Swail 4-2.
He should have reached the 2003 World Championship final, where he led Ken Doherty 15-9 in the semi-finals before the Irishman stormed back to win 17-16.
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Ken Doherty recovered from 2-1 down to edge Nigel Bond 3-2, while Mark Williams was sunk 3-0 by Stuart Bingham in the season's first major tournament.
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But Irishman Ken Doherty kissed goodbye to his hopes after losing 4-3 to Ian McCulloch, a third loss which left him propping up the six-player group headed by unbeaten Ricky Walden.
The Northern Ireland Trophy runs from August 13 to 20 and will feature the world's top 32 players including Ronnie O'Sullivan, Stephen Hendry, Ken Doherty, John Higgins and world champion Graeme Dott.
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Williams, the provisional world number 42, lost 4-1 to Ken Doherty and the exit now leaves the Welshman in serious danger of failing to secure a top 32 starting rank next season.
The opinions expressed in this commentary are solely those of Ken Ballen and Patrick Doherty.
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