Most possibilities led to a contradiction, and the few remaining could be tested by hand.

The arguments given above when taken together seem to lead to a contradiction.

This led to a contradiction because the Virginia law, which was supposedly still in force, had no such requirement.

For a large number of positions, the test would lead to a logical contradiction, ruling out that setting.

If the test did not lead to a contradiction, the machine would stop.

This leads to a contradiction, since the sphere is not flat.

Since our supposition led to a contradiction, there must not be any such function, f.

The procedure is to show that assuming "p" leads to a logical contradiction.

So the proposition of a walk crossing each bridge once leads to a contradiction.

Thus both options lead us to a contradiction and we have an inconsistent theory.