谓词公式为:
设M(x):x是学生,Q(x):x是老师, R(x):x是骗子, S(x,y):x相信y
前提:∃x(M(x) ∧∀y(Q(y)→S(x,y))), ∀x(M(x)→∀y(R(y)→┐S(x,y)))
结论;∀x(Q(x)→┐R(x))
证明;
(1) ∃x(M(x) ∧∀y(Q(y)→S(x,y))) P
(2) M(a) ∧∀y(Q(y)→S(a,y) ) ES(1)
(3) M(a)→∀y(R(y)→┐S(a,y)) US(2)
(4) M(a) T(2)I
(5) ∀y(R(y)→┐S(a,y)) T(3)(4)I
(6) ∀y(Q(y)→S(a,y)) T(1)I
(7) R(b)→┐S(a,b) US(5)
(8) Q(b)→S(a,b) US(6)
(9) S(a,b) →┐R(b) T(7)E
(10) Q(b)→┐R(b) T(8)(9)I
(11) ∀x( Q(x)→┐R(x)) UG(10)