I refute the dream XOR lemma as stated in a 1995 paper by Goldreich, Nisan, and Wigderson. I also give a counterexample to the XOR lemma for low-degree polynomials.

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I refute the 1995 dream XOR lemma conjecture by Goldreich, Nisan, and Wigderson. I also give a counterexample to the XOR lemma for low-degree polynomials.