Infinitely presented graphical small cancellation groups are acylindrically hyperbolic

We prove that infinitely presented graphical Gr(7) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C(7)-groups and, hence, classical C′(1/6)-groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical C′(1/6)-groups that provide new examples of divergence functions of groups.