ACR PIC TALKED OUT OF ALT READBACK OF FL200 AS FO INPUTS FL220 IN ALT ALERTER.

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DURING DEP FROM COS; CONTACTED ZDV. CLB CLRNC WAS 16000 FT. ZDV ISSUED A CLB CLRNC ON COURSE TO FL200. I READ BACK FL200; BUT THE FO UNDERSTOOD AND SET FL220 IN THE ALT ALERT WINDOW. WE THEN BOTH ACKNOWLEDGED THE CLRNC INCORRECTLY AS CLB AND MAINTAIN FL220. LEAVING FL200; ZDV RPTED TFC(FLT OF 2 F-15'S) N AT 12 - 1 O'CLOCK POS. WE BOTH SAW AND ACKNOWLEDGED THE 2 ACFT. LEAVING FL210; WE RECEIVED A TA; AND NOTED THE TFC AT 12 O'CLOCK; PASSING R TO L -- THEIR RANGE ABOUT 10 NM. AT FL215; WE RECEIVED AN RA; FOLLOWED IMMEDIATELY BY A CLR OF CONFLICT MESSAGE. WE OBSERVED THE FLT AT 11-12 O'CLOCK POS; MOVING R TO L; BUT DID NOT CONSIDER THEM A COLLISION RISK AT ANY TIME. AT THAT TIME; WE WERE QUERIED BY ZDV TO CONFIRM ALT AS FL200. I STATED THAT I HAD READ BACK FL220 AS OUR CLRNC LIMIT. THIS STATEMENT WAS LATER PROVEN INCORRECT; UPON REVIEW OF TAPES. CONTRIBUTING FACTORS INCLUDE FATIGUE FROM MINIMUM CREW REST; PRECEDED BY A 6 HR FLT DAY WHICH INCLUDED MECHANICAL IRREGULARITIES AND DEICING DELAYS. ANOTHER FACTOR WAS THE FACT THAT WE HAD THE TFC IN SIGHT AT ALL TIMES; DID NOT CONSIDER IT A RISK TO OUR RTE OF FLT; AND FAILED TO CONSIDER ALT DEV AS A POTENTIAL PROB. CONTRIBUTING WAS OUR PAST EXPERIENCE OF RECEIVING TA'S AND RA'S DURING FLT AT ALT AS WELL AS IN TERMINAL AREAS; WHERE ALT DEVS WERE NOT A FACTOR. THE TA/RA ALERT SIMPLY DID NOT CLUE US INTO THE FACT THAT WE HAD (POSSIBLY) EXCEEDED A CLRNC LIMIT. LOSS OF SEPARATION CAUSED DEN TO FILE A RPT ON THE INCIDENT.