How to show that the Peano Arithmetic theory is not scapegoat?
Note:
Peano Arithmetic is a consistent theory.
A theory T is scapegoat if for every formula $A$ with only one free variable there exist a closed term $s$ such that $T$ proves: $$(\exists x \; (\neg A(x)) )\Rightarrow \neg A(s)$$
("$\neg$" means "not"). I think we can start by assuming that the theory is scapegoat then we get a contradiction, but how!?