I · 06:00

Axiom Dawn

From three primitives, an entire architecture of truth begins. The grid extends — infinite, patient, ready to bear weight.

A1
P ∨ ¬P
A2
P → (Q → P)
A3
(P → Q) → ((Q → R) → (P → R))
given — axiom schema (Hilbert)
II · 09:00

Conjunction Plaza

Two premises, one merging. The wedge assembles itself from converging strokes; mass joins mass.

P
premise A
Q
premise B
∧
P ∧ Q
∧-introduction — from P and Q, infer P ∧ Q
III · 12:00

Implication Bridge

A diagonal span built from interlocking blocks. Each footing is a justified step; together they carry the proof across.

P
P → Q
Q
Q → R
R
premise
premise
MP
premise
MP
modus ponens — from P and P → Q, infer Q. Iterate.
IV · 17:00

Negation Void

Around an absent center, propositions and their mirrors orbit in pairs. The hexagon at the heart is excluded middle made visible.

P
¬P
Q
¬Q
P ∧ Q
¬(P ∧ Q)
P
P∨Q
P∧Q
P→Q
P↔Q
tertium non datur — for any P, either P or its negation holds.
V · 19:30

Quantifier Forest

A grove of identical objects: ∀x sweeps the rows; one gold trunk stands as &exists;x — the witness.

∀-introduction — uniform claim across the domain
VI · 21:00

QED — Twilight

All structures collapse upward into a single tower. Axiom, conjunction, implication, negation, quantifier — one theorem rests upon them.

axioms
P, P → Q
Q, Q → R
R
Theorem

{P, P → Q, Q → R} ⊢ R

Q.E.D.