Proofgold Proof

Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : ((((ι → ι → ι) → (ι → ι) → ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι) → ι → ο . ∀ x1 : (((((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι) → ι) → ((ι → (ι → ι) → ι → ι) → ι) → ο . ∀ x2 : ((ι → ι → (ι → ι) → ι → ι) → ι → ι) → ι → ο . ∀ x3 : ((ι → ι) → ι → (ι → ι → ι) → ι) → (ι → ι → ι → ι → ι) → ((ι → ι → ι) → ι → ι) → ο . ... ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι) → ι . x3 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 (Inj1 (setsum (setsum 0 0) (x10 0 0)))) (λ x8 x9 x10 x11 . setsum x9 ...) ... ⟶ x2 (λ x8 : ι → ι → (ι → ι) → ι → ι . λ x9 . x7 x9 (λ x10 . Inj0 (Inj1 0))) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . x12) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . x9) (Inj1 (Inj0 0)) ⟶ x2 (λ x8 : ι → ι → (ι → ι) → ι → ι . λ x9 . 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 : ι → ι → (ι → ι) → ι → ι . λ x9 . x7) (setsum (setsum (setsum (Inj0 0) (Inj0 0)) 0) 0) ⟶ In (Inj0 0) x7) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . In (setsum 0 (setsum 0 0)) x5 ⟶ x2 (λ x8 : ι → ι → (ι → ι) → ι → ι . λ x9 . setsum (Inj1 0) (setsum 0 (x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x11 0) 0 (λ x10 . x7) (Inj0 0)))) 0 ⟶ x1 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι . x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum (x9 (λ x11 . Inj0 0)) 0) x5 (λ x9 . setsum x7 0) x5) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x1 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι . Inj0 0) (λ x8 : ι → (ι → ι) → ι → ι . 0) ⟶ x1 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι . 0) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 (x6 (λ x9 x10 . Inj1 (setsum 0 0)) (λ x9 : ι → ι . x8 0 (λ x10 . setsum 0 0) 0) (Inj0 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . x2 (λ x8 : ι → ι → (ι → ι) → ι → ι . λ x9 . Inj0 0) 0 ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . setsum x10 x11) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum (x8 (x7 (λ x11 x12 : ι → ι . λ x13 . setsum 0 0) (λ x11 x12 . setsum 0 0) (setsum 0 0) (x8 0 (λ x11 . 0) 0)) (λ x11 . Inj1 0) (Inj1 (setsum 0 0))) 0) (x4 (λ x8 : (ι → ι) → ι . λ x9 x10 . 0))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ι → ι . x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum (Inj1 (Inj0 x9)) x9) (Inj0 (Inj1 (Inj0 x4))) ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . x11) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . Inj1 (x8 (Inj0 0) (λ x11 . Inj0 (x10 0)) (Inj0 (Inj1 0)))) (Inj1 (x7 (λ x8 x9 . setsum (setsum 0 0) x8) 0))) ⟶ False.