Large Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 15.0
Human-Machine Interface; Situational Awareness; Training / Qualification
Conflict Airborne Conflict; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Air Traffic Control Issued Advisory / Alert; Air Traffic Control Separated Traffic
Human Factors; Procedure
Aircraft X was climbing southbound to 34000 feet requesting 35000 feet. Had traffic; Aircraft Y westbound at 34000 feet. Loss of separation was about 8 minutes away. I was acting OJT Instructor at the sector. Student stopped Aircraft X at 33000 feet for separation. We discussed that Aircraft X had plenty of time to climb above Aircraft Y. The student asked Aircraft X 'If I climb you to 35000 feet how long to you will be level?' The pilot responded the he could be level in 2 1/2 mins. At this time we had 5 minutes until loss of separation. So we climbed Aircraft X to 35000 feet. Two min later Aircraft X altitude is showing 34100 feet. I watched for another hit and his altitude still said 34100 feet. Student then asked the pilot to verify that he was climbing to 35000 feet. The pilot responded that he was LEVEL at 35000 feet. By this time another hit has shown him at 34100 feet. At this point I took over the frequencies. We had 1 1/2 min till loss of separation and also targets appeared likely to merge. I informed Aircraft X that he was level at 34000 feet and not 35000 feet and that I needed him at 35000 feet in 1 minute. He said he would comply. Seeing an imminent safety situation I also descended Aircraft Y to 33000 feet. Separation was lost.It was an unusual and unfortunate situation. If I had reacted quicker separation my not have been lost. However; I believe my actions did maintain a safe situation.
ZID ARTCC Controller reported a loss of separation event between southbound and westbound traffic.  Reportedly; one of the flight crews leveled off at FL314 rather than continue climbing to FL350 as instructed.