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Proof step 1 from proof neq-01 (conclusion)

⊦ ¬ a ∈ y ∧ ¬ a ∈ z ∧ a ≠ c → y + c ' + z ≠ y1 + a ' + x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
y + c ' + z = y1 + a ' + x ⊦ a = c, a ∈ z, a ∈ y

Rule argument

Additional information