ZID ARTCC TRAINEE CTLR HAD A LOSS OF SEPARATION BTWN A BE40 CLBING AND A HS25 DSNDING.

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ACFT Y WAS A DAYTON; OH; ARR DSNDING TO 12000 FT. ACFT X WAS A COLUMBUS; OH; DEP; CLBING TO 11000 FT. BOTH ACFT WERE WBOUND; AND ON CONVERGING COURSES. I WAS THE TRAINEE; WITH AN INSTRUCTOR WATCHING AND AN FPL D-SIDE. I WAS FOCUSED ON ANOTHER AREA OF DEPS OUT OF CINCINNATI; OH; AND BY THE TIME I GOT BACK TO ACFT Y AND ACFT X; THEY WERE CONVERGING AND I NEEDED A PLAN TO GET ACFT X CLBING AND ON COURSE; AND ACFT Y DOWN INTO DAYTON APCH AIRSPACE. I THEN TURNED ACFT X TO A 260 DEG HDG TO TURN AWAY FROM ACFT Y. ACFT WERE STILL SEPARATED AT THIS POINT BY ALT. I HEARD MY INSTRUCTOR TELL ME TO 'TURN HIM TO A 340 DEG HDG' WHICH I DID; TURNING ACFT X TO A 340 DEG HDG. INSTRUCTOR TOLD ME NOT TO TURN ACFT X AT THIS TIME; BECAUSE HE ACTUALLY SAID 'WHAT I WOULD HAVE DONE WAS TURN ACFT X TO A 340 DEG HDG.' I THEN TOLD ACFT X TO 'DISREGARD; FLY HDG 260 DEGS.' THERE WAS NO READBACK; WHICH ALL 3 OF US MISSED. MY D-SIDE HAD GOTTEN ME A LOWER ALT FROM APCH FOR ACFT Y; WHICH I DSNDED TO 10000 FT. ACFT X WAS ACTUALLY IN THE TURN TO A 340 DEG HDG TURNING INTO THE PATH OF ACFT Y. SEPARATION WAS LOST. SUPPLEMENTAL INFO FROM ACN 635573: TRAINEE TURNED ACFT X TO A RIDICULOUS HDG. TOLD HIM TO TURN HIM BACK. I MISSED A NON READBACK.