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"can you prove to me Bush lied?"

Is that really necessary? Sometimes the president is just an unbriefed, useful idiot with plausible deniability.

Like, the president in the movie Independence Day...he didn't know about aliens until Data told him!

Bush was very briefed, and while IDK if and how much idiot he was, in his case, he is guilty until shown otherwise.

He is the son of a former president and head of CIA, and a member of Skull & Bones, so trust me, he was informed.