The minimization principle $\textsf{MIN}(\triangleleft)$ studied in bounded arithmetic says that a strict linear ordering $\triangleleft$ on any finite interval $[0,\dots,n)$ has the minimal element. We shall prove that bounded arithmetic theory $\textsf{T}^1_2(\triangleleft)$ augmented by instances of the pigeonhole principle for all $Δ^b_1(\triangleleft)$ formulas does not prove $\textsf{MIN}(\triangleleft)$.

翻译：有界算术中研究的极小化原理 $\textsf{MIN}(\triangleleft)$ 指出，任意有限区间 $[0,\dots,n)$ 上的严格线性序 $\triangleleft$ 均具有极小元。我们将证明，通过在 $\textsf{T}^1_2(\triangleleft)$ 有界算术理论中添加所有 $Δ^b_1(\triangleleft)$ 公式的鸽巢原理实例，仍无法证明 $\textsf{MIN}(\triangleleft)$。