[{name:"Test",keys:[["key1","key2"],["key3"],["key4","key5","key6"],["key7"]]}]

db.collection.aggregate([{$addFields:{dupkeys:{"$map":{input:"$keys",in:{"$setIntersection":["$$this",["key3","key1","key4","key7"]]}}},total:{$size:"$keys"}}},{$addFields:{nonMatched:{$size:{$filter:{input:"$dupkeys",cond:{$ne:["$$this",[]]}}}}}},{$match:{$expr:{$eq:["$total","$nonMatched"]}}}])