B767-300 FLC INITIATE TCASII EVASIVE MANEUVER AS SDF DATA CTLR ISSUES TA. FLC STATES SDF INCONSISTENT WITH TA ISSUANCE.

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TOOK OFF FROM SDF RWY 35L AT XA15L; CLRED TO 5000 FT HDG 330 DEGS. NEXT HDG WAS 300 DEGS IN CLB. HANDED OFF TO DEP CTL. CLRED TO 7000 FT; HDG 270 DEGS. AT THIS POINT; WE WERE CLBING THROUGH 5000 FT; TURNING TO 270 DEGS; WHEN TCASII CALLED 'TFC.' I OBSERVED TARGET ON TCASII AT 1 O'CLOCK POS AND LESS THAN 1 MI; NO ALT TAG. I INCREASED BANK ANGLE IN THE L TURN TO 45 DEGS; WHICH PROMPTED 'BANK ANGLE' CALLOUTS. THEN GOT RA TO DSND. LOWERED NOSE AND DSNDED TO 5000 FT ON 270 DEG HDG; EXCEEDING 300 KTS. REDUCED THRUST AND EXTENDED SPD BRAKES; SLOWING TO 250 KTS. CLR OF CONFLICT; WE WERE TURNED TO 230 DEGS TO INTERCEPT OUR COURSE AND CLB TO 7000 FT. FO HAD SEVERAL COMS WITH ATC DURING CONFLICT. AS WE GOT THE TCASII RA; ATC ADVISED 'POP-UP' VFR TFC; 1 O'CLOCK POS; LESS THAN 1/2 MI AT 6000 FT; THEN CHANGED IT TO ALT UNKNOWN (HE MAY HAVE BEEN READING OUR ALT AT 6000 FT). FO RPTED WE WERE RESPONDING TO A TCASII RA. WE NEVER SAW THE CONFLICT ACFT; AS WE WERE IN AND OUT OF A LAYER OF CLOUDS. THIS IS THE SECOND TIME THIS EXACT SCENARIO HAS HAPPENED TO ME; FLYING A B767 OFF OF RWY 35L FROM SDF AND CLBING THROUGH 5000 FT INTO A CONFLICT. SUPPLEMENTAL INFO FROM ACN 571369: AT APPROX 5500 FT TCASII RA DIRECTED AN IMMEDIATE DSCNT. HAVING FLOWN OUT OF KSDF ON A REGULAR BASIS; I'VE OBSERVED TFC CONFLICTS OFTEN WITHOUT WARNING FROM ATC. OFTEN TIMES; WE FIND OUT THAT ATC KNEW OF THE TFC; BUT DID NOT CALL IT OUT TO US. THIS PROB HAS BEEN WITH SDF APCH/DEP. THE TCASII ALERT WAS VITAL TO THE SAFE RESOLUTION.