NON ADHERENCE TO ATC CLRNC INSTRUCTION. OPPOSITE DIRECTION CLBING TFC. ALT TIME CLRNC RESTR NOT MET. POTENTIAL CONFLICT LTSS.

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ON CLBOUT TO FL280; THE CTLR ADVISED OF OPPOSITE DIRECTION TFC AT FL290; AND QUERIED IF WE COULD BE LEVEL AT FL310 IN 2 MINS OR LESS. THE CAPT (PF) SAID WE COULD; SO I RELAYED TO THE CTLR THAT WE COULD MEET THE RESTR. HE THEN CLRED US TO FL310 WITH THE PROVISION THAT WE BE LEVEL IN 2 MINS OR LESS. WE HAD BEEN IN ICING CONDITIONS AND HAD ANTI-ICE 'ON;' WHICH DIMINISHED OUR CLB CAPABILITY; AND FOR AN UNKNOWN REASON; THE CAPT WAS CLBING AT A SPD WELL BELOW THE OPTIMUM CLB SPD; FURTHER REDUCING OUR CLB RATE. YET; HE ASSURED ME WE COULD MEET THE RESTR. AT ABOUT FL300; IT WAS APPARENT THAT WE WOULD BE UNABLE TO MEET THE RESTR; AND SUGGESTED TO THE CAPT WE SHOULD SECURE THE ANTI-ICE AND CONSIDER MAX-CONTINUOUS THRUST TO ENHANCE OUR CLB RATE. I THEN ADVISED THE CTLR THAT OUR RATE OF CLB HAD DROPPED OFF (I SHOULD HAVE USED STRONGER LANGUAGE) IMPLYING THAT WE WOULD BE UNABLE TO MEET OUR CLB RESTR. THE CTLR THEN ISSUED HDG CHANGES TO US AND THE OTHER ACFT. I WATCHED THE CAPT ENTER THE HDG IN THE AUTOPLT FLT GUIDANCE; THEN LOOKED AT THE TCASII TO MONITOR THE OTHER ACFT. I GLANCED BACK UP TO REALIZE THE CAPT HAD ENTERED BUT NOT SELECTED THE HDG; THUS WE HAD NOT TURNED. I IMMEDIATELY POINTED THIS OUT TO HIM; BUT BY THEN WE WERE PAST THE OTHER ACFT. NO TA'S OR RA'S WERE ISSUED BY TCASII; AND LATER CONVERSATION WITH ATC BY PHONE SUGGESTED WE HAD ADEQUATE VERT SEPARATION. THIS WAS THE FIRST FLT THIS CREW HAD FLOWN TOGETHER; AND IT TAKES A WHILE SOMETIMES TO LEARN TO WORK WITH SOMEONE. MORE ASSERTIVENESS ON MY PART COULD HAVE HELPED AVERT THIS SIT; AS COULD BETTER COCKPIT DISCIPLINE AND SITUATIONAL AWARENESS.