A traditional problem in paleontology is the mistaken belief
that all reptiles with a diapsid skull morphology are members of a single clade: the traditional Diapsida. Adding taxa splits this traditional clade in two. Members of the Lepidosauramorpha developed this skull morphology independently from members of the Archosauromorpha in the large reptile tree (LRT, 1908+ taxa). In the LRT, this latter clade can continue to be called Diapsida because the clade name Lepidosauriformes is suitable for the other convergent clade in the new Lepidosauromorpha (traditional definitions apply).
Unfortunately,
the university textbook, Vertebrate Paleontology, 4th ed by Michael J Benton follows invalid tradition as Benton’s cladogram (Fig. 1) presents a monophyletic Diapsida. The Benton cladogram features too few taxa and all are suprageneric. Unfortunately, this is what they teach at the university level. Amateurs have had to step in where professors have dropped the ball, relying on others to do the work because, well… this is a lot of work. And there is no reward or book royalties, only vilification.

As documented ten years ago,
the reptiles (= amniotes) had their first dichotomy shortly after the genesis of the amnion. That dichotomy split reptiles into Archosauromorpha and Lepidosauromorpha. Benton 2014 was not aware of that division, as discussed earlier.

The following two subsets of the LRT
document the basal members of the diapsid-grade Lepidosauriformes within the Lepidosauromorpha (Fig. 3) and basal members of the diapsid-grade Diapsida within the Archosauromorpha (Fig. 4).


Moving on from ‘diapsids’ to ‘turtles’
Benton 2014 was clueless with regards to turtle outgroups and internally inconsistent. In figure 1 (above) Benton’s turtles nest close to enaliosaurs (sea reptiles) and lepidosaurs. This compares to figure 2 (above) where Benton’s turtles nest close to pterosaurs and dinosaurs. So Benton presents a cladogram (Fig. 2) in which there are no taxa between turtles and pterosaurs. Just let that sink in. This is taught in university classrooms.

By contrast
in the LRT (subset Fig. 5) turtles are derived twice from pareiasaurs, once for softshell turtles and again for hardshell turtles (Fig. 6). The LRT tests all competing candidates. Oddly, considering the widespread interest in turtle origins, no other published cladograms include the pertinent taxa recovered by the LRT. By excluding pertinent outgroup taxa, Benton 2014 follows recent misguided attempts at solving turtle origins with cherry-picked taxa. The LRT accidentally stumbles upon dual turtle ancestry by simply adding taxa and letting the software decide the tree topology. The critical mass of taxa in the LRT seems to have been reached: Turtles have not migrated from small horned pareiasaurs since then.
Since Benton once again nested pterosaurs with dinosaurs
and Scleromochlus (Figs. 1, 2) here are the taxa from the LRT (Fig. 7) that nest closer to pterosaurs when they are given the opportunity to do so (see Peters 2000, 2007) and are correctly scored from first-hand observation, tracing and reconstruction. This is what you get when you create a cladogram, admit a wide gamut of taxa and let the taxa nest themselves.

References
Benton MJ 2014. Vertebrate Paleontology 4th ed. Wiley-Blackwell 480pp.
Peters D 2000b. A Redescription of Four Prolacertiform Genera and Implications for Pterosaur Phylogenesis. Rivista Italiana di Paleontologia e Stratigrafia 106 (3): 293–336.
Peters D 2007. The origin and radiation of the Pterosauria. In D. Hone ed. Flugsaurier. The Wellnhofer pterosaur meeting, 2007, Munich, Germany. p. 27.
https://www.researchgate.net/publication/328388481_The_dual_origin_of_turtles_from_pareiasaurs