F100 CREW HAD A RWY INCURSION AT MDW.

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MDW WAS TAKING OFF ON RWY 31C AND LNDG ON RWY 4R. WE RECEIVED CLRNC TO TAXI TXWY Y; TXWY P; AND TXWY E TO RWY 31C FOR TKOF. I PROCEEDED DOWN TXWY Y; THEN TXWY P; AND LOOKED L TO WHERE I THOUGHT TXWY E WOULD BE; BUT THERE WERE NUMEROUS BARRICADES ON THAT TXWY. ATIS AT XA53Z STATED 'USE CAUTION FOR BARRICADES AT TXWY E AND TXWY P.' I WAS PRESUPPOSED TO THINK THAT TXWY WAS CLOSED; BECAUSE THE PREVIOUS NIGHT; WE GOT TAXI CLRNC TXWY Y; TXWY P; TXWY G TO RWY 31C; WHICH CROSSES RWY 31R ON TXWY P. I PROCEEDED ACROSS RWY 31R; AND THEN SAW ONLY TXWY G TO GET TO RWY 31C. I LOOKED N AND SAW A B737 ACFT WAS INDEED GETTING THROUGH ON TXWY E; AND THEN THOUGHT THE CTLR DID IN FACT WANT US ON TXWY E; AND THIS TXWY WOULD NOT HAVE CROSSED RWY 31R TO GET TO RWY 31C. I THEN REALIZED I HAD CROSSED RWY 31R WITHOUT PROPER CLRNC. IT WAS NOT BEING USED FOR TKOF OR LNDGS; BUT IT WAS NOT NOTAMED OUT; AND IT PROBABLY COULD HAVE BEEN USED. WHEN WE CROSSED; BOTH I AND THE FO VISUALLY AND VERBALLY CONFIRMED THE RWY'S PATH WAS CLR IN BOTH DIRECTIONS; AS I DO XING EVERY RWY. JUST WHEN I WAS GOING TO CALL GND CTL TO CONFIRM MY ERROR; HE STATED 'CONTINUE ON TXWY G TO RWY 31C; AND CONTACT TWR.' WE TOOK OFF NORMALLY WITHOUT ANY FURTHER PROBS OR COMMENTS. CONCLUSION; I DID NOT FOLLOW TAXI INSTRUCTIONS; AND I BELIEVE I HAVE BECOME YET ANOTHER RWY INCURSION STATISTIC. CONTRIBUTING FACTORS; I WAS INFLUENCED BY THE PREVIOUS DAY'S TAXI RTE; BY WHAT I MISINTERPED AS A CLOSED TXWY; AND NOT QUERYING THE CTLR FOR WHAT I THOUGHT WAS A SIMPLE ERROR ON HIS PART; TXWY E; WHEN HE MUST HAVE MEANT TXWY G. SUPPLEMENTAL 579683: I EVEN WROTE IT DOWN AS I TYPICALLY DO AT BUSY OR STRANGE ARPTS. I BEGAN RUNNING THE BEFORE TKOF CHKLIST. AS I WAS RUNNING THE BEFORE TKOF CHKLIST; THE CAPT CONTINUED TO TAXI ON TXWY P AND CROSSED RWY 31R INSTEAD OF TURNING L ONTO TXWY E PRIOR TO RWY 31R. AFTER 1 MIN OR 2; WE CHANGED OVER TO MDW TWR; WERE CLRED FOR TKOF; AND NOBODY EVER SAID ANYTHING ABOUT OUR MISTAKE. I ALWAYS FOLLOW ALONG ON THE COM CHART PAGE WHEN WE TAXI; EVEN AT DFW; BUT THIS TIME I WAS JUST 'HEADS DOWN' IN THE COCKPIT AT THE WRONG TIME.