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      Cain 'willing to take lie detector test' to clear harassment allegations

      Cain denied all harassment allegations at a press conference. / AP photo

      Hermain Cain not only denied all sexual harassment allegations against him at a press conference on Tuesday, he also said he'd take a lie detector test to prove his innocence.

      But here's the catch--Cain said he would not submit to a test without a good reason.

      Four women have accused the Republican presidential candidate of sexually harassing them during his time as head of the National Restaurant Association in Washington.

      Cain held the news conference in response to the latest allegations from Sharon Bialek, the only woman to come forward publically. Bialek said Cain put his hand under her skirt and pushed her head toward his crotch when she asked for her job at the National Restaurant Association back in 1997.

      Cain said the encounter "simply did not happen" and that he didn't even recognize her or remember her name.

      He also said he will not back out of the presidential race, despite the allegations.

      Do you believe Cain? Should he take a lie detector test to prove his innocence? Weigh in below and on our Facebook page.

      (The Associated Press contributed to this report)