ACR X TCASII RA HAD LTSS FROM ACR Y. SYS ERROR. EVASIVE ACTION TAKEN.

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I WAS ASKED TO WORK SECTOR D-7 BY A SUPVR. THE R-CTLR WAS EXTREMELY BUSY WITH WX DEVS; AN EMER DEPS AND ARRS ETC. AS SOON AS I PLUGGED INTO THE D-POS; SLC APCH CALLED AND WANTED APPROVAL FOR ACR X A SLC DEP TO BE ON COURSE J9. I APPROVED THIS AND TOLD THE R-MAN THAT ACR X WOULD BE ON COURSE. SINCE WE HAD AN ARR ACR Y DSNDING TO 16000 THE R- MAN INITIATED A HDOF. THE ACFT WERE DUE TO CROSS WELL INSIDE APCH'S AIRSPACE. I SAW THAT THEY WERE CLBING ACR X TO 16000 AND THAT HE WOULD BE IN CONFLICT WITH ACR Y. I IMMEDIATELY CALLED APCH ON THE LANDLINE TO INITIATE SOME SEPARATION AND THEY TOLD ME TO TURN ACR Y W. WE GAVE ACR Y ALMOST AN 80 DEG TURN TO THE R THINKING THAT THE APCH CTLR WOULD TURN ACR X E. THIS DID NOT HAPPEN AND APCH LET THESE 2 ACFT PASS VERY CLOSE. SUPPLEMENTAL INFO FROM ACN 212458. I WAS WORKING A SECTOR AT SLC APCH CTL. THE NBOUND DEP SECTOR (LAKE) THROUGH HIS COORDINATOR PAINTED OUT ACR X CLBING NBOUND THROUGH MY AIRSPACE TO JOIN J9 AND RADAR HANDED THAT ACFT OFF TO SLC CTR. I APPROVED THE POINT OUT AND NEVER TALKED TO THE OUTBOUND ACFT. THE ACFT'S ROUTING WAS APPROVED BY SLC CTR BECAUSE IT WAS NOT THE NORMAL DEP PROC. AN INBOUND ACR Y WAS HANDED OFF TO ME BY SLC CTR DSNDING TO 16000. BOTH ACFT WERE NOSE-TO-NOSE AT SAME ALT. SLC CTR KEPT ACR Y (ARR); LAKE STILL HAD ACR X. I CALLED SLC CTR ON THE LANDLINE AND TOLD THEM TO TURN ACR Y WBOUND AND THAT I WAS NOT TALKING TO HIM. I DID NOT GET ACR Y ON MY FREQ UNTIL AFTER THEY PASSED. MIN SEPARATION WAS LOST. SUPPLEMENTAL INFO FROM 212567. WE WERE WITH SLC DEP CTL ON AN ASSIGNED HDG OF 360 DEG AT AN ASSIGNED ALT OF 16000 FT. I WAS FLYING ACR X AT 320 KIAS. TCASII INDICATED A CONFLICT AT 12 O'CLOCK LEVEL. THE FO SIGHTED THE TFC; AND SOON THEREAFTER I SPOTTED LNDG LIGHTS AT 12 O'CLOCK LEVEL; AS I PREPARED TO TAKE EVASIVE ACTION; THE TFC BEGAN TO MOVE TO THE L IN MY WINDSCREEN. IT BEGAN A R TURN TO THE W WHILE MAINTAINING ALT; WHICH WAS THE SAME AS OURS. THE TFC PASSED TO OUR L AT AN APPROX DISTANCE OF 4000. IT WAS ANOTHER ACR Y AT THIS TIME SLC DEP CTL ISSUED A TA. 'TFC 11 O'CLOCK LESS THAN A MI.' THIS CALL CAME AS THE TFC WAS PASSING; MUCH TOO LATE TO ASSIST IN AVOIDING THE CONFLICT. THE FO TOLD DEP WE HAD BEEN WATCHING THE OPPOSING TFC ON TCASII. WE WERE THEN TOLD TO CONTACT SLC CTR.