A ZAU controller described a loss of separation event that occurred when a time to climb instruction was issued using required phraseology that he contended may be outdated and ineffective.

Narrative

Aircraft X entered sector eastbound level at FL370. Aircraft X made a request for climb to FL390. After a traffic scan; I asked the pilot if they could be level at FL390 in less than two minutes to avoid westbound traffic at FL380; to which he replied affirmative. I climbed the aircraft to FL390; and asked him to 'hurry up'. A few moments later; I cleared Aircraft X direct CRL; about a five degree left turn. He read back the clearance; but still had not shown out of FL370. I waited a few more moments and then observed the aircraft leaving FL370. I asked him if they could now be level in one minute and they replied that they were distracted putting clearance into the computer; hadn't started up in time; and could not be level at 390 in one minute. I turned Aircraft X twenty five degrees to the left. I then told Aircraft Y; a westbound aircraft at FL380; to turn twenty degrees to their left for the climbing traffic. I called the traffic for both aircraft; and Aircraft X told me that they had Aircraft Y in sight. However; a loss of separation occurred when they passed 4.3 miles and 600ft. I feel that this situation could have been avoided by both ATC and the pilots. The phraseology; we as controllers are required to issue for a time to climb clearance; is far too complicated and verbose to be effectively utilized. Therefore; I think we typically just expedite aircraft; and expect compliance from the cockpit. In this case; it seems the pilot was distracted by the clearance issued after the expedited climb; and forgot to climb for almost a full minute. I have almost no knowledge of what happens inside a cockpit once I give a pilot a clearance; because familiarization flights have not been available. I really believe I would benefit greatly from having the experience of seeing how pilots handle these situations inside the cockpit. I believe that would be a great training tool for the newer generation of controllers that have no means to understand what goes on in the air. Beyond that; I would also recommend a change in the time climb clearance. Currently; it is not a useful tool to prevent this type of incident. I choose to not even attempt to use that phraseology as it is currently written; because it is confusing and unnecessarily long. Had I been able to give the pilot a time to be level in a simple and clear manner; it may have been an extra reminder to the flight deck that they needed to start up right away.