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    The polynomial boundedness criterion is encoding-relative... — Carmelics
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    Challenges→Resolution is not polynomially bounded.

    The polynomial boundedness criterion is encoding-relative, so no single tautology family establishes system-wide unprovability across all representations.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Different encodings of the same problem can yield different proof lengths, showing no single tautology family captures inherent difficulty.
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    • 2.Representation-dependent hardness is empirically observed in SAT solvers, where encoding choices dramatically affect provability.
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    • 3.If unprovability were encoding-independent, a single lower bound would apply universally—but no such bound exists across all formalizations.
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    Reasons Against

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    Reason against
    ?
    • 1.Cook-Reckhow theorem treats proof systems abstractly; encoding differences are artifacts, not reflections of underlying computational limits.
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    • 2.If encoding-relative unprovability holds, proof complexity becomes undefined—we cannot meaningfully compare hardness across different representations.
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    • 3.Polynomial simulation between complete proof systems means some tautology families do establish consistent unprovability despite encoding variation.
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    Related

    Cook-Reckhow theorem treats proof systems abstractly; encoding differences are a...Different encodings of the same problem can yield different proof lengths, showi...If encoding-relative unprovability holds, proof complexity becomes undefined—we ...If unprovability were encoding-independent, a single lower bound would apply uni...
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    Polynomial simulation between complete proof systems means some tautology famili...Representation-dependent hardness is empirically observed in SAT solvers, where ...Resolution is not polynomially bounded.

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