Date: 201711
Local time of day: 1201-1800
Location: FLL.Airport, FL
Flight conditions: Mixed
Light: Daylight
Aircraft: B737 Next Generation Undifferentiated
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class E FLL
ATC / advisory: TRACON FLL
Aircraft component: TCAS Software
Component problem: Malfunctioning
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Human-Machine Interface; Confusion
Second reporter function: Pilot Not Flying; First Officer
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Less Severe; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Automation Aircraft TA; Automation Aircraft RA; Person Flight Crew; Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Separated Traffic; Flight Crew Took Evasive Action; Flight Crew Requested ATC Assistance / Clarification; Flight Crew FLC Overrode Automation
Contributing factors: Airspace Structure; Procedure; Aircraft
Primary problem: Aircraft

Narrative: We were on arrival into FLL when Approach warned us of an unknown VFR aircraft at 7;400 FT and that it appeared to be descending. We were cleared to 6;000 FT. A few seconds later the aircraft appeared on our TCAS and a TA announced. I was descending at 1;000 FT a minute and immediately hit Level Change and pulled my throttles to idle to increase my descent. At this time; the VFR aircraft was indicating 400 FT above me. Next; (this all happened simultaneously) ATC gave us a Traffic Alert and a turn away to heading 360 and descend immediately. We received an RA that told us to climb. I had a hard time hearing the TCAS instructions due to the low volume of the voice and ATC on the radio.  I looked at the red VVI indicator the TCAS presented and we were down in the bottom quarter of the required VVI and increasing descent rate due to my increased descent with Level Change that I performed earlier. It did not make sense to me to immediately reverse my descent into a climb and climb into the traffic. Next; the TCAS said monitor Vertical Speed and my FO spotted and directed me visually to the traffic. I noticed that the VFR twin aircraft was 700 FT above me and the gap was increasing due to my descent. I also visually turned away from the aircraft and was shortly clear of the conflict.  The rest of the flight continued without incident. One big concern is that the TCAS wanted me to climb into the traffic.  Within a few seconds; I would have gone from 2;500 fpm down to over 3;000 fpm down to be outside the TCAS commanded VVI red line and safe.  Instead; it wanted me to climb and get above 3;000 fpm climb. I deemed that would put us in more danger to execute.  It also helped that we got the aircraft visual and maneuvered away. Also; ATC gave us a turn and instructions far too late to help. Instead; they caused more trouble because they were talking at the same time as the TCAS. I have never disagreed with a TCAS instruction and I am surprised that I had to this time. However; it did not make sense.  I would be happy to discuss this with anyone.


Second narrative: [Report narrative contained no additional information.]


Synopsis: B737NG flight crew reported ATC issued a traffic alert to descend while TCAS was commanding a climb with traffic observed above.