Search for blocks/addresses/...

Proofgold Signed Transaction

vin
PrBec../bd4b3..
PUbei../37a84..
vout
PrBec../31452.. 363.92 bars
TMGxH../ac0c0.. ownership of 619f0.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMGae../79cc6.. ownership of e254e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMTTU../3f667.. ownership of a3378.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMJVU../ee17f.. ownership of 3cd94.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMbpj../0ad2e.. ownership of 751ed.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMPbX../553c9.. ownership of 39232.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMMVF../86dfc.. ownership of 002b6.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMHQ2../359c5.. ownership of 107f0.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMdz4../984f3.. ownership of c6930.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMF5h../9d2dd.. ownership of 1eab9.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMLmS../73b0d.. ownership of 44176.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMVB2../af838.. ownership of d25a4.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMN8Z../1b2ae.. ownership of 1cb9d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMYZA../60665.. ownership of f4df1.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMHDG../79d9e.. ownership of bc887.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMHdk../a6a1f.. ownership of f4d6f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMFCK../7e8ca.. ownership of ead0e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMLEe../b98da.. ownership of 7828f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMFAE../0b608.. ownership of 57e52.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMJPH../a1d43.. ownership of 249ae.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMZvo../cbb8f.. ownership of 536b2.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMSr6../02933.. ownership of 6219e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMJYe../269a6.. ownership of ee98d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
TMbuF../c7e49.. ownership of d949a.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0
PUYCz../39b12.. doc published by PrGVS..
Known 8106d..notI : ∀ x0 : ο . (x0 ⟶ False) ⟶ not x0
Known TrueITrueI : True
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)
Theorem 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) (proof)