ALT BUST CREATES POTENTIAL CONFLICT. CTLR ATTEMPTS SALVAGE BY INSTRUCTING ACFT TO DSND BACK TO ORIGINAL ALT. PIC TAKES ACFT AND PERFORMS EVASIVE ACTION CLB AND USES TCASII BASED DECISION TO CLB TO AVOID TFC.

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ON CLBOUT OF CLE ARPT INITIAL LEVEL OFF WAS AT 5000 FT. DEP THEN CLRED THE FLT TO 6000 FT. I MISTAKENLY DIALED IN 8000 FT MSL. WE HAD A CONFLICT WITH 7000 FT MSL TFC. AT THE TIME DEP NOTIFIED US OF THE CONFLICT WE WERE ALREADY CLBING THROUGH 7500 FT MSL. WE CONTINUED CLBING TO 8000 FT. SEPARATION ESTIMATED TO BE IN EXCESS OF 1000 FT VERT AND 2 1/2 - 3 MI HORIZ. WE DID GET VISUAL CONTACT AT THE TIME OF DEP'S INITIAL CONFLICT CALL. ALTHOUGH DEP INSTRUCTED US TO DSND AT THAT POINT; THE SAFER COURSE OF ACTION WAS TO CONTINUE CLB TO 8000 FT. SUPPLEMENTAL INFORMATION FROM ACN 260995: AFTER LEVELING OFF AT 5000 FT MSL; WE WERE GIVEN CLRNC TO CLB TO 6000 FT. THE CAPT PLACED 8000 FT IN THE ALT ALERTER AND I AM UNSURE IF THERE WERE HDG VECTORS DURING OUR CLB. AT ABOUT 7600 FT MSL THE CTLR ADVISED US TO DSND TO 6000 FT. I BEGAN A DSCNT AND THE CAPT; WHO HAD BEEN OBSERVING TFC ON TCASII; TOOK THE ACFT AND CLBED VISUALLY CLR OF THE 7000 FT TFC. WE CLBED THROUGH ABOUT 8500 FT MSL AND WERE GIVEN A NORTHERLY HDG AND 11000 FT.