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I find most Natural Deduction proof systems only allow for close formulas, which are not convenient for FOLs without a constant. Most Sequent Calculus systems instead allow for open formulas, but it is hard for me to read something like Γ⊢ϕ(x). I wonder if there is a Fitch-style Natural Deduction system(book/material) that allows for open formulas, i.e., it must include the universal generalization rule like: $\frac {\phi(x)} {\forall x \phi}$

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Dag Prawitz' systems in his book Natural Deduction (1965) seem to meet your requirements.

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