B763 CREW ON DEP; RECEIVED A 'DSND' RA FROM TCASII. HOWEVER; WITH TFC IN SIGHT THE CREW MAINTAINED A POSITIVE CLB TO KEEP VISUAL SEPARATION.

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OUR FLT DEPARTED SDF RWY 17R WITH AN ASSIGNED HDG OF 190 DEGS. WITHIN 10 SECONDS OF OUR INITIAL CHK ON WITH DEP CTL; TCASII ISSUED A TA. WE WERE IN A BUSY PHASE OF FLT RIGHT AFTER TKOF AND THE VOICE WAS SOMEWHAT UNSETTLING. CLBING THROUGH APPROX 5000 FT MSL; WE WERE ABLE TO VISUALLY ACQUIRE THE CONFLICT ACFT. THE VISUAL CONTACT OCCURRED ABOUT 5 SECONDS AFTER THE TCASII ALERT. IMMEDIATELY AFTER I SAW THE ACFT WHICH WAS IN A R TURN DIRECTLY TOWARDS US AT THE SAME ALT; AN RA INSTRUCTED US TO DSND. WE WERE AT THE SAME ALT AND APPROX 1 MI ON A COLLISION COURSE. THE CAPT ELECTED TO MAINTAIN THE PRESENT COURSE AND POSITIVE CLB RATE DUE TO THE FACT THAT WE WERE IN VISUAL CONTACT. THE TCASII THEN CHANGED ITS MIND AND INSTRUCTED US TO 'MAINTAIN VERT SPD' (APPROX 2500 FPM CLB). THE CONFLICT ACFT PASSED ABOUT 300 FT BELOW US AND 300 FT TO THE R OF US. WE QUERIED THE CTLR ABOUT HIS KNOWLEDGE OF THE ACFT. HE SAID HE DID NOT KNOW ABOUT IT; BUT LATER STATED 'HE'S 1000 FT BELOW YOU.' WE RESPONDED BY ASKING THE CTLR TO MARK THE TAPE. AN INVESTIGATION IS UNDER WAY. SUPPLEMENTAL INFO FROM ACN 509871: OUR FLT ACFT Y; SDF TO CLE. TKOF RWY 17L. CLRNC: RWY HDG CLB TO 5000 FT MSL. ON DEP; SDF DEP CTLR TOLD US TO TURN R DIRECT ABB (NABB) VOR; MAINTAIN 5000 FT. SDF HAD PARALLEL RWY OPS FROM RWY 17R. (FO'S (MY) LEG.) WE QUESTIONED ATC BECAUSE NORMALLY WHEN DEPARTING RWY 17L WE'RE GIVEN A L TURN DIRECT ABB VOR. WHILE TURNING DIRECT ABB; WE NOTICED ANOTHER ACFT; ACFT X; LEVEL AT 5000 FT OFF RWY 17R. I INITIATED A DSCNT (70 DEGS APPROX 4700 FT) AND WE MISSED ACFT BY PARAMETERS LISTED ABOVE. ONCE CLR OF TFC; I LEVELED OFF AT 5000 FT AND CONTINUED FLT. PROB AROSE WHEN SDF DEP GAVE US A NONSTANDARD TURN INTO PARALLEL RWY OPS; DURING NUMEROUS DEPS. THE PROB WAS DISCOVERED BY BOTH ACFT; VISUALLY (ACFT Y) AND VIA TCASII (ACFT X). EVIDENTLY ATC WAS VERY BUSY WITH NUMEROUS DEPS. AS A RESULT OF TASK SATURATION; ACFT WERE VECTORED INADVERTENTLY INTO EACH OTHER. AS A FLC; WE COULD HAVE 'INSISTED' ON A TURN AWAY FROM PARALLEL OPS. ATC SHOULDN'T HAVE TURNED US INTO RWY 17R DEPS UNLESS ABSOLUTELY POSITIVE OF NO CONFLICTS. PERHAPS LATE NIGHT OPS (FATIGUE) PLAYED A ROLE. TASK SATURATION AND SITUATIONAL AWARENESS NEED TO BE IMPROVED. SDF IS AN ATC TRAINING FACILITY; I DON'T KNOW IF THIS WAS A FACTOR.