Rulings
Q1: Do I have to delete all of my Digimon for this card's Start of Your Main Phase effect even when I have 0 cards in my Digi-Egg deck and can't place a card in digivolution cards?
Yes, you must delete them.
Q2: If Leviamon and Leviamon (X Antibody) are in this card's digivolution cards, are they considered "cards with different names"?
Yes, they are. When cards such as Leviamon and Leviamon (X Antibody) differ in that one has {{EffectLinkArchetype|X Antibody}} and the other doesn't, you can reference the cards as if they have different names.
Q3: Does Gate of Deadly Sins itself in digivolution cards also count for this card's "if this Digimon has 5 or more digivolution cards with different names"?
Yes, it does.
Q4: If multiple copies of this card are in digivolution cards, does its inherited effect overlap?
Yes, that's correct.
Q5: Do I have to activate this card's inherited effect when a Digimon card would be played?
No, you can choose not to.
Q6: Can I also activate this card's inherited effect when a Digimon would be played by an effect?
Yes, that's correct.
Q7: Can I use this card's inherited effect to reduce the digivolution cost by 3 even if this card has 5 or more digivolution cards with different names?
Yes, you can.
Data Sources
Lv.- Gate of Deadly Sins EX6-006 R - [Breeding] [Start of Your Main Phase] Place the top card of your Digi-Egg deck as this Digimon's bottom digivolution card, and delete all of your Digimon. If this effect deleted, place 1 [Seven Great Demon Lords] trait card from your trash as this Digimon's bottom digivolution card. [Breeding] [End of Opponent's Turn] By deleting this Digimon with 7 or more digivolution cards with different names, you may play 1 [Ogudomon] from your trash without paying the cost. --- Inherited: [Breeding] [Your Turn] [Once Per Turn] When a [Seven Great Demon Lords] trait Digimon card would be played, you may reduce the play cost by 3. If this Digimon has 5 or more digivolution cards with different names, you may reduce the play cost by 4 instead.
Lv.- Gate of Deadly Sins EX6-006 R - [Breeding] [Start of Your Main Phase] Place the top card of your Digi-Egg deck as this Digimon's bottom digivolution card, and delete all of your Digimon. If this effect deleted, place 1 [Seven Great Demon Lords] trait card from your trash as this Digimon's bottom digivolution card. [Breeding] [End of Opponent's Turn] By deleting this Digimon with 7 or more digivolution cards with different names, you may play 1 [Ogudomon] from your trash without paying the cost. --- Inherited: [Breeding] [Your Turn] [Once Per Turn] When a [Seven Great Demon Lords] trait Digimon card would be played, you may reduce the play cost by 3. If this Digimon has 5 or more digivolution cards with different names, you may reduce the play cost by 4 instead.
- Gate of Deadly Sins EX6-006 R [Breeding] [Start of Your Main Phase] Place the top card of your Digi-Egg deck as this Digimon's bottom digivolution card and delete all of your Digimon. If this effect deleted, place 1 card with the [Seven Great Demon Lords] trait from your trash as this Digimon's bottom digivolution card. [Breeding] [End of Opponent's Turn] By deleting this Digimon with 7 or more cards with different names in its digivolution cards, you may play 1 [Ogudomon] from your trash without paying the cost. --- Inherited: [Breeding] [Your Turn] [Once Per Turn] When one of your Digimon with the [Seven Great Demon Lords] trait would be played, you may reduce the play cost by 3. If this Digimon has 5 or more cards with different names in its digivolution cards, you may reduce the play cost by 4 instead.
Lv.- 大罪の門 EX6-006 R ［育成］【自分のメインフェイズ開始時】自分のデジタマデッキの上から1枚をこのデジモンの進化元の下に置き、自分のデジモン全てを消滅させる。この効果で消滅したなら、自分のトラッシュから、特徴に「七大魔王」を持つカード1枚をこのデジモンの進化元の下に置く。 ［育成］【相手のターン終了時】進化元に名称の異なるカードが7枚以上あるこのデジモンを消滅させることで、自分のトラッシュから、「オグドモン」1枚をコストを支払わずに登場できる。 --- Inherited: ［育成］【自分のターン】[ターンに1回]特徴に「七大魔王」を持つデジモンカードが登場するとき、支払う登場コスト-3できる。このデジモンの進化元に名称の異なるカードが5枚以上あるなら、代わりに支払う登場コスト-4できる。