Medium Large Transport
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (mon) 6
Situational Awareness; Workload; Distraction
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action
Human Factors; Procedure; Weather
[Aircraft X] was enroute to ZZZ1 from the southwest level at FL310. [Aircraft Y] was a departure that was climbing well at first but then slowed the climb as they got higher. [Aircraft Y] was enroute to ZZZ2 as well to the West. The sector was beginning to get busy as the URET/EDST (User Request and Evaluation Tool/En-route Display Support Tool) was beginning to fill. Odd routes were in play for weather as well as big in trail to ZZZ3.  Many aircraft were converging over ZZZ2 and the data blocks were beginning to get overlapped. I tried my best to keep the data blocks apart as I usually do but with so many aircraft coming into the sector and having to coordinate data blocks became secondary. I did not have a D-side or any help. The [Aircraft Y] and [Aircraft X] begin to flash and I told [Aircraft Y] to fly heading 360 expedite and told the Aircraft X to fly heading 180 expedite. [Aircraft Y] reported the [Aircraft X] in sight. A supervisor came up behind me and told me to descend the [Aircraft X] to FL290 which I issued. A few seconds passed and Aircraft X said they were climbing due to an RA. Once the aircraft were seperated laterally I resumed them back on course.With weather deviations and odd reroutes being issued to aircraft already en route; I should have had a D-side. My one supervisor; was walking behind me several times as I was getting more busy but told 2 controllers returning from break to get other people instead of giving me a D-side. The other supervisor offered what help he could at the time by offering suggestions but it was still about 10 minutes before I got a D-side; and another 30 minutes before I got relief.  Data block over lappage was one factor that I could have avoided to help me see the situation sooner; however constantly moving 15 data blocks can be just as damaging as not moving them.  With all this technology and ERAM (En Route Automation Modernization) and why hasn't there been a feature for auto data block separation?
I was the Captain and non-flying pilot this evening to ZZZ1.  We were about 40 minutes into the flight; somewhere near ZZZ2 VOR and level at FL310 when we saw traffic approaching opposite direction and in a climb on our MFD.  I called ATC 'Center; [Aircraft X.]'  His response was '[Aircraft X] turn heading 180 and expedite!' (This was a significant turn; maybe 40 degrees or so to the right and we knew why.)  While in the turn; this traffic is showing -200 [FT] below us and approaching. We got a RA to climb and we reacted accordingly. While climbing at full power and in a right hand turn while ATC gave us instructions to descend to FL290 twice. This happened fast and when I heard clear of conflict; I stopped to evaluate what had just happened. I told him that we had climbed to 31;600 feet complying with an RA and his response was 'roger'. I waited a minute and then said 'We were instructed to climb via TCAS; why were you giving us a descent with traffic 200 feet below?' He responded with 'maintain FL310'. I know that we are all human; but the fact that he would not acknowledge what had just happened was frustrating. I politely asked for a number that I could call him on the ground; and that is when we had a brief explanation that traffic was climbing and he thought a descent for us would offset a conflict. I was still confused but thanked him for the phone number. I still have not called; I don't know what else to say. Paperwork is necessary; but I am fortunate that no one was hurt. We are trained to comply with the TCAS above all and this instance is a good example of why that is.
ZME Controller and two pilots report of a loss of separation. Controller descends aircraft to get away from conflicting traffic but the aircraft receives a RA and it tells pilots to climb.  Controller couldn't see data tag and assumed descending was the best option. Pilot questioned Controller as to why they said descend and RA said to climb.