ACR X TCASII TA RA WITH VFR SMT EVASIVE ACTION TAKEN CLB AND TURN. SEE AND AVOID CONCEPT.

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I WAS FLYING ACR X ON VNAV AND LNAV DSNDING AND LEVELING OFF AT 13000 FT. WE WERE 20 MI W OF CLOVIS. I HAD THE VNAV PROGRAMMED FOR 20 W AT 10000 FT AND 250 KTS. I WAS CALCULATING MY ARR BECAUSE CTR WAS KEEPING ME SLIGHTLY HIGH. ZOA TOLD THE SMT TO LEVEL AT 12500 FT BECAUSE OF A TFC CONFLICT. I WAS LOOKING OUTSIDE; BELOW; AND TO THE R BECAUSE I KNEW WE WOULD BE GOING 500 FT ABOVE HIM. TCASII SHOWED: WHITE THEN YELLOW; BELOW AND TO THE R; BUT STILL CLBING. ALMOST IMMEDIATELY; TCASII WENT RED WITH AURAL WARNING 'CLB; CLB.' THE CAPT; WHO WAS MONITORING TCASII; DISENGAGED THE AUTOPLT AND CLBED TO THE L. TCASII SAID CLB AT 4000 FPM. THE SMT PASSED TO THE R ABOUT 200 FT BELOW AND 1/2 - 1 MI AWAY. CTR GAVE US NO INSTRUCTIONS UNTIL WE ADVISED THEM OF OUR DEV. SUPPLEMENTAL INFORMATION FROM ACN 242271: ATC ADVISED US OF TFC 5 MI S OF US CLBING VFR THROUGH OUR ALT. WE HAD OUR TCASII ON 5 MI RANGE AND HAD HIM AT OUR 3 O'CLOCK POS AND CLOSING. AS WE LEVELED AT 13000 FT THE TCASII SIGNAL WENT FROM WHITE TO YELLOW; THEN RED ON THE SCREEN. AT -4 RED WE GOT A FULL RED CIRCLE ON OUR WORM AND AN AURAL 'CLB; CLB' AT THE 200 FT DIFFERENCE. THE SIGNAL WAS APCHING OUR INNER CIRCLE. I PUNCHED THE AUTOPLT OFF; PULLED THE ACFT INTO A 15-17 DEG NOSE UP ATTITUDE WITH A 25 DEG L BANK AWAY FROM THE TFC.