Let x0 of type ((ι → ((ι → ι) → 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 → 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 be given.
Assume H0:
∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 x9 . 0) (λ x8 . 0) = Inj1 (setsum (x1 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x9 x10 x11 x12 . x12) (Inj0 0)) x5).
Assume H1:
∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x8 x9 . x7 (λ x10 . setsum (x7 (λ x11 . x3 (λ x12 x13 . 0) (λ x12 . 0)) (λ x11 x12 . 0) (Inj0 0)) x9) (λ x10 x11 . Inj1 (x1 (λ x12 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x13 x14 x15 x16 . x15) (x1 (λ x12 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x13 x14 x15 x16 . 0) 0))) (x6 (Inj0 0))) (λ x8 . 0) = x7 (λ x8 . setsum 0 (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . x1 (λ x10 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x11 x12 x13 x14 . x2 (λ x15 . λ x16 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x15 : ((ι → ι) → ι → ι) → ι → ι . λ x16 x17 . 0)) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 (x2 (λ x13 . λ x14 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . 0))) 0 (x6 0) (λ x9 . Inj0 (setsum 0 0)) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι . setsum 0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (setsum 0 0) (x7 (λ x9 . 0) (λ x9 x10 . 0) 0) (λ x9 . x7 (λ x10 . 0) (λ x10 x11 . 0) 0) 0))) (λ x8 x9 . setsum (x2 (λ x10 . λ x11 : ((ι → ι) → ι) → ι → ι → ι . x0 (λ x12 : ι → ((ι → ι) → ι) → ι . x10) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x13) (x2 (λ x12 . λ x13 : ((ι → ι) → ι) → ι → ι → ι . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . 0)) (x11 (λ x12 : ι → ι . 0) 0 0) (λ x12 . x0 (λ x13 : ι → ((ι → ι) → ι) → ι . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) 0 0 (λ x13 . 0) 0) 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . 0)) (x3 (λ x10 x11 . 0) (λ x10 . x9))) (x1 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x9 x10 x11 x12 . Inj1 (x3 (λ x13 x14 . Inj0 0) (λ x13 . setsum 0 0))) (setsum (x3 (λ x8 x9 . x9) (λ x8 . Inj0 0)) (setsum (setsum 0 0) (x1 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x9 x10 x11 x12 . 0) 0)))).
Assume H2:
∀ x4 x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x8 . λ x9 : ((ι → ι) → ι) → ι → ι → ι . x9 (λ x10 : ι → ι . x3 (λ x11 x12 . Inj0 (x10 0)) (λ x11 . x1 (λ x12 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x13 x14 x15 x16 . x1 (λ x17 : ((ι → ι → ι) → ι → ι → ι) → ι . λ x18 x19 x20 x21 . 0) 0) (setsum 0 0))) (Inj0 x8) 0) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 x10 . 0) = x6 (λ x8 : ι → ι . 0) 0 (λ x8 . x6 (λ x9 : ι → ι . x7) (x2 (λ x9 . λ x10 : ((ι → ι) → ι) → ι → ι → ι . Inj1 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . 0)) (λ x9 . 0)).
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 : ι → ((ι → ι) → ι) → ι . setsum ... ...) ... ... ... ... ... = ...) ⟶ False.