定理机器证明的研究已有将近50年的历史，并已经在数理逻辑、初等代数和几何学等学科取得显著成功。

There has been a lot of success in the study of automated theorem proving during the past 50 years.

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数学从萌芽时期开始，历经了初等数学时期、变量数学时期、近代数学时期和现代数学时期。人们已经从数学的内容、表现形式、作用等方面为研究数学的特点提供了框架。

People had already provided the frame for the research of mathematical characteristics from the aspects of the content, forms of expression, the role and the research procedure of mathematics.

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数学从萌芽时期开始，历经了初等数学时期、变量数学时期、近代数学时期和现代数学时期。人们已经从数学的内容、表现形式、作用等方面为研究数学的特点提供了框架。

People had already provided the frame for the research of mathematical characteristics from the aspects of the content, forms of expression, the role and the research procedure of mathematics.

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