ACR FLT CREW MAKES ERRORS DURING TAXI TO RWY 6C AT CLE. XING THE ACTIVE RWY WITHOUT CLRNC AND MAKING FURTHER ERRORS BEFORE DEPARTING ON RWY 6L.

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THE CAPT TAXIED UP TO SPOT X AND I CONTACTED CLEVELAND GND CTL. THEY INSTRUCTED US TO TAXI TO RWY 6C. THIS WAS UNUSUAL AS THE ATIS HAD STATED THAT RWY 24C WAS BEING USED FOR DEP. WE BOTH BRIEFLY LOOKED AT THE ARPT DIAGRAMS WE EACH HAD OUT AND STARTED TO TAXI. THE CAPT SAID SOMETHING LIKE 'OK; ROMEO TO LIMA' AND THAT SIGNALED TO ME THAT HE KNEW WHERE HE WAS GOING; AND SO I STARTED THE BEFORE TKOF CHKLIST WHICH IS DONE WHILE TAXIING AND REQUIRES MY ATTN TO BE INSIDE THE ACFT. ON THE FIRST FLT OF THE DAY THERE ARE EXTRA ITEMS ON THIS CHKLIST WHICH NEEDS TO BE DONE INCLUDING CHKING THE ANTI-ICE SYS. AS I TURNED BOTH WINGS' ANTI-ICE ON AND THEN THE ENG COWL'S ANTI-ICE AND THEN ENGAGED THE ISOLATION VALVE; THE CAPT NOTED THAT HE THOUGHT I DIDN'T NEED TO TURN ON THE WHOLE SYS; I JUST NEEDED TO CHK THE ISOLATION VALVE. I NOTED THIS AND WE CONTINUED. I ASSUME THAT HE WAS WATCHING TO MAKE SURE THAT I WAS DOING EVERYTHING CORRECTLY. SHORTLY AFTER THIS; THE CAPT SAID SOMETHING LIKE 'WAIT; OK; NO THIS RWY IS CLOSED.' THIS IMMEDIATELY CAUGHT MY ATTN AND I LOOKED UP TO SEE WHERE WE WERE. I NOTICED A RWY SIGN AND A HOLD SHORT BAR AND CONES AND RED CONSTRUCTION LIGHTS SO I CONTINUED WITH THE CHKLIST ASSUMING THAT THE CAPT STILL KNEW WHERE WE WERE; AND ALSO ASSUMING WE DID NOT NEED ADDITIONAL CLRNC AS THE RWY WAS CLOSED. WHEN I LOOKED UP AGAIN; I REALIZED THAT WE WERE NOW TAXIING ONTO RWY 6C/24C; AN ACTIVE RWY. WE WERE ALREADY PAST THE HOLD SHORT BAR SO I SAID 'HURRY UP! GET ACROSS!' THE CAPT ADVANCED THE PWR AND WE TAXIED ACROSS QUICKLY. AFTER XING; WE SLOWED AND TURNED L ON TXWY G. AS WE HEADED SW ON TXWY G; THE GND CTLR NOTICED THAT WE HAD CROSSED THE RWY AND INSTRUCTED US TO CONTINUE TAXI TO RWY 6C VIA TXWY G. I READ BACK THE INSTRUCTION AND WE CONTINUED AHEAD ON TXWY G. THE CAPT AT THIS POINT WAS SAYING SOMETHING TO THE EFFECT OF 'OH MAN; WE JUST CROSSED AN ACTIVE RWY! WHAT WAS I DOING? OH MAN.' I KNEW HIS MIND WAS NOT ON THE AIRPLANE; I WAS STILL JUST SEARCHING OUTSIDE FOR A LOCATION SIGN. WHEN I FOUND ONE IT SAID TXWY G AND I COMPARED THAT TO THE ARPT DIAGRAM. I DID NOT NOTICE THAT WE WOULD NEED TO STOP ON TXWY G AND HOLD SHORT OF RWY 6C AT TXWY P. WE CONTINUED TAXIING SW ON TXWY G. WHEN WE WERE NEARING TXWY T; GND INSTRUCTED US TO CONTINUE OUR TAXI TO RWY 6L. NEITHER THE CAPT NOR I NOTICED THAT WE HAD EVEN PASSED TXWY P AND WHEN GND GAVE THIS INSTRUCTION I NOTICED HOW DISTURBED THIS EVENT HAD MADE ME. WE CONTINUED TAXI AND FINISHED ALL OF OUR CHKLISTS AND THE REMAINDER OF THE FLT WAS SAFE AND UNEVENTFUL. THERE WERE A NUMBER OF MISTAKES MADE AND I DO BELIEVE THAT MY FOCUS INSIDE THE AIRPLANE AS OPPOSED TO CHKING OUR LOCATION AGAINST WHERE THE CAPT WAS TAXIING THE AIRPLANE WAS A MAJOR FACTOR. I KNOW FOR SURE THAT WE HEADED OUT OF THE RAMP AREA ON TXWY R; BUT AFTER I STARTED THE CHKLIST WE MISSED THE L TURN ONTO TXWY L; I DID NOT NOTICE THIS AND NEITHER DID THE CAPT. IN ADDITION; I HAD BEEN TO THIS ARPT LESS THAN 1 WK BEFORE; AND HAD NOTICED THE NONSTANDARD HOLD SHORT CONFIGN BTWN RWY 6C/24C AND RWY 6R/24L. MY ASSUMPTION WAS THAT THE CAPT; WHO CAME UP WITH THE TAXI RTE; WAS ALSO FAMILIAR. SO AS WE ENTERED RWY 6R/24C (THE CLOSED RWY) I SHOULD HAVE KNOWN THAT THE HOLD SHORT LINE FOR RWY 6C/24C WAS THE FIRST HOLD SHORT BAR AND NOT THE SECOND ONE; AS IS THE CASE AT MOST OTHER ARPTS; AND THE WAY PLTS ARE MOST ACCUSTOMED TO (USUALLY XING THE HOLD SHORT LINE WITH THE SEGMENTED LINES TOWARDS YOU). AT THIS ARPT DUE TO THE CLOSE PROX OF RWYS 6C/24C AND RWYS 6R/24L THE HOLD SHORT LINES WERE REVERSED WITH THE FIRST HOLD SHORT BAR WE ENCOUNTERED AFTER ENTERING RWY 6R/24L BEING THE ONE WE NEEDED TO STOP AT. UNTIL THE CAPT AND I REVIEWED THIS AFTER THE INCIDENT WE BOTH DID NOT REALIZE HOW CONFUSING THAT CONFIGN CAN BE; AND HOW IT CAN LEAD TO A RWY INCURSION.