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

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I WAS ADMINISTERING OJT AT A HIGH ALT SECTOR. THE DEVELOPMENTAL I HAD CHARGE HAD APPROX 50 HRS TIME AT HIS FIRST RADAR POS. THE PRINCIPAL ACFT INVOLVED; ONE WBOUND LEVEL AT FL310; THE OTHER SBOUND AT FL280; REQUESTING FL310. THE ACFT WERE ON CONVERGING COURSES. MY ATTN WAS DIVERTED FOR A MOMENT BECAUSE OF A JOB-RELATED FUNCTION. THEN MY ATTN WAS RETURNED TO THE SCOPE; THE 2 ACFT WERE IN CLOSE PROX AND THE STATUS OF THE DATA BLOCKS WERE CHANGED BY THE TRAINEE. THE SBOUND ACFT; ACR X ALT INDICATED CLBING TO FL310 AND IN HDOF STATUS; NOT AN UNUSUAL PROC. THE WBOUND ACFT WAS IN HDOF STATUS. I ASKED THE TRAINEE TO WHAT ALT WAS ACR X CLBING? HIS RESPONSE WAS TO FL290. I THOUGHT EVERYTHING WAS IN ORDER AND VERY ROUTINE. NEXT; WE OBSERVED ACR X MODE C READOUT TO INDICATE HE WAS CLBING THROUGH FL290. I ASKED THE TRAINEE TO CHK ON THE ALT OF ACR X. THE PLT REPLIED HE WAS OUT OF FL298 FOR FL310. STANDARD SEPARATION WAS ALREADY LOST; BUT THE ACFT WAS IMMEDIATELY DSNDED TO FL290. THE PLT CLAIMED HE WAS ISSUED A CLRNC TO FL310 AND READ IT BACK. AFTER REVIEWING THE TAPES; THE TRAINEE DID; IN FACT; ISSUE A CLRNC TO FL310. THERE WERE A NUMBER OF THINGS WRONG WITH THIS SITUATION. NO ALTS WERE MARKED ON THE FLT PROGRESS STRIPS; THE DATA BLOCKS WERE NOT UPDATED PROPERLY; TFC INFO WAS NEVER ISSUED TO EITHER ACFT; AND THE INSTRUCTOR DID NOT DEVOTE 100 PERCENT OF HIS ATTN TO THE TRAINEE. BECAUSE OF MANY OTHER INFLUENCES; EVEN JOB RELATED; 100 PERCENT DEVOTION TO THE TRAINEE IS NOT REALISTIC. THE TRAINEE HAD TAKEN AN EVALUATION EARLIER IN THE DAY; THEN HAD TAKEN OJT INSTRUCTION FROM ANOTHER INSTRUCTOR. I BELIEVE THE TRAINEE TO HAVE BEEN MENTALLY FATIGUED AS TO WHY HE ISSUED FL310 AS OPPOSED TO FL290 AND WAS CERTAIN HE ISSUED FL290. HE PROBABLY SHOULD NOT HAVE BEEN REQUIRED TO TAKE OJT AT THIS POINT. AS TO THE INSTRUCTOR; THE ONLY SUGGESTION I CAN OFFER IS THAT; IF YOUR ATTN IS DRAWN AWAY AND A CTLED SITUATION IS INVOLVED; VERIFY THE SITUATION DIRECTLY WITH THE PLT INSTEAD OF THE TRAINEE.