AA 4588 then DL 2342 at JFK
Cleveland → New York → Atlanta
Timetable, New York time
12:29AA 4588 from Cleveland at the gate
11:30DL 2342 to Atlanta leaves the gate
23 h 01 apart on the timetable, overnight
DL 2342 leaves 23 h 01 after AA 4588 arrives on the timetable: more than half a day, so not a connection we count.