That is simply incorrect. It's not my understanding of logic. It's textbook logic. Ask any professor of logic and philosophy.
Sure it is, but it comes with its own assumptions and biases which you continually fail to acknowledge. If you start from a faulty assumption any conclusion you draw will be faulty.
Again, I do accept the idea of a greater good, even of a incredibly great good. Even if said greater good is great enough to deserve the most horrible suffering, omnipotence, omniscience and omnibenevolence would make the achievement of said greater good possible without the suffering. But suffering exists, therefore God cannot have all said attributes simulataneously.
Which still assumes that the suffering serves no purpose. It assumes you know better than God what purpose suffering might serve. You're clearly coming at everything based on the assumption it serves no purpose at all and therefore must be bad. Take away that assumption and your circle collapses on itself.
Whatever picture that might be, it could have been painted without the suffering because that is what omnipotence, omniscience and omnibenevolence allow for.
If suffering served no purpose, perhaps. If suffering served a purpose then perhaps not.
If you want to endlessly speculate why God didn't create a world where everything is just as we want it to be, where we can eat whatever we want without getting fat, where people can have free will without ever using that will to harm anyone else - in other words if you want to demand explanations for why God didn't do it your way, take a read of the last five chapters of Job.
Any sort of example that includes beings that don't have the tri-omni attributes will prove itself irrelevant because it will not address the ability to achieve said goal in a way that doesn't involve suffering. When you are omnipotent, you can achieve any logical goal, otherwise you are not omnipotent. If you admit that God does not have one of the 3 attributes, then the entire issue resolves itself.
If He is not omnipotent, He doesn't stop suffering because He cannot do so at the moment, but He will be able to do so at one point in time.
If He is not omnibenevolent, He doesn't stop the suffering because He doesn't want the well-being of all creatures at all time, but He wants the well-being of most creatures at most time.
If He is not omniscient, He doesn't stop the suffering because He doesn't know how to do it at this moment, but He will know at some point in time.
... unless suffering is a way to greater well-being later. I know, I know, that silly God should have made it differently so we could have all the rewards with none of the work. While he's at it maybe we could all have ripped physiques without having to lift weights and healthy hearts even if we spend all our days stuffing our faces with chemical garbage. Hey, think how much extra time we'd have for fun if we didn't need to think about exercise.... we could have hedonism on earth forever with no consequences.
Oh, but wait, then he'd have to get rid of all sorts of other things - you know, can't have any suffering if someone's spouse decides to leave them, or grieving when a loved one dies, or pain if we don't pay attention and cut ourselves with a sharp tool. Think how much easier life would be if someone could just decide to throw their kids out in the cold because they were bored of being parents, knowing the kids would be just fine because there was no suffering. I can only imagine the chaos as people expressed their own selfish desires with nothing to restrain them. Maybe silly god should just have done away with free will and made a load of automatons who never really loved anything because they had no option to do anything else.
Just think how much easier it would be if a silly god hadn't said "this is how I want you to live, these are the consequences of choosing for me and these are the consequences of choosing against me" because it would be so much better if he could only have said "this is what I'd prefer but, you know, you do whatever you want with no consequences because, well, let's all sing kumbaya together because all that matters is that everybody is happy."
When you get promoted to God maybe you can show us how it should be done.