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An interpretation creates a link between symbols, on one hand, and objects, relations or functions, on the other hand. Examples of interpretations are the links between names and people in the real world or the links between Numbers (which are objects in the world of mathematics), and the corresponding symbols (1, 2, …). To discuss intended/extended ...


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An $n^k$ prover implies that the set $\{\left(\varphi,1^n\right)|\text{$\varphi$ has a proof of length $\le n$}\}$ is in $P$, since we can simply run the prover for $n^k$ steps and check whether it yields a valid proof. It remains to show that this language is NP complete. This follows from a straightforward reduction from SAT. Given a CNF $\varphi$ over the ...


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