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Emil Jeřábek's construction works indeed. Assume the formula $A$ has the propositional variables $x = \langle x_1,..,x_n \rangle$ and $y$ is some fresh variable. We can then construct $B$ as a formula $(y \rightarrow A) \wedge (\neg y \rightarrow C)$ whereby the formula $C$ needs to be further specified. For the formula $C$ we assume the threshold given ...

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