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We consider the problem of automatically establishing that a given syntax-guided-synthesis (SyGuS) problem is unrealizable (i.e., has no solution). We formulate the problem of proving that a SyGuS problem is unrealizable over a finite set of examples as one of solving a set of equations: the solution yields an overapproximation of the set of possible outputs that any term in the search space can produce on the given examples. If none of the possible outputs agrees with all of the examples, ourdoi:10.1145/3385412.3385979 arXiv:2004.00878v1 fatcat:gnkkuhwtmzfr7afyj5rep7sajq