ACR X UNAUTHORIZED DSCNT THROUGH OCCUPIED ALT HAD LTSS FROM ACR Y. ACR X TCASII RA DSND. EVASIVE ACTION TAKEN.

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WHILE ON THE ALB 2A STAR TO EDDF ACR X CLRED TO CROSS ALB AT FL250. UPON XING ALB THE CTLR THEN CLRED US TO FL210. AS THE ACFT WAS BEING FLOWN WITH THE AUTOPLT ENGAGED; I RESET THE ALT WINDOW ON THE MODE CTL PANEL TO 21000 FT AND PROGRAMMED THE FMS TO DSND. AS I WAS DOING THIS; THE CAPT WAS BEGINNING THE DSCNT CHKLIST. AS WE WERE PASSING APPROX FL243; THE TCASII GAVE A TA; WHICH WAS FOLLOWED BY THE OFF DUTY PLT CALLING ACR Y AT APPROX 10 O'CLOCK AND CO-ALT XING FROM L TO R. WE FOLLOWED TCASII COMMANDS AND AT FL225 QUESTIONED THE CTLR ABOUT THE TFC CONFLICT. HE STATED THAT HE HAD NOT CLRED US TO FL210. IN ADDITION TO THE 3 PLTS IN THE COCKPIT; AN FAA EXAMINER WAS ON THE SECOND JUMPSEAT AND SAID HE HEARD US CLRED TO FL210. WE THEN PULLED THE CIRCUIT BREAKER ON THE VOICE RECORDER TO PRESERVE IT AND PROCEEDED TO FRANKFURT UNEVENTFULLY FROM THIS POINT. ACR Y WAS A SIMILAR TYPE AS OURS. AFTER THE FLT; OUR AREA OF UNCERTAINTY ON OUR PART WAS WHO; IF ANY OF US; READ BACK THE CLRNC TO ATC. I BELIEVE PART OF THE UNCERTAINTY IS DUE TO THE FACT THAT THIS WAS DAY 6 OF A 7 DAY ATL-ZRH-BOM-FRA-ATL ROTATION WHICH INVOLVES CHANGING 9 1/2 TIME ZONES. AS A FURTHER FACTOR TO CREW FATIGUE; OUR COMPANY PROVIDES NO REST STATION FOR THE OFF DUTY PLT WHICH ALLOWS HIM TO GET ANY SLEEP; OUR REST AREA IS A COCKPIT JUMPSEAT WHICH RECLINES. I FEEL AT BEST; AFTER THE FIRST 2 HRS OF THIS FLT WE WERE ALL FUNCTIONING AT A LEVEL WELL BELOW THAT WHICH IS NECESSARY FOR THIS OP.