This seems to me to be nonsense, not a contradiction. Presumably, the way this is laid out, the first three statements are the hypothesis, and the fourth is the conclusion. Because Phil being gone and John being dead have nothing to do with Tim having bread, it seems to me that this can be reduced to
Tim has bread ==> Tim doesn't have bread
This is not a contradiction. If Tim has bread, then it is not true that he doesn't have bread, so the first statement does not imply the second. If Tim indeed doesn't have bread, then the first statement isn't true, so any statement at all could be appear as the conclusion, and the implication would be true, but meaningless.
BTW, in English, we don't say someone has "a bread": we say someone has bread or has a loaf of bread.