The North West's two remaining teams bowed out of Sunday's replays, meaning none of the eight North West sides made it past the first hurdle - the worst display in the competition's history.
Ardmore made the long trek to Cork and travelled home empty handed after being on the wrong side of a 37-run loss.
Syden Aiman hit 6 fours and a six in a well composed 85 as the Munster men posted 220/9 - vital late runs too for Eshan O'Sullivan (35).
Edrees took three wickets, while there were two apiece for Aviwe Mgijima, Rachit Gaur and Dharm Singh.
The chase started steadily with Mgijima (43), Conor King (25) and Harry immermann (29) taking the Bleachgreen side to 105 for 2 as drinks approached.
However, they lost their way to be bowled out for 183. Cork now host Pembroke in the second round on Sunday.
Carrickfergus eased into the second round as they beat the last remaining hope of the North West, chasing 241 to win by six wickets with almost five overs to spare.
Gary McClintock (61) and DJ Dougherty (43) shared an opening stand of 80 to lay the foundations for a big total, but the Tyrone side lost wickets at regular intervals, with big hitting William McClintock one of four wickets for Michael Rippon (4-34).
The tail rallied with 20's for Joe Robinson and Gary Neely getting them to 241.
A second wicket stand of 123 between Craig Averill (14 fours) and Iain Parkhill (8 fours) - both making 72 ensured a comfortable chase.
Michael Rippon (38*) and skipper CJ van der Walt (30*) applying the last rites with plenty to spare.
Carrick now take on The Hills at Middle Road on Sunday.