[AndrewC]

Replace your schemata with actual formulas and then we'll talk about what's a tautology and what's not.

I ate supper at home or I did not eat supper at home.

I ate supper at home or I did not eat supper at MacDonald's

[AndrewC]

I am going to bed or I am not going to bed.

.

.

I am going to bed.

[Vive ut Vivas]

I ate supper at home or I did not eat supper at home.

Tautology. (Certainly not hard to verify algorithmically.)

I ate supper at home or I did not eat supper at MacDonald's

Give these propositions truth values and then either the disjunction or its negation becomes formally verifiable.