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