ARTCC RADAR CTLR CLBED AN ACR A320 THROUGH AN ALT OCCUPIED BY AN OPPOSITE DIRECTION ACR DC10. POTENTIAL CONFLICT LTSS WAS SEEN BY THE CTLR AT THE SAME TIME THE CONFLICT ALERT ACTIVATED. BOTH ACFT WERE TURNED; BUT NOT BEFORE SEPARATION WAS LOST. CTLR HAD ABOUT 15 ACFT ON HIS FREQ WHEN THIS OCCURRED.

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ACR X AT FL350; WBOUND ON J96; REQUESTED CLB TO FL390. I ISSUED TFC TO ACR X AND TOLD HIM TO STAND BY. I HAD TFC; 15 OR MORE ACFT ON FREQ WITH 3 OR MORE BEING SEQUENCED FOR PHX ARR; 1 UNKNOWN ACFT ON MY FREQ AND CLBING ACFT FROM PHX. AFTER ACR X PASSED EBOUND TFC AT FL370; I CLBED ACR X TO FL390; THE DIVERTED MY ATTN TO OTHER TFC SITS. I LOOKED BACK TO ACR X AND SAW THAT HE WAS IN CONFLICTION WITH ACR Y WHO WAS EBOUND ON J96; CONFLICT ALERT WENT OFF AT THIS TIME ALSO. I HAD ACR X STOP CLB AND TURN L TO 160 DEGS AND ACR Y TURN L TO 350 DEGS. THE 2 ACFT PASSED BY ABOUT 4.6 MI AND 1600 FT. THE SECTOR OVERLYING THIS SECTOR HAD BEEN CLOSED ABOUT 30 MINS EARLIER BECAUSE THE SUPVR DID NOT THINK THERE WAS ENOUGH TFC TO JUSTIFY HAVING IT OPEN. IF THE SECTOR ABOVE HAD BEEN OPEN I FEEL THIS ERROR WOULD NOT HAVE OCCURRED. ACR Y WOULD HAVE BEEN IN THAT SECTOR AND I WOULD NOT HAVE BEEN ABLE TO CLB ACR X WITHOUT CALLING THE SECTOR ABOVE. FOR SOME REASON I DID NOT HAVE A FLT STRIP ON ACR Y. ALSO THIS WAS THE FIRST DAY FOR USING NEW FLT STRIP PRINTERS THAT ARE UNABLE TO PRINT IN RED AND STRIPES WERE DIFFICULT TO READ (NOT BEING ACCUSTOMED TO THE NEW FORMAT).