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