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