ACR X CLB TO OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR.

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I STARTED TO CLR ACR Y TO CLB FROM FL290 TO MAINTAIN FL310; BUT CHANGED THE CLRNC TO MAINTAIN FL290 AND EXPECT A HIGHER ALT AFTER STL. SHORTLY THEREAFTER; I NOTICED ACR X AT FL295. I ASKED HIM TO VERIFY LEVEL AT FL290. ACR X REPLIED THAT I HAD CLRED HIM TO FL310. I INSTRUCTED ACR X TO EXPEDITE DSCNT BACK TO FL290. I ALSO INSTRUCTED ACR Y WBOUND TFC AT FL310 TO TURN 40 DEGS R. LOSS OF SEPARATION OCCURRED AND WAS REESTABLISHED AFTER THE ACFT PASSED EACH OTHER. I BELIEVED THAT ACR X HAD ACCEPTED THE CLRNC TO MAINTAIN FL290 WHEN HE ACKNOWLEDGED WITH AN 'OK.' WHAT SEEMS TO HAVE HAPPENED IS THAT WHEN ACR X HEARD THE CLRNC TO MAINTAIN FL310 HE IMMEDIATELY READ BACK HIS ACKNOWLEDGEMENT. I NEVER UNKEYED MY MIKE; SO THAT I WAS CLRING THE ACFT TO MAINTAIN FL290 AT THE SAME TIME ACR X WAS READING BACK FL310. WHEN ACR X UNKEYED HIS MIKE ALL HE HEARD WAS 'EXPECT HIGHER ALT AFTER STL.' IN RETROSPECT; I SHOULD HAVE GOTTEN CONCLUSIVE CONFIRMATION THAT IT WAS ACR X THAT SAID 'OK' AND THAT HE DEFINITELY KNEW TO MAINTAIN FL290. ACR X SHOULD NOT HAVE BEEN IN SUCH A HURRY TO GET TO ALT (REQUESTED FL330) AS TO ALLOW ME TO UNKEY OR FINISH SPEAKING. SUPPLEMENTAL INFO FROM ACN 243059: ACR X COPIED AND READ BACK CLRNC FROM FL290 TO FL310. UPON CLBING THROUGH FL305 CTLR ASKED IF WE WERE LEVEL AT FL290. I SAID NO AND HE SAID WE WERE TO RETURN TO FL290. IMMEDIATE DSCNT INITIATED. NO HDG CHANGE WAS ISSUED. HE THEN TOLD US THAT WE WERE NOT CLRED TO FL310. I REPLIED THAT WE COPIED AND READ BACK CLRNC TO FL310 AND COULD EXPECT HIGHER E OF STL. BOTH PLTS HEARD FL310 AS CLRED ALT. NO EVASIVE ACTION WAS REQUIRED. ONE ACR Y FLT WAS GIVEN A 40 DEG HDG CHANGE.