Abstract
For classes of formulas containing at most two atomic sub-formulas the decision problem of first-order predicate logic with identity and function variables is treated. The class of all formulas of the form Q (α ∨ β), where Q is prefix and α, β are atomic formulas or negated atomic formulas, is decidable with respect to satisfiability. The class of all formulas of the form ∀x1...∀x6(α ∨ β) is a conservative reduction class and therefore is undecidable.
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