The content here will have two parts: First, I give a fairly straightforward,
inductive version of the problem of evil. After that, I link in the material from PART A to show that, although my argument is inductive, it's still strong enough to count as "proof."
So here's the initial argument:
(1) If God existed he would be omniscient, omnipotent, and omnibenevolent.
(2) If an omniscient, omnipotent, and omnibenevolent being existed, there would be no unnecessary suffering.
(3) But it's really, really, really, really, really, likely that unnecessary suffering exists.
(4) So it's really, really, really, really, really, likely that no omniscient, omnipotent, and omnibenevolent being exists.
(C1): It's really, really, really, really, really, likely that God doesn't exist.
Note that by "unnecessary suffering" in (2) and (3) I mean suffering that doesn't accomplish some greater end. In other words, a case of suffering will be an "unnecessary" case of suffering if an omniscient, omnipotent, and omnibenevolent being could "swoop in" and fix the problem without leaving
This is where the stuff from PART A comes in. I'll admit that there are some examples of horrible suffering which we
might be able to link to some higher good. So we can say stuff like "Yeah, the holocaust was really bad, but God had to allow it in order for us to have free will." But there are other examples of which we won't be able to find an easy purpose for (e.g. childhood leukemia) and (2) and (3) are worded so that I only need one example of that.
So once we have such an example, PART A makes it so that I only have to show that it's really, really, really, really, unlikely that God's serving a higher purpose with childhood leukemia. That part of the argument goes like this:
(5) People are intellectually obligated to believe conclusions that the available evidence suggests are really, really, really, really, really, likely to be true.
(6) People are intellectually obligated not to believe things that the the available evidence suggests are really, really, really, really, really, likely not to be true.
(7) The available evidence suggests that it's really, really, really, really, really, likely that God doesn't exist.
(C2) So people are intellectually obligated to believe that God does not exist and not to believe that God does exist.
Finally, to complete the last leg of the journey, as discussed in PART A, and obligation like the one in (C2) is enough to count as "proof." So we have proof that God doesn't exist. Q.E.D.