I cannot help you with that logic stuff but "than" is used for comparisons (bigger than, wider than etc.), what you were looking for is "then", since it appears in almost every line of yours, I can only assume it's not a typo but a logical flaw.
What surprises me about the actual logic stuff, to me it looks like 3 and 4 only work if 2 is true, that would mean to me that 3 and 4 always apply both, because if H -> F then H and F are consistent and then F -> H, or not? (I only ever did logic in german and it's been a while)
1 is a precondition for 2, 3 and 4 and as such it should be implied that they can be met simultaneously, which leaves me to believe that there is something I'm misunderstanding, could be the term "consistent" in 2.
I'm assuming it has something to do with 3 and 4 and Hypothesis H and F cannot circle-prove/justify eachother or so.
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