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Proofgold Signed Transaction

vin
Pr7Mr../f3852..
PUaSE../cef38..
vout
Pr7Mr../cdf5f.. 9.82 bars
TMZw6../11d50.. negprop ownership controlledby PrGVS.. upto 0
TMZd9../82820.. negprop ownership controlledby PrGVS.. upto 0
TMYs8../8e7dd.. negprop ownership controlledby PrGVS.. upto 0
TMX44../aa45f.. negprop ownership controlledby PrGVS.. upto 0
TMWjc../4bbc4.. negprop ownership controlledby PrGVS.. upto 0
TMU7b../7cd9e.. negprop ownership controlledby PrGVS.. upto 0
TMRZq../ed110.. negprop ownership controlledby PrGVS.. upto 0
TMRJh../18c37.. negprop ownership controlledby PrGVS.. upto 0
TMRh4../17b39.. negprop ownership controlledby PrGVS.. upto 0
TMPqd../31324.. negprop ownership controlledby PrGVS.. upto 0
TMPBi../e218b.. negprop ownership controlledby PrGVS.. upto 0
TMNG8../1a024.. negprop ownership controlledby PrGVS.. upto 0
TMNdw../6e0dd.. negprop ownership controlledby PrGVS.. upto 0
TMMyu../34867.. negprop ownership controlledby PrGVS.. upto 0
TMLuH../cb519.. negprop ownership controlledby PrGVS.. upto 0
TML87../a70e5.. negprop ownership controlledby PrGVS.. upto 0
TMJiV../8e653.. negprop ownership controlledby PrGVS.. upto 0
TMJ8v../c7d86.. negprop ownership controlledby PrGVS.. upto 0
TMHYR../151d0.. negprop ownership controlledby PrGVS.. upto 0
TMHwN../1c772.. negprop ownership controlledby PrGVS.. upto 0
TMHfF../b7558.. negprop ownership controlledby PrGVS.. upto 0
TMGYZ../bdd34.. negprop ownership controlledby PrGVS.. upto 0
TMGma../891d9.. negprop ownership controlledby PrGVS.. upto 0
TMFRS../5d1f4.. negprop ownership controlledby PrGVS.. upto 0
TMFLv../1c8e2.. negprop ownership controlledby PrGVS.. upto 0
TMFjE../eafc4.. negprop ownership controlledby PrGVS.. upto 0
TMFah../a8bbd.. negprop ownership controlledby PrGVS.. upto 0
TMdnh../f17c5.. negprop ownership controlledby PrGVS.. upto 0
TMcBv../d6354.. negprop ownership controlledby PrGVS.. upto 0
TMc8b../5bd82.. negprop ownership controlledby PrGVS.. upto 0
TMbKC../5fdba.. negprop ownership controlledby PrGVS.. upto 0
TMbgC../d0b79.. negprop ownership controlledby PrGVS.. upto 0
TMbGa../b4a60.. negprop ownership controlledby PrGVS.. upto 0
TMbbF../f5004.. negprop ownership controlledby PrGVS.. upto 0
TMaTT../4ba7a.. negprop ownership controlledby PrGVS.. upto 0
TMa1H../fde73.. negprop ownership controlledby PrGVS.. upto 0
TMNAo../ddcd5.. ownership of f1111.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMQH6../a4d09.. ownership of 08ad3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMQzr../7f205.. ownership of 586ae.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMbYW../7bd2d.. ownership of 66135.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMdkp../cc457.. ownership of 2d8bb.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNqC../df9a0.. ownership of d7611.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMFQC../c383f.. ownership of ca986.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYYk../ba23b.. ownership of 03a35.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMPQc../d2f04.. ownership of 932cb.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMXuy../5cd43.. ownership of be7d0.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTdA../fd49d.. ownership of e4e0f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMWPH../2b86b.. ownership of eac01.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMZNw../54519.. ownership of 7fcf2.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMQUb../50521.. ownership of cbf80.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMbeb../820e4.. ownership of 9baf5.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMMiS../9ceae.. ownership of 6f76d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMRaf../c93ca.. ownership of 6a8d7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNcD../282b9.. ownership of fb3da.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYfq../8f65b.. ownership of 54407.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYkV../7e4e1.. ownership of 1951d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNpR../91af6.. ownership of 2082d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMM9d../7e888.. ownership of 6c4f5.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMcve../d2b8b.. ownership of 98889.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMJ5A../76f45.. ownership of 1e086.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMQtb../42f62.. ownership of 66506.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNqX../7b6b8.. ownership of aa5e4.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMJHg../11719.. ownership of 4eeed.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNgd../90eb9.. ownership of 4effb.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMM8p../f208e.. ownership of cc30f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMHkN../fe274.. ownership of d484c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTh4../cd45f.. ownership of 33ee6.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMa72../889fe.. ownership of d7121.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTbe../47c2c.. ownership of 6858c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNgk../73a81.. ownership of 0a24d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMM4k../dcae3.. ownership of 433fa.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMM63../5105a.. ownership of 0dd56.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNUt../b51fb.. ownership of 550a7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMY8a../c364d.. ownership of e614b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TML36../41b8e.. ownership of f1e3e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNph../eefd3.. ownership of 350a7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMbX8../04eea.. ownership of a248f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMRKq../a1aec.. ownership of 7e1f5.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMQWC../24f09.. ownership of 7af28.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMUcd../0fab4.. ownership of 3f550.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYjy../706ec.. ownership of b9f6e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMPMr../7e1a3.. ownership of b82b7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMT41../6c585.. ownership of 8bcc9.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMdBP../9a82a.. ownership of 1f9c3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMVpV../1df59.. ownership of 72ada.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMVHn../51042.. ownership of 7a405.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMS1v../54a8e.. ownership of 3003b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMNqr../2155a.. ownership of 6f950.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMWre../34a8d.. ownership of 4d46e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMFCV../a7544.. ownership of 1f3a3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMUEd../eec2a.. ownership of 286ff.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMKaF../b2543.. ownership of 277ae.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMWop../48a3b.. ownership of 84b22.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMU4B../a5df3.. ownership of 4d170.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMWnn../9c8e6.. ownership of e07c2.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYVQ../b1a47.. ownership of 9a313.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMaUp../7f812.. ownership of db1af.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TML3m../5ef70.. ownership of 5264f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMd3x../cc2d3.. ownership of 4f3f6.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMM8p../909ae.. ownership of 5e406.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMcHW../39e8f.. ownership of 08f46.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMVvH../ef785.. ownership of 511ec.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMPSj../5e239.. ownership of 436a3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMH7z../de374.. ownership of 56215.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMSFC../56d86.. ownership of 6da2e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMaXG../096e9.. ownership of 1eeec.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMdfT../a713b.. ownership of e82b5.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMHNd../040e0.. ownership of c0c7a.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTki../0b7fb.. ownership of 4f699.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTBq../e6813.. ownership of 50f1b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
PUPLh../1178f.. doc published by PrGVS..
Known notEnotE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Theorem 4f699.. : ∀ x0 : ο . not x0 ⟶ x0 ⟶ ∀ x1 : ο . x1 (proof)
Known d06ba.. : not (∀ x0 : (((((ι → ι) → ι) → ι → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ο . ∀ x1 : (ι → 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 → ο . (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (setsum (x4 (Inj1 0) (λ x8 x9 . setsum (setsum 0 0) (setsum 0 0)) x5 0) (setsum (x4 (Inj0 0) (λ x8 x9 . 0) (setsum 0 0) 0) (setsum (Inj1 0) 0))) (Inj1 (setsum x6 0)) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . setsum 0 (setsum (x9 (Inj1 0) (x9 0 0)) x7)) (x4 (setsum (x4 (setsum 0 0) (λ x8 x9 . setsum 0 0) x5 (setsum 0 0)) x7) (λ x8 x9 . x9) (setsum (Inj1 (x4 0 (λ x8 x9 . 0) 0 0)) (Inj1 (Inj1 0))) 0) ⟶ x3 (λ x8 x9 . x9) (setsum x5 0) (Inj1 0) x6) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . In (Inj1 0) (setsum 0 0) ⟶ x3 (λ x8 x9 . 0) (setsum 0 (setsum 0 (Inj1 0))) 0 (Inj1 0) ⟶ x1 (λ x8 . setsum (setsum (Inj0 (x5 0 (λ x9 . 0))) x8) 0) (λ x8 : ((ι → ι) → ι) → ι . Inj1 0) (Inj1 (setsum (Inj1 (setsum 0 0)) (x5 0 (λ x8 . 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι . In (Inj1 (x4 (setsum (x6 (λ x8 . 0) 0) (setsum 0 0)))) (setsum (x4 (setsum (Inj0 0) 0)) (x4 0)) ⟶ x2 (λ x8 x9 . x7 (λ x10 . 0)) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 x10 . setsum (Inj0 0) 0)) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 . In (setsum 0 (setsum (setsum (Inj0 0) 0) (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 0) (λ x8 x9 . 0) (λ x8 . x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 x10 . 0) (λ x9 . 0))))) (Inj1 (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . setsum x10 0) (λ x8 x9 . x8) (λ x8 . Inj1 (Inj1 0)))) ⟶ x2 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 x10 . Inj1 (Inj0 0)) ⟶ x1 (λ x8 . Inj1 0) (λ x8 : ((ι → ι) → ι) → ι . setsum (setsum (setsum (setsum 0 0) (Inj1 0)) (setsum 0 x7)) 0) (setsum (setsum (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0) (x6 0 (λ x8 : ι → ι . 0) 0 0) 0) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0) (setsum 0 0) (setsum 0 0))) (setsum 0 (x6 x7 (λ x8 : ι → ι . setsum 0 0) (setsum 0 0) (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x8 x9 . x8) 0 (Inj1 0) (setsum 0 0) ⟶ x1 (λ x8 . setsum (Inj0 x8) (setsum 0 (setsum 0 (setsum 0 0)))) (λ x8 : ((ι → ι) → ι) → ι . 0) 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x1 (λ x8 . x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) 0)) (λ x8 : ((ι → ι) → ι) → ι . Inj1 0) (x5 0) ⟶ x1 (λ x8 . setsum (x5 0) (Inj0 0)) (λ x8 : ((ι → ι) → ι) → ι . Inj0 0) (setsum (setsum 0 0) (Inj0 (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . x9 0 0) (Inj1 (setsum 0 (x6 (λ x8 : ι → ι → ι . λ x9 . Inj0 0) (λ x8 : ι → ι . λ x9 . x9))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj1 (setsum (x7 (x4 0) (λ x8 : ι → ι . λ x9 . setsum 0 0)) 0)) (Inj0 0) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . setsum 0 (x7 (x6 (setsum 0 0) (λ x10 : ι → ι . λ x11 . Inj1 0) (λ x10 . setsum 0 0)) (λ x10 : ι → ι . λ x11 . setsum (x10 0) 0))) (Inj1 (setsum (x4 (Inj1 0)) (Inj0 0))) ⟶ x3 (λ x8 x9 . setsum (setsum (x6 (setsum 0 0) (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . x10)) (Inj1 0)) (Inj0 0)) 0 0 (x7 0 (λ x8 : ι → ι . λ x9 . x9))) ⟶ False)
Known 2c194.. : not (∀ x0 : ((((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) → 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) → ι) → ι) → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In (Inj1 (setsum (setsum (Inj0 0) (x5 0)) (x5 0))) (Inj1 (Inj0 (x5 (x7 0)))) ⟶ x3 (λ x8 . setsum (setsum (Inj0 (Inj1 0)) (Inj1 (setsum 0 0))) x6) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . setsum 0 (x8 (λ x10 : ι → ι . λ x11 . setsum (setsum 0 0) 0) (x7 (x7 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . x3 (λ x8 . Inj0 (setsum (setsum (Inj0 0) x8) (x6 (λ x9 x10 x11 . x11) (λ x9 . 0) (λ x9 . 0) (Inj0 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . x8 (λ x10 : ι → ι . λ x11 . x10 (Inj1 0)) (Inj0 0)) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . λ x9 . x9) (λ x8 . setsum (setsum 0 0) 0) x4 (λ x8 : ι → ι . λ x9 . 0) 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι) → ι → ι → ι . ∀ x7 . x3 (λ x8 . setsum (Inj1 0) (Inj1 (x5 0 (setsum 0 0) (λ x9 . x6 (λ x10 . 0) (λ x10 . 0) 0 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . x8 (λ x11 : ι → ι . λ x12 . Inj1 0) (x8 (λ x11 : ι → ι . λ x12 . 0) 0)))) ⟶ x2 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . 0) 0 (Inj0 (setsum (Inj1 (x5 0 0 (λ x8 . 0))) (x4 (λ x8 : ι → ι → ι . λ x9 x10 . Inj0 0)))) (λ x8 . 0) 0) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x6 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x7 . In x7 (Inj0 (x5 (λ x8 x9 : ι → ι . λ x10 . Inj1 (setsum 0 0)) (Inj0 0) (x6 0 (λ x8 x9 . setsum 0 0) (x4 0 (λ x8 . 0) 0 0) 0) x7)) ⟶ x2 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . setsum (setsum x8 (x9 (λ x10 x11 . Inj1 0) (λ x10 . setsum 0 0))) (setsum x8 (Inj0 (x9 (λ x10 x11 . 0) (λ x10 . 0))))) 0 0 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 (x9 0)) (x6 (Inj1 0) (λ x8 x9 . setsum 0 0) (setsum 0 0) (Inj1 0)) (Inj1 (setsum 0 0)) (setsum (Inj1 0) 0))) 0 ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum 0 (Inj0 (setsum (Inj0 0) (setsum 0 0)))) (λ x8 x9 x10 . x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x7 : ι → ι . In (Inj0 (setsum (Inj1 (x7 0)) 0)) (setsum (setsum 0 (setsum (Inj0 0) (x5 (λ x8 : (ι → ι) → ι → ι . 0)))) (Inj1 (Inj1 0))) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . Inj1 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 x9 x10 . x8) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . x8 (λ x9 . λ x10 : ι → ι . 0) (x7 0)) (λ x8 . 0) 0 (λ x8 : ι → ι . λ x9 . x7 (Inj0 (Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . 0) 0)))) (setsum (Inj1 0) (setsum (Inj1 (Inj0 0)) (setsum (x7 0) (Inj0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι . In x5 (setsum x6 (setsum 0 0)) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . λ x9 . x9) (λ x8 . Inj1 (Inj1 x8)) 0 (λ x8 : ι → ι . λ x9 . Inj0 (x8 x9)) x5 ⟶ x3 (λ x8 . Inj1 (setsum x6 (setsum 0 x8))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . Inj0 (setsum (Inj1 (x9 (λ x10 . 0))) (x7 (x7 0 0 0) (Inj1 0) (Inj1 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum x6 (Inj1 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 x9 x10 . Inj1 (Inj0 0)) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 (Inj1 (Inj1 (Inj1 0))))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6 0 0 (λ x9 . 0) 0) (λ x8 x9 x10 . 0) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6 (x8 (λ x9 : ι → ι → ι . λ x10 x11 . x9 (x8 (λ x12 : ι → ι → ι . λ x13 x14 . 0)) (setsum 0 0))) (setsum 0 (setsum (Inj0 0) 0)) (λ x9 . setsum 0 (setsum (x6 0 0 (λ x10 . 0) 0) 0)) (setsum (Inj1 (setsum 0 0)) (x8 (λ x9 : ι → ι → ι . λ x10 x11 . 0)))) (λ x8 x9 x10 . x10)) ⟶ False)
Known 95285.. : not (∀ x0 : ((ι → ι → ι → ι) → ι → ι → ι) → ι → ο . ∀ x1 : ((ι → ι) → ι) → (ι → ι) → ι → ο . ∀ x2 : (ι → ι) → ι → ο . ∀ x3 : (ι → ι → ι → ι → ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ο . (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . In (setsum 0 (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . setsum 0 0) 0) (λ x8 . 0) (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . 0))))) (setsum (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . Inj1 0) (x6 (λ x10 : (ι → ι) → ι → ι . 0))) (λ x8 . Inj1 (setsum 0 0)) 0) (setsum (x6 (λ x8 : (ι → ι) → ι → ι . 0)) (setsum (setsum 0 0) (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj0 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . x8 (x6 (λ x10 : (ι → ι) → ι → ι . 0)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . In (Inj1 (setsum (x5 (λ x8 x9 x10 . Inj0 0) (setsum 0 0) (setsum 0 0)) (setsum x6 (x7 (λ x8 . 0))))) x6 ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum (Inj1 0) x12)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj1 (Inj1 (Inj0 (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum 0 (setsum (Inj0 0) 0))) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj0 (Inj0 (x9 (x7 (λ x10 . 0)) (x7 (λ x10 . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . In (Inj0 x7) (setsum 0 0) ⟶ x2 (λ x8 . 0) x6 ⟶ x2 (λ x8 . 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . x6) x4 ⟶ In x5 (Inj1 0)) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (x5 (λ x8 : ι → ι → ι . 0)) (x5 (λ x8 : ι → ι → ι . Inj0 (x8 (Inj1 0) (setsum 0 0)))) ⟶ x1 (λ x8 : ι → ι . Inj0 0) (λ x8 . 0) (x5 (λ x8 : ι → ι → ι . 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : ι → ι . x6 (λ x9 . x7) (Inj1 (Inj0 (Inj1 0)))) (λ x8 . setsum (x6 (λ x9 . setsum x9 0) (Inj1 (Inj1 0))) 0) (setsum 0 (Inj1 0)) ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . setsum x7 (setsum x10 (x8 (setsum 0 0) 0 (setsum 0 0)))) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) 0 ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) (Inj1 x7)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . x10) (Inj0 0) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . 0)) ⟶ False)
Known acf72.. : not (∀ x0 : (((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) → ο . ∀ x2 : (ι → ι) → (ι → ι → ι) → ο . ∀ x3 : (((ι → ι) → ι) → ι → ι) → ((ι → ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . In (Inj1 (x5 0)) (Inj0 (Inj1 (Inj1 (setsum 0 0)))) ⟶ x2 (λ x8 . x7 (λ x9 . setsum (setsum (setsum 0 0) 0) (x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0))) (λ x9 : ι → ι . λ x10 . setsum 0 (x7 (λ x11 . Inj0 0) (λ x11 : ι → ι . λ x12 . 0)))) (λ x8 x9 . 0) ⟶ x3 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x8 (λ x10 . setsum (setsum 0 0) (Inj0 0))) 0) (λ x8 : ι → ι → ι . Inj0 0) (λ x8 : (ι → ι) → ι . 0) (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x7 (setsum x9 (Inj1 0))) (Inj0 (setsum 0 (Inj1 0)))) (λ x8 : ι → ι → ι . 0) (λ x8 : (ι → ι) → ι . setsum x6 (setsum (x8 (λ x9 . Inj0 0)) (x7 0))) (setsum (setsum (x7 0) x5) (Inj1 (setsum (Inj1 0) (setsum 0 0)))) ⟶ In (Inj0 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . In (Inj1 x7) (Inj0 (Inj0 x5)) ⟶ x3 (λ x8 : (ι → ι) → ι . λ x9 . Inj0 (setsum (setsum (Inj0 0) 0) (setsum 0 (x8 (λ x10 . 0))))) (λ x8 : ι → ι → ι . 0) (λ x8 : (ι → ι) → ι . x6) (Inj0 0) ⟶ x2 (λ x8 . Inj0 x6) (λ x8 x9 . setsum (setsum 0 0) x6)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 . 0) (λ x8 x9 . 0) ⟶ In (Inj0 x6) (setsum x6 (Inj1 (Inj0 (Inj0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . In (Inj0 0) (Inj1 (setsum x6 0)) ⟶ x2 (λ x8 . Inj0 0) (λ x8 x9 . setsum (x7 (setsum 0 0)) 0) ⟶ x1 (λ x8 x9 . 0) (λ x8 : ι → ι . x6)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x8 x9 . setsum (setsum 0 (setsum (Inj1 0) x7)) (Inj1 (setsum x6 x6))) (λ x8 : ι → ι . 0) ⟶ x1 (λ x8 x9 . x6) (λ x8 : ι → ι . x7)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 . 0) (λ x8 x9 . Inj1 0) ⟶ x0 (λ x8 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) (x7 (setsum (Inj0 (setsum 0 0)) (setsum (setsum 0 0) (Inj0 0))) (Inj1 (setsum 0 (setsum 0 0)))) (setsum 0 (setsum (x4 (setsum 0 0) 0 (λ x8 . setsum 0 0) (setsum 0 0)) (setsum (x7 0 0) (Inj1 0)))) (λ x8 : ι → ι . λ x9 . setsum x9 (Inj0 x9))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) x6 x5 (λ x8 : ι → ι . λ x9 . setsum (Inj1 (setsum (Inj1 0) x9)) (Inj0 x9)) ⟶ x2 (λ x8 . Inj0 (x7 0)) (λ x8 x9 . x6)) ⟶ False)
Known 748af.. : not (∀ x0 : (ι → ι) → ι → ο . ∀ x1 : (ι → (ι → ι) → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι) → ο . ∀ x2 : (ι → ι) → ι → ι → ι → ο . ∀ x3 : (((ι → ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι → ι) → ι → ι) → ι → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . In (Inj1 (setsum (Inj0 (setsum 0 0)) x4)) (Inj1 (x7 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . Inj1 (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (x5 (setsum (Inj1 (Inj1 0)) 0))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum (x8 (λ x12 x13 x14 . Inj1 (Inj1 0)) (λ x12 . Inj0 0) (x10 (x10 0 0) 0)) (Inj1 0)) x7 ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → ι → ι . x2 (λ x8 . x7 (λ x9 : ι → ι . 0) (Inj0 (setsum 0 0))) 0 (Inj1 0) (Inj0 (setsum (x5 (Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : ι → ι . 0) 0)) (x6 x4))) ⟶ x2 (λ x8 . Inj0 0) (setsum x4 (Inj0 (x5 0 (λ x8 : ι → ι . setsum 0 0)))) x4 0) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . 0) (Inj0 (Inj1 x4)) (Inj0 (setsum (Inj0 0) 0)) (setsum (setsum x4 0) 0) ⟶ In x7 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι → ι . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum 0 (Inj0 (Inj1 (x10 0 0)))) (Inj1 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0 (setsum (Inj0 (setsum 0 0)) 0) (λ x9 . x6) (x8 (setsum (Inj1 0) 0) (λ x9 . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ False) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . In (Inj1 (Inj0 (setsum 0 (x6 (λ x8 x9 x10 . 0))))) (Inj0 (setsum x4 0)) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7 ⟶ x0 (λ x8 . Inj0 (Inj0 (setsum (x5 0) (Inj1 0)))) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . In (Inj1 0) x4 ⟶ x0 (λ x8 . setsum 0 (Inj0 (x6 (λ x9 : ι → ι . λ x10 . 0)))) (setsum x7 x7) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) (Inj1 (Inj1 x5))) ⟶ False)
Known 56955.. : not (∀ x0 : (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 → ο . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι → ι → ι) → ι) → ι → ο . ∀ x3 : (ι → ι) → ((ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι) → ο . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ι → ι . In (Inj1 (Inj1 x4)) x4 ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . 0) (setsum (x7 0 x4) (Inj0 (setsum (Inj0 0) 0))) (λ x8 : (ι → ι) → ι → ι . setsum (Inj0 (setsum x5 x5)) (Inj1 0)) ⟶ x3 (λ x8 . x6 (λ x9 : (ι → ι) → ι . setsum (Inj1 (setsum 0 0)) (x7 (Inj1 0) 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum (Inj1 (setsum x7 (Inj1 0))) 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) (setsum (setsum (x5 (λ x8 : (ι → ι) → ι . setsum 0 0)) (Inj0 (Inj1 0))) (x4 (Inj1 (setsum 0 0)) (Inj0 0))) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . Inj0 x8) (Inj1 (setsum x7 (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . Inj0 (setsum (Inj1 (setsum 0 0)) x6)) (Inj0 (Inj0 (Inj1 (Inj1 0)))) ⟶ x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . In (setsum 0 (setsum (setsum (x5 (λ x8 . λ x9 : ι → ι . λ x10 . 0)) (setsum 0 0)) (Inj1 (Inj0 0)))) (Inj0 (setsum (Inj0 (Inj0 0)) 0)) ⟶ x3 (λ x8 . setsum 0 (Inj0 (Inj1 (Inj0 0)))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . 0) ⟶ x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . setsum (Inj1 0) (Inj1 0)) (setsum 0 (setsum 0 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) (setsum (x7 (x5 0 (λ x8 x9 . 0))) (setsum x6 x6)) ⟶ In (Inj1 (setsum (Inj0 (setsum 0 0)) (setsum (Inj1 0) (setsum 0 0)))) (x4 (λ x8 x9 . setsum (setsum x6 0) (Inj0 (x7 0))) (setsum 0 0) (λ x8 . 0) (setsum (x7 (setsum 0 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . x7) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum 0 (Inj0 (setsum (x8 0 (λ x11 . 0) 0) 0))) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . x8) (setsum (setsum (Inj0 0) x4) 0) (λ x8 : (ι → ι) → ι → ι . Inj1 (setsum 0 (x6 (x5 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . Inj0 0) (setsum 0 (x7 (λ x8 : (ι → ι) → ι → ι . setsum (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (Inj1 0)))) (λ x8 : (ι → ι) → ι → ι . x5) ⟶ False) ⟶ False)
Known 16fbe.. : not (∀ x0 : (ι → ι) → ι → ι → ο . ∀ x1 : ((ι → ι) → ι) → ((ι → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ο . ∀ x2 : (ι → ι) → ((((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → 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 → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι → ο . (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 . 0) (setsum 0 (Inj1 (setsum x7 (setsum 0 0)))) (setsum (x4 (x6 (Inj0 0) (setsum 0 0)) (λ x8 x9 . x9)) (setsum 0 x7)) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . 0) (λ x8 : ι → ι → ι → ι . 0) (λ x8 x9 x10 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 0)) (setsum (Inj0 (setsum (Inj1 0) (Inj1 0))) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . In x7 (Inj1 (Inj1 (Inj0 x6))) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . 0) (λ x8 : ι → ι → ι → ι . setsum (Inj1 (Inj1 (setsum 0 0))) 0) (λ x8 x9 x10 . setsum 0 (Inj0 (Inj1 (Inj0 0)))) 0 ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . Inj1 (setsum (Inj1 (x8 0 (λ x10 . 0))) 0)) (λ x8 : ι → ι → ι → ι . setsum (Inj1 0) (setsum 0 0)) (λ x8 x9 x10 . x9) (x4 (λ x8 : ι → ι → ι . setsum x7 (setsum (Inj0 0) (x8 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . setsum (Inj1 0) (Inj1 0)) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . Inj0 (Inj0 (setsum 0 0))) 0) (λ x8 : (ι → ι) → ι . λ x9 x10 . Inj0 (Inj1 0)) (Inj1 (Inj0 (setsum 0 0))) (λ x8 . setsum (Inj1 0) (setsum 0 (setsum (Inj0 0) x5))) 0 ⟶ x2 (λ x8 . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . setsum (setsum x10 0) (setsum (Inj1 (Inj1 0)) (setsum (x8 (λ x12 : ι → ι . 0)) x10))) (λ x8 : (ι → ι) → ι . λ x9 x10 . Inj1 (x8 (λ x11 . setsum (setsum 0 0) (Inj0 0)))) (setsum (Inj1 (Inj0 x6)) (Inj1 (setsum 0 (Inj1 0)))) (λ x8 . Inj1 (Inj0 (setsum (Inj0 0) (Inj0 0)))) (setsum x7 (Inj1 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . In x7 (Inj0 0) ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x10) (λ x8 : (ι → ι) → ι . λ x9 x10 . 0) (Inj1 (setsum x7 (setsum (Inj0 0) 0))) (λ x8 . x8) (setsum (Inj1 (x4 (Inj0 0))) (Inj1 x7)) ⟶ x2 Inj0 (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x8 (λ x12 : ι → ι . 0)) (λ x8 : (ι → ι) → ι . λ x9 x10 . setsum x7 0) (setsum (setsum 0 0) 0) (λ x8 . Inj0 (Inj0 x5)) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (setsum (Inj0 (Inj0 (Inj1 0))) (setsum 0 x5)) (x4 (setsum (setsum x5 (setsum 0 0)) (Inj1 x5))) ⟶ x2 (λ x8 . setsum (x7 (λ x9 x10 x11 . 0)) x5) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 . x8 (λ x11 . setsum x10 0)) (setsum 0 (setsum (Inj1 0) (Inj0 x5))) (λ x8 . x7 (λ x9 x10 x11 . setsum (setsum (setsum 0 0) (Inj1 0)) (Inj0 (Inj1 0)))) (Inj1 (Inj1 0)) ⟶ x1 (λ x8 : ι → ι . 0) (λ x8 : ι → ι → ι → ι . Inj1 0) (λ x8 x9 x10 . x10)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x8 : ι → ι . Inj1 (setsum (x7 (λ x9 . λ x10 : ι → ι . 0)) (setsum 0 0))) (λ x8 : ι → ι → ι → ι . x6 (λ x9 x10 . x9) (λ x9 : ι → ι . λ x10 . x8 0 (x8 (setsum 0 0) (Inj1 0) (Inj0 0)) 0) (λ x9 . Inj1 (Inj0 0))) (λ x8 x9 x10 . x9) ⟶ x0 (λ x8 . setsum 0 (Inj1 (setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0))))) 0 (setsum (setsum (setsum (x6 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0)) 0) (setsum 0 (setsum 0 0))) (x6 (λ x8 x9 . x7 (λ x10 . λ x11 : ι → ι . Inj1 0)) (λ x8 : ι → ι . λ x9 . x8 (setsum 0 0)) (λ x8 . setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0)))))) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x7 . x0 (λ x8 . 0) (setsum (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . 0) (Inj0 0) 0)) x7) (setsum (x4 (λ x8 x9 x10 . Inj0 (setsum 0 0))) 0) ⟶ x0 (λ x8 . setsum (setsum (Inj1 (Inj0 0)) (setsum (Inj0 0) 0)) (x5 0 (Inj0 (setsum 0 0)))) (Inj1 (Inj1 (x5 (x6 (λ x8 : (ι → ι) → ι → ι . 0) 0 0) (Inj0 0)))) (Inj1 (Inj1 (Inj1 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x8 . x5) 0 (setsum 0 x5) ⟶ False) ⟶ False)
Known 5be0e.. : not (∀ 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 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι . In (x7 (setsum 0 0) (λ x8 . 0) (setsum (setsum (setsum 0 0) (Inj0 0)))) (x7 (setsum (setsum (x4 0) (setsum 0 0)) (x4 (Inj0 0))) (λ x8 . setsum 0 (setsum (setsum 0 0) (setsum 0 0))) (λ x8 . 0)) ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . setsum (x9 (λ x13 : ι → ι . x13 (x13 0))) (setsum 0 (x9 (λ x13 : ι → ι . 0)))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . x7 0 (λ x11 . setsum (setsum (setsum 0 0) (Inj0 0)) (Inj1 (setsum 0 0))) (λ x11 . setsum (x8 (setsum 0 0) (λ x12 . 0) (x8 0 (λ x12 . 0) 0)) (Inj0 0))) (Inj1 (Inj0 (setsum (Inj1 0) 0))) ⟶ x3 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 (setsum (setsum (setsum 0 0) x9) 0)) (λ x8 x9 x10 x11 . x8) (λ x8 : ι → ι → ι . λ x9 . 0)) ⟶ (∀ 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 (setsum (setsum x11 (Inj0 0)) x10)) (λ x8 : ι → ι → ι . λ x9 . x8 0 (Inj0 0)) ⟶ 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)
Known 3311e.. : not (∀ x0 : (ι → ι) → ι → ο . ∀ x1 x2 : ((ι → ι) → ι) → ι → ι → ο . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → ι → (((ι → ι) → ι) → ι → ι) → ο . (∀ x4 x5 x6 x7 . In (setsum (setsum (setsum (Inj1 0) 0) (Inj0 (Inj0 0))) (setsum (setsum 0 0) (Inj0 (setsum 0 0)))) (setsum (setsum (setsum (setsum 0 0) x4) x7) 0) ⟶ x1 (λ x8 : ι → ι . setsum (setsum (Inj0 x5) (Inj0 0)) 0) (Inj0 (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (Inj0 0)))) (setsum (Inj0 (setsum 0 (Inj1 0))) 0) ⟶ x3 (λ x8 . λ x9 : (ι → ι) → ι . x9 (λ x10 . x8)) x5 (λ x8 : (ι → ι) → ι . λ x9 . Inj0 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x8 . λ x9 : (ι → ι) → ι . setsum (x9 (λ x10 . setsum (setsum 0 0) x8)) 0) 0 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x8 (λ x10 . x8 (λ x11 . setsum 0 0))) 0) ⟶ False) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι . x0 (λ x8 . 0) (x6 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x2 (λ x8 : ι → ι . setsum (setsum (x8 0) 0) (x7 (λ x9 . 0) (λ x9 x10 . setsum (Inj0 0) 0) (x6 (Inj0 0)))) 0 (x7 (λ x8 . Inj1 (x5 0 (λ x9 . 0))) (λ x8 x9 . x8) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 : ι → ι . x6) (setsum (setsum x4 x7) (setsum 0 0)) (Inj0 0) ⟶ x0 (λ x8 . Inj0 (x5 0 (λ x9 : ι → ι . λ x10 . Inj1 (Inj0 0)) (λ x9 . 0))) (setsum x6 (Inj0 (Inj0 (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 . 0) (Inj1 x4) ⟶ x1 (λ x8 : ι → ι . setsum 0 (Inj0 (Inj1 (Inj1 0)))) x4 (setsum 0 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . x1 (λ x8 : ι → ι . setsum 0 x5) (setsum (Inj1 0) (setsum (Inj0 (setsum 0 0)) 0)) (Inj1 (x7 (λ x8 : (ι → ι) → ι . x6 (Inj0 0) (λ x9 . Inj1 0)) (Inj1 (Inj0 0)) (Inj0 (setsum 0 0)) 0)) ⟶ In (Inj0 (Inj0 (x7 (λ x8 : (ι → ι) → ι . x8 (λ x9 . 0)) x5 (Inj1 0) (Inj0 0)))) (x4 x5)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . In (setsum x7 (setsum 0 0)) (Inj0 x7) ⟶ x0 (λ x8 . x8) (Inj1 0) ⟶ x0 (λ x8 . x6 0 (setsum 0 (Inj0 0))) (setsum (setsum (Inj1 x5) 0) (setsum (x6 0 x4) (setsum (Inj1 0) (x6 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . x0 (λ x8 . x6 (λ x9 . Inj1 0)) (Inj1 (setsum 0 (Inj1 (setsum 0 0)))) ⟶ False) ⟶ False)
Known 63b62.. : not (∀ x0 : (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 → 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) → (((ι → ι → ι) → ι) → ι) → (ι → ι) → ο . (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι . In (Inj0 x6) (setsum 0 (setsum 0 0)) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . Inj1 x6) (setsum (Inj0 (Inj1 (setsum 0 0))) (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (x7 (λ x8 . setsum 0 0) 0 0) (setsum (x7 (setsum x6) (Inj1 (Inj1 0)) 0) x5) (λ x8 . 0) (x7 (λ x8 . Inj0 0) (x4 (setsum (Inj1 0) (Inj0 0)) (λ x8 . x6) (λ x8 . 0) 0) (Inj0 (setsum x5 (Inj1 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι . x6) (λ x8 . x5)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x11 0) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 . 0) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . Inj0 (x7 0 (Inj0 0) (λ x10 . 0) (Inj0 (setsum 0 0)))) x6 (x4 (λ x8 x9 : ι → ι . 0) (x4 (λ x8 x9 : ι → ι . 0) (Inj0 (Inj0 0)) 0 0) (setsum (setsum 0 x6) (setsum (Inj0 0) (Inj1 0))) x6) x6 (λ x8 . setsum (Inj1 (setsum (x7 0 0 (λ x9 . 0) 0) (setsum 0 0))) (setsum (setsum 0 (setsum 0 0)) (setsum x8 (Inj0 0)))) (Inj1 (x7 (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (setsum 0 0)) (λ x8 . Inj0 (Inj1 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . In x7 (setsum (Inj0 (x4 (λ x8 . 0))) 0) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . 0) (x4 (λ x8 . x5)) (Inj1 (Inj0 (setsum (Inj1 0) 0))) (Inj0 0) (λ x8 . Inj1 0) (Inj0 (Inj0 0))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . 0) x6 0 x7 (λ x8 . setsum 0 (Inj0 (Inj1 (Inj1 0)))) (x4 (λ x8 . 0) (λ x8 : ι → ι . Inj1 x6) (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 . setsum x5 0)) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum (Inj0 (Inj1 (x11 0))) (x9 0)) (λ x8 : (ι → ι → ι) → ι . 0) Inj0 ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (x7 (x9 (λ x11 x12 . setsum 0 0)) (λ x11 : ι → ι . x10)) 0) (Inj1 0) x5 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (x9 (λ x11 x12 . 0)) (x8 0 (λ x11 : ι → ι . Inj0 (x11 0)))) (Inj0 (setsum (Inj1 0) (setsum x4 (setsum 0 0)))) (setsum x7 (Inj1 (setsum (setsum 0 0) 0))) (λ x8 : ι → ι . λ x9 . x7) (λ x8 . 0) ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . x10) (Inj0 x7) 0 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . x8)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . Inj0 (Inj1 (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . 0) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . setsum (Inj1 (Inj1 (setsum 0 0))) (setsum (x9 0 (λ x10 . setsum 0 0)) x7)) (λ x8 : ι → ι . setsum 0 (x6 (x6 0 0) x5))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In x6 (x5 (setsum (x4 0 (Inj1 0)) (x4 x6 (Inj0 0)))) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . setsum (x9 0 (λ x10 . 0)) (x9 (Inj1 (x9 0 (λ x10 . 0))) (λ x10 . x8))) (λ x8 : ι → ι . x8 0) ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (setsum (Inj0 (Inj1 0)) (Inj1 (setsum 0 0))) (x8 (setsum (x9 (λ x11 x12 . 0)) (setsum 0 0)) (λ x11 : ι → ι . x8 (setsum 0 0) (λ x12 : ι → ι . x10)))) (x4 (x4 (x4 (setsum 0 0) (Inj1 0)) (x7 0)) (setsum (setsum (x4 0 0) (setsum 0 0)) 0)) (x5 (x4 (setsum 0 (x5 0)) 0)) (λ x8 : ι → ι . λ x9 . Inj0 (setsum (Inj1 (Inj0 0)) 0)) (λ x8 . Inj1 (setsum (x7 (setsum 0 0)) (Inj1 x6)))) ⟶ False)
Known bfeb0.. : not (∀ x0 : (ι → ι) → ι → (ι → ι) → ο . ∀ x1 : (((((ι → ι) → 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 → ο . ∀ x3 : ((ι → (ι → ι) → ι) → ι → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 . In (Inj1 0) x7 ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . Inj1 0) (Inj0 0)) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . In (setsum (x4 (setsum x7 (x6 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 (λ x8 . 0) 0)) (Inj1 (Inj1 0)) 0) (Inj1 0)) (Inj0 x7) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . Inj1 (setsum 0 (Inj1 x7))) (x6 (λ x8 . λ x9 : ι → ι . λ x10 . setsum (setsum x10 0) (Inj1 (setsum 0 0))) (Inj0 (x4 0 0 (setsum 0 0))) (λ x8 . Inj0 0) (Inj1 0)) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . setsum (Inj0 (x8 x9 (λ x10 . Inj0 0))) (Inj1 x9)) (setsum (setsum (x5 (setsum 0 0) (λ x8 x9 . setsum 0 0)) (setsum (setsum 0 0) (x6 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 (λ x8 . 0) 0))) x7)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum (setsum (setsum 0 (setsum 0 0)) (x10 0)) 0) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x10 (setsum (setsum (setsum 0 0) 0) (x10 (Inj0 0)))) (setsum 0 (setsum (x4 (Inj0 0) x5) (Inj1 0))) ⟶ x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x8 (setsum x7 (Inj0 x7))) (Inj0 (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x1 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → (ι → ι) → ι → ι → ι . In x5 (Inj0 (Inj0 (x7 (λ x8 . x7 (λ x9 . 0) (λ x9 . 0) 0 0) (λ x8 . 0) (Inj0 0) (Inj0 0)))) ⟶ x1 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 . x6 (setsum (Inj0 (x6 0 0)) (setsum 0 0)) (Inj0 (x6 (Inj0 0) 0))) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum 0 x9) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . x7 (λ x10 . x10) (λ x10 . x8 (Inj0 (x8 0 (λ x11 . 0))) (λ x11 . setsum x11 (setsum 0 0))) (setsum 0 (setsum (x7 (λ x10 . 0) (λ x10 . 0) 0 0) (Inj0 0))) (setsum x9 0)) (Inj1 (x7 (λ x8 . 0) (λ x8 . setsum (setsum 0 0) (Inj0 0)) (x7 (λ x8 . Inj0 0) (λ x8 . Inj0 0) (Inj1 0) (setsum 0 0)) (x6 (x6 0 0) 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj0 0) (setsum (Inj0 (setsum (Inj1 0) (x6 0 0))) 0) ⟶ x0 (setsum x5) (Inj0 (x7 (setsum (Inj0 0) (x6 0 0)) (λ x8 : ι → ι . λ x9 . setsum (Inj0 0) 0))) (λ x8 . x6 x5 (setsum (Inj0 x5) (x6 x8 (setsum 0 0)))) ⟶ x0 (λ x8 . 0) (x4 (λ x8 . x5)) (λ x8 . Inj0 (setsum x5 (x6 (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 x7 : ι → ι . x0 (λ x8 . Inj1 (Inj0 (x5 (λ x9 : (ι → ι) → ι . Inj0 0) (x6 0) (λ x9 . setsum 0 0)))) (setsum 0 (Inj1 0)) (λ x8 . 0) ⟶ x0 (λ x8 . x5 (λ x9 : (ι → ι) → ι . 0) x8 (λ x9 . 0)) (Inj1 (Inj1 (x7 0))) (λ x8 . setsum (setsum (Inj0 (x7 0)) (Inj0 0)) (Inj1 (Inj0 (x7 0))))) ⟶ False)
Known ebfdd.. : not (∀ x0 : (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 → ι) → ι) → ι → ι → ο . ∀ x3 : ((ι → ι → (ι → ι) → ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι → ι → ι) → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . Inj1 (Inj0 x11)) (λ x8 : ι → ι → ι → ι . setsum x6 (Inj1 (Inj0 (setsum 0 0)))) (Inj0 (setsum (setsum (x4 0) 0) 0))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 . In (setsum 0 x5) (setsum (Inj0 0) (Inj1 0)) ⟶ x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . setsum (Inj0 x11) (Inj0 (Inj0 (x10 (λ x13 . 0) 0)))) (λ x8 : ι → ι → ι → ι . 0) 0 ⟶ x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . setsum 0 (Inj1 (setsum (Inj1 0) 0))) (λ x8 : ι → ι → ι → ι . x5) (setsum x7 (Inj0 (Inj0 0)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x11) (λ x8 : ι → ι → ι → ι . x5) (Inj0 x5) ⟶ x2 (λ x8 . x7 x5) (λ x8 : ι → ι . 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . setsum (x8 (λ x10 . Inj1 (setsum 0 0))) (setsum (setsum (x8 (λ x10 . 0)) (x7 0)) (Inj0 (Inj0 0)))) (Inj1 (Inj1 (setsum x5 (Inj1 0)))) (setsum (Inj1 (setsum (setsum 0 0) x5)) (setsum (Inj1 x6) (Inj1 (Inj1 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj0 x5) (Inj1 (Inj1 (Inj0 0))) ⟶ x2 (λ x8 . x6) (λ x8 : ι → ι . Inj0 (Inj0 0)) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . 0) (Inj1 (setsum 0 (Inj0 0))) x5 ⟶ x2 (λ x8 . 0) (λ x8 : ι → ι . x5) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . Inj1 0) (Inj1 x5) x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι . ∀ x7 . In (setsum (Inj1 (setsum (setsum 0 0) (setsum 0 0))) (setsum (Inj0 (x5 0)) 0)) (Inj1 (setsum (setsum (Inj1 0) (setsum 0 0)) (Inj0 (x6 (λ x8 x9 x10 . 0) (λ x8 . 0) (λ x8 . 0))))) ⟶ x0 (λ x8 x9 . setsum (setsum 0 0) (x6 (λ x10 x11 x12 . Inj0 (Inj1 0)) (λ x10 . 0) (λ x10 . x8))) (λ x8 : ι → ι . Inj0 (setsum (x6 (λ x9 x10 x11 . Inj0 0) (λ x9 . 0) (λ x9 . Inj0 0)) 0)) (Inj0 (setsum (setsum (setsum 0 0) 0) (Inj0 (setsum 0 0)))) (λ x8 : ι → ι . Inj0 (setsum 0 0)) (setsum x7 (Inj0 (Inj0 0))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . x11) (Inj1 (setsum (Inj0 0) 0)) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . In (Inj0 0) (Inj1 (setsum 0 (Inj0 x6))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . 0) 0 (λ x8 . λ x9 : ι → ι . x9 (setsum 0 (Inj1 x7))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum (setsum 0 (Inj0 (Inj0 0))) (Inj1 (x9 (λ x13 . setsum 0 0) (λ x13 . x13) x11))) x6 (λ x8 . λ x9 : ι → ι . setsum (setsum 0 0) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . In (x5 0) (setsum (Inj0 (setsum 0 (x5 0))) (setsum x7 (setsum (setsum 0 0) 0))) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → ι . x8 (setsum (x8 (x5 0)) (Inj0 0))) (Inj1 x6) (λ x8 : ι → ι . Inj1 (setsum (setsum (x8 0) x6) (Inj1 (setsum 0 0)))) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . x8) (λ x8 : ι → ι . setsum 0 (setsum 0 (x7 (x5 (λ x9 . 0))))) 0 (λ x8 : ι → ι . Inj1 (Inj0 0)) (x7 0) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → ι . x8 0) (setsum (setsum 0 (Inj1 (Inj1 0))) 0) (λ x8 : ι → ι . 0) (Inj0 (Inj1 0))) ⟶ False)
Known 7a4d9.. : not (∀ x0 : (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 → ι) → ι) → ι) → ο . ∀ x2 : ((ι → ι) → ι → ι) → (ι → ((ι → ι) → ι → ι) → ι) → ο . ∀ x3 : ((((ι → ι) → ι) → ι → ι) → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . setsum 0 x5) ⟶ x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj1 0) x6) (setsum (Inj0 0) (setsum (Inj1 (x4 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj0 x7) 0) (Inj1 x7) ⟶ False) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . setsum (x8 (setsum 0 (setsum 0 0))) x7) (λ x8 . λ x9 : (ι → ι) → ι → ι . x6 (λ x10 x11 . setsum (setsum x11 (setsum 0 0)) x11)) ⟶ x2 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . λ x9 : (ι → ι) → ι → ι . Inj1 (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 : ι → ι . Inj1) (λ x8 . λ x9 : (ι → ι) → ι → ι . 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . In (Inj1 0) (setsum (Inj0 (x4 (setsum 0 0) (Inj1 0) (Inj1 0) (setsum 0 0))) 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 (setsum 0 (Inj1 0))) (x9 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . x11) (λ x8 : (ι → ι) → ι . 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (setsum 0 (Inj0 0)) (setsum (Inj0 0) 0)) (λ x8 : (ι → ι) → ι . setsum (Inj0 (x7 (setsum 0 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj0 (setsum (setsum 0 0) (Inj0 0))) (setsum (setsum (setsum 0 0) 0) (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . 0) (λ x8 : (ι → ι) → ι . setsum 0 (Inj0 x6)) ⟶ In (Inj1 (Inj1 0)) x7) ⟶ (∀ x4 x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . x7) ⟶ x0 (λ x8 . λ x9 : ι → ι . x6) (λ x8 : ι → (ι → ι) → ι . 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . Inj0 (setsum 0 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ In (setsum 0 0) (Inj0 0)) ⟶ False)
Known 9033d.. : not (∀ x0 : ((ι → ι → (ι → ι) → ι) → ι) → ι → ι → ο . ∀ x1 : (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) → ο . (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 . λ x9 : ι → ι . x9 (Inj1 (Inj0 x6))) (λ x8 : (ι → ι) → ι . setsum (Inj1 (setsum x6 0)) (Inj0 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x7 . In (setsum (Inj0 (setsum (Inj0 0) 0)) (Inj1 0)) (Inj0 x7) ⟶ x3 (λ x8 . λ x9 : ι → ι . x8) (λ x8 : (ι → ι) → ι . Inj0 (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) 0))) ⟶ x3 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x8 . x5) (setsum x5 (x6 (Inj1 0) (Inj1 (Inj0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x6 (x8 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0)) 0) (x6 0 x4) (λ x8 x9 . Inj1 (x7 (λ x10 . Inj1 x9) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) 0 (λ x8 x9 . setsum (Inj0 0) x7) ⟶ In (Inj0 (Inj0 (setsum x6 (Inj0 0)))) (Inj0 (setsum (Inj0 (setsum 0 0)) (setsum (x4 0 0 (λ x8 . 0) 0) x7)))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . In (Inj1 x5) (Inj1 (setsum (Inj1 (x6 (λ x8 x9 : ι → ι . λ x10 . 0) (λ x8 x9 . 0))) (Inj1 (setsum 0 0)))) ⟶ x1 (λ x8 . x6 (λ x9 x10 : ι → ι . λ x11 . Inj0 0) (λ x9 x10 . setsum (Inj0 0) 0)) (setsum 0 (setsum (setsum 0 (setsum 0 0)) (setsum 0 0))) ⟶ x1 (λ x8 . 0) (setsum 0 (Inj0 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (Inj1 (setsum (Inj1 (setsum 0 0)) (Inj1 0))) ⟶ False) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . In x5 (setsum (setsum 0 0) (Inj1 (setsum (Inj0 0) x4))) ⟶ x1 (λ x8 . x7) (Inj1 0) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι . setsum (setsum x7 0) (x6 0)) 0 (setsum (Inj0 (setsum 0 (Inj0 0))) 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι . 0) (setsum 0 (Inj0 (setsum x5 (Inj1 0)))) (setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj0 (Inj1 0))) ⟶ In (Inj1 (Inj1 (Inj1 0))) (setsum 0 (setsum 0 (Inj1 0)))) ⟶ False)
Known 8e3ed.. : not (∀ x0 : ((ι → ι → ι) → ι) → ι → ο . ∀ x1 : (ι → ι) → (((ι → ι → ι) → ι → ι) → ι) → ο . ∀ x2 : (ι → (ι → ι → 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) → ο . (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 x10 . Inj1 (setsum (Inj0 x9) 0))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum (Inj1 0) (setsum (Inj0 (setsum 0 0)) x7)) (λ x8 : (ι → ι) → ι . x6) (λ x8 : ι → ι . λ x9 x10 . x10) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . Inj1 (x10 (λ x11 . setsum (setsum 0 0) 0))) (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 x10 . setsum x10 x7)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (x4 (λ x8 . λ x9 : ι → ι . x6) (λ x8 : ι → ι . λ x9 . Inj1 (Inj0 (setsum 0 0))) (setsum 0 (setsum (setsum 0 0) 0)) x5) (setsum 0 (setsum (setsum (setsum 0 0) 0) x7)) ⟶ x0 (λ x8 : ι → ι → ι . x7) (Inj1 (setsum x5 (Inj1 x6))) ⟶ x2 (λ x8 . λ x9 : ι → ι → ι → ι . Inj1 0) (λ x8 . x5) (λ x8 . 0) x6 0) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . In (x6 (Inj0 (setsum (Inj1 0) (Inj1 0)))) (setsum (x5 (x5 0 (λ x8 : ι → ι . setsum 0 0) (λ x8 . Inj1 0) (setsum 0 0)) (λ x8 : ι → ι . setsum (x6 0) 0) (λ x8 . x5 0 (λ x9 : ι → ι . 0) (λ x9 . x7) (setsum 0 0)) 0) (x4 (λ x8 x9 . Inj1 (setsum 0 0)))) ⟶ x2 (λ x8 . λ x9 : ι → ι → ι → ι . x6 (Inj1 x7)) (λ x8 . x8) (λ x8 . setsum 0 0) (x5 0 (λ x8 : ι → ι . x5 0 (λ x9 : ι → ι . setsum (setsum 0 0) (setsum 0 0)) (λ x9 . Inj1 (x6 0)) 0) (λ x8 . setsum (x5 (setsum 0 0) (λ x9 : ι → ι . Inj0 0) (λ x9 . Inj0 0) (Inj1 0)) (Inj1 0)) (x4 (λ x8 x9 . 0))) (x6 0) ⟶ x0 (λ x8 : ι → ι → ι . x5 (Inj1 0) (λ x9 : ι → ι . Inj0 0) Inj1 (Inj1 0)) (Inj1 (x6 (Inj0 x7)))) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . In x5 x5 ⟶ x1 (λ x8 . Inj1 x5) (λ x8 : (ι → ι → ι) → ι → ι . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . In (Inj0 (setsum (Inj0 (Inj1 0)) 0)) (Inj0 (setsum (x4 (Inj1 0)) x6)) ⟶ x1 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι → ι . x5) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum (Inj1 (setsum 0 0)) (Inj1 x8)) (λ x8 : (ι → ι) → ι . Inj1 (setsum (Inj1 0) 0)) (λ x8 : ι → ι . λ x9 x10 . x10)) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . In (Inj0 0) (setsum (x6 (setsum (setsum 0 0) (Inj1 0)) (λ x8 : ι → ι . x5)) (x6 0 (λ x8 : ι → ι . x5))) ⟶ x0 (λ x8 : ι → ι → ι . 0) (setsum 0 (Inj1 (setsum (Inj0 0) (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . 0) (λ x8 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → ι . Inj1 (setsum (setsum (setsum 0 0) 0) (setsum (Inj0 0) 0))) 0 ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum 0 (x10 (λ x11 . setsum 0 0))) (λ x8 : (ι → ι) → ι . Inj0 (Inj1 (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . λ x9 x10 . setsum (x8 0) x7)) ⟶ False)
Known 29cbb.. : not (∀ x0 : (ι → ι) → ι → ο . ∀ x1 : (((ι → ι → ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ο . ∀ x2 : (((((ι → ι) → ι) → ι → ι) → ι) → ι) → ((ι → ι → ι) → ((ι → ι) → ι) → ι) → ι → ((ι → ι) → ι) → ο . ∀ x3 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ο . (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . In (setsum 0 (setsum (x6 (λ x8 . Inj0 0)) 0)) (setsum (x6 (λ x8 . Inj0 (setsum 0 0))) (Inj0 (setsum (setsum 0 0) (x6 (λ x8 . 0))))) ⟶ x0 (λ x8 . setsum (Inj1 (Inj1 (setsum 0 0))) (x6 (λ x9 . Inj0 x8))) (x4 (Inj1 (Inj1 (Inj0 0))) (setsum 0 (Inj1 (x6 (λ x8 . 0))))) ⟶ x3 (λ x8 . x7) (x5 (λ x8 : ι → ι → ι . λ x9 . setsum 0 (Inj1 (x8 0 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 . setsum (Inj1 x7) (x6 (λ x10 . x10)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 . In (x4 (λ x8 : (ι → ι) → ι . 0)) (Inj1 (setsum (Inj1 0) (setsum (Inj0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . Inj0 0) (Inj0 (Inj0 (x5 0 (λ x8 . 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 . 0) ⟶ x0 (λ x8 . Inj0 (Inj0 (Inj1 x8))) (x6 (λ x8 : (ι → ι) → ι . x5 (setsum 0 0) (setsum (Inj0 0))) (setsum (x4 (λ x8 : (ι → ι) → ι . Inj1 0)) 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 . x3 (λ x8 . Inj1 0) 0 (λ x8 : (ι → ι) → ι → ι . λ x9 . 0) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x8 : ι → ι → ι . λ x9 : (ι → ι) → ι . setsum (x9 (λ x10 . x8 (setsum 0 0) 0)) (setsum 0 0)) (setsum (Inj1 (Inj0 (setsum 0 0))) (Inj0 0)) (λ x8 : ι → ι . x7)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x2 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι . x5) (λ x8 : ι → ι → ι . λ x9 : (ι → ι) → ι . 0) (Inj1 (Inj0 0)) (λ x8 : ι → ι . setsum (setsum (Inj1 (x6 0 0 0)) (setsum x7 (x8 0))) x5) ⟶ x3 (λ x8 . Inj0 (Inj1 (setsum (Inj0 0) (setsum 0 0)))) (x6 0 0 0) (λ x8 : (ι → ι) → ι → ι . λ x9 . Inj0 (Inj1 0))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x8 . setsum (setsum (setsum (Inj1 0) 0) (Inj1 (setsum 0 0))) 0) (setsum (setsum (setsum 0 (setsum 0 0)) (setsum x5 x4)) (Inj1 0)) (λ x8 : (ι → ι) → ι → ι . λ x9 . x7) ⟶ x1 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . Inj1 x7) (λ x8 x9 . setsum x6 0) (λ x8 . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . Inj0 (Inj0 (setsum x7 (setsum 0 0)))) (λ x8 x9 . x7) (λ x8 . 0) ⟶ x3 (λ x8 . 0) 0 (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 (x8 (λ x9 . x7) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 . x5) (Inj0 0) ⟶ x0 (λ x8 . setsum x5 (Inj1 (Inj1 (x6 0)))) (setsum (Inj1 (setsum 0 (Inj1 0))) (setsum (x6 x7) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x8 . setsum (setsum (setsum x8 (x6 0 0 0 0)) x8) (setsum 0 0)) (setsum (x5 (λ x8 : ι → ι . λ x9 x10 . setsum x9 (setsum 0 0)) (λ x8 . x8)) (setsum (x6 (setsum 0 0) (setsum 0 0) (Inj1 0) (x7 0)) (setsum 0 (x6 0 0 0 0)))) ⟶ False) ⟶ False)
Known 91710.. : not (∀ x0 : (ι → ι) → (ι → ι) → ι → ο . ∀ x1 : (ι → ι) → (ι → ι) → (ι → (ι → ι) → ι → ι) → ο . ∀ x2 : (ι → ι) → ((((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) → ο . (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x8 . x7) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x8 (λ x9 : ι → ι . λ x10 . setsum (x8 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . x8 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0) 0) (setsum (setsum 0 0) x10)) (λ x9 . Inj1 0) 0) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum (Inj0 (x6 (λ x9 : (ι → ι) → ι → ι . 0))) (Inj1 0)) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . x8 x7 (λ x11 . setsum (x8 (Inj0 0) (λ x12 . x11)) (Inj1 x11)))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (Inj1 x5) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . Inj1 (setsum (setsum 0 0) 0)) (λ x8 x9 . x9) 0 (setsum 0 x6)) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum x6 x6) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . setsum (setsum (Inj1 (Inj1 0)) 0) (Inj0 (Inj0 x7))) ⟶ x1 (λ x8 . setsum 0 0) (λ x8 . setsum (setsum (setsum (Inj0 0) (Inj1 0)) x5) x7) (λ x8 . λ x9 : ι → ι . λ x10 . 0)) ⟶ (∀ x4 x5 x6 x7 . In (setsum (Inj1 (Inj0 (Inj1 0))) x5) (Inj1 0) ⟶ x2 (λ x8 . setsum (Inj1 0) (Inj1 (setsum 0 (setsum 0 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 . Inj0 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) ⟶ x0 (λ x8 . x8) (λ x8 . 0) (setsum (Inj1 (Inj1 x7)) (setsum (Inj0 (Inj0 0)) (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x8 . Inj0 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 . x8) (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (x9 0))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι → ι . ∀ x7 . In x7 (setsum x7 (x5 (x5 (x6 0 0) (setsum 0 0)) (x5 (x6 0 0) 0))) ⟶ x1 (λ x8 . x7) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . λ x10 . x8) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . setsum x9 x7)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x8 . Inj0 (Inj1 0)) (λ x8 . Inj0 (x7 (λ x9 . setsum 0 (Inj0 0)) (λ x9 : ι → ι . Inj1 0) x8 0)) (Inj0 (setsum 0 (x4 (λ x8 : (ι → ι) → ι . Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . In (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . x8 (setsum (setsum 0 0) (setsum 0 0)) (Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . 0)))) 0 0) (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . x6 (λ x9 : (ι → ι) → ι → ι . setsum 0 0)))) ⟶ x0 (λ x8 . 0) (λ x8 . 0) (Inj0 0) ⟶ x2 (λ x8 . setsum 0 (setsum (Inj1 0) (setsum (Inj0 0) (Inj0 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (setsum (setsum 0 0) 0)) (x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 (x10 0)) (setsum (Inj0 0) (Inj0 0))))) ⟶ False)
Known 05d15.. : not (∀ x0 : ((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) → ((ι → ι) → ι) → (ι → ι) → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ο . ∀ x2 : (ι → ι) → (ι → ι) → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . In (setsum (Inj0 0) 0) (Inj0 (Inj1 x5)) ⟶ x3 (λ x8 . setsum x8 (setsum (setsum (Inj0 0) 0) (setsum 0 x5))) x4) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x8 . setsum (Inj0 (Inj1 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0)))) (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (x5 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 x9) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x9 (λ x11 . setsum 0 (Inj1 0))) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . Inj1 (setsum (setsum (x6 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (λ x10 . 0)) (setsum 0 0)) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj1 (setsum 0 (Inj1 (x4 0 0 (λ x8 . 0) 0)))) (setsum (setsum (Inj0 (Inj1 0)) 0) x5) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (x10 (setsum (x10 0) (setsum 0 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . 0) ⟶ x2 (λ x8 . Inj1 x7) (setsum (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → ι . In (x7 (λ x8 x9 . 0) (λ x8 x9 . Inj1 (setsum (x7 (λ x10 x11 . 0) (λ x10 x11 . 0)) (setsum 0 0)))) (Inj0 0) ⟶ x2 (λ x8 . 0) (λ x8 . 0) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj1 (Inj1 0)) (λ x8 . λ x9 x10 : ι → ι . λ x11 . setsum (Inj1 (Inj1 (setsum 0 0))) (x9 0)) (λ x8 . 0) (Inj1 (x4 (λ x8 . x8)))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 . 0) (λ x8 . 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 0)) (Inj1 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . x11 (Inj1 (Inj0 x10))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . 0) ⟶ x3 (λ x8 . 0) (Inj0 (Inj1 (x5 (λ x8 x9 . 0) (λ x8 : ι → ι . setsum 0 0) (λ x8 . 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . In (Inj0 (Inj1 0)) (x5 (Inj0 (setsum 0 0)) (λ x8 . 0)) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . 0) (λ x8 . λ x9 x10 : ι → ι . λ x11 . setsum (Inj0 (x10 (setsum 0 0))) (Inj0 x11)) (λ x8 . x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (setsum (x7 0) (Inj0 0)) 0) 0 (λ x9 . setsum (setsum (Inj1 0) (setsum 0 0)) (setsum x9 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0) 0 (λ x10 . 0))))) (setsum (setsum 0 (setsum (setsum 0 0) (setsum 0 0))) (Inj0 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj1 x6) (λ x8 . λ x9 x10 : ι → ι . λ x11 . 0) (λ x8 . Inj0 (setsum (Inj1 (setsum 0 0)) 0)) (Inj0 x5) ⟶ x2 (λ x8 . x6) (λ x8 . x7 (λ x9 : ι → ι → ι . setsum (setsum x6 (setsum 0 0)) 0))) ⟶ False)
Known 6993e.. : not (∀ 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 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . In (Inj0 0) x6 ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (setsum (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0))) (setsum 0 0)) x5) (setsum (Inj1 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0)))) (Inj1 0) (λ x8 : ι → ι . x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (Inj0 x5) ⟶ x3 (λ x8 : ι → ι → ι . λ x9 . x8 (Inj0 0) (Inj0 0)) x5 (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι → ι . λ x9 . Inj0 x6) (setsum (setsum (setsum (Inj0 0) (setsum 0 0)) 0) (setsum 0 (x5 (λ x8 . setsum 0 0)))) (λ x8 : (ι → ι) → ι . x8 (λ x9 . Inj1 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 x9 . λ x10 : ι → ι . x7) (λ x8 . setsum (Inj0 (setsum (Inj0 0) 0)) x7)) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x8 x9 . Inj1 0) (λ x8 : ι → ι . setsum 0 (x7 (Inj1 (setsum 0 0)) (λ x9 . Inj1 (setsum 0 0)))) (λ x8 : ι → ι → ι . λ x9 x10 . x7 (Inj0 x9) (λ x11 . x8 (setsum (Inj0 0) (Inj1 0)) x10)) 0 ⟶ x2 (λ x8 x9 . 0) (λ x8 : ι → ι . Inj0 0) (λ x8 : ι → ι → ι . λ x9 x10 . Inj1 (Inj0 (Inj0 (Inj1 0)))) (x7 (x4 (λ x8 x9 . setsum 0 (Inj0 0)) (λ x8 : ι → ι . λ x9 . x6 0 (λ x10 : ι → ι . x7 0 (λ x11 . 0))) (λ x8 . Inj1 0)) (λ x8 . Inj1 (Inj0 (Inj1 0))))) ⟶ (∀ 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 (Inj1 (setsum 0 0)))) ⟶ 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)) (setsum (setsum 0 (Inj1 (setsum 0 0))))) ⟶ (∀ 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)
Known 30bb5.. : not (∀ x0 : ((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) → ο . ∀ x2 : ((ι → ι → ι) → ι → ι → ι → ι) → (ι → ι) → ι → ο . ∀ x3 : (ι → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι) → ι → ι → ο . (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . setsum (setsum (setsum (Inj1 0) (Inj0 0)) (x9 (λ x11 x12 . x10) (λ x11 . Inj1 0))) (x7 (λ x11 : (ι → ι) → ι . x9 (λ x12 x13 . Inj0 0) (λ x12 . 0)))) (setsum (setsum (Inj1 (setsum 0 0)) 0) (Inj1 (Inj1 (setsum 0 0)))) (setsum (setsum (Inj0 (setsum 0 0)) (Inj1 0)) (Inj0 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . setsum 0 (setsum (setsum x8 (Inj0 0)) (Inj1 (setsum 0 0)))) (Inj1 x7) (x5 x4 (λ x8 x9 . x7) (λ x8 . setsum x6 0) (x5 (x5 (setsum 0 0) (λ x8 x9 . Inj1 0) (λ x8 . Inj1 0) (Inj0 0)) (λ x8 x9 . Inj1 (setsum 0 0)) (λ x8 . setsum 0 0) 0)) ⟶ x1 (λ x8 . Inj1 0) (λ x8 : ι → ι → ι → ι . x5 (Inj0 (Inj0 0)) (λ x9 x10 . setsum 0 0) (λ x9 . x6) (setsum (x8 0 x7 (Inj0 0)) (x5 0 (λ x9 x10 . Inj1 0) (λ x9 . Inj1 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : ι → ι → ι . λ x9 x10 x11 . 0) (λ x8 . x7) (x6 (setsum (Inj0 0) (setsum (setsum 0 0) 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . In (Inj0 (Inj1 (setsum (setsum 0 0) (setsum 0 0)))) (setsum 0 0) ⟶ x2 (λ x8 : ι → ι → ι . λ x9 x10 x11 . Inj0 (setsum (Inj0 (Inj0 0)) 0)) (λ x8 . x7 (λ x9 : (ι → ι) → ι . Inj1 (setsum 0 0)) (λ x9 x10 . Inj1 x9)) (setsum x5 0) ⟶ x1 (λ x8 . setsum 0 (x7 (λ x9 : (ι → ι) → ι . x6 (setsum 0 0)) (λ x9 x10 . Inj1 (setsum 0 0)))) (λ x8 : ι → ι → ι → ι . Inj0 (Inj0 (Inj0 (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . In (setsum (setsum (x4 (λ x8 x9 : ι → ι . λ x10 . 0) x5) (setsum (Inj0 0) x6)) 0) (Inj0 (setsum (Inj0 (Inj1 0)) x5)) ⟶ x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . 0) 0 x7 ⟶ x1 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι → ι . x1 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . x6) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x7 (λ x9 . Inj0 (Inj1 0)) (x8 (Inj1 (setsum 0 0)) (λ x9 : ι → ι . λ x10 . 0) (x8 (setsum 0 0) (λ x9 : ι → ι . λ x10 . x9 0) 0)) (x7 (λ x9 . setsum (setsum 0 0) (Inj1 0)) (Inj0 (setsum 0 0)) x6)) (λ x8 x9 . Inj0) (λ x8 : ι → ι → ι . Inj0 (setsum (setsum (Inj1 0) (setsum 0 0)) (setsum (Inj1 0) 0))) (λ x8 : ι → ι . x6) (λ x8 . x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . In (setsum 0 (setsum (setsum (Inj0 0) (setsum 0 0)) 0)) (Inj1 (Inj1 x7)) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) (λ x8 x9 x10 . Inj0 (Inj1 x8)) (λ x8 : ι → ι → ι . 0) (λ x8 : ι → ι . x6 (setsum 0 (Inj1 (x8 0)))) (λ x8 . Inj1 (Inj1 (Inj0 (x5 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x8 (x8 (setsum (Inj1 0) (x8 0 (λ x9 : ι → ι . λ x10 . 0) 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x8 0 (λ x11 : ι → ι . λ x12 . 0) 0)) (setsum 0 0)) (λ x9 : ι → ι . λ x10 . 0) (setsum (Inj1 x6) x6)) (λ x8 x9 x10 . Inj1 (setsum (Inj0 (Inj1 0)) x9)) (λ x8 : ι → ι → ι . 0) (λ x8 : ι → ι . x8 x6) (λ x8 . setsum x8 (Inj1 (setsum x5 (setsum 0 0)))) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x8 0 (λ x9 : ι → ι . λ x10 . Inj0 (setsum 0 0)) (setsum x6 (Inj1 (Inj1 0)))) (λ x8 x9 x10 . 0) (λ x8 : ι → ι → ι . Inj1 (setsum x5 0)) (λ x8 : ι → ι . 0) (λ x8 . setsum 0 0)) ⟶ False)
Known 6c860.. : not (∀ 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)
Known 1b96e.. : not (∀ x0 : ((((ι → ι) → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι) → (ι → ι) → ο . ∀ x1 : (ι → (ι → ι) → ι) → ι → ο . ∀ x2 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → ο . ∀ x3 : (ι → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι) → ο . (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . setsum 0 (x9 (setsum (setsum 0 0) (setsum 0 0)) (Inj1 0) 0)) (λ x8 . x7) ⟶ x3 (λ x8 . Inj0 (x6 (setsum (Inj0 0) (x6 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . x7)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . x3 (λ x8 . setsum (Inj0 0) (Inj0 0)) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . 0) (Inj1 0)) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . In (Inj1 0) (setsum x7 (Inj0 (setsum 0 (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . 0))))) ⟶ x2 (λ x8 . setsum (Inj1 0) (Inj0 0)) (Inj1 (setsum 0 0)) (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 (Inj1 (Inj0 0))) (setsum x6 0)) ⟶ x2 (λ x8 . 0) x7 (λ x8 : (ι → ι) → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . In x7 (Inj1 (setsum (setsum (setsum 0 0) (setsum 0 0)) (x5 (setsum 0 0) (setsum 0 0) (λ x8 . 0) 0))) ⟶ x2 (λ x8 . Inj1 x6) (x5 (Inj0 (setsum x6 0)) x7 (λ x8 . x7) x4) (λ x8 : (ι → ι) → ι → ι . Inj1 x7) ⟶ x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 . x8)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . In (setsum (setsum (x6 (λ x8 : (ι → ι) → ι . λ x9 . setsum 0 0) (setsum 0 0) (λ x8 . setsum 0 0)) (Inj0 (setsum 0 0))) (setsum 0 (Inj0 (Inj1 0)))) (x6 (λ x8 : (ι → ι) → ι . x7) 0 (λ x8 . 0)) ⟶ x1 (λ x8 . λ x9 : ι → ι . x9 0) (Inj1 (setsum (x7 (Inj0 0)) (x7 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 x7 . In (setsum x4 x7) (Inj1 (setsum (setsum (setsum 0 0) 0) x4)) ⟶ x1 (λ x8 . λ x9 : ι → ι . 0) 0 ⟶ x3 (λ x8 . x7) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . setsum 0 x6)) ⟶ (∀ x4 : (ι → ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 . 0) ⟶ x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . Inj0 (setsum x7 x7)) (λ x8 . Inj1 (Inj1 0))) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . x7) (λ x8 . Inj1 0) ⟶ In x7 (x4 (setsum 0 (x4 (Inj0 0))))) ⟶ False)
Known c13a6.. : not (∀ x0 : (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 → ο . ∀ x2 : ((((ι → 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 → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . In (x7 0) x4 ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 (x6 (λ x10 . Inj0 0) (λ x10 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . 0) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (setsum 0 (Inj1 x6)) (Inj1 (Inj1 (x5 (Inj1 0) (λ x8 : ι → ι . λ x9 . 0)))) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) x4 ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (Inj0 0))) 0) 0 (λ x8 . 0) (λ x8 . setsum (Inj0 (Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . 0)))) 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum (setsum 0 0) (Inj0 0)) (setsum (Inj1 0) (setsum 0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x6 0) 0 (λ x8 . 0) (λ x8 . 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 : ((ι → ι) → ι) → ι . x8 (λ x9 : ι → ι . x7)) 0 (λ x8 . Inj0 (x6 (λ x9 . setsum x8 (Inj0 0)) (λ x9 : ι → ι . λ x10 . setsum x7 (setsum 0 0)) (λ x9 . 0) 0)) (λ x8 . setsum x8 (Inj0 0)) ⟶ False) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . x2 (λ x8 : ((ι → ι) → ι) → ι . Inj0 (setsum (x8 (λ x9 : ι → ι . Inj1 0)) 0)) 0 (λ x8 . 0) (λ x8 . Inj1 (Inj0 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 x9 . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj1 (setsum (setsum (x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) 0 0) (setsum 0 0)) (setsum 0 (x8 (λ x10 : ι → ι . 0))))) (λ x8 . Inj0 (setsum (x6 (λ x9 : (ι → ι) → ι . x9 (λ x10 . 0)) (λ x9 . 0) 0 0) (x6 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 . x7 0 (λ x10 x11 . 0) (λ x10 . 0) 0) (x5 0 0) 0))) (λ x8 . setsum (Inj0 (setsum 0 0)) (Inj1 0)) (Inj1 (x5 (x7 (Inj0 0) (λ x8 x9 . setsum 0 0) (λ x8 . setsum 0 0) (x5 0 0)) (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj0 (x6 0)) (λ x8 . 0) (λ x8 . x7) (x6 0) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . 0) 0 (λ x8 . Inj1 (x5 x8 (λ x9 : ι → ι . 0))) (λ x8 . setsum (Inj0 x8) (x6 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj0 x7) (Inj0 x5) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x5) x7 (λ x8 . Inj0 (setsum (Inj1 (setsum 0 0)) 0)) (λ x8 . 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . x9 (λ x12 x13 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj0 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . In (Inj1 0) (Inj1 (setsum 0 0)) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj0 (setsum 0 (setsum (Inj0 0) (x9 (λ x10 x11 . 0))))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj1 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . setsum 0 (x5 (λ x9 . 0)))) ⟶ False)
Known 29cb8.. : not (∀ x0 : ((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 → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ο . ∀ x3 : (ι → (ι → ι) → ι) → ι → ι → ο . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ι . In (Inj1 0) (Inj1 (x7 (λ x8 . setsum (Inj0 0) (Inj1 0)))) ⟶ x1 (λ x8 . Inj1 0) (λ x8 . λ x9 : ι → ι → ι . setsum (setsum (setsum (Inj1 0) 0) 0) (setsum (setsum (setsum 0 0) 0) (setsum 0 (x9 0 0)))) (λ x8 : ι → ι → ι . 0) (Inj0 (Inj0 (setsum 0 (x5 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . x6 (λ x10 : ι → ι . λ x11 . x10 (Inj0 (x9 0)))) (x6 (λ x8 : ι → ι . λ x9 . x6 (λ x10 : ι → ι . λ x11 . setsum (setsum 0 0) (Inj1 0)))) (setsum (Inj0 0) 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ι → ι . setsum (setsum x8 (setsum (Inj1 0) (setsum 0 0))) 0) (x5 (λ x8 : ι → ι → ι . x6 (λ x9 : ι → ι → ι . setsum 0 (setsum 0 0)) x7)) (x5 (λ x8 : ι → ι → ι . Inj0 0)) ⟶ In (Inj0 (setsum (setsum 0 0) (Inj0 (setsum 0 0)))) (Inj0 0)) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (setsum (setsum 0 (setsum (x4 (λ x8 . 0) (λ x8 : ι → ι . 0)) x6)) (setsum (x4 (λ x8 . Inj1 0) (λ x8 : ι → ι . setsum 0 0)) 0)) (Inj1 (Inj1 (setsum (Inj1 0) 0))) ⟶ x3 (λ x8 . λ x9 : ι → ι . 0) (Inj0 (setsum x5 x5)) 0 ⟶ x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι . Inj0 (x8 (λ x9 x10 . 0))) x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . In (setsum (setsum (setsum (x7 (λ x8 . 0) 0) 0) (x7 (λ x8 . Inj1 0) (setsum 0 0))) x6) (Inj0 x6) ⟶ x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι . x5 (λ x9 x10 x11 . setsum (Inj1 x10) (Inj0 (Inj0 0))) (x5 (λ x9 x10 x11 . Inj0 0) 0)) (Inj1 (setsum (setsum x6 (Inj1 0)) (Inj0 (Inj0 0)))) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . x7 (λ x9 . 0) (setsum 0 0)) (setsum (Inj0 0) x6) (λ x8 . setsum (Inj0 (Inj0 (Inj0 0))) (setsum (x5 (λ x9 x10 x11 . Inj1 0) (setsum 0 0)) (setsum 0 0))) (Inj0 x6)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (x5 (Inj1 0) (λ x9 : ι → ι . setsum 0 0) (λ x9 . setsum 0 0)) (x7 (λ x9 : ι → ι . setsum 0 0))) (setsum (setsum 0 (setsum 0 0)) (setsum (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (x8 0 0 (λ x9 . 0) 0)))) x6 (λ x8 . Inj1 (Inj1 (x5 (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (λ x9 : ι → ι . x8) (λ x9 . Inj1 0)))) 0 ⟶ x1 (λ x8 . setsum (setsum 0 0) 0) (λ x8 . λ x9 : ι → ι → ι . x9 x8 (x9 (Inj1 (setsum 0 0)) (Inj1 (x9 0 0)))) (λ x8 : ι → ι → ι . x6) (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x8 . x7 (λ x9 : (ι → ι) → ι → ι . Inj1 (x7 (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0)))) (λ x8 . λ x9 : ι → ι → ι . Inj0 0) (λ x8 : ι → ι → ι . Inj1 (setsum 0 x6)) (setsum 0 (setsum (Inj1 0) 0)) ⟶ In (setsum 0 (setsum 0 (Inj1 (setsum 0 0)))) (Inj0 (setsum (Inj1 (Inj1 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . x7) (λ x8 : ι → ι → ι . x5 (setsum x7 (setsum (Inj1 0) 0))) x7 ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj0 (setsum (setsum x6 x6) x7)) 0 (λ x8 . x8) (Inj0 x7)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (Inj1 (x5 0)) 0) (x6 (λ x9 : ι → ι . λ x10 . Inj0 0))) (Inj1 x7) (λ x8 . x6 (λ x9 : ι → ι . λ x10 . x9 0)) x7 ⟶ In (x6 (λ x8 : ι → ι . λ x9 . setsum (Inj0 (Inj0 0)) (Inj0 (x8 0)))) (Inj1 (setsum (x4 (setsum 0 0)) (setsum (x6 (λ x8 : ι → ι . λ x9 . 0)) (Inj0 0))))) ⟶ False)
Known ee98d.. : not (∀ x0 : ((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 → ι → ι) → ο . ∀ x2 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (((ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ο . ∀ x3 : (ι → ι) → (ι → ι → ι → ι → ι) → ο . (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 . Inj0 (setsum (Inj0 0) x5)) (λ x8 x9 x10 x11 . x10) ⟶ x3 (λ x8 . Inj1 (Inj0 (Inj1 (Inj1 0)))) (λ x8 x9 x10 x11 . x11)) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . In (x6 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (Inj1 (x9 0)))) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0)) ⟶ x3 (λ x8 . Inj1 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0))) (λ x8 x9 x10 x11 . 0) ⟶ x3 (λ x8 . 0) (λ x8 x9 x10 x11 . x11)) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 x7) (λ x8 : (ι → ι) → ι → ι → ι . λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj0 0) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x9 (setsum 0 0)) (λ x8 : (ι → ι) → ι → ι → ι . λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x9 (λ x12 . x9 (λ x13 . 0) (x10 (setsum 0 0))) (setsum (Inj0 (x9 (λ x12 . 0) 0)) (setsum (setsum 0 0) x11))) ⟶ x3 (λ x8 . x7 0) (λ x8 x9 x10 x11 . x8)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . 0) (λ x8 : (ι → ι) → ι . setsum (setsum x7 x5) (setsum (Inj1 x5) 0)) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum 0 (Inj1 (Inj1 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : ι → ι → ι . x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum (setsum (Inj0 (Inj0 0)) (setsum (Inj0 0) 0)) x10) ⟶ False) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . x9 (Inj0 (Inj0 x10)) (x9 x10 0 (setsum (Inj0 0) (setsum 0 0))) x10) (λ x8 : (ι → ι) → ι . x6) ⟶ x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . x9 0 (setsum (setsum (Inj1 0) (Inj1 0)) 0) (setsum (setsum 0 0) (Inj1 (setsum 0 0)))) (λ x8 : (ι → ι) → ι . setsum (setsum x5 (Inj0 0)) (Inj1 x7))) ⟶ (∀ x4 : ((ι → ι) → ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → ι . In (Inj1 (x5 (λ x8 . 0) (setsum (setsum 0 0) x6) (setsum (Inj1 0) (x5 (λ x8 . 0) 0 0)))) (Inj1 (Inj0 0)) ⟶ x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . 0) (λ x8 : (ι → ι) → ι . setsum (setsum 0 (x5 (λ x9 . 0) (Inj0 0) 0)) (x8 (λ x9 . x8 (λ x10 . 0)))) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . x8 (setsum (Inj1 (setsum 0 0)) 0) (λ x12 x13 . setsum (Inj1 x12) (setsum 0 (Inj1 0)))) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum 0 (setsum (Inj1 (setsum 0 0)) (setsum (setsum 0 0) x11)))) ⟶ False)
Known 536b2.. : not (∀ x0 : (((((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 → 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) → (ι → ι) → ι → ι) → ι → ι) → ι → ι → ο . (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 . x2 (λ x8 . 0) (x6 (λ x8 . λ x9 : ι → ι . Inj1 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 x9 : ι → ι . λ x10 . x7) (λ x8 : ι → ι . λ x9 . Inj1 (Inj0 (setsum (setsum 0 0) 0))) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum x7 0) (setsum (setsum (Inj0 (setsum 0 0)) x5) (Inj0 0)) (setsum 0 x4)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → ι) → ι → (ι → ι) → ι . x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj1 (x7 (λ x11 : ι → ι . setsum (setsum 0 0) (x11 0)) (setsum (setsum 0 0) (setsum 0 0)) (λ x11 . x9 (λ x12 x13 . Inj0 0) (λ x12 . Inj1 0) 0))) (setsum 0 (Inj0 (Inj0 (setsum 0 0)))) (Inj1 x6) ⟶ In (setsum (Inj1 x6) x4) (Inj1 x5)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι → ι . In (Inj1 x5) (setsum 0 (Inj1 (x7 (λ x8 . Inj1 0) (λ x8 x9 . setsum 0 0) 0 0))) ⟶ x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . 0) (Inj0 0) (λ x8 . λ x9 : ι → ι . setsum 0 (x7 (λ x10 . x10) (λ x10 x11 . x11) (Inj0 (x6 (λ x10 : (ι → ι) → ι → ι . 0))) (Inj0 0))) ⟶ x2 (λ x8 . x8) 0 (λ x8 x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x7 Inj1 (λ x10 x11 . x11) (x8 (setsum (x6 (λ x10 : (ι → ι) → ι → ι . 0)) x9)) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . In (Inj0 0) (setsum (Inj1 0) (Inj0 (setsum (Inj1 0) x4))) ⟶ x2 (λ x8 . 0) 0 (λ x8 x9 : ι → ι . λ x10 . Inj0 (Inj0 (Inj0 (Inj1 0)))) (λ x8 : ι → ι . λ x9 . setsum x6 (setsum (x7 (λ x10 . 0) (setsum 0 0) (λ x10 . setsum 0 0) (Inj0 0)) 0)) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (setsum (x9 (λ x11 x12 . 0) (λ x11 . x8 (λ x12 : ι → ι → ι . λ x13 : ι → ι . 0)) (Inj1 0)) (setsum (setsum 0 0) 0)) (x9 (λ x11 x12 . x10) (λ x11 . Inj1 (setsum 0 0)) (Inj1 (Inj0 0)))) (setsum (x7 (λ x8 . Inj1 (x7 (λ x9 . 0) 0 (λ x9 . 0) 0)) x5 (λ x8 . Inj1 0) (Inj1 (Inj1 0))) x6) 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . In (Inj0 (Inj1 (setsum 0 (Inj0 0)))) (Inj1 (setsum (setsum (setsum 0 0) 0) (x7 (λ x8 . x7 (λ x9 . 0) (λ x9 : ι → ι . λ x10 . 0)) (λ x8 : ι → ι . λ x9 . Inj0 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) 0) (x7 (λ x11 . x10) (λ x11 : ι → ι . λ x12 . x9 (λ x13 x14 . 0) (λ x13 . setsum 0 0) (setsum 0 0)))) (Inj1 (Inj1 (setsum (Inj0 0) (setsum 0 0)))) (Inj0 x4) ⟶ x1 (λ x8 . Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . x10))) (λ x8 : ((ι → ι) → ι → ι) → ι . Inj0 (Inj1 (setsum (setsum 0 0) (Inj1 0)))) (λ x8 x9 . Inj0 (x7 (λ x10 . setsum (setsum 0 0) (Inj0 0)) (λ x10 : ι → ι . λ x11 . Inj1 (x10 0)))) (x7 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . setsum (x6 (λ x10 . 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x8 . 0) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . Inj1 (setsum x6 x8)) 0 ⟶ In (Inj1 (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) (Inj0 (setsum (Inj1 x6) (x4 (λ x8 . 0))))) ⟶ (∀ x4 x5 x6 x7 . In x7 (setsum (Inj0 (setsum 0 (setsum 0 0))) x6) ⟶ x2 (λ x8 . Inj0 (setsum (Inj0 x8) (setsum (setsum 0 0) 0))) (Inj0 (setsum x5 0)) (λ x8 x9 : ι → ι . λ x10 . Inj0 (Inj1 (setsum (setsum 0 0) x7))) (λ x8 : ι → ι . λ x9 . Inj1 (setsum 0 (setsum 0 (setsum 0 0)))) ⟶ x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . Inj0 x7) (Inj1 x5) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . setsum (setsum (setsum 0 (Inj0 0)) 0) (Inj1 (Inj1 (setsum 0 0)))) (setsum (Inj1 (setsum x5 0)) x7) (λ x8 . λ x9 : ι → ι . setsum (Inj1 (setsum (x6 (λ x10 : (ι → ι) → ι → ι . 0)) x8)) x7) ⟶ x1 (setsum (Inj1 (Inj1 x7))) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . setsum x9 (setsum (Inj1 (setsum 0 0)) x9)) (Inj0 (x6 (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 0) 0)))) ⟶ False)
Known 57e52.. : not (∀ x0 : (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) → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → (ι → ι) → ι) → ι) → (ι → ι) → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 0) (λ x8 . setsum (x7 (setsum 0 x8)) (Inj0 0)) (λ x8 . x8) (x7 (setsum 0 (Inj0 0))) ⟶ x3 (λ x8 . setsum x6 (Inj1 0)) (Inj0 (setsum (x7 0) (setsum (Inj1 0) (Inj1 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x8 0) (λ x8 . 0) 0) (Inj1 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . Inj1 0) 0 ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 (setsum 0 x9)) (λ x8 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 (setsum 0 (Inj1 0)))) (λ x8 . x8) (Inj1 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0)) (λ x8 : ι → ι . λ x9 . Inj0 0) (λ x8 . 0) x6))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 . setsum (setsum x6 x6) x7) (Inj1 0) ⟶ x2 (λ x8 . setsum 0 0) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . setsum x6 (setsum 0 (x5 0))) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . setsum 0 (x7 (setsum (Inj1 0) (Inj0 0)))) ⟶ In (setsum (Inj0 (x5 x4)) 0) (Inj1 (Inj1 (setsum 0 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . In (Inj0 (Inj1 (x5 (λ x8 x9 . 0)))) (x5 (λ x8 x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x11 0) (Inj0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x8 : ι → ι . Inj0 (x5 (λ x9 x10 . x9))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj0 x10) (λ x8 : ι → ι . Inj1 (Inj0 (x5 (λ x9 x10 . x8 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . In (x5 (Inj1 (setsum (setsum 0 0) (x4 0))) (x7 (λ x8 . setsum (Inj0 0) (x5 0 0)) (λ x8 x9 . Inj1 (setsum 0 0)))) x6 ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj1 (x9 x10 (λ x13 . 0) (setsum 0 0)))) (λ x8 : ι → ι . Inj0 0) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . x8) (λ x8 . x5 (x7 (λ x9 . x9) (λ x9 x10 . x8)) (setsum 0 (x7 (λ x9 . Inj0 0) (λ x9 x10 . setsum 0 0)))) 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . In (x7 (λ x8 : (ι → ι) → ι . 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : (ι → ι) → ι . setsum (Inj1 0) 0)) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . 0) (λ x8 . Inj1 (setsum (setsum (setsum 0 0) (x5 0 0 (λ x9 . 0))) (Inj1 (x7 (λ x9 : (ι → ι) → ι . 0))))) (setsum 0 (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . λ x10 : ι → ι → ι . setsum x9 (Inj0 (x10 (setsum 0 0) 0))) (λ x8 . x5 (λ x9 : ι → ι . setsum (Inj1 0) (setsum (setsum 0 0) 0)) (λ x9 x10 . 0) (Inj1 (setsum (setsum 0 0) (x6 0))) 0) (λ x8 . 0) (Inj0 (x5 (λ x8 : ι → ι . 0) (λ x8 x9 . Inj0 0) (setsum 0 (x4 (λ x8 . 0))) (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum x12 (Inj1 x12)) (λ x8 : ι → ι . Inj0 (setsum (Inj0 0) 0))) ⟶ False)
Known ead0e.. : not (∀ x0 : (ι → ι → ι) → ((ι → ι) → ((ι → ι) → ι) → ι) → ο . ∀ x1 : ((ι → ι) → ι → ι → ι) → ι → ο . ∀ x2 : (ι → (ι → (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) → (ι → ι) → ι) → ι → ι) → ι → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 (Inj1 (Inj1 (Inj0 0)))) 0 ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . Inj0 (x6 (λ x10 . setsum (setsum 0 0) 0))) (Inj0 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . x9) (setsum 0 (setsum (setsum (Inj0 0) 0) (x5 (λ x8 . x5 (λ x9 . 0) (λ x9 x10 . 0)) (λ x8 x9 . 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . x9) (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . x8) (setsum (Inj1 0) (setsum (setsum (setsum 0 0) 0) (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . λ x9 . setsum (x8 (Inj0 (Inj0 0))) (Inj1 (Inj1 (setsum 0 0)))) (Inj0 (Inj1 (setsum (setsum 0 0) x4))) ⟶ x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . 0) (setsum (x7 (setsum x4 (Inj1 0))) x4) (λ x8 : ι → ι . λ x9 . x9) (Inj1 (setsum 0 (Inj0 (x7 0))))) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . setsum (setsum x8 (x9 (Inj1 0) (λ x12 . x11) 0)) 0) (Inj1 (setsum (x4 (λ x8 . 0) (λ x8 . x8)) 0)) (λ x8 : ι → ι . λ x9 . setsum (setsum (x7 (Inj1 0)) (x7 (Inj0 0))) (Inj1 (x8 0))) (x5 (λ x8 . Inj1 0)) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . 0) (Inj0 (Inj1 (setsum 0 (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . 0) 0 (λ x8 : ι → ι . λ x9 . 0) (setsum 0 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 0) (x7 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . setsum (Inj0 0) 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 . In (Inj0 x4) (setsum 0 (x6 (λ x8 . setsum (Inj0 0) (setsum 0 0)) (setsum x4 (Inj1 0)) 0)) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . x10) 0 ⟶ x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . setsum 0 x8) (x6 (λ x8 . setsum (setsum x8 x8) 0) 0 (setsum x4 (Inj0 x5))) (λ x8 : ι → ι . λ x9 . Inj1 0) (setsum 0 (Inj1 x7))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . In (x6 0 (λ x8 : ι → ι . Inj0 0)) x7 ⟶ x0 (λ x8 x9 . setsum x9 x9) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . x9 (λ x10 . setsum (Inj1 (Inj1 0)) 0)) ⟶ x0 (λ x8 x9 . setsum x9 (setsum (Inj0 (setsum 0 0)) (Inj1 (x6 0 (λ x10 : ι → ι . 0))))) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 x9 . Inj0 0) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . Inj0 0) ⟶ In (Inj1 (setsum 0 (x4 (λ x8 : ι → ι . x6) (λ x8 . x5 0)))) x7) ⟶ False)
Known bc887.. : not (∀ x0 : (ι → ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ο . ∀ x1 : (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 → ο . (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . In (Inj0 x6) (setsum (setsum 0 0) (setsum x6 (Inj0 (setsum 0 0)))) ⟶ x2 (λ x8 . Inj0 (Inj0 0)) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . x10) (setsum (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 (setsum 0 0))) 0) ⟶ x3 (λ x8 . λ x9 : ι → ι → ι . Inj0 x8) x5 (setsum (setsum (setsum 0 (setsum 0 0)) (Inj0 0)) 0)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : ι → ι → ι . 0) x7 (setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (Inj0 0))) (setsum 0 (Inj1 (setsum 0 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι → ι . x7) (setsum (x4 (λ x8 : (ι → ι) → ι → ι . x7)) x6) (Inj0 (Inj1 (setsum (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . In (Inj0 0) (setsum 0 (x5 (Inj0 (setsum 0 0)) (λ x8 : ι → ι . λ x9 . Inj0 0))) ⟶ x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . x8) x7 (x6 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj1 0) (λ x8 x9 . 0)) ⟶ x2 (λ x8 . x8) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . x10) (setsum (Inj0 0) (x6 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 0) (λ x8 x9 . x9)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In (Inj0 (Inj1 0)) (setsum (setsum (Inj0 0) (setsum (setsum 0 0) (setsum 0 0))) (setsum 0 (setsum (Inj0 0) (x4 0 0)))) ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . 0) (setsum (setsum 0 (setsum (setsum 0 0) (Inj0 0))) (Inj1 x6)) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . Inj0 0) (x4 0 (x5 (setsum (Inj1 0) 0)))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ι → ι → ι . 0) 0 0 ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . x9 (λ x10 . setsum (Inj1 (Inj0 0)) (setsum 0 0))) 0) ⟶ (∀ x4 x5 x6 x7 . In (Inj0 x6) (setsum (setsum x4 (setsum x5 (setsum 0 0))) (Inj1 (setsum x5 0))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . x7) 0 ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . setsum 0 0) x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (Inj1 0) x5 ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . 0) 0 ⟶ x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . Inj1 0) (Inj1 (Inj1 (x4 (λ x8 : (ι → ι) → ι → ι . 0)))) (Inj1 (setsum (setsum (Inj0 0) 0) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . 0) (x4 0) x7 ⟶ False) ⟶ False)
Known 1cb9d.. : not (∀ x0 : (((((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) → ι → ι) → ο . ∀ x2 : (ι → ι) → (ι → ι) → (ι → (ι → ι) → ι) → ο . ∀ x3 : (ι → (ι → (ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . x2 (λ x8 . setsum x5 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . setsum 0 x8) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . x7) x5 (Inj0 0) (Inj1 (Inj0 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 . 0) x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . setsum x8 (Inj0 0)) 0 (setsum 0 0) 0 (λ x8 . Inj1 (Inj0 (Inj0 (setsum 0 0)))) (setsum (setsum (x5 (λ x8 x9 x10 . x10) (setsum 0 0) 0) 0) (setsum (x5 (λ x8 x9 x10 . Inj0 0) 0 0) 0)) ⟶ In (x5 (λ x8 x9 x10 . Inj1 (Inj0 (setsum 0 0))) (Inj1 (x7 (λ x8 : (ι → ι) → ι → ι . x6 (λ x9 . 0)) (setsum 0 0) (x7 (λ x8 : (ι → ι) → ι → ι . 0) 0 0))) (x7 (λ x8 : (ι → ι) → ι → ι . 0) (x5 (λ x8 x9 x10 . 0) 0 (Inj0 0)) (Inj1 x4))) (Inj1 (Inj0 (Inj0 x4)))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . 0) (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 0) (λ x8 : ι → ι . setsum (x8 0) 0) (setsum (setsum 0 0)) (setsum (x4 0) (Inj1 0))) (Inj1 (setsum (setsum 0 0) x5))) ⟶ x2 (λ x8 . Inj1 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x8 . 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . x8) ⟶ x2 (λ x8 . Inj0 (Inj0 (x6 (setsum 0 0)))) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj0 (x4 (Inj1 (Inj1 0)) (λ x8 x9 . x6 0 (λ x10 : ι → ι . λ x11 . Inj1 0)) (setsum 0 (Inj1 0)) 0)) (x7 (setsum (x7 (setsum 0 0) (λ x8 : ι → ι . λ x9 . setsum 0 0)) (setsum (x4 0 (λ x8 x9 . 0) 0 0) (Inj0 0))) (λ x8 : ι → ι . λ x9 . setsum (Inj0 (Inj1 0)) 0)) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . x7 0 (λ x9 : ι → ι . λ x10 . Inj0 (Inj1 0))) (setsum (x7 (setsum (setsum 0 0) (x4 0 (λ x8 x9 . 0) 0 0)) (λ x8 : ι → ι . λ x9 . x6 0 (λ x10 : ι → ι . λ x11 . setsum 0 0))) x5) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . setsum (Inj1 (Inj1 0)) (Inj1 (Inj1 0))) (λ x8 x9 x10 x11 . 0) (λ x8 . λ x9 : ι → ι . λ x10 . setsum (setsum (Inj0 0) 0) (Inj1 (Inj1 x10)))) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . x6 (Inj1 (setsum (Inj0 0) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . 0) 0 0))) (setsum (Inj0 (setsum 0 0)) (setsum (Inj0 0) 0))) (λ x8 x9 x10 x11 . x8) (λ x8 . λ x9 : ι → ι . λ x10 . 0) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . Inj0) (Inj0 (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum (Inj0 0) (Inj1 0)) (λ x8 : ι → ι . λ x9 . Inj1 0) 0 (Inj0 0))) (setsum (setsum (x6 (Inj0 0) (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0))) 0) (x6 0 (Inj1 (Inj1 0)))) (Inj0 (Inj1 (setsum (x6 0 0) (Inj0 0)))) (λ x8 . x8) (setsum (setsum 0 (Inj0 (setsum 0 0))) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (λ x8 : ι → ι . λ x9 . Inj0 (Inj0 0)) (Inj1 (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0))) (setsum (setsum 0 0) (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0)))))) ⟶ (∀ x4 : ((ι → ι) → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . In (setsum (setsum 0 (Inj0 (Inj0 0))) (x4 (λ x8 : ι → ι . λ x9 x10 . Inj0 (Inj0 0)))) (x4 (λ x8 : ι → ι . λ x9 x10 . 0)) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . Inj0 (setsum x8 x7)) (Inj0 x7) (Inj0 (setsum x7 0)) (Inj0 (setsum (Inj1 0) (setsum x5 x7))) (λ x8 . x8) 0 ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . x5) (setsum (Inj0 0) (Inj0 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x6 x7 . In (Inj0 (Inj1 (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 x10 . Inj1 0)))) (Inj1 (x4 (Inj1 0) (setsum (setsum 0 0) 0))) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . 0) (Inj1 x7) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . setsum x7 0) (λ x8 x9 x10 x11 . setsum (Inj0 x9) x9) (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (setsum (x9 0) 0))) ⟶ False)
Known 44176.. : not (∀ x0 : (ι → ι) → ((ι → ι) → ι → ι → ι) → ι → ο . ∀ x1 : (ι → ((ι → ι → ι) → ι) → ι) → (ι → ι → ι → ι) → ο . ∀ x2 : (ι → ι → ι) → ι → ο . ∀ x3 : (((ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι) → ι) → ι → ι → ο . (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 x7 . In x6 (setsum x6 (Inj1 (Inj1 (Inj1 0)))) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . setsum (Inj0 0) 0) x4 (Inj0 0)) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In (Inj1 (setsum (setsum (setsum 0 0) (setsum 0 0)) x7)) (Inj0 (setsum (x6 x7) x7)) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . Inj1 (setsum 0 0)) 0 (Inj0 (Inj0 (setsum (setsum 0 0) (Inj0 0)))) ⟶ x2 (λ x8 x9 . 0) (setsum (Inj0 0) (setsum (x6 0) (x6 (x4 (λ x8 x9 . 0) 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . In (x5 0 Inj1) (Inj1 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (Inj1 0)) (λ x8 . 0) (setsum 0 0) 0)) ⟶ x2 (λ x8 x9 . Inj1 (setsum (x6 (λ x10 . λ x11 : ι → ι . Inj1 0) (λ x10 x11 . 0)) (x6 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 . x9)))) (setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) (setsum (Inj1 0) (Inj1 0))) 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 x9 . setsum x9 (Inj1 (setsum (setsum 0 0) 0))) (setsum (x4 (setsum (Inj1 0) (setsum 0 0)) (λ x8 . Inj0 x5)) (setsum (x4 (Inj1 0) (λ x8 . Inj0 0)) (Inj1 0))) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . Inj0 (x8 (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) 0 (Inj1 (Inj1 0)))) (setsum (setsum (Inj0 (setsum 0 0)) x7) x5) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . In (Inj0 (x7 (λ x8 . 0) 0)) (Inj1 (Inj0 x4)) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . In (setsum 0 (setsum (x7 0) x5)) (Inj1 0) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 0) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 x8)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . In (x4 (Inj0 (Inj1 x5)) (λ x8 : ι → ι . setsum (x7 (λ x9 . x8 0)) (x8 (setsum 0 0))) (λ x8 . 0)) (setsum (Inj1 x6) x6) ⟶ x2 (λ x8 . Inj1) (x7 (λ x8 . x7 (λ x9 . 0))) ⟶ x0 (λ x8 . 0) (λ x8 : ι → ι . λ x9 x10 . setsum (setsum (Inj0 x9) (Inj1 (Inj1 0))) (Inj0 (setsum (Inj0 0) (x8 0)))) (setsum x5 (setsum (setsum 0 (Inj1 0)) (x4 0 (λ x8 : ι → ι . Inj0 0) (λ x8 . x6))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . setsum 0) x6 ⟶ x0 (λ x8 . x7) (λ x8 : ι → ι . λ x9 x10 . x7) (setsum (Inj0 (Inj1 (x4 (λ x8 : (ι → ι) → ι . 0) (λ x8 . 0)))) (x4 (λ x8 : (ι → ι) → ι . 0) Inj1))) ⟶ False)
Known c6930.. : not (∀ x0 : (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) → ο . ∀ x2 : (ι → 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 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (setsum x5 (Inj0 x6)) (setsum 0 (x4 (λ x8 : ι → ι → ι . Inj0 (Inj0 0)))) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → (ι → ι) → ι → ι . 0) (setsum 0 (Inj0 (setsum x6 (Inj0 0)))) ⟶ x3 (λ x8 : ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x7) (λ x8 : (ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x3 (λ x8 : ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x9) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . Inj1 x6) ⟶ In (Inj0 0) (setsum (setsum x6 (setsum x5 0)) (Inj0 (setsum x6 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . In (x4 (λ x8 : ι → ι → ι . x7 (λ x9 x10 x11 . x10) 0)) (Inj1 (x7 (λ x8 x9 x10 . 0) (setsum 0 (Inj0 0)))) ⟶ x1 (λ x8 . Inj1 (Inj1 0)) (λ x8 : ι → ι → ι → ι . setsum 0 (Inj1 (setsum (setsum 0 0) (x8 0 0 0)))) (λ x8 . setsum (x7 (λ x9 x10 x11 . 0) (Inj1 x8)) (Inj1 x8)) (λ x8 : ι → ι . 0) (λ x8 . x5) ⟶ x2 (λ x8 . setsum (setsum 0 (Inj0 x5)) (Inj1 0)) (λ x8 . λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . 0))) (Inj0 (x4 (λ x8 : ι → ι → ι . 0))) (setsum 0 0) (setsum (x7 (λ x8 x9 x10 . setsum (Inj0 0) (setsum 0 0)) (x6 (λ x8 : ι → ι → ι . setsum 0 0) (λ x8 x9 . x7 (λ x10 x11 x12 . 0) 0) (setsum 0 0))) (x4 (λ x8 : ι → ι → ι . x7 (λ x9 x10 x11 . setsum 0 0) (x6 (λ x9 : ι → ι → ι . 0) (λ x9 x10 . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . In (Inj0 (Inj1 (setsum (x4 0) (setsum 0 0)))) (Inj0 0) ⟶ x2 (λ x8 . Inj0 (x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) 0) 0 (x6 (Inj1 0)) 0)) (λ x8 . λ x9 : (ι → ι) → ι . 0) (Inj1 (x4 (Inj0 0))) (x6 (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (Inj1 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 0 0) 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (setsum 0 0) (x6 0) 0))) (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 0) (x4 (x6 0)) (setsum (Inj1 0) (Inj1 0)) 0) (Inj0 (x4 0))) ⟶ x2 (λ x8 . setsum 0 (Inj0 (x6 (setsum 0 0)))) (λ x8 . λ x9 : (ι → ι) → ι . x8) (Inj0 (x6 (setsum 0 (setsum 0 0)))) (Inj0 x5) (Inj0 (setsum x5 (x4 (x4 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x1 (λ x8 . Inj0 (setsum (Inj1 (Inj1 0)) x8)) (λ x8 : ι → ι → ι → ι . Inj1 (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) 0 0 0)) (λ x8 . setsum 0 (Inj1 (Inj1 x7))) (λ x8 : ι → ι . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x8 . x5 (Inj1 (setsum 0 (Inj1 0))) (λ x9 . setsum (setsum (Inj1 0) x9) x8)) (λ x8 : ι → ι → ι → ι . Inj0 (Inj0 (Inj0 (x7 0)))) (λ x8 . Inj1 (Inj0 (setsum (Inj0 0) (x6 0 0)))) (λ x8 : ι → ι . x6 (setsum (x6 0 (setsum 0 0)) (x6 (Inj0 0) (x8 0))) (Inj0 (setsum (setsum 0 0) (Inj0 0)))) (λ x8 . 0) ⟶ x1 (λ x8 . x6 (Inj1 (x5 0 (λ x9 . x8))) 0) (λ x8 : ι → ι → ι → ι . setsum (Inj0 (Inj0 (Inj1 0))) 0) (λ x8 . Inj0 (setsum (setsum (Inj0 0) (x7 0)) 0)) (λ x8 : ι → ι . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . In x7 x4 ⟶ x0 (λ x8 . Inj0) (λ x8 : ι → (ι → ι) → ι → ι . Inj0 (setsum x7 0)) (Inj0 (x5 (Inj0 x7) (λ x8 x9 . 0) (λ x8 . 0))) ⟶ x0 (λ x8 x9 . Inj0 x8) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 x6) (setsum (setsum 0 (Inj1 x6)) (setsum (Inj1 0) (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . ∀ x6 x7 . x0 (λ x8 x9 . setsum x7 x6) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 (x8 x7 (λ x9 . setsum x6 (x8 0 (λ x10 . 0) 0)) 0)) (Inj0 (x4 (x4 (Inj1 0)))) ⟶ In (Inj1 (setsum (x4 (setsum 0 0)) (x4 (setsum 0 0)))) (Inj1 (Inj0 0))) ⟶ False)
Known 002b6.. : not (∀ x0 : ((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 → 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) → ι) → ι) → ο . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 0) (Inj1 (setsum (Inj0 0) (x5 0 (Inj0 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum x7 (setsum (x6 (setsum 0 0)) 0)) (λ x8 : (ι → ι) → ι . setsum (x8 (λ x9 . 0)) (Inj1 (Inj0 (Inj0 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . setsum 0 x7) (setsum (Inj1 0) (setsum (Inj0 0) (Inj1 (Inj1 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 . In (Inj1 (setsum 0 (setsum 0 0))) (Inj1 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x8 (Inj0 (setsum 0 0)) (x9 (setsum 0 0)))) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . setsum (setsum (setsum (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (setsum 0 0)) (Inj1 (setsum 0 0))) (x9 (λ x11 . setsum (Inj1 0) (x8 (λ x12 . λ x13 : ι → ι . 0))) (λ x11 . 0))) (x4 (λ x8 x9 : ι → ι . λ x10 . x8 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) 0 ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x6 x7 . In (Inj0 (x4 (λ x8 x9 x10 . 0))) (Inj0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 x7) 0 ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj1 (x9 x8)) (λ x8 : ι → ι . Inj1 (setsum (x8 (setsum 0 0)) (Inj0 (Inj0 0)))) (λ x8 . Inj1 (Inj0 0)) (λ x8 x9 . 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (x10 (λ x12 . 0) x8)) (λ x8 : ι → ι . setsum x7 (setsum (setsum 0 (setsum 0 0)) x7)) (λ x8 . 0) (λ x8 x9 . 0) ⟶ In (Inj1 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 0) x4 (λ x8 . setsum 0 0) x7) (Inj0 0))) (setsum (setsum x7 (setsum 0 (setsum 0 0))) (setsum (setsum (setsum 0 0) x4) x6))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In x7 (setsum 0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 (setsum 0 (Inj0 0))) (x6 (setsum (setsum (x6 0) 0) (x6 (Inj1 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 0) (x6 (Inj0 (setsum (setsum 0 0) 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (Inj0 (Inj1 0)) x5 ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . x8 x9) (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0)) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . 0) 0) ⟶ False)
Known 751ed.. : not (∀ x0 : (((((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 → ο . ∀ x3 : (ι → ι) → ι → ι → ο . (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 : (ι → ι → ι) → ι . In (setsum (setsum (setsum (x4 0) (setsum 0 0)) (Inj0 0)) (setsum (x6 (λ x8 x9 . Inj1 0)) 0)) (Inj1 (setsum (setsum (Inj1 0) (setsum 0 0)) 0)) ⟶ x3 (λ x8 . 0) 0 (setsum (setsum (x7 (λ x8 x9 . setsum 0 0)) 0) (Inj1 (Inj1 (Inj0 0)))) ⟶ x3 (λ x8 . setsum (Inj1 (setsum (x7 (λ x9 x10 . 0)) (setsum 0 0))) (Inj1 (setsum 0 (x5 (λ x9 : (ι → ι) → ι . 0))))) (x4 (x7 (λ x8 x9 . setsum 0 (Inj1 0)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . In (Inj0 0) x7 ⟶ x3 (λ x8 . Inj0 0) 0 x6 ⟶ x3 (λ x8 . 0) (setsum 0 0) (Inj0 (Inj1 0))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . 0) (λ x8 : ι → (ι → ι) → ι . setsum x7) ⟶ x2 (λ x8 . 0) (x4 (λ x8 x9 : ι → ι . Inj1 (Inj0 0)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . In (setsum x4 (setsum (Inj0 (setsum 0 0)) (setsum 0 x7))) (Inj1 0) ⟶ x2 (λ x8 . Inj1 (Inj1 0)) (setsum 0 x7) ⟶ x2 (λ x8 . x7) (Inj0 (Inj1 0))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 . In (Inj1 (setsum (Inj1 0) (Inj1 (x6 (λ x8 : ι → ι . 0))))) (Inj0 (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x2 (λ x8 . Inj0 (x6 (λ x9 : ι → ι . setsum (Inj0 0) 0))) x5 ⟶ x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . Inj0 (Inj0 (x6 (λ x10 : ι → ι . x7)))) (λ x8 : ι → (ι → ι) → ι . λ x9 . setsum 0 (setsum (setsum (Inj1 0) x9) (Inj0 x7)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . setsum (setsum 0 (setsum x9 0)) 0) (λ x8 : ι → (ι → ι) → ι . setsum 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . setsum (Inj0 0) x6) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . x7) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . x6 (λ x10 : ι → ι → ι . λ x11 x12 . setsum 0 (setsum (Inj0 0) (setsum 0 0))) (λ x10 x11 . setsum x9 (x8 (λ x12 : ι → ι . setsum 0 0) (λ x12 . Inj0 0) x9)) x9 (setsum (Inj0 0) (Inj0 (setsum 0 0)))) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . setsum (x6 (λ x10 : ι → ι → ι . λ x11 x12 . setsum x12 0) (λ x10 x11 . x10) x7 (Inj0 (setsum 0 0))) 0) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) 0)) (setsum (Inj1 (setsum 0 0)) (Inj1 (setsum 0 0))))) ⟶ False)
Known a3378.. : not (∀ x0 : (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 → ι) → ι → ο . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι . In (Inj1 (setsum x4 (Inj0 (Inj0 0)))) x4 ⟶ x0 (λ x8 . 0) (λ x8 . Inj1 (Inj1 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 . setsum (setsum 0 x8) (setsum (Inj1 (Inj0 0)) (Inj0 0))) (setsum (Inj1 (Inj0 (Inj1 0))) x4) 0 ⟶ x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . x5) (λ x8 : ((ι → ι) → ι) → ι → ι . x6 (Inj1 (x6 0))) x5 (λ x8 . x8) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . Inj0 0) (λ x8 : ((ι → ι) → ι) → ι → ι . x7) (Inj1 (setsum (Inj1 (Inj1 0)) (setsum (Inj0 0) x5))) (λ x8 . 0) (setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 x7)) ⟶ In (Inj0 x4) x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . In (setsum (Inj1 (Inj0 (x7 (λ x8 : (ι → ι) → ι → ι . 0)))) 0) (Inj1 (Inj1 0)) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) (Inj1 0) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x6 (λ x9 x10 . 0) (λ x9 : ι → ι . λ x10 . Inj1 (Inj0 (Inj0 0)))) (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x5) (Inj0 x5)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι . setsum (Inj0 (setsum (Inj1 0) (setsum 0 0))) (setsum (x7 (λ x9 : (ι → ι) → ι . setsum 0 0)) (setsum 0 0))) (x5 (λ x8 . Inj1 (setsum (Inj0 0) (Inj0 0))) (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj1 0))) (λ x8 . 0) (Inj0 (Inj0 (Inj0 0)))) Inj1 (setsum (Inj1 (x5 (λ x8 . x8) (setsum 0 0) (λ x8 . 0) 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . 0))))) ⟶ x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . 0) (λ x8 x9 x10 . x9)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) (λ x8 x9 x10 . setsum x9 (Inj0 (setsum x8 x8))) ⟶ In (setsum (x6 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . Inj0 (setsum 0 0)) x4) (setsum 0 (Inj1 0))) (Inj1 x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 . In (setsum (setsum 0 0) 0) (x5 0 0 (λ x8 . setsum (Inj0 (Inj1 0)) 0)) ⟶ x0 (λ x8 . x6) (λ x8 . 0) (λ x8 . 0) x7 x7 ⟶ x0 (λ x8 . Inj0 0) (λ x8 . Inj1 0) (λ x8 . setsum 0 (x5 0 (setsum (setsum 0 0) (Inj1 0)) (λ x9 . x8))) 0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . In (setsum (x5 (Inj1 0)) 0) (setsum (Inj0 x7) (Inj1 (setsum x7 (setsum 0 0)))) ⟶ x0 (λ x8 . Inj1 0) (λ x8 . 0) (λ x8 . Inj1 (x5 0)) (x5 (Inj1 0)) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . setsum 0 (setsum (setsum 0 0) (setsum (Inj0 0) (setsum 0 0)))) (x5 (setsum 0 x4))) ⟶ False)
Known 619f0.. : not (∀ x0 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ο . ∀ x1 : (ι → ι) → (ι → ι) → ο . ∀ x2 : ((((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι → ι → ι → ι) → ι → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . x3 (λ x8 . 0) 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (x7 x4) (Inj0 0) ⟶ x3 (λ x8 . x7 x6) (setsum (x7 (setsum (setsum 0 0) x6)) 0) ⟶ x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (x8 (λ x12 x13 : ι → ι . Inj0 0) x10 (λ x12 . 0) (Inj0 (setsum 0 0))) (setsum (setsum (Inj0 0) (Inj0 0)) (Inj1 x11))) (setsum (setsum (Inj0 (setsum 0 0)) (setsum (x5 (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 . 0)) (setsum 0 0))) (setsum (x5 (λ x8 : (ι → ι) → ι . Inj1 0) (λ x8 : ι → ι . λ x9 . x9)) (Inj1 (Inj1 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . Inj1 (Inj0 x9)) (setsum (Inj1 (Inj0 (setsum 0 0))) (Inj1 (setsum (Inj0 0) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . In (Inj0 (setsum (x7 0 (λ x8 : ι → ι . λ x9 . 0) (setsum 0 0) (x6 0)) (x6 (setsum 0 0)))) (Inj0 (Inj1 0)) ⟶ x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . 0) (setsum (x6 (Inj1 (x6 0))) (Inj0 (x7 (setsum 0 0) (λ x8 : ι → ι . λ x9 . 0) x4 (x7 0 (λ x8 : ι → ι . λ x9 . 0) 0 0)))) ⟶ x3 (λ x8 . setsum (setsum (x6 (Inj1 0)) (x6 x5)) (x7 (setsum (Inj0 0) (x7 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)) (λ x9 : ι → ι . λ x10 . Inj0 0) (Inj0 (x7 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)) (x7 x8 (λ x9 : ι → ι . λ x10 . setsum 0 0) 0 (Inj1 0)))) (Inj0 x4)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . In (Inj1 (Inj0 0)) (setsum (x4 (setsum (Inj1 0) (setsum 0 0)) (λ x8 x9 . x8) (setsum (Inj1 0) (x4 0 (λ x8 x9 . 0) 0 0)) x6) (setsum (x4 (Inj1 0) (λ x8 x9 . Inj1 0) (setsum 0 0) 0) (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x0 (λ x8 . Inj1 x6) (λ x8 : ι → ι → ι → ι . 0) ⟶ x1 (λ x8 . Inj1 (setsum 0 (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0))))) (λ x8 . setsum (x5 (λ x9 x10 . x10)) (setsum 0 (Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . In (x7 (setsum 0 0) (λ x8 x9 . Inj1 (Inj1 0))) (setsum (Inj1 x4) (x6 (λ x8 : ι → ι . λ x9 x10 . setsum x9 0) (setsum (setsum 0 0) (x6 (λ x8 : ι → ι . λ x9 x10 . 0) 0 0)) (x6 (λ x8 : ι → ι . λ x9 x10 . Inj0 0) x4 0))) ⟶ x1 (λ x8 . setsum 0 (setsum 0 (Inj1 0))) (λ x8 . setsum (x5 0 (λ x9 : ι → ι . λ x10 . 0)) (setsum (setsum 0 (setsum 0 0)) (Inj0 (Inj1 0)))) ⟶ x1 (λ x8 . Inj1 (x6 (λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 0) (x9 0)) (Inj0 (Inj0 0)) (Inj0 (x5 0 (λ x9 : ι → ι . λ x10 . 0))))) (λ x8 . 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x7 : ι → ι → ι → ι . In x4 (x7 0 (Inj1 (setsum (Inj0 0) (Inj0 0))) x5) ⟶ x0 (λ x8 . setsum x8 (setsum x8 0)) (λ x8 : ι → ι → ι → ι . 0) ⟶ x0 (λ x8 . x7 (setsum 0 0) (setsum x8 0) (Inj1 0)) (λ x8 : ι → ι → ι → ι . 0)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 . setsum (setsum 0 0) 0) (λ x8 : ι → ι → ι → ι . setsum (setsum 0 0) (setsum (Inj1 0) 0)) ⟶ x3 (λ x8 . 0) (Inj0 (setsum (Inj0 0) (Inj1 (setsum 0 0))))) ⟶ False)
Theorem e82b5.. : (∀ x0 : (((((ι → ι) → ι) → ι → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ο . ∀ x1 : (ι → 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 → ο . (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (setsum (x4 (Inj1 0) (λ x8 x9 . setsum (setsum 0 0) (setsum 0 0)) x5 0) (setsum (x4 (Inj0 0) (λ x8 x9 . 0) (setsum 0 0) 0) (setsum (Inj1 0) 0))) (Inj1 (setsum x6 0)) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . setsum 0 (setsum (x9 (Inj1 0) (x9 0 0)) x7)) (x4 (setsum (x4 (setsum 0 0) (λ x8 x9 . setsum 0 0) x5 (setsum 0 0)) x7) (λ x8 x9 . x9) (setsum (Inj1 (x4 0 (λ x8 x9 . 0) 0 0)) (Inj1 (Inj1 0))) 0) ⟶ x3 (λ x8 x9 . x9) (setsum x5 0) (Inj1 0) x6) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . In (Inj1 0) (setsum 0 0) ⟶ x3 (λ x8 x9 . 0) (setsum 0 (setsum 0 (Inj1 0))) 0 (Inj1 0) ⟶ x1 (λ x8 . setsum (setsum (Inj0 (x5 0 (λ x9 . 0))) x8) 0) (λ x8 : ((ι → ι) → ι) → ι . Inj1 0) (Inj1 (setsum (Inj1 (setsum 0 0)) (x5 0 (λ x8 . 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι . In (Inj1 (x4 (setsum (x6 (λ x8 . 0) 0) (setsum 0 0)))) (setsum (x4 (setsum (Inj0 0) 0)) (x4 0)) ⟶ x2 (λ x8 x9 . x7 (λ x10 . 0)) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 x10 . setsum (Inj0 0) 0)) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 . In (setsum 0 (setsum (setsum (Inj0 0) 0) (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 0) (λ x8 x9 . 0) (λ x8 . x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 x10 . 0) (λ x9 . 0))))) (Inj1 (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . setsum x10 0) (λ x8 x9 . x8) (λ x8 . Inj1 (Inj1 0)))) ⟶ x2 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 x10 . Inj1 (Inj0 0)) ⟶ x1 (λ x8 . Inj1 0) (λ x8 : ((ι → ι) → ι) → ι . setsum (setsum (setsum (setsum 0 0) (Inj1 0)) (setsum 0 x7)) 0) (setsum (setsum (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0) (x6 0 (λ x8 : ι → ι . 0) 0 0) 0) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0) (setsum 0 0) (setsum 0 0))) (setsum 0 (x6 x7 (λ x8 : ι → ι . setsum 0 0) (setsum 0 0) (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x8 x9 . x8) 0 (Inj1 0) (setsum 0 0) ⟶ x1 (λ x8 . setsum (Inj0 x8) (setsum 0 (setsum 0 (setsum 0 0)))) (λ x8 : ((ι → ι) → ι) → ι . 0) 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x1 (λ x8 . x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) 0)) (λ x8 : ((ι → ι) → ι) → ι . Inj1 0) (x5 0) ⟶ x1 (λ x8 . setsum (x5 0) (Inj0 0)) (λ x8 : ((ι → ι) → ι) → ι . Inj0 0) (setsum (setsum 0 0) (Inj0 (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . x9 0 0) (Inj1 (setsum 0 (x6 (λ x8 : ι → ι → ι . λ x9 . Inj0 0) (λ x8 : ι → ι . λ x9 . x9))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj1 (setsum (x7 (x4 0) (λ x8 : ι → ι . λ x9 . setsum 0 0)) 0)) (Inj0 0) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι . setsum 0 (x7 (x6 (setsum 0 0) (λ x10 : ι → ι . λ x11 . Inj1 0) (λ x10 . setsum 0 0)) (λ x10 : ι → ι . λ x11 . setsum (x10 0) 0))) (Inj1 (setsum (x4 (Inj1 0)) (Inj0 0))) ⟶ x3 (λ x8 x9 . setsum (setsum (x6 (setsum 0 0) (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . x10)) (Inj1 0)) (Inj0 0)) 0 0 (x7 0 (λ x8 : ι → ι . λ x9 . x9))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 6da2e.. : (∀ x0 : ((((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) → 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) → ι) → ι) → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In (Inj1 (setsum (setsum (Inj0 0) (x5 0)) (x5 0))) (Inj1 (Inj0 (x5 (x7 0)))) ⟶ x3 (λ x8 . setsum (setsum (Inj0 (Inj1 0)) (Inj1 (setsum 0 0))) x6) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . setsum 0 (x8 (λ x10 : ι → ι . λ x11 . setsum (setsum 0 0) 0) (x7 (x7 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . x3 (λ x8 . Inj0 (setsum (setsum (Inj0 0) x8) (x6 (λ x9 x10 x11 . x11) (λ x9 . 0) (λ x9 . 0) (Inj0 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . x8 (λ x10 : ι → ι . λ x11 . x10 (Inj1 0)) (Inj0 0)) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . λ x9 . x9) (λ x8 . setsum (setsum 0 0) 0) x4 (λ x8 : ι → ι . λ x9 . 0) 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι) → ι → ι → ι . ∀ x7 . x3 (λ x8 . setsum (Inj1 0) (Inj1 (x5 0 (setsum 0 0) (λ x9 . x6 (λ x10 . 0) (λ x10 . 0) 0 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . x8 (λ x11 : ι → ι . λ x12 . Inj1 0) (x8 (λ x11 : ι → ι . λ x12 . 0) 0)))) ⟶ x2 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . 0) 0 (Inj0 (setsum (Inj1 (x5 0 0 (λ x8 . 0))) (x4 (λ x8 : ι → ι → ι . λ x9 x10 . Inj0 0)))) (λ x8 . 0) 0) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x6 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x7 . In x7 (Inj0 (x5 (λ x8 x9 : ι → ι . λ x10 . Inj1 (setsum 0 0)) (Inj0 0) (x6 0 (λ x8 x9 . setsum 0 0) (x4 0 (λ x8 . 0) 0 0) 0) x7)) ⟶ x2 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . setsum (setsum x8 (x9 (λ x10 x11 . Inj1 0) (λ x10 . setsum 0 0))) (setsum x8 (Inj0 (x9 (λ x10 x11 . 0) (λ x10 . 0))))) 0 0 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 (x9 0)) (x6 (Inj1 0) (λ x8 x9 . setsum 0 0) (setsum 0 0) (Inj1 0)) (Inj1 (setsum 0 0)) (setsum (Inj1 0) 0))) 0 ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum 0 (Inj0 (setsum (Inj0 0) (setsum 0 0)))) (λ x8 x9 x10 . x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x7 : ι → ι . In (Inj0 (setsum (Inj1 (x7 0)) 0)) (setsum (setsum 0 (setsum (Inj0 0) (x5 (λ x8 : (ι → ι) → ι → ι . 0)))) (Inj1 (Inj1 0))) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . Inj1 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 x9 x10 . x8) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . x8 (λ x9 . λ x10 : ι → ι . 0) (x7 0)) (λ x8 . 0) 0 (λ x8 : ι → ι . λ x9 . x7 (Inj0 (Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . 0) 0)))) (setsum (Inj1 0) (setsum (Inj1 (Inj0 0)) (setsum (x7 0) (Inj0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι . In x5 (setsum x6 (setsum 0 0)) ⟶ x1 (λ x8 : (ι → (ι → ι) → ι) → ι → ι → ι . λ x9 . x9) (λ x8 . Inj1 (Inj1 x8)) 0 (λ x8 : ι → ι . λ x9 . Inj0 (x8 x9)) x5 ⟶ x3 (λ x8 . Inj1 (setsum x6 (setsum 0 x8))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . Inj0 (setsum (Inj1 (x9 (λ x10 . 0))) (x7 (x7 0 0 0) (Inj1 0) (Inj1 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum x6 (Inj1 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 x9 x10 . Inj1 (Inj0 0)) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 (Inj1 (Inj1 (Inj1 0))))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6 0 0 (λ x9 . 0) 0) (λ x8 x9 x10 . 0) ⟶ x0 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6 (x8 (λ x9 : ι → ι → ι . λ x10 x11 . x9 (x8 (λ x12 : ι → ι → ι . λ x13 x14 . 0)) (setsum 0 0))) (setsum 0 (setsum (Inj0 0) 0)) (λ x9 . setsum 0 (setsum (x6 0 0 (λ x10 . 0) 0) 0)) (setsum (Inj1 (setsum 0 0)) (x8 (λ x9 : ι → ι → ι . λ x10 x11 . 0)))) (λ x8 x9 x10 . x10)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 436a3.. : (∀ x0 : ((ι → ι → ι → ι) → ι → ι → ι) → ι → ο . ∀ x1 : ((ι → ι) → ι) → (ι → ι) → ι → ο . ∀ x2 : (ι → ι) → ι → ο . ∀ x3 : (ι → ι → ι → ι → ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ο . (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . In (setsum 0 (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . setsum 0 0) 0) (λ x8 . 0) (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . 0))))) (setsum (x7 (λ x8 . λ x9 : ι → ι . x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 . Inj1 0) (x6 (λ x10 : (ι → ι) → ι → ι . 0))) (λ x8 . Inj1 (setsum 0 0)) 0) (setsum (x6 (λ x8 : (ι → ι) → ι → ι . 0)) (setsum (setsum 0 0) (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj0 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . x8 (x6 (λ x10 : (ι → ι) → ι → ι . 0)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . In (Inj1 (setsum (x5 (λ x8 x9 x10 . Inj0 0) (setsum 0 0) (setsum 0 0)) (setsum x6 (x7 (λ x8 . 0))))) x6 ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum (Inj1 0) x12)) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj1 (Inj1 (Inj0 (Inj1 0)))) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 (setsum 0 (setsum (Inj0 0) 0))) (λ x8 : ι → ι . λ x9 : ι → ι → ι . Inj0 (Inj0 (x9 (x7 (λ x10 . 0)) (x7 (λ x10 . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . In (Inj0 x7) (setsum 0 0) ⟶ x2 (λ x8 . 0) x6 ⟶ x2 (λ x8 . 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . x6) x4 ⟶ In x5 (Inj1 0)) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (x5 (λ x8 : ι → ι → ι . 0)) (x5 (λ x8 : ι → ι → ι . Inj0 (x8 (Inj1 0) (setsum 0 0)))) ⟶ x1 (λ x8 : ι → ι . Inj0 0) (λ x8 . 0) (x5 (λ x8 : ι → ι → ι . 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : ι → ι . x6 (λ x9 . x7) (Inj1 (Inj0 (Inj1 0)))) (λ x8 . setsum (x6 (λ x9 . setsum x9 0) (Inj1 (Inj1 0))) 0) (setsum 0 (Inj1 0)) ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . setsum x7 (setsum x10 (x8 (setsum 0 0) 0 (setsum 0 0)))) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) 0 ⟶ x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . 0) (Inj1 x7)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 : ι → ι → ι → ι . λ x9 x10 . x10) (Inj0 0) ⟶ x3 (λ x8 x9 x10 x11 x12 . Inj1 0) (λ x8 : ι → ι . λ x9 : ι → ι → ι . 0)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 08f46.. : (∀ x0 : (((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) → ο . ∀ x2 : (ι → ι) → (ι → ι → ι) → ο . ∀ x3 : (((ι → ι) → ι) → ι → ι) → ((ι → ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . In (Inj1 (x5 0)) (Inj0 (Inj1 (Inj1 (setsum 0 0)))) ⟶ x2 (λ x8 . x7 (λ x9 . setsum (setsum (setsum 0 0) 0) (x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0))) (λ x9 : ι → ι . λ x10 . setsum 0 (x7 (λ x11 . Inj0 0) (λ x11 : ι → ι . λ x12 . 0)))) (λ x8 x9 . 0) ⟶ x3 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x8 (λ x10 . setsum (setsum 0 0) (Inj0 0))) 0) (λ x8 : ι → ι → ι . Inj0 0) (λ x8 : (ι → ι) → ι . 0) (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x7 (setsum x9 (Inj1 0))) (Inj0 (setsum 0 (Inj1 0)))) (λ x8 : ι → ι → ι . 0) (λ x8 : (ι → ι) → ι . setsum x6 (setsum (x8 (λ x9 . Inj0 0)) (x7 0))) (setsum (setsum (x7 0) x5) (Inj1 (setsum (Inj1 0) (setsum 0 0)))) ⟶ In (Inj0 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 x7 . In (Inj1 x7) (Inj0 (Inj0 x5)) ⟶ x3 (λ x8 : (ι → ι) → ι . λ x9 . Inj0 (setsum (setsum (Inj0 0) 0) (setsum 0 (x8 (λ x10 . 0))))) (λ x8 : ι → ι → ι . 0) (λ x8 : (ι → ι) → ι . x6) (Inj0 0) ⟶ x2 (λ x8 . Inj0 x6) (λ x8 x9 . setsum (setsum 0 0) x6)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 . 0) (λ x8 x9 . 0) ⟶ In (Inj0 x6) (setsum x6 (Inj1 (Inj0 (Inj0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . In (Inj0 0) (Inj1 (setsum x6 0)) ⟶ x2 (λ x8 . Inj0 0) (λ x8 x9 . setsum (x7 (setsum 0 0)) 0) ⟶ x1 (λ x8 x9 . 0) (λ x8 : ι → ι . x6)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x8 x9 . setsum (setsum 0 (setsum (Inj1 0) x7)) (Inj1 (setsum x6 x6))) (λ x8 : ι → ι . 0) ⟶ x1 (λ x8 x9 . x6) (λ x8 : ι → ι . x7)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 . 0) (λ x8 x9 . Inj1 0) ⟶ x0 (λ x8 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) (x7 (setsum (Inj0 (setsum 0 0)) (setsum (setsum 0 0) (Inj0 0))) (Inj1 (setsum 0 (setsum 0 0)))) (setsum 0 (setsum (x4 (setsum 0 0) 0 (λ x8 . setsum 0 0) (setsum 0 0)) (setsum (x7 0 0) (Inj1 0)))) (λ x8 : ι → ι . λ x9 . setsum x9 (Inj0 x9))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . 0) x6 x5 (λ x8 : ι → ι . λ x9 . setsum (Inj1 (setsum (Inj1 0) x9)) (Inj0 x9)) ⟶ x2 (λ x8 . Inj0 (x7 0)) (λ x8 x9 . x6)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 4f3f6.. : (∀ x0 : (ι → ι) → ι → ο . ∀ x1 : (ι → (ι → ι) → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι) → ο . ∀ x2 : (ι → ι) → ι → ι → ι → ο . ∀ x3 : (((ι → ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι → ι) → ι → ι) → ι → ο . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . In (Inj1 (setsum (Inj0 (setsum 0 0)) x4)) (Inj1 (x7 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . Inj1 (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (x5 (setsum (Inj1 (Inj1 0)) 0))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum (x8 (λ x12 x13 x14 . Inj1 (Inj1 0)) (λ x12 . Inj0 0) (x10 (x10 0 0) 0)) (Inj1 0)) x7 ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → ι → ι . x2 (λ x8 . x7 (λ x9 : ι → ι . 0) (Inj0 (setsum 0 0))) 0 (Inj1 0) (Inj0 (setsum (x5 (Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : ι → ι . 0) 0)) (x6 x4))) ⟶ x2 (λ x8 . Inj0 0) (setsum x4 (Inj0 (x5 0 (λ x8 : ι → ι . setsum 0 0)))) x4 0) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . 0) (Inj0 (Inj1 x4)) (Inj0 (setsum (Inj0 0) 0)) (setsum (setsum x4 0) 0) ⟶ In x7 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι → ι . x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . setsum 0 (Inj0 (Inj1 (x10 0 0)))) (Inj1 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) (λ x8 : ι → (ι → ι) → ι . x5 0 (setsum (Inj0 (setsum 0 0)) 0) (λ x9 . x6) (x8 (setsum (Inj1 0) 0) (λ x9 . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ False) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . In (Inj1 (Inj0 (setsum 0 (x6 (λ x8 x9 x10 . 0))))) (Inj0 (setsum x4 0)) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) x7 ⟶ x0 (λ x8 . Inj0 (Inj0 (setsum (x5 0) (Inj1 0)))) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . In (Inj1 0) x4 ⟶ x0 (λ x8 . setsum 0 (Inj0 (x6 (λ x9 : ι → ι . λ x10 . 0)))) (setsum x7 x7) ⟶ x3 (λ x8 : (ι → ι → ι → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) (Inj1 (Inj1 x5))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem db1af.. : (∀ x0 : (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 → ο . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι → ι → ι) → ι) → ι → ο . ∀ x3 : (ι → ι) → ((ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι) → ο . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ι → ι . In (Inj1 (Inj1 x4)) x4 ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . 0) (setsum (x7 0 x4) (Inj0 (setsum (Inj0 0) 0))) (λ x8 : (ι → ι) → ι → ι . setsum (Inj0 (setsum x5 x5)) (Inj1 0)) ⟶ x3 (λ x8 . x6 (λ x9 : (ι → ι) → ι . setsum (Inj1 (setsum 0 0)) (x7 (Inj1 0) 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum (Inj1 (setsum x7 (Inj1 0))) 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) (setsum (setsum (x5 (λ x8 : (ι → ι) → ι . setsum 0 0)) (Inj0 (Inj1 0))) (x4 (Inj1 (setsum 0 0)) (Inj0 0))) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . Inj0 x8) (Inj1 (setsum x7 (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . Inj0 (setsum (Inj1 (setsum 0 0)) x6)) (Inj0 (Inj0 (Inj1 (Inj1 0)))) ⟶ x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . In (setsum 0 (setsum (setsum (x5 (λ x8 . λ x9 : ι → ι . λ x10 . 0)) (setsum 0 0)) (Inj1 (Inj0 0)))) (Inj0 (setsum (Inj0 (Inj0 0)) 0)) ⟶ x3 (λ x8 . setsum 0 (Inj0 (Inj1 (Inj0 0)))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . 0) ⟶ x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . setsum (Inj1 0) (Inj1 0)) (setsum 0 (setsum 0 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x8 : ((ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 x10 . 0) (setsum (x7 (x5 0 (λ x8 x9 . 0))) (setsum x6 x6)) ⟶ In (Inj1 (setsum (Inj0 (setsum 0 0)) (setsum (Inj1 0) (setsum 0 0)))) (x4 (λ x8 x9 . setsum (setsum x6 0) (Inj0 (x7 0))) (setsum 0 0) (λ x8 . 0) (setsum (x7 (setsum 0 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x8 . x7) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . setsum 0 (Inj0 (setsum (x8 0 (λ x11 . 0) 0) 0))) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . x8) (setsum (setsum (Inj0 0) x4) 0) (λ x8 : (ι → ι) → ι → ι . Inj1 (setsum 0 (x6 (x5 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . Inj0 0) (setsum 0 (x7 (λ x8 : (ι → ι) → ι → ι . setsum (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (Inj1 0)))) (λ x8 : (ι → ι) → ι → ι . x5) ⟶ False) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem e07c2.. : (∀ x0 : (ι → ι) → ι → ι → ο . ∀ x1 : ((ι → ι) → ι) → ((ι → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ο . ∀ x2 : (ι → ι) → ((((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → 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 → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι → ο . (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 . 0) (setsum 0 (Inj1 (setsum x7 (setsum 0 0)))) (setsum (x4 (x6 (Inj0 0) (setsum 0 0)) (λ x8 x9 . x9)) (setsum 0 x7)) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . 0) (λ x8 : ι → ι → ι → ι . 0) (λ x8 x9 x10 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 0)) (setsum (Inj0 (setsum (Inj1 0) (Inj1 0))) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . In x7 (Inj1 (Inj1 (Inj0 x6))) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . 0) (λ x8 : ι → ι → ι → ι . setsum (Inj1 (Inj1 (setsum 0 0))) 0) (λ x8 x9 x10 . setsum 0 (Inj0 (Inj1 (Inj0 0)))) 0 ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . Inj1 (setsum (Inj1 (x8 0 (λ x10 . 0))) 0)) (λ x8 : ι → ι → ι → ι . setsum (Inj1 0) (setsum 0 0)) (λ x8 x9 x10 . x9) (x4 (λ x8 : ι → ι → ι . setsum x7 (setsum (Inj0 0) (x8 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x8 . setsum (Inj1 0) (Inj1 0)) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . Inj0 (Inj0 (setsum 0 0))) 0) (λ x8 : (ι → ι) → ι . λ x9 x10 . Inj0 (Inj1 0)) (Inj1 (Inj0 (setsum 0 0))) (λ x8 . setsum (Inj1 0) (setsum 0 (setsum (Inj0 0) x5))) 0 ⟶ x2 (λ x8 . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . setsum (setsum x10 0) (setsum (Inj1 (Inj1 0)) (setsum (x8 (λ x12 : ι → ι . 0)) x10))) (λ x8 : (ι → ι) → ι . λ x9 x10 . Inj1 (x8 (λ x11 . setsum (setsum 0 0) (Inj0 0)))) (setsum (Inj1 (Inj0 x6)) (Inj1 (setsum 0 (Inj1 0)))) (λ x8 . Inj1 (Inj0 (setsum (Inj0 0) (Inj0 0)))) (setsum x7 (Inj1 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . In x7 (Inj0 0) ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x10) (λ x8 : (ι → ι) → ι . λ x9 x10 . 0) (Inj1 (setsum x7 (setsum (Inj0 0) 0))) (λ x8 . x8) (setsum (Inj1 (x4 (Inj0 0))) (Inj1 x7)) ⟶ x2 Inj0 (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x8 (λ x12 : ι → ι . 0)) (λ x8 : (ι → ι) → ι . λ x9 x10 . setsum x7 0) (setsum (setsum 0 0) 0) (λ x8 . Inj0 (Inj0 x5)) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (setsum (Inj0 (Inj0 (Inj1 0))) (setsum 0 x5)) (x4 (setsum (setsum x5 (setsum 0 0)) (Inj1 x5))) ⟶ x2 (λ x8 . setsum (x7 (λ x9 x10 x11 . 0)) x5) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 . x8 (λ x11 . setsum x10 0)) (setsum 0 (setsum (Inj1 0) (Inj0 x5))) (λ x8 . x7 (λ x9 x10 x11 . setsum (setsum (setsum 0 0) (Inj1 0)) (Inj0 (Inj1 0)))) (Inj1 (Inj1 0)) ⟶ x1 (λ x8 : ι → ι . 0) (λ x8 : ι → ι → ι → ι . Inj1 0) (λ x8 x9 x10 . x10)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x8 : ι → ι . Inj1 (setsum (x7 (λ x9 . λ x10 : ι → ι . 0)) (setsum 0 0))) (λ x8 : ι → ι → ι → ι . x6 (λ x9 x10 . x9) (λ x9 : ι → ι . λ x10 . x8 0 (x8 (setsum 0 0) (Inj1 0) (Inj0 0)) 0) (λ x9 . Inj1 (Inj0 0))) (λ x8 x9 x10 . x9) ⟶ x0 (λ x8 . setsum 0 (Inj1 (setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0))))) 0 (setsum (setsum (setsum (x6 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0)) 0) (setsum 0 (setsum 0 0))) (x6 (λ x8 x9 . x7 (λ x10 . λ x11 : ι → ι . Inj1 0)) (λ x8 : ι → ι . λ x9 . x8 (setsum 0 0)) (λ x8 . setsum 0 (x7 (λ x9 . λ x10 : ι → ι . 0)))))) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x7 . x0 (λ x8 . 0) (setsum (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . 0) (Inj0 0) 0)) x7) (setsum (x4 (λ x8 x9 x10 . Inj0 (setsum 0 0))) 0) ⟶ x0 (λ x8 . setsum (setsum (Inj1 (Inj0 0)) (setsum (Inj0 0) 0)) (x5 0 (Inj0 (setsum 0 0)))) (Inj1 (Inj1 (x5 (x6 (λ x8 : (ι → ι) → ι → ι . 0) 0 0) (Inj0 0)))) (Inj1 (Inj1 (Inj1 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x8 . x5) 0 (setsum 0 x5) ⟶ False) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 84b22.. : (∀ 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 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι . In (x7 (setsum 0 0) (λ x8 . 0) (setsum (setsum (setsum 0 0) (Inj0 0)))) (x7 (setsum (setsum (x4 0) (setsum 0 0)) (x4 (Inj0 0))) (λ x8 . setsum 0 (setsum (setsum 0 0) (setsum 0 0))) (λ x8 . 0)) ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 x12 . setsum (x9 (λ x13 : ι → ι . x13 (x13 0))) (setsum 0 (x9 (λ x13 : ι → ι . 0)))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι . x7 0 (λ x11 . setsum (setsum (setsum 0 0) (Inj0 0)) (Inj1 (setsum 0 0))) (λ x11 . setsum (x8 (setsum 0 0) (λ x12 . 0) (x8 0 (λ x12 . 0) 0)) (Inj0 0))) (Inj1 (Inj0 (setsum (Inj1 0) 0))) ⟶ x3 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 (setsum (setsum (setsum 0 0) x9) 0)) (λ x8 x9 x10 x11 . x8) (λ x8 : ι → ι → ι . λ x9 . 0)) ⟶ (∀ 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 (setsum (setsum x11 (Inj0 0)) x10)) (λ x8 : ι → ι → ι . λ x9 . x8 0 (Inj0 0)) ⟶ 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) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 286ff.. : (∀ x0 : (ι → ι) → ι → ο . ∀ x1 x2 : ((ι → ι) → ι) → ι → ι → ο . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → ι → (((ι → ι) → ι) → ι → ι) → ο . (∀ x4 x5 x6 x7 . In (setsum (setsum (setsum (Inj1 0) 0) (Inj0 (Inj0 0))) (setsum (setsum 0 0) (Inj0 (setsum 0 0)))) (setsum (setsum (setsum (setsum 0 0) x4) x7) 0) ⟶ x1 (λ x8 : ι → ι . setsum (setsum (Inj0 x5) (Inj0 0)) 0) (Inj0 (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (Inj0 0)))) (setsum (Inj0 (setsum 0 (Inj1 0))) 0) ⟶ x3 (λ x8 . λ x9 : (ι → ι) → ι . x9 (λ x10 . x8)) x5 (λ x8 : (ι → ι) → ι . λ x9 . Inj0 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x8 . λ x9 : (ι → ι) → ι . setsum (x9 (λ x10 . setsum (setsum 0 0) x8)) 0) 0 (λ x8 : (ι → ι) → ι . λ x9 . setsum (x8 (λ x10 . x8 (λ x11 . setsum 0 0))) 0) ⟶ False) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι . x0 (λ x8 . 0) (x6 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x2 (λ x8 : ι → ι . setsum (setsum (x8 0) 0) (x7 (λ x9 . 0) (λ x9 x10 . setsum (Inj0 0) 0) (x6 (Inj0 0)))) 0 (x7 (λ x8 . Inj1 (x5 0 (λ x9 . 0))) (λ x8 x9 . x8) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 : ι → ι . x6) (setsum (setsum x4 x7) (setsum 0 0)) (Inj0 0) ⟶ x0 (λ x8 . Inj0 (x5 0 (λ x9 : ι → ι . λ x10 . Inj1 (Inj0 0)) (λ x9 . 0))) (setsum x6 (Inj0 (Inj0 (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 . 0) (Inj1 x4) ⟶ x1 (λ x8 : ι → ι . setsum 0 (Inj0 (Inj1 (Inj1 0)))) x4 (setsum 0 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . x1 (λ x8 : ι → ι . setsum 0 x5) (setsum (Inj1 0) (setsum (Inj0 (setsum 0 0)) 0)) (Inj1 (x7 (λ x8 : (ι → ι) → ι . x6 (Inj0 0) (λ x9 . Inj1 0)) (Inj1 (Inj0 0)) (Inj0 (setsum 0 0)) 0)) ⟶ In (Inj0 (Inj0 (x7 (λ x8 : (ι → ι) → ι . x8 (λ x9 . 0)) x5 (Inj1 0) (Inj0 0)))) (x4 x5)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . In (setsum x7 (setsum 0 0)) (Inj0 x7) ⟶ x0 (λ x8 . x8) (Inj1 0) ⟶ x0 (λ x8 . x6 0 (setsum 0 (Inj0 0))) (setsum (setsum (Inj1 x5) 0) (setsum (x6 0 x4) (setsum (Inj1 0) (x6 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . x0 (λ x8 . x6 (λ x9 . Inj1 0)) (Inj1 (setsum 0 (Inj1 (setsum 0 0)))) ⟶ False) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 4d46e.. : (∀ x0 : (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 → 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) → (((ι → ι → ι) → ι) → ι) → (ι → ι) → ο . (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι . In (Inj0 x6) (setsum 0 (setsum 0 0)) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . Inj1 x6) (setsum (Inj0 (Inj1 (setsum 0 0))) (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (x7 (λ x8 . setsum 0 0) 0 0) (setsum (x7 (setsum x6) (Inj1 (Inj1 0)) 0) x5) (λ x8 . 0) (x7 (λ x8 . Inj0 0) (x4 (setsum (Inj1 0) (Inj0 0)) (λ x8 . x6) (λ x8 . 0) 0) (Inj0 (setsum x5 (Inj1 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι . x6) (λ x8 . x5)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x11 0) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 . 0) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . Inj0 (x7 0 (Inj0 0) (λ x10 . 0) (Inj0 (setsum 0 0)))) x6 (x4 (λ x8 x9 : ι → ι . 0) (x4 (λ x8 x9 : ι → ι . 0) (Inj0 (Inj0 0)) 0 0) (setsum (setsum 0 x6) (setsum (Inj0 0) (Inj1 0))) x6) x6 (λ x8 . setsum (Inj1 (setsum (x7 0 0 (λ x9 . 0) 0) (setsum 0 0))) (setsum (setsum 0 (setsum 0 0)) (setsum x8 (Inj0 0)))) (Inj1 (x7 (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (setsum 0 0)) (λ x8 . Inj0 (Inj1 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . In x7 (setsum (Inj0 (x4 (λ x8 . 0))) 0) ⟶ x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . 0) (x4 (λ x8 . x5)) (Inj1 (Inj0 (setsum (Inj1 0) 0))) (Inj0 0) (λ x8 . Inj1 0) (Inj0 (Inj0 0))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 . λ x9 : ((ι → ι) → ι → ι) → ι . 0) x6 0 x7 (λ x8 . setsum 0 (Inj0 (Inj1 (Inj1 0)))) (x4 (λ x8 . 0) (λ x8 : ι → ι . Inj1 x6) (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 . setsum x5 0)) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum (Inj0 (Inj1 (x11 0))) (x9 0)) (λ x8 : (ι → ι → ι) → ι . 0) Inj0 ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (x7 (x9 (λ x11 x12 . setsum 0 0)) (λ x11 : ι → ι . x10)) 0) (Inj1 0) x5 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (x9 (λ x11 x12 . 0)) (x8 0 (λ x11 : ι → ι . Inj0 (x11 0)))) (Inj0 (setsum (Inj1 0) (setsum x4 (setsum 0 0)))) (setsum x7 (Inj1 (setsum (setsum 0 0) 0))) (λ x8 : ι → ι . λ x9 . x7) (λ x8 . 0) ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . x10) (Inj0 x7) 0 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . x8)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . Inj0 (Inj1 (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . 0) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . setsum (Inj1 (Inj1 (setsum 0 0))) (setsum (x9 0 (λ x10 . setsum 0 0)) x7)) (λ x8 : ι → ι . setsum 0 (x6 (x6 0 0) x5))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In x6 (x5 (setsum (x4 0 (Inj1 0)) (x4 x6 (Inj0 0)))) ⟶ x0 (λ x8 . λ x9 : ι → (ι → ι) → ι . setsum (x9 0 (λ x10 . 0)) (x9 (Inj1 (x9 0 (λ x10 . 0))) (λ x10 . x8))) (λ x8 : ι → ι . x8 0) ⟶ x1 (λ x8 : ι → ((ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum (setsum (Inj0 (Inj1 0)) (Inj1 (setsum 0 0))) (x8 (setsum (x9 (λ x11 x12 . 0)) (setsum 0 0)) (λ x11 : ι → ι . x8 (setsum 0 0) (λ x12 : ι → ι . x10)))) (x4 (x4 (x4 (setsum 0 0) (Inj1 0)) (x7 0)) (setsum (setsum (x4 0 0) (setsum 0 0)) 0)) (x5 (x4 (setsum 0 (x5 0)) 0)) (λ x8 : ι → ι . λ x9 . Inj0 (setsum (Inj1 (Inj0 0)) 0)) (λ x8 . Inj1 (setsum (x7 (setsum 0 0)) (Inj1 x6)))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 3003b.. : (∀ x0 : (ι → ι) → ι → (ι → ι) → ο . ∀ x1 : (((((ι → ι) → 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 → ο . ∀ x3 : ((ι → (ι → ι) → ι) → ι → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 . In (Inj1 0) x7 ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . Inj1 0) (Inj0 0)) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . In (setsum (x4 (setsum x7 (x6 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 (λ x8 . 0) 0)) (Inj1 (Inj1 0)) 0) (Inj1 0)) (Inj0 x7) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . Inj1 (setsum 0 (Inj1 x7))) (x6 (λ x8 . λ x9 : ι → ι . λ x10 . setsum (setsum x10 0) (Inj1 (setsum 0 0))) (Inj0 (x4 0 0 (setsum 0 0))) (λ x8 . Inj0 0) (Inj1 0)) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . setsum (Inj0 (x8 x9 (λ x10 . Inj0 0))) (Inj1 x9)) (setsum (setsum (x5 (setsum 0 0) (λ x8 x9 . setsum 0 0)) (setsum (setsum 0 0) (x6 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 (λ x8 . 0) 0))) x7)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum (setsum (setsum 0 (setsum 0 0)) (x10 0)) 0) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x10 (setsum (setsum (setsum 0 0) 0) (x10 (Inj0 0)))) (setsum 0 (setsum (x4 (Inj0 0) x5) (Inj1 0))) ⟶ x2 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . x8 (setsum x7 (Inj0 x7))) (Inj0 (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x1 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 . 0) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → (ι → ι) → ι → ι → ι . In x5 (Inj0 (Inj0 (x7 (λ x8 . x7 (λ x9 . 0) (λ x9 . 0) 0 0) (λ x8 . 0) (Inj0 0) (Inj0 0)))) ⟶ x1 (λ x8 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι . λ x9 . x6 (setsum (Inj0 (x6 0 0)) (setsum 0 0)) (Inj0 (x6 (Inj0 0) 0))) (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι . setsum 0 x9) ⟶ x3 (λ x8 : ι → (ι → ι) → ι . λ x9 . x7 (λ x10 . x10) (λ x10 . x8 (Inj0 (x8 0 (λ x11 . 0))) (λ x11 . setsum x11 (setsum 0 0))) (setsum 0 (setsum (x7 (λ x10 . 0) (λ x10 . 0) 0 0) (Inj0 0))) (setsum x9 0)) (Inj1 (x7 (λ x8 . 0) (λ x8 . setsum (setsum 0 0) (Inj0 0)) (x7 (λ x8 . Inj0 0) (λ x8 . Inj0 0) (Inj1 0) (setsum 0 0)) (x6 (x6 0 0) 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj0 0) (setsum (Inj0 (setsum (Inj1 0) (x6 0 0))) 0) ⟶ x0 (setsum x5) (Inj0 (x7 (setsum (Inj0 0) (x6 0 0)) (λ x8 : ι → ι . λ x9 . setsum (Inj0 0) 0))) (λ x8 . x6 x5 (setsum (Inj0 x5) (x6 x8 (setsum 0 0)))) ⟶ x0 (λ x8 . 0) (x4 (λ x8 . x5)) (λ x8 . Inj0 (setsum x5 (x6 (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 x7 : ι → ι . x0 (λ x8 . Inj1 (Inj0 (x5 (λ x9 : (ι → ι) → ι . Inj0 0) (x6 0) (λ x9 . setsum 0 0)))) (setsum 0 (Inj1 0)) (λ x8 . 0) ⟶ x0 (λ x8 . x5 (λ x9 : (ι → ι) → ι . 0) x8 (λ x9 . 0)) (Inj1 (Inj1 (x7 0))) (λ x8 . setsum (setsum (Inj0 (x7 0)) (Inj0 0)) (Inj1 (Inj0 (x7 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 72ada.. : (∀ x0 : (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 → ι) → ι) → ι → ι → ο . ∀ x3 : ((ι → ι → (ι → ι) → ι) → ι → ((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι → ι → ι) → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . Inj1 (Inj0 x11)) (λ x8 : ι → ι → ι → ι . setsum x6 (Inj1 (Inj0 (setsum 0 0)))) (Inj0 (setsum (setsum (x4 0) 0) 0))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 . In (setsum 0 x5) (setsum (Inj0 0) (Inj1 0)) ⟶ x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . setsum (Inj0 x11) (Inj0 (Inj0 (x10 (λ x13 . 0) 0)))) (λ x8 : ι → ι → ι → ι . 0) 0 ⟶ x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . setsum 0 (Inj1 (setsum (Inj1 0) 0))) (λ x8 : ι → ι → ι → ι . x5) (setsum x7 (Inj0 (Inj0 0)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 : ι → ι → (ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x11) (λ x8 : ι → ι → ι → ι . x5) (Inj0 x5) ⟶ x2 (λ x8 . x7 x5) (λ x8 : ι → ι . 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . setsum (x8 (λ x10 . Inj1 (setsum 0 0))) (setsum (setsum (x8 (λ x10 . 0)) (x7 0)) (Inj0 (Inj0 0)))) (Inj1 (Inj1 (setsum x5 (Inj1 0)))) (setsum (Inj1 (setsum (setsum 0 0) x5)) (setsum (Inj1 x6) (Inj1 (Inj1 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj0 x5) (Inj1 (Inj1 (Inj0 0))) ⟶ x2 (λ x8 . x6) (λ x8 : ι → ι . Inj0 (Inj0 0)) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . 0) (Inj1 (setsum 0 (Inj0 0))) x5 ⟶ x2 (λ x8 . 0) (λ x8 : ι → ι . x5) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . Inj1 0) (Inj1 x5) x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι . ∀ x7 . In (setsum (Inj1 (setsum (setsum 0 0) (setsum 0 0))) (setsum (Inj0 (x5 0)) 0)) (Inj1 (setsum (setsum (Inj1 0) (setsum 0 0)) (Inj0 (x6 (λ x8 x9 x10 . 0) (λ x8 . 0) (λ x8 . 0))))) ⟶ x0 (λ x8 x9 . setsum (setsum 0 0) (x6 (λ x10 x11 x12 . Inj0 (Inj1 0)) (λ x10 . 0) (λ x10 . x8))) (λ x8 : ι → ι . Inj0 (setsum (x6 (λ x9 x10 x11 . Inj0 0) (λ x9 . 0) (λ x9 . Inj0 0)) 0)) (Inj0 (setsum (setsum (setsum 0 0) 0) (Inj0 (setsum 0 0)))) (λ x8 : ι → ι . Inj0 (setsum 0 0)) (setsum x7 (Inj0 (Inj0 0))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . x11) (Inj1 (setsum (Inj0 0) 0)) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . In (Inj0 0) (Inj1 (setsum 0 (Inj0 x6))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . 0) 0 (λ x8 . λ x9 : ι → ι . x9 (setsum 0 (Inj1 x7))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum (setsum 0 (Inj0 (Inj0 0))) (Inj1 (x9 (λ x13 . setsum 0 0) (λ x13 . x13) x11))) x6 (λ x8 . λ x9 : ι → ι . setsum (setsum 0 0) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . In (x5 0) (setsum (Inj0 (setsum 0 (x5 0))) (setsum x7 (setsum (setsum 0 0) 0))) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → ι . x8 (setsum (x8 (x5 0)) (Inj0 0))) (Inj1 x6) (λ x8 : ι → ι . Inj1 (setsum (setsum (x8 0) x6) (Inj1 (setsum 0 0)))) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . x8) (λ x8 : ι → ι . setsum 0 (setsum 0 (x7 (x5 (λ x9 . 0))))) 0 (λ x8 : ι → ι . Inj1 (Inj0 0)) (x7 0) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → ι . x8 0) (setsum (setsum 0 (Inj1 (Inj1 0))) 0) (λ x8 : ι → ι . 0) (Inj0 (Inj1 0))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 8bcc9.. : (∀ x0 : (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 → ι) → ι) → ι) → ο . ∀ x2 : ((ι → ι) → ι → ι) → (ι → ((ι → ι) → ι → ι) → ι) → ο . ∀ x3 : ((((ι → ι) → ι) → ι → ι) → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . setsum 0 x5) ⟶ x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj1 0) x6) (setsum (Inj0 0) (setsum (Inj1 (x4 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj0 x7) 0) (Inj1 x7) ⟶ False) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . setsum (x8 (setsum 0 (setsum 0 0))) x7) (λ x8 . λ x9 : (ι → ι) → ι → ι . x6 (λ x10 x11 . setsum (setsum x11 (setsum 0 0)) x11)) ⟶ x2 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . λ x9 : (ι → ι) → ι → ι . Inj1 (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 : ι → ι . Inj1) (λ x8 . λ x9 : (ι → ι) → ι → ι . 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . In (Inj1 0) (setsum (Inj0 (x4 (setsum 0 0) (Inj1 0) (Inj1 0) (setsum 0 0))) 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 (setsum 0 (Inj1 0))) (x9 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . x11) (λ x8 : (ι → ι) → ι . 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (setsum 0 (Inj0 0)) (setsum (Inj0 0) 0)) (λ x8 : (ι → ι) → ι . setsum (Inj0 (x7 (setsum 0 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj0 (setsum (setsum 0 0) (Inj0 0))) (setsum (setsum (setsum 0 0) 0) (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . 0) (λ x8 : (ι → ι) → ι . setsum 0 (Inj0 x6)) ⟶ In (Inj1 (Inj1 0)) x7) ⟶ (∀ x4 x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . x7) ⟶ x0 (λ x8 . λ x9 : ι → ι . x6) (λ x8 : ι → (ι → ι) → ι . 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . Inj0 (setsum 0 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ In (setsum 0 0) (Inj0 0)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem b9f6e.. : (∀ x0 : ((ι → ι → (ι → ι) → ι) → ι) → ι → ι → ο . ∀ x1 : (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) → ο . (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x8 . λ x9 : ι → ι . x9 (Inj1 (Inj0 x6))) (λ x8 : (ι → ι) → ι . setsum (Inj1 (setsum x6 0)) (Inj0 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x7 . In (setsum (Inj0 (setsum (Inj0 0) 0)) (Inj1 0)) (Inj0 x7) ⟶ x3 (λ x8 . λ x9 : ι → ι . x8) (λ x8 : (ι → ι) → ι . Inj0 (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) 0))) ⟶ x3 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x8 . x5) (setsum x5 (x6 (Inj1 0) (Inj1 (Inj0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x6 (x8 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0)) 0) (x6 0 x4) (λ x8 x9 . Inj1 (x7 (λ x10 . Inj1 x9) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x2 (λ x8 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) 0 (λ x8 x9 . setsum (Inj0 0) x7) ⟶ In (Inj0 (Inj0 (setsum x6 (Inj0 0)))) (Inj0 (setsum (Inj0 (setsum 0 0)) (setsum (x4 0 0 (λ x8 . 0) 0) x7)))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . In (Inj1 x5) (Inj1 (setsum (Inj1 (x6 (λ x8 x9 : ι → ι . λ x10 . 0) (λ x8 x9 . 0))) (Inj1 (setsum 0 0)))) ⟶ x1 (λ x8 . x6 (λ x9 x10 : ι → ι . λ x11 . Inj0 0) (λ x9 x10 . setsum (Inj0 0) 0)) (setsum 0 (setsum (setsum 0 (setsum 0 0)) (setsum 0 0))) ⟶ x1 (λ x8 . 0) (setsum 0 (Inj0 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (Inj1 (setsum (Inj1 (setsum 0 0)) (Inj1 0))) ⟶ False) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . In x5 (setsum (setsum 0 0) (Inj1 (setsum (Inj0 0) x4))) ⟶ x1 (λ x8 . x7) (Inj1 0) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι . setsum (setsum x7 0) (x6 0)) 0 (setsum (Inj0 (setsum 0 (Inj0 0))) 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι . 0) (setsum 0 (Inj0 (setsum x5 (Inj1 0)))) (setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj0 (Inj1 0))) ⟶ In (Inj1 (Inj1 (Inj1 0))) (setsum 0 (setsum 0 (Inj1 0)))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 7af28.. : (∀ x0 : ((ι → ι → ι) → ι) → ι → ο . ∀ x1 : (ι → ι) → (((ι → ι → ι) → ι → ι) → ι) → ο . ∀ x2 : (ι → (ι → ι → 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) → ο . (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 x10 . Inj1 (setsum (Inj0 x9) 0))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum (Inj1 0) (setsum (Inj0 (setsum 0 0)) x7)) (λ x8 : (ι → ι) → ι . x6) (λ x8 : ι → ι . λ x9 x10 . x10) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . Inj1 (x10 (λ x11 . setsum (setsum 0 0) 0))) (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 x10 . setsum x10 x7)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (x4 (λ x8 . λ x9 : ι → ι . x6) (λ x8 : ι → ι . λ x9 . Inj1 (Inj0 (setsum 0 0))) (setsum 0 (setsum (setsum 0 0) 0)) x5) (setsum 0 (setsum (setsum (setsum 0 0) 0) x7)) ⟶ x0 (λ x8 : ι → ι → ι . x7) (Inj1 (setsum x5 (Inj1 x6))) ⟶ x2 (λ x8 . λ x9 : ι → ι → ι → ι . Inj1 0) (λ x8 . x5) (λ x8 . 0) x6 0) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . In (x6 (Inj0 (setsum (Inj1 0) (Inj1 0)))) (setsum (x5 (x5 0 (λ x8 : ι → ι . setsum 0 0) (λ x8 . Inj1 0) (setsum 0 0)) (λ x8 : ι → ι . setsum (x6 0) 0) (λ x8 . x5 0 (λ x9 : ι → ι . 0) (λ x9 . x7) (setsum 0 0)) 0) (x4 (λ x8 x9 . Inj1 (setsum 0 0)))) ⟶ x2 (λ x8 . λ x9 : ι → ι → ι → ι . x6 (Inj1 x7)) (λ x8 . x8) (λ x8 . setsum 0 0) (x5 0 (λ x8 : ι → ι . x5 0 (λ x9 : ι → ι . setsum (setsum 0 0) (setsum 0 0)) (λ x9 . Inj1 (x6 0)) 0) (λ x8 . setsum (x5 (setsum 0 0) (λ x9 : ι → ι . Inj0 0) (λ x9 . Inj0 0) (Inj1 0)) (Inj1 0)) (x4 (λ x8 x9 . 0))) (x6 0) ⟶ x0 (λ x8 : ι → ι → ι . x5 (Inj1 0) (λ x9 : ι → ι . Inj0 0) Inj1 (Inj1 0)) (Inj1 (x6 (Inj0 x7)))) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . In x5 x5 ⟶ x1 (λ x8 . Inj1 x5) (λ x8 : (ι → ι → ι) → ι → ι . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . In (Inj0 (setsum (Inj0 (Inj1 0)) 0)) (Inj0 (setsum (x4 (Inj1 0)) x6)) ⟶ x1 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι → ι . x5) ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum (Inj1 (setsum 0 0)) (Inj1 x8)) (λ x8 : (ι → ι) → ι . Inj1 (setsum (Inj1 0) 0)) (λ x8 : ι → ι . λ x9 x10 . x10)) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . In (Inj0 0) (setsum (x6 (setsum (setsum 0 0) (Inj1 0)) (λ x8 : ι → ι . x5)) (x6 0 (λ x8 : ι → ι . x5))) ⟶ x0 (λ x8 : ι → ι → ι . 0) (setsum 0 (Inj1 (setsum (Inj0 0) (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . 0) (λ x8 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x8 : ι → ι → ι . Inj1 (setsum (setsum (setsum 0 0) 0) (setsum (Inj0 0) 0))) 0 ⟶ x3 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι . setsum 0 (x10 (λ x11 . setsum 0 0))) (λ x8 : (ι → ι) → ι . Inj0 (Inj1 (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . λ x9 x10 . setsum (x8 0) x7)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem a248f.. : (∀ x0 : (ι → ι) → ι → ο . ∀ x1 : (((ι → ι → ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ο . ∀ x2 : (((((ι → ι) → ι) → ι → ι) → ι) → ι) → ((ι → ι → ι) → ((ι → ι) → ι) → ι) → ι → ((ι → ι) → ι) → ο . ∀ x3 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ο . (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . In (setsum 0 (setsum (x6 (λ x8 . Inj0 0)) 0)) (setsum (x6 (λ x8 . Inj0 (setsum 0 0))) (Inj0 (setsum (setsum 0 0) (x6 (λ x8 . 0))))) ⟶ x0 (λ x8 . setsum (Inj1 (Inj1 (setsum 0 0))) (x6 (λ x9 . Inj0 x8))) (x4 (Inj1 (Inj1 (Inj0 0))) (setsum 0 (Inj1 (x6 (λ x8 . 0))))) ⟶ x3 (λ x8 . x7) (x5 (λ x8 : ι → ι → ι . λ x9 . setsum 0 (Inj1 (x8 0 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 . setsum (Inj1 x7) (x6 (λ x10 . x10)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 . In (x4 (λ x8 : (ι → ι) → ι . 0)) (Inj1 (setsum (Inj1 0) (setsum (Inj0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . Inj0 0) (Inj0 (Inj0 (x5 0 (λ x8 . 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 . 0) ⟶ x0 (λ x8 . Inj0 (Inj0 (Inj1 x8))) (x6 (λ x8 : (ι → ι) → ι . x5 (setsum 0 0) (setsum (Inj0 0))) (setsum (x4 (λ x8 : (ι → ι) → ι . Inj1 0)) 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 . x3 (λ x8 . Inj1 0) 0 (λ x8 : (ι → ι) → ι → ι . λ x9 . 0) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι . 0) (λ x8 : ι → ι → ι . λ x9 : (ι → ι) → ι . setsum (x9 (λ x10 . x8 (setsum 0 0) 0)) (setsum 0 0)) (setsum (Inj1 (Inj0 (setsum 0 0))) (Inj0 0)) (λ x8 : ι → ι . x7)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x2 (λ x8 : (((ι → ι) → ι) → ι → ι) → ι . x5) (λ x8 : ι → ι → ι . λ x9 : (ι → ι) → ι . 0) (Inj1 (Inj0 0)) (λ x8 : ι → ι . setsum (setsum (Inj1 (x6 0 0 0)) (setsum x7 (x8 0))) x5) ⟶ x3 (λ x8 . Inj0 (Inj1 (setsum (Inj0 0) (setsum 0 0)))) (x6 0 0 0) (λ x8 : (ι → ι) → ι → ι . λ x9 . Inj0 (Inj1 0))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x8 . setsum (setsum (setsum (Inj1 0) 0) (Inj1 (setsum 0 0))) 0) (setsum (setsum (setsum 0 (setsum 0 0)) (setsum x5 x4)) (Inj1 0)) (λ x8 : (ι → ι) → ι → ι . λ x9 . x7) ⟶ x1 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . Inj1 x7) (λ x8 x9 . setsum x6 0) (λ x8 . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x8 : (ι → ι → ι → ι) → ι . λ x9 . Inj0 (Inj0 (setsum x7 (setsum 0 0)))) (λ x8 x9 . x7) (λ x8 . 0) ⟶ x3 (λ x8 . 0) 0 (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 (x8 (λ x9 . x7) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 . x5) (Inj0 0) ⟶ x0 (λ x8 . setsum x5 (Inj1 (Inj1 (x6 0)))) (setsum (Inj1 (setsum 0 (Inj1 0))) (setsum (x6 x7) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x8 . setsum (setsum (setsum x8 (x6 0 0 0 0)) x8) (setsum 0 0)) (setsum (x5 (λ x8 : ι → ι . λ x9 x10 . setsum x9 (setsum 0 0)) (λ x8 . x8)) (setsum (x6 (setsum 0 0) (setsum 0 0) (Inj1 0) (x7 0)) (setsum 0 (x6 0 0 0 0)))) ⟶ False) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem f1e3e.. : (∀ x0 : (ι → ι) → (ι → ι) → ι → ο . ∀ x1 : (ι → ι) → (ι → ι) → (ι → (ι → ι) → ι → ι) → ο . ∀ x2 : (ι → ι) → ((((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) → ο . (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x8 . x7) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x8 (λ x9 : ι → ι . λ x10 . setsum (x8 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . x8 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0) 0) (setsum (setsum 0 0) x10)) (λ x9 . Inj1 0) 0) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum (Inj0 (x6 (λ x9 : (ι → ι) → ι → ι . 0))) (Inj1 0)) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . x8 x7 (λ x11 . setsum (x8 (Inj0 0) (λ x12 . x11)) (Inj1 x11)))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . In (Inj1 x5) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . Inj1 (setsum (setsum 0 0) 0)) (λ x8 x9 . x9) 0 (setsum 0 x6)) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum x6 x6) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . setsum (setsum (Inj1 (Inj1 0)) 0) (Inj0 (Inj0 x7))) ⟶ x1 (λ x8 . setsum 0 0) (λ x8 . setsum (setsum (setsum (Inj0 0) (Inj1 0)) x5) x7) (λ x8 . λ x9 : ι → ι . λ x10 . 0)) ⟶ (∀ x4 x5 x6 x7 . In (setsum (Inj1 (Inj0 (Inj1 0))) x5) (Inj1 0) ⟶ x2 (λ x8 . setsum (Inj1 0) (Inj1 (setsum 0 (setsum 0 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 . Inj0 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) ⟶ x0 (λ x8 . x8) (λ x8 . 0) (setsum (Inj1 (Inj1 x7)) (setsum (Inj0 (Inj0 0)) (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x8 . Inj0 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 . x8) (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (x9 0))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι → ι . ∀ x7 . In x7 (setsum x7 (x5 (x5 (x6 0 0) (setsum 0 0)) (x5 (x6 0 0) 0))) ⟶ x1 (λ x8 . x7) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . λ x10 . x8) ⟶ x3 (λ x8 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (λ x8 : ι → (ι → ι) → ι . λ x9 x10 . setsum x9 x7)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x8 . Inj0 (Inj1 0)) (λ x8 . Inj0 (x7 (λ x9 . setsum 0 (Inj0 0)) (λ x9 : ι → ι . Inj1 0) x8 0)) (Inj0 (setsum 0 (x4 (λ x8 : (ι → ι) → ι . Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . In (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . x8 (setsum (setsum 0 0) (setsum 0 0)) (Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . 0)))) 0 0) (Inj1 (x6 (λ x8 : (ι → ι) → ι → ι . x6 (λ x9 : (ι → ι) → ι → ι . setsum 0 0)))) ⟶ x0 (λ x8 . 0) (λ x8 . 0) (Inj0 0) ⟶ x2 (λ x8 . setsum 0 (setsum (Inj1 0) (setsum (Inj0 0) (Inj0 0)))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (setsum (setsum 0 0) 0)) (x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 (x10 0)) (setsum (Inj0 0) (Inj0 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 550a7.. : (∀ x0 : ((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) → ((ι → ι) → ι) → (ι → ι) → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ο . ∀ x2 : (ι → ι) → (ι → ι) → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . In (setsum (Inj0 0) 0) (Inj0 (Inj1 x5)) ⟶ x3 (λ x8 . setsum x8 (setsum (setsum (Inj0 0) 0) (setsum 0 x5))) x4) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x8 . setsum (Inj0 (Inj1 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0)))) (Inj1 (setsum (setsum 0 0) (Inj0 0)))) (x5 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 x9) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x9 (λ x11 . setsum 0 (Inj1 0))) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . Inj1 (setsum (setsum (x6 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (λ x10 . 0)) (setsum 0 0)) 0))) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj1 (setsum 0 (Inj1 (x4 0 0 (λ x8 . 0) 0)))) (setsum (setsum (Inj0 (Inj1 0)) 0) x5) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (x10 (setsum (x10 0) (setsum 0 0)))) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . 0) ⟶ x2 (λ x8 . Inj1 x7) (setsum (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → ι . In (x7 (λ x8 x9 . 0) (λ x8 x9 . Inj1 (setsum (x7 (λ x10 x11 . 0) (λ x10 x11 . 0)) (setsum 0 0)))) (Inj0 0) ⟶ x2 (λ x8 . 0) (λ x8 . 0) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj1 (Inj1 0)) (λ x8 . λ x9 x10 : ι → ι . λ x11 . setsum (Inj1 (Inj1 (setsum 0 0))) (x9 0)) (λ x8 . 0) (Inj1 (x4 (λ x8 . x8)))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 . 0) (λ x8 . 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 0)) (Inj1 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x1 (λ x8 : ι → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . x11 (Inj1 (Inj0 x10))) (λ x8 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . 0) ⟶ x3 (λ x8 . 0) (Inj0 (Inj1 (x5 (λ x8 x9 . 0) (λ x8 : ι → ι . setsum 0 0) (λ x8 . 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . In (Inj0 (Inj1 0)) (x5 (Inj0 (setsum 0 0)) (λ x8 . 0)) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . 0) (λ x8 . λ x9 x10 : ι → ι . λ x11 . setsum (Inj0 (x10 (setsum 0 0))) (Inj0 x11)) (λ x8 . x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (setsum (x7 0) (Inj0 0)) 0) 0 (λ x9 . setsum (setsum (Inj1 0) (setsum 0 0)) (setsum x9 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0) 0 (λ x10 . 0))))) (setsum (setsum 0 (setsum (setsum 0 0) (setsum 0 0))) (Inj0 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj1 x6) (λ x8 . λ x9 x10 : ι → ι . λ x11 . 0) (λ x8 . Inj0 (setsum (Inj1 (setsum 0 0)) 0)) (Inj0 x5) ⟶ x2 (λ x8 . x6) (λ x8 . x7 (λ x9 : ι → ι → ι . setsum (setsum x6 (setsum 0 0)) 0))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 433fa.. : (∀ 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 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . In (Inj0 0) x6 ⟶ x0 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (setsum (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0))) (setsum 0 0)) x5) (setsum (Inj1 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0)))) (Inj1 0) (λ x8 : ι → ι . x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (Inj0 x5) ⟶ x3 (λ x8 : ι → ι → ι . λ x9 . x8 (Inj0 0) (Inj0 0)) x5 (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ι → ι → ι . λ x9 . Inj0 x6) (setsum (setsum (setsum (Inj0 0) (setsum 0 0)) 0) (setsum 0 (x5 (λ x8 . setsum 0 0)))) (λ x8 : (ι → ι) → ι . x8 (λ x9 . Inj1 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 x9 . λ x10 : ι → ι . x7) (λ x8 . setsum (Inj0 (setsum (Inj0 0) 0)) x7)) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x8 x9 . Inj1 0) (λ x8 : ι → ι . setsum 0 (x7 (Inj1 (setsum 0 0)) (λ x9 . Inj1 (setsum 0 0)))) (λ x8 : ι → ι → ι . λ x9 x10 . x7 (Inj0 x9) (λ x11 . x8 (setsum (Inj0 0) (Inj1 0)) x10)) 0 ⟶ x2 (λ x8 x9 . 0) (λ x8 : ι → ι . Inj0 0) (λ x8 : ι → ι → ι . λ x9 x10 . Inj1 (Inj0 (Inj0 (Inj1 0)))) (x7 (x4 (λ x8 x9 . setsum 0 (Inj0 0)) (λ x8 : ι → ι . λ x9 . x6 0 (λ x10 : ι → ι . x7 0 (λ x11 . 0))) (λ x8 . Inj1 0)) (λ x8 . Inj1 (Inj0 (Inj1 0))))) ⟶ (∀ 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 (Inj1 (setsum 0 0)))) ⟶ 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)) (setsum (setsum 0 (Inj1 (setsum 0 0))))) ⟶ (∀ 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) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 6858c.. : (∀ x0 : ((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) → ο . ∀ x2 : ((ι → ι → ι) → ι → ι → ι → ι) → (ι → ι) → ι → ο . ∀ x3 : (ι → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι) → ι → ι → ο . (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . setsum (setsum (setsum (Inj1 0) (Inj0 0)) (x9 (λ x11 x12 . x10) (λ x11 . Inj1 0))) (x7 (λ x11 : (ι → ι) → ι . x9 (λ x12 x13 . Inj0 0) (λ x12 . 0)))) (setsum (setsum (Inj1 (setsum 0 0)) 0) (Inj1 (Inj1 (setsum 0 0)))) (setsum (setsum (Inj0 (setsum 0 0)) (Inj1 0)) (Inj0 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . setsum 0 (setsum (setsum x8 (Inj0 0)) (Inj1 (setsum 0 0)))) (Inj1 x7) (x5 x4 (λ x8 x9 . x7) (λ x8 . setsum x6 0) (x5 (x5 (setsum 0 0) (λ x8 x9 . Inj1 0) (λ x8 . Inj1 0) (Inj0 0)) (λ x8 x9 . Inj1 (setsum 0 0)) (λ x8 . setsum 0 0) 0)) ⟶ x1 (λ x8 . Inj1 0) (λ x8 : ι → ι → ι → ι . x5 (Inj0 (Inj0 0)) (λ x9 x10 . setsum 0 0) (λ x9 . x6) (setsum (x8 0 x7 (Inj0 0)) (x5 0 (λ x9 x10 . Inj1 0) (λ x9 . Inj1 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : ι → ι → ι . λ x9 x10 x11 . 0) (λ x8 . x7) (x6 (setsum (Inj0 0) (setsum (setsum 0 0) 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . In (Inj0 (Inj1 (setsum (setsum 0 0) (setsum 0 0)))) (setsum 0 0) ⟶ x2 (λ x8 : ι → ι → ι . λ x9 x10 x11 . Inj0 (setsum (Inj0 (Inj0 0)) 0)) (λ x8 . x7 (λ x9 : (ι → ι) → ι . Inj1 (setsum 0 0)) (λ x9 x10 . Inj1 x9)) (setsum x5 0) ⟶ x1 (λ x8 . setsum 0 (x7 (λ x9 : (ι → ι) → ι . x6 (setsum 0 0)) (λ x9 x10 . Inj1 (setsum 0 0)))) (λ x8 : ι → ι → ι → ι . Inj0 (Inj0 (Inj0 (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 x7 . In (setsum (setsum (x4 (λ x8 x9 : ι → ι . λ x10 . 0) x5) (setsum (Inj0 0) x6)) 0) (Inj0 (setsum (Inj0 (Inj1 0)) x5)) ⟶ x3 (λ x8 . λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . 0) 0 x7 ⟶ x1 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι → ι . x1 (λ x8 . 0) (λ x8 : ι → ι → ι → ι . x6) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x7 (λ x9 . Inj0 (Inj1 0)) (x8 (Inj1 (setsum 0 0)) (λ x9 : ι → ι . λ x10 . 0) (x8 (setsum 0 0) (λ x9 : ι → ι . λ x10 . x9 0) 0)) (x7 (λ x9 . setsum (setsum 0 0) (Inj1 0)) (Inj0 (setsum 0 0)) x6)) (λ x8 x9 . Inj0) (λ x8 : ι → ι → ι . Inj0 (setsum (setsum (Inj1 0) (setsum 0 0)) (setsum (Inj1 0) 0))) (λ x8 : ι → ι . x6) (λ x8 . x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . In (setsum 0 (setsum (setsum (Inj0 0) (setsum 0 0)) 0)) (Inj1 (Inj1 x7)) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) (λ x8 x9 x10 . Inj0 (Inj1 x8)) (λ x8 : ι → ι → ι . 0) (λ x8 : ι → ι . x6 (setsum 0 (Inj1 (x8 0)))) (λ x8 . Inj1 (Inj1 (Inj0 (x5 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x8 (x8 (setsum (Inj1 0) (x8 0 (λ x9 : ι → ι . λ x10 . 0) 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x8 0 (λ x11 : ι → ι . λ x12 . 0) 0)) (setsum 0 0)) (λ x9 : ι → ι . λ x10 . 0) (setsum (Inj1 x6) x6)) (λ x8 x9 x10 . Inj1 (setsum (Inj0 (Inj1 0)) x9)) (λ x8 : ι → ι → ι . 0) (λ x8 : ι → ι . x8 x6) (λ x8 . setsum x8 (Inj1 (setsum x5 (setsum 0 0)))) ⟶ x0 (λ x8 : ι → ((ι → ι) → ι → ι) → ι → ι . x8 0 (λ x9 : ι → ι . λ x10 . Inj0 (setsum 0 0)) (setsum x6 (Inj1 (Inj1 0)))) (λ x8 x9 x10 . 0) (λ x8 : ι → ι → ι . Inj1 (setsum x5 0)) (λ x8 : ι → ι . 0) (λ x8 . setsum 0 0)) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 33ee6.. : (∀ 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) ⟶ ∀ x0 : ο . x0 (proof)
Theorem cc30f.. : (∀ x0 : ((((ι → ι) → ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι) → (ι → ι) → ο . ∀ x1 : (ι → (ι → ι) → ι) → ι → ο . ∀ x2 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → ο . ∀ x3 : (ι → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι) → ο . (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . setsum 0 (x9 (setsum (setsum 0 0) (setsum 0 0)) (Inj1 0) 0)) (λ x8 . x7) ⟶ x3 (λ x8 . Inj0 (x6 (setsum (Inj0 0) (x6 0)))) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . x7)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . x3 (λ x8 . setsum (Inj0 0) (Inj0 0)) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . 0) (Inj1 0)) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . In (Inj1 0) (setsum x7 (Inj0 (setsum 0 (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . 0))))) ⟶ x2 (λ x8 . setsum (Inj1 0) (Inj0 0)) (Inj1 (setsum 0 0)) (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 (Inj1 (Inj0 0))) (setsum x6 0)) ⟶ x2 (λ x8 . 0) x7 (λ x8 : (ι → ι) → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . In x7 (Inj1 (setsum (setsum (setsum 0 0) (setsum 0 0)) (x5 (setsum 0 0) (setsum 0 0) (λ x8 . 0) 0))) ⟶ x2 (λ x8 . Inj1 x6) (x5 (Inj0 (setsum x6 0)) x7 (λ x8 . x7) x4) (λ x8 : (ι → ι) → ι → ι . Inj1 x7) ⟶ x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 . x8)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → ι . In (setsum (setsum (x6 (λ x8 : (ι → ι) → ι . λ x9 . setsum 0 0) (setsum 0 0) (λ x8 . setsum 0 0)) (Inj0 (setsum 0 0))) (setsum 0 (Inj0 (Inj1 0)))) (x6 (λ x8 : (ι → ι) → ι . x7) 0 (λ x8 . 0)) ⟶ x1 (λ x8 . λ x9 : ι → ι . x9 0) (Inj1 (setsum (x7 (Inj0 0)) (x7 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 x7 . In (setsum x4 x7) (Inj1 (setsum (setsum (setsum 0 0) 0) x4)) ⟶ x1 (λ x8 . λ x9 : ι → ι . 0) 0 ⟶ x3 (λ x8 . x7) (λ x8 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 . setsum 0 x6)) ⟶ (∀ x4 : (ι → ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . 0) (λ x8 . 0) ⟶ x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . Inj0 (setsum x7 x7)) (λ x8 . Inj1 (Inj1 0))) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x0 (λ x8 : ((ι → ι) → ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . x7) (λ x8 . Inj1 0) ⟶ In x7 (x4 (setsum 0 (x4 (Inj0 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 4eeed.. : (∀ x0 : (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 → ο . ∀ x2 : ((((ι → 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 → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . In (x7 0) x4 ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 (x6 (λ x10 . Inj0 0) (λ x10 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . 0) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (setsum 0 (Inj1 x6)) (Inj1 (Inj1 (x5 (Inj1 0) (λ x8 : ι → ι . λ x9 . 0)))) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) x4 ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (Inj0 0))) 0) 0 (λ x8 . 0) (λ x8 . setsum (Inj0 (Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . 0)))) 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum (setsum 0 0) (Inj0 0)) (setsum (Inj1 0) (setsum 0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x6 0) 0 (λ x8 . 0) (λ x8 . 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 : ((ι → ι) → ι) → ι . x8 (λ x9 : ι → ι . x7)) 0 (λ x8 . Inj0 (x6 (λ x9 . setsum x8 (Inj0 0)) (λ x9 : ι → ι . λ x10 . setsum x7 (setsum 0 0)) (λ x9 . 0) 0)) (λ x8 . setsum x8 (Inj0 0)) ⟶ False) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . x2 (λ x8 : ((ι → ι) → ι) → ι . Inj0 (setsum (x8 (λ x9 : ι → ι . Inj1 0)) 0)) 0 (λ x8 . 0) (λ x8 . Inj1 (Inj0 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 x9 . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj1 (setsum (setsum (x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) 0 0) (setsum 0 0)) (setsum 0 (x8 (λ x10 : ι → ι . 0))))) (λ x8 . Inj0 (setsum (x6 (λ x9 : (ι → ι) → ι . x9 (λ x10 . 0)) (λ x9 . 0) 0 0) (x6 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 . x7 0 (λ x10 x11 . 0) (λ x10 . 0) 0) (x5 0 0) 0))) (λ x8 . setsum (Inj0 (setsum 0 0)) (Inj1 0)) (Inj1 (x5 (x7 (Inj0 0) (λ x8 x9 . setsum 0 0) (λ x8 . setsum 0 0) (x5 0 0)) (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj0 (x6 0)) (λ x8 . 0) (λ x8 . x7) (x6 0) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . 0) 0 (λ x8 . Inj1 (x5 x8 (λ x9 : ι → ι . 0))) (λ x8 . setsum (Inj0 x8) (x6 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj0 x7) (Inj0 x5) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x5) x7 (λ x8 . Inj0 (setsum (Inj1 (setsum 0 0)) 0)) (λ x8 . 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . x9 (λ x12 x13 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj0 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . In (Inj1 0) (Inj1 (setsum 0 0)) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj0 (setsum 0 (setsum (Inj0 0) (x9 (λ x10 x11 . 0))))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj1 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . setsum 0 (x5 (λ x9 . 0)))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 66506.. : (∀ x0 : ((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 → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ο . ∀ x3 : (ι → (ι → ι) → ι) → ι → ι → ο . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ι . In (Inj1 0) (Inj1 (x7 (λ x8 . setsum (Inj0 0) (Inj1 0)))) ⟶ x1 (λ x8 . Inj1 0) (λ x8 . λ x9 : ι → ι → ι . setsum (setsum (setsum (Inj1 0) 0) 0) (setsum (setsum (setsum 0 0) 0) (setsum 0 (x9 0 0)))) (λ x8 : ι → ι → ι . 0) (Inj0 (Inj0 (setsum 0 (x5 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι . x6 (λ x10 : ι → ι . λ x11 . x10 (Inj0 (x9 0)))) (x6 (λ x8 : ι → ι . λ x9 . x6 (λ x10 : ι → ι . λ x11 . setsum (setsum 0 0) (Inj1 0)))) (setsum (Inj0 0) 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ι → ι . setsum (setsum x8 (setsum (Inj1 0) (setsum 0 0))) 0) (x5 (λ x8 : ι → ι → ι . x6 (λ x9 : ι → ι → ι . setsum 0 (setsum 0 0)) x7)) (x5 (λ x8 : ι → ι → ι . Inj0 0)) ⟶ In (Inj0 (setsum (setsum 0 0) (Inj0 (setsum 0 0)))) (Inj0 0)) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (setsum (setsum 0 (setsum (x4 (λ x8 . 0) (λ x8 : ι → ι . 0)) x6)) (setsum (x4 (λ x8 . Inj1 0) (λ x8 : ι → ι . setsum 0 0)) 0)) (Inj1 (Inj1 (setsum (Inj1 0) 0))) ⟶ x3 (λ x8 . λ x9 : ι → ι . 0) (Inj0 (setsum x5 x5)) 0 ⟶ x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι . Inj0 (x8 (λ x9 x10 . 0))) x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . In (setsum (setsum (setsum (x7 (λ x8 . 0) 0) 0) (x7 (λ x8 . Inj1 0) (setsum 0 0))) x6) (Inj0 x6) ⟶ x2 (λ x8 . 0) (λ x8 : (ι → ι → ι) → ι . x5 (λ x9 x10 x11 . setsum (Inj1 x10) (Inj0 (Inj0 0))) (x5 (λ x9 x10 x11 . Inj0 0) 0)) (Inj1 (setsum (setsum x6 (Inj1 0)) (Inj0 (Inj0 0)))) ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . x7 (λ x9 . 0) (setsum 0 0)) (setsum (Inj0 0) x6) (λ x8 . setsum (Inj0 (Inj0 (Inj0 0))) (setsum (x5 (λ x9 x10 x11 . Inj1 0) (setsum 0 0)) (setsum 0 0))) (Inj0 x6)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (x5 (Inj1 0) (λ x9 : ι → ι . setsum 0 0) (λ x9 . setsum 0 0)) (x7 (λ x9 : ι → ι . setsum 0 0))) (setsum (setsum 0 (setsum 0 0)) (setsum (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (x8 0 0 (λ x9 . 0) 0)))) x6 (λ x8 . Inj1 (Inj1 (x5 (x5 0 (λ x9 : ι → ι . 0) (λ x9 . 0)) (λ x9 : ι → ι . x8) (λ x9 . Inj1 0)))) 0 ⟶ x1 (λ x8 . setsum (setsum 0 0) 0) (λ x8 . λ x9 : ι → ι → ι . x9 x8 (x9 (Inj1 (setsum 0 0)) (Inj1 (x9 0 0)))) (λ x8 : ι → ι → ι . x6) (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x8 . x7 (λ x9 : (ι → ι) → ι → ι . Inj1 (x7 (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0)))) (λ x8 . λ x9 : ι → ι → ι . Inj0 0) (λ x8 : ι → ι → ι . Inj1 (setsum 0 x6)) (setsum 0 (setsum (Inj1 0) 0)) ⟶ In (setsum 0 (setsum 0 (Inj1 (setsum 0 0)))) (Inj0 (setsum (Inj1 (Inj1 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x8 . 0) (λ x8 . λ x9 : ι → ι → ι . x7) (λ x8 : ι → ι → ι . x5 (setsum x7 (setsum (Inj1 0) 0))) x7 ⟶ x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . Inj0 (setsum (setsum x6 x6) x7)) 0 (λ x8 . x8) (Inj0 x7)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x8 : ι → ι → (ι → ι) → ι → ι . setsum (setsum (Inj1 (x5 0)) 0) (x6 (λ x9 : ι → ι . λ x10 . Inj0 0))) (Inj1 x7) (λ x8 . x6 (λ x9 : ι → ι . λ x10 . x9 0)) x7 ⟶ In (x6 (λ x8 : ι → ι . λ x9 . setsum (Inj0 (Inj0 0)) (Inj0 (x8 0)))) (Inj1 (setsum (x4 (setsum 0 0)) (setsum (x6 (λ x8 : ι → ι . λ x9 . 0)) (Inj0 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 98889.. : (∀ x0 : ((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 → ι → ι) → ο . ∀ x2 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (((ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ο . ∀ x3 : (ι → ι) → (ι → ι → ι → ι → ι) → ο . (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x8 . Inj0 (setsum (Inj0 0) x5)) (λ x8 x9 x10 x11 . x10) ⟶ x3 (λ x8 . Inj1 (Inj0 (Inj1 (Inj1 0)))) (λ x8 x9 x10 x11 . x11)) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . In (x6 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (Inj1 (x9 0)))) (x4 (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . λ x10 . 0)) ⟶ x3 (λ x8 . Inj1 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0))) (λ x8 x9 x10 x11 . 0) ⟶ x3 (λ x8 . 0) (λ x8 x9 x10 x11 . x11)) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 x7) (λ x8 : (ι → ι) → ι → ι → ι . λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj0 0) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x9 (setsum 0 0)) (λ x8 : (ι → ι) → ι → ι → ι . λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x9 (λ x12 . x9 (λ x13 . 0) (x10 (setsum 0 0))) (setsum (Inj0 (x9 (λ x12 . 0) 0)) (setsum (setsum 0 0) x11))) ⟶ x3 (λ x8 . x7 0) (λ x8 x9 x10 x11 . x8)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . 0) (λ x8 : (ι → ι) → ι . setsum (setsum x7 x5) (setsum (Inj1 x5) 0)) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum 0 (Inj1 (Inj1 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : ι → ι → ι . x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . 0) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum (setsum (Inj0 (Inj0 0)) (setsum (Inj0 0) 0)) x10) ⟶ False) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . x9 (Inj0 (Inj0 x10)) (x9 x10 0 (setsum (Inj0 0) (setsum 0 0))) x10) (λ x8 : (ι → ι) → ι . x6) ⟶ x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . x9 0 (setsum (setsum (Inj1 0) (Inj1 0)) 0) (setsum (setsum 0 0) (Inj1 (setsum 0 0)))) (λ x8 : (ι → ι) → ι . setsum (setsum x5 (Inj0 0)) (Inj1 x7))) ⟶ (∀ x4 : ((ι → ι) → ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → ι . In (Inj1 (x5 (λ x8 . 0) (setsum (setsum 0 0) x6) (setsum (Inj1 0) (x5 (λ x8 . 0) 0 0)))) (Inj1 (Inj0 0)) ⟶ x0 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : ι → ι → ι → ι . λ x10 . 0) (λ x8 : (ι → ι) → ι . setsum (setsum 0 (x5 (λ x9 . 0) (Inj0 0) 0)) (x8 (λ x9 . x8 (λ x10 . 0)))) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 . λ x10 : (ι → ι) → ι . λ x11 . x8 (setsum (Inj1 (setsum 0 0)) 0) (λ x12 x13 . setsum (Inj1 x12) (setsum 0 (Inj1 0)))) (λ x8 : (ι → ι) → ι . λ x9 x10 x11 . setsum 0 (setsum (Inj1 (setsum 0 0)) (setsum (setsum 0 0) x11)))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 2082d.. : (∀ x0 : (((((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 → 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) → (ι → ι) → ι → ι) → ι → ι) → ι → ι → ο . (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 . x2 (λ x8 . 0) (x6 (λ x8 . λ x9 : ι → ι . Inj1 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 x9 : ι → ι . λ x10 . x7) (λ x8 : ι → ι . λ x9 . Inj1 (Inj0 (setsum (setsum 0 0) 0))) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum x7 0) (setsum (setsum (Inj0 (setsum 0 0)) x5) (Inj0 0)) (setsum 0 x4)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → ι) → ι → (ι → ι) → ι . x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj1 (x7 (λ x11 : ι → ι . setsum (setsum 0 0) (x11 0)) (setsum (setsum 0 0) (setsum 0 0)) (λ x11 . x9 (λ x12 x13 . Inj0 0) (λ x12 . Inj1 0) 0))) (setsum 0 (Inj0 (Inj0 (setsum 0 0)))) (Inj1 x6) ⟶ In (setsum (Inj1 x6) x4) (Inj1 x5)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι → ι → ι . In (Inj1 x5) (setsum 0 (Inj1 (x7 (λ x8 . Inj1 0) (λ x8 x9 . setsum 0 0) 0 0))) ⟶ x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . 0) (Inj0 0) (λ x8 . λ x9 : ι → ι . setsum 0 (x7 (λ x10 . x10) (λ x10 x11 . x11) (Inj0 (x6 (λ x10 : (ι → ι) → ι → ι . 0))) (Inj0 0))) ⟶ x2 (λ x8 . x8) 0 (λ x8 x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x7 Inj1 (λ x10 x11 . x11) (x8 (setsum (x6 (λ x10 : (ι → ι) → ι → ι . 0)) x9)) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . In (Inj0 0) (setsum (Inj1 0) (Inj0 (setsum (Inj1 0) x4))) ⟶ x2 (λ x8 . 0) 0 (λ x8 x9 : ι → ι . λ x10 . Inj0 (Inj0 (Inj0 (Inj1 0)))) (λ x8 : ι → ι . λ x9 . setsum x6 (setsum (x7 (λ x10 . 0) (setsum 0 0) (λ x10 . setsum 0 0) (Inj0 0)) 0)) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (setsum (x9 (λ x11 x12 . 0) (λ x11 . x8 (λ x12 : ι → ι → ι . λ x13 : ι → ι . 0)) (Inj1 0)) (setsum (setsum 0 0) 0)) (x9 (λ x11 x12 . x10) (λ x11 . Inj1 (setsum 0 0)) (Inj1 (Inj0 0)))) (setsum (x7 (λ x8 . Inj1 (x7 (λ x9 . 0) 0 (λ x9 . 0) 0)) x5 (λ x8 . Inj1 0) (Inj1 (Inj1 0))) x6) 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . In (Inj0 (Inj1 (setsum 0 (Inj0 0)))) (Inj1 (setsum (setsum (setsum 0 0) 0) (x7 (λ x8 . x7 (λ x9 . 0) (λ x9 : ι → ι . λ x10 . 0)) (λ x8 : ι → ι . λ x9 . Inj0 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) 0) (x7 (λ x11 . x10) (λ x11 : ι → ι . λ x12 . x9 (λ x13 x14 . 0) (λ x13 . setsum 0 0) (setsum 0 0)))) (Inj1 (Inj1 (setsum (Inj0 0) (setsum 0 0)))) (Inj0 x4) ⟶ x1 (λ x8 . Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . x10))) (λ x8 : ((ι → ι) → ι → ι) → ι . Inj0 (Inj1 (setsum (setsum 0 0) (Inj1 0)))) (λ x8 x9 . Inj0 (x7 (λ x10 . setsum (setsum 0 0) (Inj0 0)) (λ x10 : ι → ι . λ x11 . Inj1 (x10 0)))) (x7 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . setsum (x6 (λ x10 . 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x8 . 0) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . Inj1 (setsum x6 x8)) 0 ⟶ In (Inj1 (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) (Inj0 (setsum (Inj1 x6) (x4 (λ x8 . 0))))) ⟶ (∀ x4 x5 x6 x7 . In x7 (setsum (Inj0 (setsum 0 (setsum 0 0))) x6) ⟶ x2 (λ x8 . Inj0 (setsum (Inj0 x8) (setsum (setsum 0 0) 0))) (Inj0 (setsum x5 0)) (λ x8 x9 : ι → ι . λ x10 . Inj0 (Inj1 (setsum (setsum 0 0) x7))) (λ x8 : ι → ι . λ x9 . Inj1 (setsum 0 (setsum 0 (setsum 0 0)))) ⟶ x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . Inj0 x7) (Inj1 x5) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . setsum (setsum (setsum 0 (Inj0 0)) 0) (Inj1 (Inj1 (setsum 0 0)))) (setsum (Inj1 (setsum x5 0)) x7) (λ x8 . λ x9 : ι → ι . setsum (Inj1 (setsum (x6 (λ x10 : (ι → ι) → ι → ι . 0)) x8)) x7) ⟶ x1 (setsum (Inj1 (Inj1 x7))) (λ x8 : ((ι → ι) → ι → ι) → ι . 0) (λ x8 x9 . setsum x9 (setsum (Inj1 (setsum 0 0)) x9)) (Inj0 (x6 (λ x8 : (ι → ι) → ι → ι . setsum (setsum 0 0) 0)))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 54407.. : (∀ x0 : (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) → ο . ∀ x2 : (ι → ι) → (((ι → ι → ι) → (ι → ι) → ι) → ι) → (ι → ι) → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 0) (λ x8 . setsum (x7 (setsum 0 x8)) (Inj0 0)) (λ x8 . x8) (x7 (setsum 0 (Inj0 0))) ⟶ x3 (λ x8 . setsum x6 (Inj1 0)) (Inj0 (setsum (x7 0) (setsum (Inj1 0) (Inj1 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0) (λ x8 : ι → ι . λ x9 . x8 0) (λ x8 . 0) 0) (Inj1 (Inj0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x3 (λ x8 . Inj1 0) 0 ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . Inj1 (setsum 0 x9)) (λ x8 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 (setsum 0 (Inj1 0)))) (λ x8 . x8) (Inj1 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 (Inj1 0)) (λ x8 : ι → ι . λ x9 . Inj0 0) (λ x8 . 0) x6))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x8 . setsum (setsum x6 x6) x7) (Inj1 0) ⟶ x2 (λ x8 . setsum 0 0) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . setsum x6 (setsum 0 (x5 0))) (λ x8 : (ι → ι → ι) → (ι → ι) → ι . 0) (λ x8 . setsum 0 (x7 (setsum (Inj1 0) (Inj0 0)))) ⟶ In (setsum (Inj0 (x5 x4)) 0) (Inj1 (Inj1 (setsum 0 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . In (Inj0 (Inj1 (x5 (λ x8 x9 . 0)))) (x5 (λ x8 x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x11 0) (Inj0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x8 : ι → ι . Inj0 (x5 (λ x9 x10 . x9))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj0 x10) (λ x8 : ι → ι . Inj1 (Inj0 (x5 (λ x9 x10 . x8 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . In (x5 (Inj1 (setsum (setsum 0 0) (x4 0))) (x7 (λ x8 . setsum (Inj0 0) (x5 0 0)) (λ x8 x9 . Inj1 (setsum 0 0)))) x6 ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 (setsum (setsum 0 0) (setsum 0 0))) (Inj1 (x9 x10 (λ x13 . 0) (setsum 0 0)))) (λ x8 : ι → ι . Inj0 0) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . x8) (λ x8 . x5 (x7 (λ x9 . x9) (λ x9 x10 . x8)) (setsum 0 (x7 (λ x9 . Inj0 0) (λ x9 x10 . setsum 0 0)))) 0) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . In (x7 (λ x8 : (ι → ι) → ι . 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (λ x8 : ι → ι . x7 (λ x9 : (ι → ι) → ι . setsum (Inj1 0) 0)) ⟶ x0 (λ x8 x9 . λ x10 : ι → ι → ι . 0) (λ x8 . 0) (λ x8 . Inj1 (setsum (setsum (setsum 0 0) (x5 0 0 (λ x9 . 0))) (Inj1 (x7 (λ x9 : (ι → ι) → ι . 0))))) (setsum 0 (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . λ x10 : ι → ι → ι . setsum x9 (Inj0 (x10 (setsum 0 0) 0))) (λ x8 . x5 (λ x9 : ι → ι . setsum (Inj1 0) (setsum (setsum 0 0) 0)) (λ x9 x10 . 0) (Inj1 (setsum (setsum 0 0) (x6 0))) 0) (λ x8 . 0) (Inj0 (x5 (λ x8 : ι → ι . 0) (λ x8 x9 . Inj0 0) (setsum 0 (x4 (λ x8 . 0))) (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum x12 (Inj1 x12)) (λ x8 : ι → ι . Inj0 (setsum (Inj0 0) 0))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 6a8d7.. : (∀ x0 : (ι → ι → ι) → ((ι → ι) → ((ι → ι) → ι) → ι) → ο . ∀ x1 : ((ι → ι) → ι → ι → ι) → ι → ο . ∀ x2 : (ι → (ι → (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) → (ι → ι) → ι) → ι → ι) → ι → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 (Inj1 (Inj1 (Inj0 0)))) 0 ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . Inj0 (x6 (λ x10 . setsum (setsum 0 0) 0))) (Inj0 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . x9) (setsum 0 (setsum (setsum (Inj0 0) 0) (x5 (λ x8 . x5 (λ x9 . 0) (λ x9 x10 . 0)) (λ x8 x9 . 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x9 . x9) (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . x8) (setsum (Inj1 0) (setsum (setsum (setsum 0 0) 0) (Inj1 (setsum 0 0)))) (λ x8 : ι → ι . λ x9 . setsum (x8 (Inj0 (Inj0 0))) (Inj1 (Inj1 (setsum 0 0)))) (Inj0 (Inj1 (setsum (setsum 0 0) x4))) ⟶ x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . 0) (setsum (x7 (setsum x4 (Inj1 0))) x4) (λ x8 : ι → ι . λ x9 . x9) (Inj1 (setsum 0 (Inj0 (x7 0))))) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . setsum (setsum x8 (x9 (Inj1 0) (λ x12 . x11) 0)) 0) (Inj1 (setsum (x4 (λ x8 . 0) (λ x8 . x8)) 0)) (λ x8 : ι → ι . λ x9 . setsum (setsum (x7 (Inj1 0)) (x7 (Inj0 0))) (Inj1 (x8 0))) (x5 (λ x8 . Inj1 0)) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . 0) (Inj0 (Inj1 (setsum 0 (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . 0) 0 (λ x8 : ι → ι . λ x9 . 0) (setsum 0 0) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . Inj1 0) (x7 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . setsum (Inj0 0) 0))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 . In (Inj0 x4) (setsum 0 (x6 (λ x8 . setsum (Inj0 0) (setsum 0 0)) (setsum x4 (Inj1 0)) 0)) ⟶ x1 (λ x8 : ι → ι . λ x9 x10 . x10) 0 ⟶ x2 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 . setsum 0 x8) (x6 (λ x8 . setsum (setsum x8 x8) 0) 0 (setsum x4 (Inj0 x5))) (λ x8 : ι → ι . λ x9 . Inj1 0) (setsum 0 (Inj1 x7))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . In (x6 0 (λ x8 : ι → ι . Inj0 0)) x7 ⟶ x0 (λ x8 x9 . setsum x9 x9) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . x9 (λ x10 . setsum (Inj1 (Inj1 0)) 0)) ⟶ x0 (λ x8 x9 . setsum x9 (setsum (Inj0 (setsum 0 0)) (Inj1 (x6 0 (λ x10 : ι → ι . 0))))) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x8 x9 . Inj0 0) (λ x8 : ι → ι . λ x9 : (ι → ι) → ι . Inj0 0) ⟶ In (Inj1 (setsum 0 (x4 (λ x8 : ι → ι . x6) (λ x8 . x5 0)))) x7) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 9baf5.. : (∀ x0 : (ι → ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ο . ∀ x1 : (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 → ο . (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . In (Inj0 x6) (setsum (setsum 0 0) (setsum x6 (Inj0 (setsum 0 0)))) ⟶ x2 (λ x8 . Inj0 (Inj0 0)) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . x10) (setsum (x4 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 (setsum 0 0))) 0) ⟶ x3 (λ x8 . λ x9 : ι → ι → ι . Inj0 x8) x5 (setsum (setsum (setsum 0 (setsum 0 0)) (Inj0 0)) 0)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x8 . λ x9 : ι → ι → ι . 0) x7 (setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (Inj0 0))) (setsum 0 (Inj1 (setsum 0 0)))) ⟶ x3 (λ x8 . λ x9 : ι → ι → ι . x7) (setsum (x4 (λ x8 : (ι → ι) → ι → ι . x7)) x6) (Inj0 (Inj1 (setsum (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x7 . In (Inj0 0) (setsum 0 (x5 (Inj0 (setsum 0 0)) (λ x8 : ι → ι . λ x9 . Inj0 0))) ⟶ x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . x8) x7 (x6 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj1 0) (λ x8 x9 . 0)) ⟶ x2 (λ x8 . x8) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . x10) (setsum (Inj0 0) (x6 (λ x8 : (ι → ι) → ι → ι . λ x9 : ι → ι . λ x10 . Inj0 0) (λ x8 x9 . x9)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . In (Inj0 (Inj1 0)) (setsum (setsum (Inj0 0) (setsum (setsum 0 0) (setsum 0 0))) (setsum 0 (setsum (Inj0 0) (x4 0 0)))) ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . 0) (setsum (setsum 0 (setsum (setsum 0 0) (Inj0 0))) (Inj1 x6)) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . Inj0 0) (x4 0 (x5 (setsum (Inj1 0) 0)))) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x3 (λ x8 . λ x9 : ι → ι → ι . 0) 0 0 ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . x9 (λ x10 . setsum (Inj1 (Inj0 0)) (setsum 0 0))) 0) ⟶ (∀ x4 x5 x6 x7 . In (Inj0 x6) (setsum (setsum x4 (setsum x5 (setsum 0 0))) (Inj1 (setsum x5 0))) ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . x7) 0 ⟶ x2 (λ x8 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 : ι → ι → ι . λ x10 x11 . setsum 0 0) x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (Inj1 0) x5 ⟶ x1 (λ x8 . λ x9 : (ι → ι) → ι . 0) 0 ⟶ x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . Inj1 0) (Inj1 (Inj1 (x4 (λ x8 : (ι → ι) → ι → ι . 0)))) (Inj1 (setsum (setsum (Inj0 0) 0) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . 0) (x4 0) x7 ⟶ False) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 7fcf2.. : (∀ x0 : (((((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) → ι → ι) → ο . ∀ x2 : (ι → ι) → (ι → ι) → (ι → (ι → ι) → ι) → ο . ∀ x3 : (ι → (ι → (ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . x2 (λ x8 . setsum x5 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . setsum 0 x8) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . x7) x5 (Inj0 0) (Inj1 (Inj0 (setsum (Inj1 0) (setsum 0 0)))) (λ x8 . 0) x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . setsum x8 (Inj0 0)) 0 (setsum 0 0) 0 (λ x8 . Inj1 (Inj0 (Inj0 (setsum 0 0)))) (setsum (setsum (x5 (λ x8 x9 x10 . x10) (setsum 0 0) 0) 0) (setsum (x5 (λ x8 x9 x10 . Inj0 0) 0 0) 0)) ⟶ In (x5 (λ x8 x9 x10 . Inj1 (Inj0 (setsum 0 0))) (Inj1 (x7 (λ x8 : (ι → ι) → ι → ι . x6 (λ x9 . 0)) (setsum 0 0) (x7 (λ x8 : (ι → ι) → ι → ι . 0) 0 0))) (x7 (λ x8 : (ι → ι) → ι → ι . 0) (x5 (λ x8 x9 x10 . 0) 0 (Inj0 0)) (Inj1 x4))) (Inj1 (Inj0 (Inj0 x4)))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . 0) (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj1 0) (λ x8 : ι → ι . setsum (x8 0) 0) (setsum (setsum 0 0)) (setsum (x4 0) (Inj1 0))) (Inj1 (setsum (setsum 0 0) x5))) ⟶ x2 (λ x8 . Inj1 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x8 . 0) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . x8) ⟶ x2 (λ x8 . Inj0 (Inj0 (x6 (setsum 0 0)))) (λ x8 . 0) (λ x8 . λ x9 : ι → ι . 0)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ((ι → ι) → ι → ι) → ι . In (Inj0 (x4 (Inj1 (Inj1 0)) (λ x8 x9 . x6 0 (λ x10 : ι → ι . λ x11 . Inj1 0)) (setsum 0 (Inj1 0)) 0)) (x7 (setsum (x7 (setsum 0 0) (λ x8 : ι → ι . λ x9 . setsum 0 0)) (setsum (x4 0 (λ x8 x9 . 0) 0 0) (Inj0 0))) (λ x8 : ι → ι . λ x9 . setsum (Inj0 (Inj1 0)) 0)) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . x7 0 (λ x9 : ι → ι . λ x10 . Inj0 (Inj1 0))) (setsum (x7 (setsum (setsum 0 0) (x4 0 (λ x8 x9 . 0) 0 0)) (λ x8 : ι → ι . λ x9 . x6 0 (λ x10 : ι → ι . λ x11 . setsum 0 0))) x5) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . setsum (Inj1 (Inj1 0)) (Inj1 (Inj1 0))) (λ x8 x9 x10 x11 . 0) (λ x8 . λ x9 : ι → ι . λ x10 . setsum (setsum (Inj0 0) 0) (Inj1 (Inj1 x10)))) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . x6 (Inj1 (setsum (Inj0 0) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . 0) 0 0))) (setsum (Inj0 (setsum 0 0)) (setsum (Inj0 0) 0))) (λ x8 x9 x10 x11 . x8) (λ x8 . λ x9 : ι → ι . λ x10 . 0) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . Inj0) (Inj0 (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum (Inj0 0) (Inj1 0)) (λ x8 : ι → ι . λ x9 . Inj1 0) 0 (Inj0 0))) (setsum (setsum (x6 (Inj0 0) (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0))) 0) (x6 0 (Inj1 (Inj1 0)))) (Inj0 (Inj1 (setsum (x6 0 0) (Inj0 0)))) (λ x8 . x8) (setsum (setsum 0 (Inj0 (setsum 0 0))) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (λ x8 : ι → ι . λ x9 . Inj0 (Inj0 0)) (Inj1 (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0))) (setsum (setsum 0 0) (x4 (λ x8 x9 . 0) (λ x8 : ι → ι . λ x9 . 0)))))) ⟶ (∀ x4 : ((ι → ι) → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . In (setsum (setsum 0 (Inj0 (Inj0 0))) (x4 (λ x8 : ι → ι . λ x9 x10 . Inj0 (Inj0 0)))) (x4 (λ x8 : ι → ι . λ x9 x10 . 0)) ⟶ x3 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . Inj0 (setsum x8 x7)) (Inj0 x7) (Inj0 (setsum x7 0)) (Inj0 (setsum (Inj1 0) (setsum x5 x7))) (λ x8 . x8) 0 ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . x5) (setsum (Inj0 0) (Inj0 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x6 x7 . In (Inj0 (Inj1 (x5 (λ x8 : (ι → ι) → ι → ι . λ x9 x10 . Inj1 0)))) (Inj1 (x4 (Inj1 0) (setsum (setsum 0 0) 0))) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . 0) (Inj1 x7) ⟶ x1 (λ x8 : ι → (ι → ι → ι) → (ι → ι) → ι . setsum x7 0) (λ x8 x9 x10 x11 . setsum (Inj0 x9) x9) (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (setsum (x9 0) 0))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem e4e0f.. : (∀ x0 : (ι → ι) → ((ι → ι) → ι → ι → ι) → ι → ο . ∀ x1 : (ι → ((ι → ι → ι) → ι) → ι) → (ι → ι → ι → ι) → ο . ∀ x2 : (ι → ι → ι) → ι → ο . ∀ x3 : (((ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι) → ι) → ι → ι → ο . (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 x7 . In x6 (setsum x6 (Inj1 (Inj1 (Inj1 0)))) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . setsum (Inj0 0) 0) x4 (Inj0 0)) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In (Inj1 (setsum (setsum (setsum 0 0) (setsum 0 0)) x7)) (Inj0 (setsum (x6 x7) x7)) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . Inj1 (setsum 0 0)) 0 (Inj0 (Inj0 (setsum (setsum 0 0) (Inj0 0)))) ⟶ x2 (λ x8 x9 . 0) (setsum (Inj0 0) (setsum (x6 0) (x6 (x4 (λ x8 x9 . 0) 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . In (x5 0 Inj1) (Inj1 (x4 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 (Inj1 0)) (λ x8 . 0) (setsum 0 0) 0)) ⟶ x2 (λ x8 x9 . Inj1 (setsum (x6 (λ x10 . λ x11 : ι → ι . Inj1 0) (λ x10 x11 . 0)) (x6 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 . x9)))) (setsum (setsum (setsum (setsum 0 0) (setsum 0 0)) (setsum (Inj1 0) (Inj1 0))) 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 x9 . setsum x9 (Inj1 (setsum (setsum 0 0) 0))) (setsum (x4 (setsum (Inj1 0) (setsum 0 0)) (λ x8 . Inj0 x5)) (setsum (x4 (Inj1 0) (λ x8 . Inj0 0)) (Inj1 0))) ⟶ x3 (λ x8 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . λ x9 : (ι → ι → ι) → (ι → ι) → ι . Inj0 (x8 (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) 0 (Inj1 (Inj1 0)))) (setsum (setsum (Inj0 (setsum 0 0)) x7) x5) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . In (Inj0 (x7 (λ x8 . 0) 0)) (Inj1 (Inj0 x4)) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . In (setsum 0 (setsum (x7 0) x5)) (Inj1 0) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 0) ⟶ x1 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) (λ x8 x9 x10 . Inj1 x8)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . In (x4 (Inj0 (Inj1 x5)) (λ x8 : ι → ι . setsum (x7 (λ x9 . x8 0)) (x8 (setsum 0 0))) (λ x8 . 0)) (setsum (Inj1 x6) x6) ⟶ x2 (λ x8 . Inj1) (x7 (λ x8 . x7 (λ x9 . 0))) ⟶ x0 (λ x8 . 0) (λ x8 : ι → ι . λ x9 x10 . setsum (setsum (Inj0 x9) (Inj1 (Inj1 0))) (Inj0 (setsum (Inj0 0) (x8 0)))) (setsum x5 (setsum (setsum 0 (Inj1 0)) (x4 0 (λ x8 : ι → ι . Inj0 0) (λ x8 . x6))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . setsum 0) x6 ⟶ x0 (λ x8 . x7) (λ x8 : ι → ι . λ x9 x10 . x7) (setsum (Inj0 (Inj1 (x4 (λ x8 : (ι → ι) → ι . 0) (λ x8 . 0)))) (x4 (λ x8 : (ι → ι) → ι . 0) Inj1))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 932cb.. : (∀ x0 : (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) → ο . ∀ x2 : (ι → 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 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 x7 . In (setsum x5 (Inj0 x6)) (setsum 0 (x4 (λ x8 : ι → ι → ι . Inj0 (Inj0 0)))) ⟶ x0 (λ x8 x9 . 0) (λ x8 : ι → (ι → ι) → ι → ι . 0) (setsum 0 (Inj0 (setsum x6 (Inj0 0)))) ⟶ x3 (λ x8 : ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x7) (λ x8 : (ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x3 (λ x8 : ι → ι . λ x9 . λ x10 : (ι → ι) → ι → ι . x9) (λ x8 : (ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . Inj1 x6) ⟶ In (Inj0 0) (setsum (setsum x6 (setsum x5 0)) (Inj0 (setsum x6 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . In (x4 (λ x8 : ι → ι → ι . x7 (λ x9 x10 x11 . x10) 0)) (Inj1 (x7 (λ x8 x9 x10 . 0) (setsum 0 (Inj0 0)))) ⟶ x1 (λ x8 . Inj1 (Inj1 0)) (λ x8 : ι → ι → ι → ι . setsum 0 (Inj1 (setsum (setsum 0 0) (x8 0 0 0)))) (λ x8 . setsum (x7 (λ x9 x10 x11 . 0) (Inj1 x8)) (Inj1 x8)) (λ x8 : ι → ι . 0) (λ x8 . x5) ⟶ x2 (λ x8 . setsum (setsum 0 (Inj0 x5)) (Inj1 0)) (λ x8 . λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . 0))) (Inj0 (x4 (λ x8 : ι → ι → ι . 0))) (setsum 0 0) (setsum (x7 (λ x8 x9 x10 . setsum (Inj0 0) (setsum 0 0)) (x6 (λ x8 : ι → ι → ι . setsum 0 0) (λ x8 x9 . x7 (λ x10 x11 x12 . 0) 0) (setsum 0 0))) (x4 (λ x8 : ι → ι → ι . x7 (λ x9 x10 x11 . setsum 0 0) (x6 (λ x9 : ι → ι → ι . 0) (λ x9 x10 . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . In (Inj0 (Inj1 (setsum (x4 0) (setsum 0 0)))) (Inj0 0) ⟶ x2 (λ x8 . Inj0 (x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) 0) 0 (x6 (Inj1 0)) 0)) (λ x8 . λ x9 : (ι → ι) → ι . 0) (Inj1 (x4 (Inj0 0))) (x6 (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (Inj1 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . 0) 0 0 0) 0) (x7 (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 0) (setsum 0 0) (x6 0) 0))) (setsum (x7 (λ x8 . λ x9 : ι → ι . λ x10 . Inj0 0) (x4 (x6 0)) (setsum (Inj1 0) (Inj1 0)) 0) (Inj0 (x4 0))) ⟶ x2 (λ x8 . setsum 0 (Inj0 (x6 (setsum 0 0)))) (λ x8 . λ x9 : (ι → ι) → ι . x8) (Inj0 (x6 (setsum 0 (setsum 0 0)))) (Inj0 x5) (Inj0 (setsum x5 (x4 (x4 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x1 (λ x8 . Inj0 (setsum (Inj1 (Inj1 0)) x8)) (λ x8 : ι → ι → ι → ι . Inj1 (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) 0 0 0)) (λ x8 . setsum 0 (Inj1 (Inj1 x7))) (λ x8 : ι → ι . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x8 . x5 (Inj1 (setsum 0 (Inj1 0))) (λ x9 . setsum (setsum (Inj1 0) x9) x8)) (λ x8 : ι → ι → ι → ι . Inj0 (Inj0 (Inj0 (x7 0)))) (λ x8 . Inj1 (Inj0 (setsum (Inj0 0) (x6 0 0)))) (λ x8 : ι → ι . x6 (setsum (x6 0 (setsum 0 0)) (x6 (Inj0 0) (x8 0))) (Inj0 (setsum (setsum 0 0) (Inj0 0)))) (λ x8 . 0) ⟶ x1 (λ x8 . x6 (Inj1 (x5 0 (λ x9 . x8))) 0) (λ x8 : ι → ι → ι → ι . setsum (Inj0 (Inj0 (Inj1 0))) 0) (λ x8 . Inj0 (setsum (setsum (Inj0 0) (x7 0)) 0)) (λ x8 : ι → ι . 0) (λ x8 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . In x7 x4 ⟶ x0 (λ x8 . Inj0) (λ x8 : ι → (ι → ι) → ι → ι . Inj0 (setsum x7 0)) (Inj0 (x5 (Inj0 x7) (λ x8 x9 . 0) (λ x8 . 0))) ⟶ x0 (λ x8 x9 . Inj0 x8) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 x6) (setsum (setsum 0 (Inj1 x6)) (setsum (Inj1 0) (setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . ∀ x6 x7 . x0 (λ x8 x9 . setsum x7 x6) (λ x8 : ι → (ι → ι) → ι → ι . Inj1 (x8 x7 (λ x9 . setsum x6 (x8 0 (λ x10 . 0) 0)) 0)) (Inj0 (x4 (x4 (Inj1 0)))) ⟶ In (Inj1 (setsum (x4 (setsum 0 0)) (x4 (setsum 0 0)))) (Inj1 (Inj0 0))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem ca986.. : (∀ x0 : ((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 → 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) → ι) → ι) → ο . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 0) (Inj1 (setsum (Inj0 0) (x5 0 (Inj0 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum x7 (setsum (x6 (setsum 0 0)) 0)) (λ x8 : (ι → ι) → ι . setsum (x8 (λ x9 . 0)) (Inj1 (Inj0 (Inj0 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . setsum 0 x7) (setsum (Inj1 0) (setsum (Inj0 0) (Inj1 (Inj1 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 . In (Inj1 (setsum 0 (setsum 0 0))) (Inj1 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x8 (Inj0 (setsum 0 0)) (x9 (setsum 0 0)))) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . setsum (setsum (setsum (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (setsum 0 0)) (Inj1 (setsum 0 0))) (x9 (λ x11 . setsum (Inj1 0) (x8 (λ x12 . λ x13 : ι → ι . 0))) (λ x11 . 0))) (x4 (λ x8 x9 : ι → ι . λ x10 . x8 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) 0 ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x6 x7 . In (Inj0 (x4 (λ x8 x9 x10 . 0))) (Inj0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 x7) 0 ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj1 (x9 x8)) (λ x8 : ι → ι . Inj1 (setsum (x8 (setsum 0 0)) (Inj0 (Inj0 0)))) (λ x8 . Inj1 (Inj0 0)) (λ x8 x9 . 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (x10 (λ x12 . 0) x8)) (λ x8 : ι → ι . setsum x7 (setsum (setsum 0 (setsum 0 0)) x7)) (λ x8 . 0) (λ x8 x9 . 0) ⟶ In (Inj1 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 0) x4 (λ x8 . setsum 0 0) x7) (Inj0 0))) (setsum (setsum x7 (setsum 0 (setsum 0 0))) (setsum (setsum (setsum 0 0) x4) x6))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In x7 (setsum 0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 (setsum 0 (Inj0 0))) (x6 (setsum (setsum (x6 0) 0) (x6 (Inj1 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 0) (x6 (Inj0 (setsum (setsum 0 0) 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (Inj0 (Inj1 0)) x5 ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . x8 x9) (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0)) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . 0) 0) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 2d8bb.. : (∀ x0 : (((((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 → ο . ∀ x3 : (ι → ι) → ι → ι → ο . (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 : (ι → ι → ι) → ι . In (setsum (setsum (setsum (x4 0) (setsum 0 0)) (Inj0 0)) (setsum (x6 (λ x8 x9 . Inj1 0)) 0)) (Inj1 (setsum (setsum (Inj1 0) (setsum 0 0)) 0)) ⟶ x3 (λ x8 . 0) 0 (setsum (setsum (x7 (λ x8 x9 . setsum 0 0)) 0) (Inj1 (Inj1 (Inj0 0)))) ⟶ x3 (λ x8 . setsum (Inj1 (setsum (x7 (λ x9 x10 . 0)) (setsum 0 0))) (Inj1 (setsum 0 (x5 (λ x9 : (ι → ι) → ι . 0))))) (x4 (x7 (λ x8 x9 . setsum 0 (Inj1 0)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . In (Inj0 0) x7 ⟶ x3 (λ x8 . Inj0 0) 0 x6 ⟶ x3 (λ x8 . 0) (setsum 0 0) (Inj0 (Inj1 0))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . 0) (λ x8 : ι → (ι → ι) → ι . setsum x7) ⟶ x2 (λ x8 . 0) (x4 (λ x8 x9 : ι → ι . Inj1 (Inj0 0)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . In (setsum x4 (setsum (Inj0 (setsum 0 0)) (setsum 0 x7))) (Inj1 0) ⟶ x2 (λ x8 . Inj1 (Inj1 0)) (setsum 0 x7) ⟶ x2 (λ x8 . x7) (Inj0 (Inj1 0))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 . In (Inj1 (setsum (Inj1 0) (Inj1 (x6 (λ x8 : ι → ι . 0))))) (Inj0 (setsum 0 (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x2 (λ x8 . Inj0 (x6 (λ x9 : ι → ι . setsum (Inj0 0) 0))) x5 ⟶ x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . Inj0 (Inj0 (x6 (λ x10 : ι → ι . x7)))) (λ x8 : ι → (ι → ι) → ι . λ x9 . setsum 0 (setsum (setsum (Inj1 0) x9) (Inj0 x7)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x1 (λ x8 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x9 . setsum (setsum 0 (setsum x9 0)) 0) (λ x8 : ι → (ι → ι) → ι . setsum 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . setsum (Inj0 0) x6) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . x7) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . x6 (λ x10 : ι → ι → ι . λ x11 x12 . setsum 0 (setsum (Inj0 0) (setsum 0 0))) (λ x10 x11 . setsum x9 (x8 (λ x12 : ι → ι . setsum 0 0) (λ x12 . Inj0 0) x9)) x9 (setsum (Inj0 0) (Inj0 (setsum 0 0)))) ⟶ x0 (λ x8 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . λ x9 : ((ι → ι) → ι) → ι → ι . setsum (x6 (λ x10 : ι → ι → ι . λ x11 x12 . setsum x12 0) (λ x10 x11 . x10) x7 (Inj0 (setsum 0 0))) 0) (λ x8 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) 0)) (setsum (Inj1 (setsum 0 0)) (Inj1 (setsum 0 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 586ae.. : (∀ x0 : (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 → ι) → ι → ο . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι . In (Inj1 (setsum x4 (Inj0 (Inj0 0)))) x4 ⟶ x0 (λ x8 . 0) (λ x8 . Inj1 (Inj1 (setsum (setsum 0 0) (setsum 0 0)))) (λ x8 . setsum (setsum 0 x8) (setsum (Inj1 (Inj0 0)) (Inj0 0))) (setsum (Inj1 (Inj0 (Inj1 0))) x4) 0 ⟶ x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . x5) (λ x8 : ((ι → ι) → ι) → ι → ι . x6 (Inj1 (x6 0))) x5 (λ x8 . x8) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . Inj0 0) (λ x8 : ((ι → ι) → ι) → ι → ι . x7) (Inj1 (setsum (Inj1 (Inj1 0)) (setsum (Inj0 0) x5))) (λ x8 . 0) (setsum (Inj1 (Inj0 (Inj1 0))) (Inj0 x7)) ⟶ In (Inj0 x4) x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . In (setsum (Inj1 (Inj0 (x7 (λ x8 : (ι → ι) → ι → ι . 0)))) 0) (Inj1 (Inj1 0)) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) (Inj1 0) ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x6 (λ x9 x10 . 0) (λ x9 : ι → ι . λ x10 . Inj1 (Inj0 (Inj0 0)))) (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . 0) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . x5) (Inj0 x5)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι . setsum (Inj0 (setsum (Inj1 0) (setsum 0 0))) (setsum (x7 (λ x9 : (ι → ι) → ι . setsum 0 0)) (setsum 0 0))) (x5 (λ x8 . Inj1 (setsum (Inj0 0) (Inj0 0))) (x7 (λ x8 : (ι → ι) → ι . Inj0 (Inj1 0))) (λ x8 . 0) (Inj0 (Inj0 (Inj0 0)))) Inj1 (setsum (Inj1 (x5 (λ x8 . x8) (setsum 0 0) (λ x8 . 0) 0)) (Inj1 (Inj1 (x7 (λ x8 : (ι → ι) → ι . 0))))) ⟶ x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . 0) (λ x8 x9 x10 . x9)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x8 : (ι → ι → ι → ι) → ι → ι . λ x9 : (ι → ι → ι) → ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) (λ x8 x9 x10 . setsum x9 (Inj0 (setsum x8 x8))) ⟶ In (setsum (x6 (λ x8 . 0) (λ x8 : ι → ι . λ x9 . Inj0 (setsum 0 0)) x4) (setsum 0 (Inj1 0))) (Inj1 x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 . In (setsum (setsum 0 0) 0) (x5 0 0 (λ x8 . setsum (Inj0 (Inj1 0)) 0)) ⟶ x0 (λ x8 . x6) (λ x8 . 0) (λ x8 . 0) x7 x7 ⟶ x0 (λ x8 . Inj0 0) (λ x8 . Inj1 0) (λ x8 . setsum 0 (x5 0 (setsum (setsum 0 0) (Inj1 0)) (λ x9 . x8))) 0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . In (setsum (x5 (Inj1 0)) 0) (setsum (Inj0 x7) (Inj1 (setsum x7 (setsum 0 0)))) ⟶ x0 (λ x8 . Inj1 0) (λ x8 . 0) (λ x8 . Inj1 (x5 0)) (x5 (Inj1 0)) 0 ⟶ x2 (λ x8 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . setsum 0 (setsum (setsum 0 0) (setsum (Inj0 0) (setsum 0 0)))) (x5 (setsum 0 x4))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem f1111.. : (∀ x0 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ο . ∀ x1 : (ι → ι) → (ι → ι) → ο . ∀ x2 : ((((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι → ι → ι → ι) → ι → ο . ∀ x3 : (ι → ι) → ι → ο . (∀ x4 x5 x6 x7 . x3 (λ x8 . 0) 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (x7 x4) (Inj0 0) ⟶ x3 (λ x8 . x7 x6) (setsum (x7 (setsum (setsum 0 0) x6)) 0) ⟶ x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (x8 (λ x12 x13 : ι → ι . Inj0 0) x10 (λ x12 . 0) (Inj0 (setsum 0 0))) (setsum (setsum (Inj0 0) (Inj0 0)) (Inj1 x11))) (setsum (setsum (Inj0 (setsum 0 0)) (setsum (x5 (λ x8 : (ι → ι) → ι . 0) (λ x8 : ι → ι . λ x9 . 0)) (setsum 0 0))) (setsum (x5 (λ x8 : (ι → ι) → ι . Inj1 0) (λ x8 : ι → ι . λ x9 . x9)) (Inj1 (Inj1 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . Inj1 (Inj0 x9)) (setsum (Inj1 (Inj0 (setsum 0 0))) (Inj1 (setsum (Inj0 0) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . In (Inj0 (setsum (x7 0 (λ x8 : ι → ι . λ x9 . 0) (setsum 0 0) (x6 0)) (x6 (setsum 0 0)))) (Inj0 (Inj1 0)) ⟶ x2 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . λ x9 x10 x11 . 0) (setsum (x6 (Inj1 (x6 0))) (Inj0 (x7 (setsum 0 0) (λ x8 : ι → ι . λ x9 . 0) x4 (x7 0 (λ x8 : ι → ι . λ x9 . 0) 0 0)))) ⟶ x3 (λ x8 . setsum (setsum (x6 (Inj1 0)) (x6 x5)) (x7 (setsum (Inj0 0) (x7 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)) (λ x9 : ι → ι . λ x10 . Inj0 0) (Inj0 (x7 0 (λ x9 : ι → ι . λ x10 . 0) 0 0)) (x7 x8 (λ x9 : ι → ι . λ x10 . setsum 0 0) 0 (Inj1 0)))) (Inj0 x4)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . In (Inj1 (Inj0 0)) (setsum (x4 (setsum (Inj1 0) (setsum 0 0)) (λ x8 x9 . x8) (setsum (Inj1 0) (x4 0 (λ x8 x9 . 0) 0 0)) x6) (setsum (x4 (Inj1 0) (λ x8 x9 . Inj1 0) (setsum 0 0) 0) (setsum (setsum 0 0) (setsum 0 0)))) ⟶ x0 (λ x8 . Inj1 x6) (λ x8 : ι → ι → ι → ι . 0) ⟶ x1 (λ x8 . Inj1 (setsum 0 (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0))))) (λ x8 . setsum (x5 (λ x9 x10 . x10)) (setsum 0 (Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . In (x7 (setsum 0 0) (λ x8 x9 . Inj1 (Inj1 0))) (setsum (Inj1 x4) (x6 (λ x8 : ι → ι . λ x9 x10 . setsum x9 0) (setsum (setsum 0 0) (x6 (λ x8 : ι → ι . λ x9 x10 . 0) 0 0)) (x6 (λ x8 : ι → ι . λ x9 x10 . Inj0 0) x4 0))) ⟶ x1 (λ x8 . setsum 0 (setsum 0 (Inj1 0))) (λ x8 . setsum (x5 0 (λ x9 : ι → ι . λ x10 . 0)) (setsum (setsum 0 (setsum 0 0)) (Inj0 (Inj1 0)))) ⟶ x1 (λ x8 . Inj1 (x6 (λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 0) (x9 0)) (Inj0 (Inj0 0)) (Inj0 (x5 0 (λ x9 : ι → ι . λ x10 . 0))))) (λ x8 . 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x7 : ι → ι → ι → ι . In x4 (x7 0 (Inj1 (setsum (Inj0 0) (Inj0 0))) x5) ⟶ x0 (λ x8 . setsum x8 (setsum x8 0)) (λ x8 : ι → ι → ι → ι . 0) ⟶ x0 (λ x8 . x7 (setsum 0 0) (setsum x8 0) (Inj1 0)) (λ x8 : ι → ι → ι → ι . 0)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 . setsum (setsum 0 0) 0) (λ x8 : ι → ι → ι → ι . setsum (setsum 0 0) (setsum (Inj1 0) 0)) ⟶ x3 (λ x8 . 0) (Inj0 (setsum (Inj0 0) (Inj1 (setsum 0 0))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)