Introduction to Logic

Assume a language with object constant a and unary function constants f and g. Given p(a), ∀x.(p(x) ⇒ p(f(x))), and ∀x.(p(f(x)) ⇒ p(g(x))), use the Fitch system with Tree Induction to prove ∀x.p(x).

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Herbrand
Objects a, b, c
Functions f, g
Goal  Incomplete