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Solution-processed, large-area, and flexible electronics largely relies on the excellent electronic properties of sp$^2$-hybridized carbon molecules, either in the form of $\pi$-conjugated small molecules and polymers or graphene and carbon nanotubes. Carbon with sp-hybridization, the foundation of the elusive allotrope carbyne, offers vast opportunities for functionalized molecules in the form of linear carbon atomic wires (CAWs), with intriguing and even superior predicted electronic properties. While CAWs represent a vibrant field of research, to date, they have only been applied sparingly to molecular devices. The recent observation of the field-effect in microcrystalline cumulenes suggests their potential applications in solution-processed thin-film transistors but concerns surrounding the stability and electronic performance have precluded developments in this direction. In the present study, ideal field-effect characteristics are demonstrated for solution-processed thin films of tetraphenyl[3]cumulene, the shortest semiconducting CAW. Films are deposited through a scalable, large-area, meniscus-coating technique, providing transistors with hole mobilities in excess of 0.1 cm$^2$ V$^{-1}$ s$^{-1}$, as well as promising operational stability under dark conditions. These results offer a solid foundation for the exploitation of a vast class of molecular semiconductors for organic electronics based on sp-hybridized carbon systems and create a previously unexplored paradigm.