CPR X CLB THROUGH OCCUPIED ALT HAD LTSS FROM ACR Y. CTLR TRAINING IN PROGRESS. SYS ERROR.

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I HAD A TRAINEE WORKING AND IT GOT BUSY WITH HVY COMPLEX TFC. WE DECIDED TO GET A TRACKER FOR HELP. BEFORE THE INCIDENT OCCURRED; ZME WOULD NOT LET US TALK TO ACFT AT FL290 WHICH WAS IN CONFLICTION WITH AN ACFT WE WERE TALKING TO AT FL290 ALSO. FINALLY WE CALLED THEM AGAIN TO TELL THEM TO TURN AND DSND THEIR ACFT TO AVOID OURS; AS WE TURNED OURS TO AVOID. THIS WAS THE BEGINNING OF MULTIPLE CONTRIBUTING FACTORS. THEY WERE SEPARATED AFTER TURNING AND DSNDING 3 OR 4 ACFT. AN OUTSIDE FACILITY DROPPED A FLT PLAN FROM THE SYS AND OUR FLOW CTL; ZME AND OUR SECTOR WERE ALL WORKING TO GET FLT PLAN BACK IN AND A TRACK STARTED ON ACFT; YET ANOTHER FACTOR. CPR X LEVEL AT FL310 WAS CLRED TO FL390 WITH ACR Y AT FL330 OPPOSITE DIRECTION WHICH WAS TO BE STARTED DOWN WHEN CLR OF TFC. DURING THE OUTBOUND RUSH OFF OF SDF; ACR Y WAS NOT STARTED DOWN IN TIME AND CONFLICT ALERT ACTIVATED. TRAINEE TRIED TO STOP CLB OF CPR X BY DSNDING TO FL310 AGAIN. CPR X WAS INDICATING FL337 ALREADY. I STEPPED IN TO TURN AND CLB CPR X AND I CUT HIM OUT SO I TRIED TO TURN ACR Y AND NO REPLY. GO BACK TO CPR X AND CLB AND TURN. HE TURNS BUT DSNDS IN CONFUSION. STANDARD SEPARATION IS LOST. SUPPLEMENTAL INFORMATION FROM ACN 260987: ACTUAL CONFLICT: CPR X CLBING TO FL390 SWBOUND. ACR Y AT FL330 NEBOUND. I SAW THE CONFLICTION SECONDS BEFORE CONFLICT ALERT ACTIVATED. I MADE THE DECISION TO DSND CPR X BACK DOWN TO FL310. (LAST UPDATE I SAW WAS FL321.) MY TRAINER TRIED TO CORRECT THIS BY TRYING TO CONTINUE HIS CLB AND TURNED BOTH ACFT. HIS XMISSIONS KEPT GETTING BLOCKED. HE HAD TO MAKE AT LEAST 3 XMISSIONS BEFORE 1 ACFT ACKNOWLEDGED. OTHER ACFT NEVER DID ACKNOWLEDGE OR ACTUALLY TURN.