CPR X HAD LTSS FROM ACR Y. SYS ERROR.

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CPR X DEPARTED OAKLAND ENRTE TO PHOENIX ON RWY 29. OUR INITIAL CLRNC WAS TO CLB TO 10000 FT MSL ON THE RWY HDG FOR VECTORS TO THE SKYLINE 2 DEP. ON THE FIRST CONTACT WITH BAY DEP; THE CTLR DELETED THE 4 DME 2000 FT MSL XING RESTRICTION. ON THE SECOND CONTACT; SHE DIRECTED US TO TURN L TO 180 DEG AND CLB TO FL230 TO INTERCEPT THE PYE 135 DEG RADIAL ON THE SID. PASSING APPROX 5200 FT MSL; I SPOTTED TFC AT OUR 12:30 O'CLOCK POS APPROX 200-300 FT LOWER AND ABOUT 1/2 MI LATERAL SEPARATION. IT APPEARED TO BE ACR Y MLG IN A L TURN. JUST AS WE WERE ABOUT TO QUESTION THE CTLR; THE OTHER CREW ASKED THE CTLR ABOUT THE TFC OFF TO THEIR SIDE. THE CTLR RESPONDED BY SAYING THAT IT WAS CPR X CLBING THROUGH 6000 FT MSL. NO OTHER TA'S WERE ISSUED. AFTER LNDG AT PHOENIX; I TELEPHONED BAY TRACON AND SPOKE TO FAA SUPVR. HE CONFIRMED THAT A LOSS OF IFR SEPARATION HAD TAKEN PLACE; AND THAT HE WAS INVESTIGATING. HE SAID THAT ALL INDICATIONS POINTED TO A PROBABLE CTLR ERROR. HE DID ASK ABOUT OUR RATE OF CLB; APPROX 1500 FPM; AND IF WE HAD LEVELED OFF DURING THE CLB. WE HADN'T LEVELED OFF; BUT I TOLD HIM WE HAD USED A NOISE ABATEMENT CLB OUT OF OAKLAND. THAT MAY HAVE RESULTED IN LOWER RATES OF CLB THAN THE CTLR HAD ANTICIPATED. HE CONCLUDED BY STATING THAT THERE WAS NO INDICATION WE HAD DEVIATED IN ANY WAY FROM OUR CLRNC.