POTENTIAL CONFLICT LTSS OCCURS AFTER FLC DEV FROM FLT PLAN FILED ALT IN A SUPPOSED ADHERENCE TO AN ATC CLRNC.

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CLBING OUT OF CMH ARPT WHILE IN CONTACT WITH INDIANAPOLIS CTR; WE WERE INSTRUCTED TO CLB TO 'FL270.' THE CAPT READ BACK THE CLRNC TO THE CTLR ('CLB TO 270'). I HEARD THE INITIAL CLRNC AND THE CAPT'S READBACK OF IT TO 'CLB TO 270;' AND I REPEATED IT TO THE CAPT. AS WE WERE CLBING THROUGH FL250; I NOTICED OUR FILED FLT PLAN ALT WAS ONLY TO FL260. ABOUT THE TIME WE WERE CLBING THROUGH FL260 FOR FL270; THE TCASII ISSUED A TA FOR IT WAS SHOWING TFC AT 270 WITHIN 10 NM. THE CAPT TOLD ME TO DSND BACK TO FL260 AT ABOUT THE TIME TCASII ISSUED A DSND COMMAND. (MAX ALT REACHED WAS 26300 FT MSL). ATC CAME ON THE RADIO AS WE WERE DSNDING TELLING US TO CHK OUR ALT AS HE SHOWED US AT 26300 MSL. WE ADVISED ATC WE WERE LEVELING AT FL260 BUT THAT THE INITIAL CLRNC HAD BEEN TO CLB TO FL270. NOTE: BOTH THE CAPT AND MYSELF FELT UNCOMFORTABLE ABOUT THE CLB CLRNC TO FL270. IT WAS NOT OUR FLT PLANNED ALT; NOR IS IT THE CORRECT ALT FOR THE WBOUND TFC (OUR DEST WAS CHICAGO). THE SEPARATION WOULD HAVE BEEN MUCH LESS HAD WE NOT HAD TCASII ON BOARD FOR THIS IS WHAT FIRST ALERTED US TO THE CONFLICT.