Karn's Sylex

• WWizards of the Coast2022-09-09
  Official Ruling
  If a spell or an activated ability that isn’t a mana ability has a cost that requires a player to pay life, that spell or ability can’t be cast or activated.
• WWizards of the Coast2022-09-09
  Official Ruling
  Other things may still cause players to pay life, such as a resolving spell or ability.
• WWizards of the Coast2022-09-09
  Official Ruling
  Players may always pay 0 life, even if an effect says they can’t pay life.
• WWizards of the Coast2022-09-09
  Official Ruling
  Activated abilities contain a colon. They’re generally written “[Cost]: [Effect].” Some keyword abilities are activated abilities (such as cycling) and will have colons in their reminder text.
• WWizards of the Coast2022-09-09
  Official Ruling
  An activated mana ability is one that produces mana as it resolves, not one that costs mana to activate.

Rulings via Scryfall