Aphetto Alchemist does not have summoning sickness.
Steps
Activate Tevesh Szat's first loyalty ability by putting two loyalty counters on it, creating two 0/1 Thrull creature tokens.
When the Thrulls enter the battlefield, Intruder Alarm triggers twice.
Resolve the first trigger, untapping all creatures.
Activate Aphetto Alchemist by tapping it, untapping The Chain Veil.
Resolve the second Intruder Alarm trigger, untapping all creatures.
Activate Aphetto Alchemist by tapping it, untapping target artifact or creature.
Activate Ashnod's Altar twice by sacrificing the two Thrull tokens, adding ({C} magic symbol) ({C} magic symbol) ({C} magic symbol) ({C} magic symbol) .
Activate The Chain Veil by paying ({4} magic symbol) and tapping it, allowing you an additional activation of your planeswalkers' loyalty abilities this turn.
Repeat.
Results
Infinite activations of loyalty abilities of all other Planeswalkers you control.