TCASII LOGIC ACR X TCASII RA WITH VFR ACFT GOT UNSAFE RA.

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ON THE EAGUL 3 DEP FROM PHX WE EXPERIENCED A TFC CONFLICT AND A TCASII RESOLUTION WHICH I FEEL WAS UNSAFE. I WAS THE PF AND DID NOT COMPLY WITH THE RESOLUTION. I AM CONCERNED THAT THERE MAY BE A SOFTWARE PROB WITH THE TCASII IN THIS SIT. I WAS JUST COMPLETING THE TURN TO 020 DEGS AT APPROX 6 DME FROM PXR AND 3400 FT (2200 FT AGL); I OBSERVED A HIGH WING CESSNA SLIGHTLY BELOW AT 11 O'CLOCK MAYBE 4 MI AHEAD. AT THE SAME TIME WE RECEIVED A TCASII ALERT AND A CALL FROM DEP CTL FOR A TA. I IMMEDIATELY CHKED THE VSI WHICH SHOWED THE CONFLICT AT 12 O'CLOCK; 2-3 MI; 400 FT BELOW WITH OUR RATE OF CLB AT 500 FPM. (THE COPLT CONFIRMED ALL THESE FIGURES.) WE WERE AT 230 KTS ACCELERATING (VZF 228) WITH QUIET EPR (APPROX 1.57). I WAS NOT TOO CONCERNED AT THIS TIME SINCE WE WERE ABOVE THE ACFT CLBING AND HE WAS 45 DEGS OFF OUR HDG. I DID INCREASE THE BACK PRESSURE SLIGHTLY. ABOUT 15 SECONDS AFTER THE TCASII ALERT WE RECEIVED AN RA COMMANDING A 1500 FPM DSCNT. I HESITATED INITIALLY BUT DECIDED TO IGNORE THE TCASII. THE SO; COPLT AND I HAD THE TFC IN SIGHT. WE WERE AT THIS TIME AT LEAST 500 FT ABOVE AND CLBING IN EXCESS OF 500 FPM AND ONLY 2500-2800 FT ABOVE THE GND WITH RISING TERRAIN. WE RECEIVED A SECOND MORE INTENSE RA (FOR A DSCNT) AT WHICH TIME I PULLED BACK HARD INCREASING THE RATE OF CLB NEEDLE TO BEYOND VERT (GREATER THAN 1500 FPM). WITHIN 5-10 SECONDS OF THE SECOND RA WE RECEIVED MONITOR VERT SPD FOLLOWED IMMEDIATELY THEREAFTER BY A CLR OF CONFLICT. WITHIN 5 SECONDS OF THE CLR OF CONFLICT ADVISORY THE TFC DISAPPEARED BELOW THE ACFT TO THE L. I DISCUSSED THE SIT WITH DEP. HE CONFIRMED THAT THE ACFT WAS IN THE PHX PATTERN AT 3000 FT UNDER HIS CTL AND THAT HE DID NOT RECEIVE A CONFLICT ALERT. I FEEL IF I HAD FOLLOWED THE TCASII IT WOULD HAVE PUT US IN IMMINENT DANGER OF A MIDAIR FOLLOWED BY A GPWS ALERT. I FEEL THAT THE TCASII PROGRAM NEEDS WORK.