Finding a guaranteed consequent of a satisfiable sentence ### Let A = ∀x∀y(P(x,y)). A is satisfiable. Find any B such that it isn't a tautology and is a consequent of A. Now if I understand it correctly, then a correct and somewhat trivial solution to this would be any sentence logically equal to A. For example neg(∃x∃y(neg(P(x,y))). Is there anything else, or is this the only simple solution? Thank you in advance.

How about **reflexivity** \- $\forall x (P(x, x))$?

Similarly, **transitivity** $\forall x\forall y\forall z(P(x, y)\wedge P(y, z)\implies P(x, z))$ and **symmetry** $\forall x\forall y(P(x, y)\implies P(y, x))$. And there are lots of others . . .