Necessary, because if it weren’t true — if there ARE parallel lines in the non-Euclidean system of geometry with the most empirical verification — then we have no reason to think that parallel lines don’t exist. Non-Euclidean geometry could accurately describe the universe, and there could still be parallel lines.

Whether any physicists have doubted the non-Euclidean system as a description of the universe is irrelevant. The conclusion is based on the condition “IF” — if the physicists who think non-Euclidean geometry accurately describes the universe are right, then parallel lines don’t exist. We simply accept, for the purpose of analyzing the conclusion, that the “IF” part is true.

Not necessary, because the conclusion refers to a specific non-Euclidean system — the one with the most empirical verification. Other kinds of non-Euclidean systems are irrelevant.

Not necessary, because the conclusion is conditioned on the hypothetical situation that the non-Euclidean system accurately describes the universe. Whether this is in fact true doesn’t affect the argument.

Not necessary, because the existence of doubt or lack of doubt has no bearing on the reasoning. The conclusion is based on the hypothetical situation in which the non-Euclidean system accurately describes the universe. Whether anyone doubts the theory or not is irrelevant; for the purpose of evaluating the argument, we simply accept the hypothetical situation as true.