A new algorithm (WSCAN) extracts a witness from a terminating SCAN derivation, and guarantees the witness is first-order when the derivation is one-sided.
Archiv für mathematische Logik und Grundlagenforschung1(1), 17–29 (1950)
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Computing Witnesses Using the SCAN Algorithm (Extended Preprint)
A new algorithm (WSCAN) extracts a witness from a terminating SCAN derivation, and guarantees the witness is first-order when the derivation is one-sided.