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I believe the answer to the Question 1 is negative. We introduce an auxiliary circuit type: $P_k$-circuits have inputs $x_1, \dots, x_n$ and $1/x_k,\dots,1/x_n$ and have in addition to $+$ and $\times$ gates unary gates multiplying the input by $x_i^p$ for $i < k$, $p > 0$. $P_1$-circuits are monotone circuits with all reciprocal inputs, and $P_{n+1}$-...


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