Let x0 of type ((ι → ι) → (CT2 ι) → ι) → ι → ι → ι be given.
Let x1 of type (ι → (ι → ι) → ι) → (ι → ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι be given.
Let x2 of type ((ι → ((ι → ι) → ι) → ι) → (ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → ι → ι be given.
Let x3 of type ((ι → ι) → ι) → (ι → (ι → ι) → ι) → ι be given.
Assume H0:
∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι) → ι . x3 (λ x8 : ι → ι . 0) (λ x8 . λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . x3 (λ x12 : ι → ι . x12 (x11 (λ x13 x14 . 0))) (λ x12 . λ x13 : ι → ι . x11 (λ x14 x15 . x1 (λ x16 . λ x17 : ι → ι . 0) (λ x16 x17 x18 x19 . 0) (λ x16 : ι → ι . 0) 0))) x8 0) = x0 (λ x8 : ι → ι . λ x9 : (ι → ι → ι) → ι . setsum 0 0) (Inj0 (x0 (λ x8 : ι → ι . λ x9 : (ι → ι → ι) → ι . Inj1 (x7 (λ x10 : ι → ι . 0))) 0 0)) (setsum (x3 (λ x8 : ι → ι . x8 (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . 0) 0)) (λ x8 . λ x9 : ι → ι . 0)) 0).
Assume H1:
∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι . Inj1 (setsum x6 (setsum 0 0))) (λ x8 . λ x9 : ι → ι . 0) = x5 (λ x8 : (ι → ι) → ι → ι . x6).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x8 : ι → ι . λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : ι → ι . setsum (setsum (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0) 0) (setsum (x1 (λ x11 . λ x12 : ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 : ι → ι . 0) 0) (Inj0 0))) (λ x10 . λ x11 : ι → ι . x10)) (x1 (λ x8 . λ x9 : ι → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . x1 (λ x14 . λ x15 : ι → ι . 0) (λ x14 x15 x16 x17 . 0) (λ x14 : ι → ι . 0) 0) x6)) (λ x8 x9 x10 x11 . setsum (x3 (λ x12 : ι → ι . Inj1 0) (λ x12 . λ x13 : ι → ι . setsum 0 0)) (setsum (setsum 0 0) (x0 (λ x12 : ι → ι . λ x13 : (ι → ι → ι) → ι . 0) 0 0))) (λ x8 : ι → ι . x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (x3 (λ x9 : ι → ι . setsum 0 0) (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0)) (x7 (λ x9 : ι → ι → ι . setsum 0 0))) (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . ...) ...)) ... = ...) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x8 : ι → ι . λ x9 : (ι → ι → ι) → ι . 0) (x1 (λ x8 . λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . 0) 0 (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (Inj0 0))) (λ x8 x9 x10 x11 . 0) (λ x8 : ι → ι . Inj0 (Inj0 0)) (x0 (λ x8 : ι → ι . λ x9 : (ι → ι → ι) → ι . 0) (Inj1 0) x5)) x7 = setsum (x2 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x8 (x0 (λ x12 : ι → ι . λ x13 : (ι → ι → ι) → ι . 0) (x11 0) 0) (λ x12 : ι → ι . x10)) 0) 0) ⟶ False.