To apply a rule of inference, check the lines you wish to use as premises and click the button for the rule of inference. Reiteration allows you to repeat an earlier item. To delete one or more lines from a proof, check the desired lines and click Delete. When entering expressions, use Ascii characters only. Use ~ for ¬; use & for ∧; use | for ∨; use => for ⇒; use <=> for ⇔; use A for ∀; use E for ∃; and use : for . in quantified sentences. For variables, use strings of alphanumeric characters that begin with a capital letter. For example, to enter ∀x.∃y.(p(x) ∧ q(y) ⇒ r(y) ∨ ¬s(y)), write AX:EY:(p(X)&q(Y)=>r(Y)|~s(Y)).

Objects

a, b, c

Functions

f, g

Goal

Incomplete

Enter the premise you wish to add to the proof:

Select premises.
Enter your proposed conclusion:

Must be provable from selected premises via truthtable.

Enter the conclusion you wish to add to the proof:

Enter the justification for this conclusion:

Enter the symbol you wish to replace:

Enter the replacement:

Enter the sentence you wish to disjoin to the checked items:

Or Elimination:

φ∨ψ
φ⇒χ
ψ⇒χ
χ

Enter the assumption you wish to make:

Universal Introduction:

φ
Aν:φ_{τ←ν
}

Enter the placeholder you would like to replace:

τ:

Enter the variable you would like to use:

ν:

Universal Elimination:

Aν:φ
φ[ν←τ]
where τ is free for ν in φ

Enter the term you would like to use:

τ:

Existential Introduction:

φ(τ)
Eν:φ(ν)

Enter the term you would like to replace:

τ:

Enter the variable you would like to use:

ν:

Existential Elimination:

Eν:φ(ν)
ψ
φ([σ]) => ψ
where [σ] is a new Skolem constant.