Entering Data

1. To start with we hope you have clicked on the start new proof to reach the proof window, which is split into two text fields the givens and the goal.
2. Type the givens of your proof into the Givens text field and your goal in the Goal text field using the input guide provided on the left.
3. After entering your problem click Start Proof, when your syntax will be checked.
4. The letters A and E are reserved for quantifiers, as in Ax[p(x)] or Ex[q(x)]. Therefore, it's a good idea to use non-capitals for propositions to avoid mistakes. If the goal is falsity then the syntax for it is 'bottom'.)

Applying Rules

To start with we hope you have clicked on the start new proof link to reach the proof window (if not do so). As you can see the window is splitinto two text fields the givens and the goal. Type the givens of your proof into the Givens text field and your goal in the Goal text field using the input guide provided on the left (Note: While entering the givens and goal do not use A and E in your formulas as A and E are reserved for quantifiers, as in Ax[p(x)] or Ex[q(x)]. If the goal is falsity then the syntax for it is 'bottom'.) After entering your problem click Start Proof, when your syntax will be checked.

After successfully entering the proof window if you are still confused as to how to apply the rules, then read on.

A proof step can be made forwards or backwards, which is clearly explained in the Forwards and Backwards Rules option in the Help menu. Here though, as an example, is a brief summary for the rule 'Not elimination'. Using the rule forwards requires you to first select an empty line and the rule. If you can recollect how Not elimination is used you would figure out that now you need to select two contradictory formulas to derive bottom - after clicking on two contradictory lines bottom will be added to your proof in place of the ''empty line'. The same rule can also be used backwards: the important thing is to select the goal line in this case (which must be the formula 'bottom'), and the line selected after must be a Not formula of the form ~x. The new goal 'x' will appear.

Some of the rules generate boxes. For example, the For All Introduction Rule, when applied backwards, generates a box, which serves to introduce a new context. In this case it would be a context including one or more new constants, which are indicated at the top left hand of the box. Other boxes may introduce extra assumptions. Any formula derived inside a box cannot be used outside it, since they might have used assumptions local to the box. This is in accordance of the natural deduction in your logic course.

A very useful rule is called the tick rule, which is used backwards to complete a proof. If a goal formula exists as a line in the proof (either derived or assumed in the current box), then tick allows to recognise the goal can be derived. Selecting the goal and tick rule, and then the matching line results in a proof going grey as it is completed. Note that this may be a subproof only (eg one part of the proof requirement for applying Or-elimination).

We hope to have helped you start your first proof and successfully solve it, if you still have not found what you’ve been looking for try the panic situations, heuristic hints or the manual whose links are under the help menu. There is also additional help contained in the error messages that appear when the rules have been incorrectly applied and the dialog boxes used at various points in applying rules.