Herod , " ...... ALWAYS BELIEVE AND FOLLOW THE TCAS"
Even if the ATC shouts to take the opposite evasive action?
Has any one had his TCAS warning to descend and the ATC advising to climb up or vice versa??
TCAS RAs must take precedence over ATC instructions. Controllers understand that and so should pilots.
The problem occurs when the controller becomes aware of a conflict late and will try to resolve it, but is unaware of the RA. The controller may have a completely valid conflict resolution which may be contradictory to the equally valid RA. The ability of the TCAS to co-ordinate both aircraft simultaneously (or instruct one aircraft with knowledge that the other is not RA capable) with none of the latencies of voice comms means it should always take precedence.
Modern surveillance systems are now able to downlink the RA information during the event. However providing this to the controller is a long way from universal. The purpose is not for the controller to intervene in the RA, but simply to be aware of its occurrence, not risk applying potentially contradictory instructions, and be ready to deal with any consequences involving, for example, reclearance.