What the name means

BV means bit-vectors. Without the QF restriction, formulas may use quantifiers such as 'for every' and 'there exists'.

A quantifier binds a variable and states how its values matter. 'For every x' requires the body to hold for each value. 'There exists y' requires at least one suitable value. Their order can change which choices may depend on others.

Fixed-width bit-vector domains are finite, so expansion over all values is possible in principle. The number of combinations can still be enormous. Quantified formulas need a different search strategy from a single quantifier-free assignment problem.

Worked example

Choose a successor for every input

Use eight-bit x and y. Ask whether, for every x, there exists a y such that y = x + 1 at eight-bit width.

  1. For each input x, choose y to be its wrapped increment.
  2. For x = 0, choose y = 1. For x = 255, choose y = 0.
  3. The same rule supplies a valid y for every remaining input pattern.

The formula is true, so asserting it gives a sat query. The chosen y is allowed to depend on x.

This is an authored mathematical example, not captured Axeyum output. Here, sat means the constraints can all hold; unsat means they cannot.

A contrasting case

Reverse the quantifiers: there exists one y such that for every x, y = x + 1. That is unsat. Inputs zero and one would force the same y to equal both one and two.

Use cases

  • Express hardware synthesis conditions where an output choice must exist for every input.
  • Specify bit-vector relations with alternating choices, such as an input followed by a permitted response.

Modeling caution

To prove an identity for every input, ask for a counterexample: a case where the identity fails. QF_BV can express this search when the identity itself has no quantifiers.

Axeyum coverage

The examples explain the logic's meaning. They do not establish complete Axeyum support for this division. Acceptance, solving, and evidence coverage depend on the input and the solver route.

This division appears in the site's retained regression scoreboard. Read the individual slices and their source records for the tested scope.

A solver may return unknown if it cannot settle a query. That result establishes neither sat nor unsat. Parsing a declared logic name alone does not prove support for every formula in it.

Engine support documentation at the site's recorded snapshot, 03ae4a3c9, 2026-10-05.

Definitions and references

Definitions consulted September 6, 2026. The worked examples and use-case explanations are authored for this guide.