Proofgold Proof

Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with ∀ x0 : (ι → ι → ι) → ι → ο . ∀ x1 : (ι → ι) → ι → ο . ∀ x2 : (ι → ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι → ο . ∀ x3 : (ι → ι → ι → ι) → ι → ο . (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x8 x9 . setsum 0 (setsum (setsum x8 (x6 (λ x10 . 0) 0 (λ x10 . 0))) x7)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . x6 (λ x10 . Inj0 (setsum 0 0)) (setsum (Inj1 0) (setsum (Inj1 0) (x8 0))) (λ x10 . 0)) x7 ⟶ x3 (λ x8 x9 x10 . x9) 0) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . In (Inj0 0) (Inj1 (setsum 0 (setsum 0 (setsum 0 0)))) ⟶ x3 (λ x8 x9 x10 . Inj1 (Inj0 0)) (Inj1 0) ⟶ x1 (λ x8 . 0) (Inj1 (Inj0 (Inj0 (Inj0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . In (Inj0 0) (Inj0 (Inj0 (Inj1 (Inj0 0)))) ⟶ x2 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . setsum (Inj1 (setsum (Inj0 0) 0)) x6) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . In (Inj0 (setsum 0 (setsum 0 (Inj0 0)))) x6 ⟶ x2 (λ x8 x9 . setsum 0 x6) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj0 (x9 0 0)) (setsum (x5 (λ x8 x9 . Inj1 0) (x5 (λ x8 x9 . x9) (setsum 0 0))) 0) ⟶ x0 (λ x8 x9 . setsum (setsum x9 (setsum (setsum 0 0) 0)) x6) (setsum (setsum (x7 (Inj1 0) (λ x8 x9 . setsum 0 0) (λ x8 . setsum 0 0) 0) (setsum (Inj0 0) (setsum 0 0))) (setsum (Inj1 (Inj1 0)) (setsum (x4 0) (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x8 . 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x8 . 0) x5 ⟶ x1 (λ x8 . x6) 0) ⟶ (∀ x4 x5 x6 x7 . In (Inj1 (Inj0 (Inj1 0))) (Inj1 (Inj1 0)) ⟶ x0 (λ x8 x9 . x7) (setsum 0 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . 0) (x5 (Inj0 (Inj0 0))) ⟶ x3 (λ x8 x9 x10 . 0) 0) ⟶ False.