Global bounds on the Type-III Seesaw

EFM acknowledges support from the \Spanish Agencia Estatal de Investigacion" (AEI) and the EU \Fondo Europeo de Desarrollo Regional" (FEDER) through the project FPA2016-78645-P; and the Spanish MINECO through the Centro de Excelencia Severo Ochoa Program under grant SEV-2016-0597. JHG acknowledges support by the grant K125105 of the National Research, Development and Innovation Fund in Hungary. JLP acknowledges support by the \Generalitat Valenciana" (Spain) through the \plan GenT" program (CIDEGENT/2018/019).