ACR FLC ISSUED CONFLICTING SET OF CLRNCS FROM ARTCC RADAR CTLR. UNAUTH USE OF FREQ ASSIGNED TO SECTOR BY UNKNOWN CTLR.

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WE RECEIVED A MOMENTARY TCASII TA. TCASII IDENTED THE INTRUDER AT 2 O'CLOCK; 11-12 MI; PLUS 1300 FT DSNDING. THE FO AND I SEARCHED THE SECTOR VISUALLY AND WERE UNABLE TO ACQUIRE THE INTRUDER VISUALLY AND WERE UNABLE TO ACQUIRE THE INTRUDER VISUALLY. ON TCASII; WE OBSERVED THE INTRUDER PASS OUR R WING. SHORTLY AFTER THE INTRUDER PASSED US; ABOUT 1-2 MINS AFTER THE TA; ATC GAVE US A 'DSND IMMEDIATELY' FOLLOWED BY 'CORRECTION; CLB TO FL330' FOLLOWED BY 'DISREGARD' AND SHORTLY THEREAFTER; 'SAY YOUR ALT.' WE COMPLIED WITH ALL ATC INSTRUCTIONS SHOWING ALT VARIANCES OF A 100 FT DSCNT IMMEDIATELY FOLLOWED BY A 400 FT CLB; THEN DSNDING BACK TO FL310. MY FO AND I WERE SOMEWHAT CONCERNED AND CONFUSED BY THE CONFLICTING ATC INSTRUCTIONS WITHOUT ANY FOLLOW-UP FROM ATC AS TO WHAT THE PROB WAS. IN OUR OPINION; THE ATC INSTRUCTIONS WERE TOO LATE IF AT ALL NECESSARY. AS I SAID; IT WAS ONLY A MOMENTARY TA; THERE WAS NO RA. FROM OUR OBSERVATIONS ON TCASII; THE CLOSEST THE INTRUDER CAME WAS 2 O'CLOCK; HIGH AT 1300 FT AT 12 MI MOVING TO 6 O'CLOCK; PLUS 1800 FT AT 8-9 MI. AT THE TIME OF THE INCIDENT; RADIO TFC ON ZID FREQ 133.05 WAS QUITE HVY. COMPLICATING MATTERS; APPARENTLY ANOTHER CTLR WHO HAD ACCESS TO THE FREQ WAS INADVERTENTLY XMITTING ON IT; BLOCKING RADIO COM. THIS COULD VERY WELL BE ONE OF THE REASONS FOR THE LATE ATC INSTRUCTIONS. HOWEVER; I'M STILL UNSURE AS TO THE LOGIC OF THE CONFLICTING ATC INSTRUCTIONS. ALSO; WHERE WAS THE ATC SUPVR? SUPPLEMENTAL INFO FROM ACN 250024: THE FREQ 133.05 WAS BUSY AND TO ADD TO THE PROB WAS ANOTHER CTLR THAT DIDN'T REALIZE HE WAS XMITTING ON THIS FREQ AND TALKING PERSONAL BUSINESS ON THIS FREQ.