Let x0 of type (((ι → (ι → 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) → ι) → ι → ι) → ι → ι → ι be given.
Let x2 of type (ι → ι → ι) → ι → ι be given.
Let x3 of type (CT3 ι) → ((ι → (ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 : ι → ι → ι → ι . setsum (x8 x7 (x2 (λ x9 x10 . 0) (Inj1 0)) 0) 0) (λ x8 : ι → (ι → ι) → ι . x7) (λ x8 : (ι → ι) → ι . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x7) (Inj0 (x2 (λ x9 x10 . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . 0) 0 0)))) = Inj1 (x3 (λ x8 : ι → ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x10 (λ x12 : ι → ι . x3 (λ x13 : ι → ι → ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . setsum 0 0) (x3 (λ x9 : ι → ι → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . 0)) 0) (Inj0 0)) (λ x8 : ι → (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . x8 (λ x9 . x9))).
Assume H1:
∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x8 : ι → ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x3 (λ x12 : ι → ι → ι → ι . x10 (λ x13 : ι → ι . x10 (λ x14 : ι → ι . 0))) (λ x12 : ι → (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . x3 (λ x13 : ι → ι → ι → ι . x13 0 0 0) (λ x13 : ι → (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . Inj0 0))) 0 x7) (λ x8 : ι → (ι → ι) → ι . setsum (Inj1 (setsum (x2 (λ x9 x10 . 0) 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0))) 0) (λ x8 : (ι → ι) → ι . 0) = Inj0 (x4 0 (setsum (x4 (x5 0) x7 (x0 (λ x8 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . 0) 0) (x3 (λ x8 : ι → ι → ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0))) (x1 (λ x8 : ((ι → ι) → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 . 0) 0 (setsum 0 0))) 0 (Inj1 0)).
Assume H2:
∀ x4 : ((ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 x9 . x8) (Inj0 (x1 (λ x8 : ((ι → ι) → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 . x2 (λ x11 x12 . 0) (setsum 0 0)) (setsum x7 x5) x7)) = x4 (λ x8 : ι → ι . x5) (Inj1 (x4 (λ x8 : ι → ι . setsum x5 0) (Inj0 (x3 (λ x8 : ι → ι → ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0))) (x1 (λ x8 : ((ι → ι) → ι) → ι → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 . 0) (setsum 0 0) (x2 (λ x8 x9 . 0) 0)))) (x3 (λ x8 : ι → ι → ι → ι . Inj0 (x8 0 (setsum 0 0) (x8 0 0 0))) (λ x8 : ι → (ι → ι) → ι . Inj1 (x8 (x2 (λ x9 x10 . 0) 0) (λ x9 . 0))) (λ x8 : (ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . setsum (Inj1 0) x11) 0 (setsum 0 x7))).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . Inj1 (x5 (x3 (λ x9 : ι → ι → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . ...) ...) ... ... ...)) 0 = ...) ⟶ False.