Proof Designer does not automatically recognize when you have proven a statement you are trying to prove. You must tell it that you have reached your goal by using the Finish command.
If your goal is to prove some statement, then you cannot use the Finish command unless the statement you are trying to prove is in your givens list. If it is, select it in the givens list and give the Finish command. If your goal is to prove a contradiction, then you cannot use the Finish command unless there are two statements in your givens list, one of which is the negation of the other. If there are two such statements in your givens list, select both of them and give the Finish command. Note that it is not sufficient to choose two statements that contradict each other; one must actually be the negation of the other. For example, Proof Designer would not recognize the givens x∈A∩B and x∉A as achieving the goal of reaching a contradiction, even though they contradict each other. However, it would recognize x∈A and x∉A as achieving the goal of reaching a contradiction.
When you finish the last gap in a proof, Proof Designer will congratulate you on completing the proof.
Note: If you have a gap in your proof whose goal is to define some variable, then Proof Designer will automatically close the gap when you define the variable. There are two commands that you can use to accomplish this: Define and Existential Instantiation. If you have a gap that has no goal, you can simply delete it at any time.