Transform statements into clause form using parser checks. Practice implication removal, negation pushing, and distribution. Build cleaner logical expressions for lessons, assignments, and revision.
| Input | Implication-Free Form | Final CNF | Clause Count |
|---|---|---|---|
| P -> Q | !P | Q | !P | Q | 1 |
| !(P | Q) | !(P | Q) | !P & !Q | 2 |
| (P | (Q & R)) | P | (Q & R) | (P | Q) & (P | R) | 2 |
This converter uses logical equivalence rules instead of arithmetic formulas. The main transformations are:
P -> Q ≡ !P | QP <-> Q ≡ (!P | Q) & (!Q | P)!(P & Q) ≡ !P | !Q and !(P | Q) ≡ !P & !Q!!P ≡ PP | (Q & R) ≡ (P | Q) & (P | R)A CNF converter calculator changes a propositional logic expression into conjunctive normal form. CNF writes a formula as an AND of clauses. Each clause is an OR of literals. This format is important in discrete mathematics, proof systems, automated reasoning, and SAT solving. Students also use CNF when checking equivalence rules during homework and revision.
Conjunctive normal form gives a standard structure. Standard structure makes complex logic easier to inspect. You can compare clauses, count literals, and test logical workflows with less confusion. CNF is also useful for theorem proving because many algorithms expect formulas in clause form. When every statement follows one pattern, symbolic processing becomes clearer and faster.
The calculator reads your logical expression and parses its operators by precedence. It supports NOT, AND, OR, implication, and biconditional symbols. Then it removes implication rules first. After that, it pushes negations inward with De Morgan transformations. Finally, it distributes OR over AND until the expression reaches conjunctive normal form. The result includes the parsed formula, implication free form, negation normal form, final CNF, and extracted clauses.
This tool is practical for classwork, self study, and exam preparation. You can test whether a manual conversion matches the generated result. You can also review each stage and understand where distribution expands the formula. Clause counts and variable counts provide another quick validation layer. Export options help you save results for notes, worksheets, or tutoring sessions.
You may enter symbols such as !, ~, ¬, &, ∧, |, ∨, ->, and <->. Parentheses help control grouping. Clear grouping reduces mistakes and improves readable output. This calculator is designed for learners who want a clean interface, direct results, and transparent logic steps without unnecessary clutter. It works well for practice sets, demonstrations, and repeated conversions for beginners and advanced learners alike today.
After conversion, read each clause carefully and confirm the literals match your expectations. If two expressions give the same clause structure, they are easier to compare. This supports worksheets, lecture examples, proof exercises, and logic programming preparation.
CNF means conjunctive normal form. It represents a formula as an AND of clauses. Each clause contains literals joined by OR. This standard form is common in logic courses and SAT solving.
You can enter variables with letters, digits, and underscores. The calculator accepts NOT, AND, OR, implication, biconditional, parentheses, and TRUE or FALSE constants. Both ASCII and several common logic symbols are supported.
Yes. Enable the step option to view the implication free form and the negation normal form before the final CNF output. This helps you verify your manual conversion process.
CNF conversion often expands expressions during distribution. When OR is distributed over AND, one compact formula may become several clauses. That is normal and expected in many logic transformations.
A tautological clause contains both a variable and its negation, such as P and !P. Such a clause is always true. The calculator counts these clauses so you can inspect simplification opportunities.
Yes. The page includes CSV export for structured result data and PDF export for printable summaries. Both options appear after a successful conversion and work directly from the result section.
Yes. SAT solvers usually require clause based input. Even if you are not producing DIMACS files, seeing formulas in CNF helps you understand clause construction and solver ready logic structure.
Check parentheses, operator spelling, and variable placement. Most errors happen when a closing bracket is missing or two operators appear together. Clean syntax should produce a valid parse and CNF result.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.