I am not sure how to even start solving this problem. I tried to solve it using the semantic tree, but with no success. It’s an exercise from the book Mathematical Logic for Computer Science by Mordechai Ben-Ari.
Prove that the following formula has no finite models:
∀x∃yp(x,y) ∧ ∀x¬p(x,x) ∧ ∀x∀y∀z(p(x,y)∧p(y,z)→p(x,z)).
Prove that the following formula has no finite models:
∀x∃yp(x,y) ∧ ∀x¬p(x,x) ∧ ∀x∀y∀z(p(x,y)∧p(y,z)→p(x,z)).