Problem 1

Given the following premises, use the resolution and universalinstantiation to prove F(c) where c is part of the domain of x andw.

1.?x A(x)

2.?x [¬A(x)?C(x)]

3.?x,w [¬C(x)?F(w)]

Problem 2

Let the domain of the variables x, y, and w be the set {a,b,c}.Given the following premises, use resolution, universalgeneralization (Table 2 in section 1.6.7), and universalinstantiation to prove ?x B(x).

1. ¬A(x)?B(y)

2. ¬C(x)?G(w)

3. ¬G(x)

4. A(x)

Problem 3

Repeat problem 2, but prove ?w ¬C(w)

TABLE 2 Rules of Inference for Quantified Statements. Rule of Inference Name VxP(x) Universal instantiation :. P(c) P(c) for an arbitrary c .. VxP(x) Universal generalization ExP(x) Existential instantiation ..P(c) for some element c P(c) for some element c .. ExP(x) Existential generalization