The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called "Ceiling Machines." The formal ingredients of these two machines are nearly identical. But there are crucial differences, splitting the two into a "Higher Ceiling Machine" and a "Lower Ceiling Machine." A potential graph of state transitions of the Higher Ceiling Machine is then offered. This graph is termed the "canonically nondeterministic solution" or CNDS, whose accompanying problem is its own replication, i.e., the problem, "Replicate CNDS" (whose accompanying algorithm is cast in Martin-L\"of type theory). I then show that while this graph can be replicated (solved) in polynomial time by a nondeterministic machine -- of which the Higher Ceiling Machine is a canonical example -- it cannot be solved in polynomial time by a deterministic machine, of which the Lower Ceiling Machine is also canonical. It is consequently proven that P $\neq$ NP.

中文翻译：

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作为程序的机器：P $\neq$ NP

Curry-Howard 对应关系通常称为程序证明结果。我提供了这个结果的概括，可以将机器称为程序。利用这一见解，我介绍了两种新的图灵机，称为“天花板机”。这两台机器的正式成分几乎相同。但存在关键差异，将两者分为“更高的天花板机器”和“更低的天花板机器”。然后提供更高天花板机器的状态转换的潜在图。该图被称为“规范非确定性解”或 CNDS，其伴随问题是其自身的复制，即问题“复制 CNDS”（其伴随算法是类型理论的 Martin-L\）。然后我表明，虽然该图可以通过非确定性机器在多项式时间内复制（求解）——其中较高的天花板机器是一个典型的例子——但它不能通过确定性机器在多项式时间内求解，其中较低的天花板机器也是规范的。因此证明 P $\neq$ NP。