Q15,b

Consider the following first order formula: $\left ( \matrix{ \forall x \exists y : R(x,y) \\[1em] \Large \land \\[1em] \forall x \forall y : \left ( R(x,y) \implies \lnot R(y,x) \right) \\[1em] \Large \land \\[1em] \forall x \forall y \forall z : \left ( R(x,y) \land R(y,z) \implies R(x,z) \right ) \\[1em] \Large \land \\[1em] \forall x: \lnot R(x,x) }\right )$ Does it have finite models? Is it satisfiable? If so, give a countable model for it.