2. Let T = {(Vx) (P(x) (y) R(x, y)), (y) ((3x)R(y,x) (z) P(z)), (Vx)P(x)} be a theory in language L = (P, R) without equality where P, R is unary resp. binary relation symbol. (a) Applying skolemization find a theory T' (in a some extended language) such that T' is equisatisfiable with T and all axioms of T' are universal sentences. (b) Prove by tableau method that T' is unsatisfiable. (c) Let T" denote the set of open matrices of axioms of T', so T" is an open theory equiva- lent to T'. Find a conjunction of ground instances of axioms of T" that is unsatisfiable. Hint: use the tableau from (b). (d) Find some complete extension of T or explain why no such extension exists.