Logical Proof Generator Calculator

Calculator inputs

Premises

Enter one formula per line.

Target conclusion

Use the same symbol style everywhere.

Analysis mode

Maximum proof lines

Show truth-table preview rows

Accepted syntax
NOT: ~A
AND: A & B
OR: A | B
IF-THEN: A -> B
IFF: A <-> B
Grouping: (A | B) -> C

Built-in proof rules
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Disjunctive Syllogism
Simplification
Conjunction
Resolution
Contrapositive

Best use cases
Classroom practice
Symbolic reasoning drills
Quick argument validation
Counterexample discovery
Natural-deduction style checking

Reset

Example data table

Example	Premises	Conclusion	Expected outcome	Key reason
1	A → B, A	B	Derived and valid	Modus Ponens
2	A → B, B → C, A	C	Derived and valid	Chain reasoning
3	A ∨ B, ~A	B	Derived and valid	Disjunctive Syllogism

Formula used

Argument validity formula: ((P1 ∧ P2 ∧ ... ∧ Pn) → C)

Modus Ponens: P, (P → Q) ⟹ Q

Modus Tollens: (P → Q), ~Q ⟹ ~P

Hypothetical Syllogism: (P → Q), (Q → R) ⟹ (P → R)

Disjunctive Syllogism: (P ∨ Q), ~P ⟹ Q

Resolution: (P ∨ Q), (~P ∨ R) ⟹ (Q ∨ R)

Simplification: (P ∧ Q) ⟹ P and Q

Conjunction: P, Q ⟹ (P ∧ Q)

The calculator combines rule-driven derivation with exhaustive truth-table checking. If every assignment that makes all premises true also makes the conclusion true, the argument is valid.

How to use this calculator

Type each premise on a separate line in the premises box.
Enter the target statement you want to prove.
Choose hybrid, rule-based, or truth-table mode.
Set the maximum proof lines for the search depth.
Enable truth-table preview if you want sample rows displayed.
Press Generate proof to place the result above the form.
Review derived steps, validity status, and any counterexamples.
Use the CSV or PDF buttons to export the visible result.

FAQs

1. What type of logic does this calculator support?

It focuses on propositional logic with variables, negation, conjunction, disjunction, implication, and biconditional expressions. It is designed for symbolic argument practice and classroom-style proofs.

2. Does a valid truth table always mean a proof appears?

Not always. The truth-table audit can confirm validity even when the built-in derivation rules do not finish a full proof inside the selected line limit.

3. Why are some arguments marked invalid?

An argument is invalid when at least one assignment makes every premise true while making the conclusion false. The calculator lists sample counterexamples when this happens.

4. What syntax should I enter for formulas?

Use ~ for NOT, & for AND, | for OR, -> for implication, and <-> for biconditional. Parentheses are recommended for nested statements.

5. Can I test long expressions with many variables?

Yes, but exhaustive truth-table checking is capped at ten variables to keep performance practical. Rule-based proof search can still run beyond that limit.

6. What do the line references mean in the proof table?

They show which earlier statements produced the new line. This makes each derivation traceable and easier to review for teaching or self-study.

7. When should I use hybrid mode?

Hybrid mode is best when you want both a proof attempt and a formal validity check. It gives a broader picture than either method alone.

8. What do the export buttons download?

CSV exports the generated proof table. PDF captures the result summary and proof lines in a printable document for assignments, revision, or sharing.