ACR ACFT AT FL410 BECAME CONFUSED BY ZOB WHETHER TO CROSS A FIX 15 MI W OR 15 MI E AT FL270. CREW CLAIMS THE CTR VERIFIED E AT FL270. APCHING THE FIX; THE ACR RECEIVED A TCASII RA ON OPPOSITE DIRECTION TFC AT FL350.

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ORD-EWR CRUISING AT FL410. WE RECEIVED CLRNC TO CROSS 15 MI W SLT AT FL270; AND CAPT READ THAT BACK AND I VERIFIED BY POINTING AT FL270 ON MCP. WE REALIZED THAT WAS JUST 5 MI AWAY AND CAPT VERIFIED WITH ATC; 15 MI W SLT AT FL270. THEY CORRECTED US 15 MI E SLT AT FL270; AND CAPT READ BACK 15 MI E SLT; FL270. WE BEGAN OUR DSCNT TO MAKE THE RESTR. DSNDING THROUGH FL360; CTR ASKED IF WE WERE LEVEL AT FL370; AND WE REALIZED THERE MUST HAVE BEEN A MISTAKE. I TURNED THE AUTOPLT OFF AND CLBED BACK TO FL370. AT THE SAME TIME; WE RECEIVED 1 RA 'TFC' CALLOUT; AND CTR GAVE US A L 45 DEG TURN. WE HAD TFC BELOW AT FL350. NO NEAR MISS OCCURRED. THE ATC FREQ WAS BUSY. OUR INCORRECT READBACK OF FL270 WAS NOT CAUGHT BY THE CTLR 3 TIMES ON OUR READBACKS (OR POSSIBLY WE WERE GIVEN FL270 BY MISTAKE FROM ATC. BOTH PLTS THOUGHT WE HEARD FL270) AND THERE WAS CONFUSION ABOUT WHICH SIDE OF SLT VOR FOR THE XING RESTR. THIS WAS THE END OF A LONG DUTY DAY (14 HRS) AND WX DELAYS AT BOTH ORD AND EWR AT MINIMUMS. AFTER THE EVENT WE WERE GIVEN CLRNC TO FL240 I BELIEVE.