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Handbook of Automated Reasoning by Andrei Voronkov, Alan J.A. Robinson

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3.3 Extensional resolution

The ideas we have discussed so far have been directed toward proving theorems of the system T si170_e of elementary type theory, which lacks the axioms of Extensionality and Descriptions of the full system C si171_e of classical type theory. Of course, to prove a theorem A ο of C si172_e , one can in principle prove [H o A o ] in T , where H o is an appropriate conjunction of axioms of Extensionality and Descriptions, ...

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