Let x0 of type (ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι be given.
Let x1 of type (((((ι → ι) → ι) → ι → ι → ι) → ι) → ι) → (CT3 ι) → ι be given.
Let x2 of type ((CT2 ι) → ι) → ((ι → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι) → ι → ι be given.
Let x3 of type (ι → ι) → ι → ι be given.
Assume H0:
∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x8 . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . x9 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)) (λ x9 : ι → ι → ι → ι . 0)) (x5 (λ x8 : (ι → ι) → ι . x7) (λ x8 : ι → ι . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . x8 (Inj0 0)) (λ x9 : ι → ι → ι → ι . x7))) = x1 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . setsum (setsum (x3 (λ x9 . x7) 0) x7) (x8 (λ x9 : (ι → ι) → ι . λ x10 x11 . x1 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . x3 (λ x13 . 0) 0) (λ x12 : ι → ι → ι → ι . x12 0 0 0)))) (λ x8 : ι → ι → ι → ι . Inj0 x6).
Assume H1:
∀ x4 x5 x6 x7 . x3 (λ x8 . x8) (setsum (x2 (λ x8 : (ι → ι → ι) → ι . x5) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 : ι → ι . x7) 0) (Inj1 x5)) = x4.
Apply FalseE with
... ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 : (ι → ι → ι) → ι . x3 (λ x9 . setsum (x3 (λ x10 . setsum 0 0) (x3 (λ x10 . 0) 0)) x7) 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 : ι → ι . x0 (λ x11 . setsum (x8 (setsum 0 0) (λ x12 . Inj0 0) (x0 (λ x12 . 0) (λ x12 . 0) (λ x12 x13 x14 . 0) (λ x12 : ι → ι . λ x13 . 0))) 0) (λ x11 . 0) (λ x11 x12 x13 . 0) (λ x11 : ι → ι . ...)) ... = ...) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . Inj0 x5) (λ x8 : ι → ι → ι → ι . x5) = x5) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . x6) (λ x8 : ι → ι → ι → ι . 0) = setsum x4 (x3 (λ x8 . x7) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x8 . setsum 0 x8) (λ x8 . x6 (λ x9 x10 . x7 (x0 (λ x11 . x2 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 x14 : ι → ι . 0) 0) (λ x11 . x0 (λ x12 . 0) (λ x12 . 0) (λ x12 x13 x14 . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x11 x12 x13 . Inj1 0) (λ x11 : ι → ι . λ x12 . Inj1 0)))) (λ x8 x9 x10 . 0) (λ x8 : ι → ι . λ x9 . x9) = Inj0 (x3 (λ x8 . 0) (Inj1 (x6 (λ x8 x9 . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x10 : ι → ι → ι → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 . x8) (λ x8 . x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . x0 (λ x11 . setsum 0 x8) (λ x11 . x9 (λ x12 . x9 (λ x13 . 0) 0) x11) (λ x11 x12 x13 . 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 . x12) (λ x13 . 0) (λ x13 x14 x15 . setsum 0 0) (λ x13 : ι → ι . λ x14 . x2 (λ x15 : (ι → ι → ι) → ι . 0) (λ x15 : ι → (ι → ι) → ι → ι . λ x16 x17 : ι → ι . 0) 0))) x8) (λ x8 x9 x10 . x9) (λ x8 : ι → ι . λ x9 . 0) = Inj1 (Inj1 0)) ⟶ False.