ZAB CTLR ATTEMPTS TO MAINTAIN LEGAL SEPARATION AFTER OPPOSITE DIRECTION; SAME ALT TFC ADVISE OF TCASII MANEUVER.

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I WAS WORKING THE XD45-XB45 SHIFT; 8 HRS AFTER WORKING A DAY SHIFT. ZAB AND DARC ONLY; AND STILL INVESTIGATING A FATAL CRASH OF AN ACFT THAT JUST CRASHED NEAR THE SECTOR 21/15 BOUNDARY. COORD WAS BEING ACCOMPLISHED WITH THE OMIC AND OTHER AGENCIES REGARDING THE ACCIDENT. ADDITIONALLY; THERE WERE PROBS WITH THE 'FLUSHED FLT PROGRESS STRIPS' AND ALL DATA WAS HAVING TO BE CHKED/PASSED MANUALLY. MODERATE TURB WAS A PROB AT MOST ALTS FROM THE ROCKIES W. AT THIS TIME; ACFT X CHKED IN OVER LVS AT FL390 EBOUND. ACFT Y WAS WBOUND AT FL390. AT ONE POINT; I RAN OUT THE VECTOR LINES AND OBSERVED THAT THE 2 ACFT WOULD PASS APPROX 12 MI APART. AT THAT TIME I WENT BACK TO THE PREVIOUSLY MENTIONED TASKS. ACFT X STATED THAT HE WAS CLBING DUE TO TFC. I IMMEDIATELY DSNDED ACFT Y TO FL370 AND TOLD HIM TO EXPEDITE. I THEN CLBED AFT X TO FL410. IT APPEARED THAT I ACHIEVED VERT SEPARATION VERY QUICKLY AS ACFT Y RPTED LEVEL AT FL370. IT APPEARED THAT I ACHIEVED VERT SEPARATION BEFORE LATERAL SEPARATION WAS LOST. DURING THIS EVENT; NUMEROUS RADIO XMISSIONS WERE NOT READABLE DUE TO MANY ACFT TALKING AT THE SAME TIME. ACFT X WAS SUBSEQUENTLY CLRED BACK TO FL390; AND ACFT Y STAYED AT FL370. NO CONFLICT ALERT WAS ACTIVATED; NO OEDP HAD ALERTED; AND IT APPEARED THAT I HAD ACHIEVED SEPARATION. I HEARD 3 DAYS LATER THAT ACFT Y HAD FILED AN NMAC RPT. DUE TO THE FACT THAT THE ZAB COMPUTER WAS NOT CERTIFIED OPERATIONAL; IT HAS YET TO BE DETERMINED THE EXACT 'OFFICIAL' SEPARATION THAT EXISTED. THE BEST ESTIMATE SO FAR IS A 4.2 NM LATERALLY; AND 1 RADAR HIT AT ABOUT 1100 FT VERTLY. THE VOICE TAPES HAVE NOT YET BEEN MATCHED TO THE RADAR DATA TO VERIFY THE TIME/POS OF THE ALT RPT. ALL OTHER RADAR HITS SHOWED THAT THE ACFT WERE SEPARATED. CAUSAL FACTORS: ZAB COMPUTER SYS SHUT DOWN (NO CONFLICT ALERT/OEDP); AND INACCURATE VECTOR LINES IN DARC MODE. DISTR/PREOCCUPATION WITH THE FATAL ACCIDENT; AND OTHER PROBS (SUCH AS FLT PLAN PROCESSING). THE SHIFT SCHEDULE OF 8 HRS ON; 8 HRS OFF; THEN 8 MORE HRS ON MAY HAVE CAUSED FATIGUE TO THE POINT OF LOSING AWARENESS. ONCE I BELIEVED THAT THE 2 ACFT WERE SEPARATED; I DID NOT NOTICE THE CONFLICTION UNTIL ACFT X STATED THAT HE WAS CLBING. TOTAL TIME FROM THE TIME THAT I THOUGHT THE 2 ACFT WERE NOT GOING TO BE IN CONFLICTION UNTIL THE INCIDENT WAS APPROX 8-9 MINS. BEFORE LEAVING FREQ; ACFT Y ASKED IF SEPARATION HAD BEEN LOST. I STATED 'NO' BECAUSE; ON THE 200 NM SCALE THAT WE HAVE TO WORK ON THE MID; IT APPEARED THAT SEPARATION HAD BEEN MAINTAINED.