In order to show that a sequent is not valid, we provide a \emph{counter example}, which is a model that satisfies all premises but falsifies the conclusion.

This is a consequence of soundness. We know from the definition of soundness that

$$\varphi_1, \varphi_2,\!..., \varphi_n \nmodels \psi \qquad \Rightarrow \qquad \varphi_1, \varphi_2,\!..., \varphi_n \nvdash \psi$$

A counterexample is enough to tell us that the left-hand side of this implication is true, hence the sequent is not valid.
