We show this in a couple of steps. First, as a consequence of how we constructed these fractional parts, we can rewrite any xk as the difference between the k-th multiple of r and the associated integer part vk. After making these substitutions for indices h and g, we get:
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，这一点在爱思助手中也有详细论述
For SAT problems with 10 variables and 200 clauses, it usually output SAT as expected, but the assignment was never valid (Examples: first, second). Once it claimed a SAT formula was UNSAT. For this reason I didn't bother testing with more variables for the SAT case.
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