∀x:P(x) →S(x) Premise (1)
∀x:S(x) →R(x) Equivalent Premise (3) Modus Tollens
∀x : P(x) → R(x) Rule of Syllogism
¬ ∃x: (Q(x) ∧ R(x)) Premise (2)
∀x : P(x) → ¬ Q(x) Rule of Disjunction
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