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Proofgold Signed Transaction

vin
PrEvg../e5537..
PUbXo../3060e..
vout
PrEvg../18146.. 0.36 bars
TMbVg../2307e.. ownership of 29aed.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJSY../2a892.. ownership of c2130.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFEG../3f870.. ownership of 5d0c6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZV8../43e77.. ownership of 20cee.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSc1../a3bec.. ownership of 21cd8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSyD../434ed.. ownership of bb94b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMF8z../501b8.. ownership of de260.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMEsA../9a027.. ownership of 5bbbd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMajf../1e9b3.. ownership of 5920d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNb8../77e91.. ownership of ad41d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFe8../701e3.. ownership of ed937.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFwX../42a0c.. ownership of 8691a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdaR../ddf14.. ownership of 7e7e4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJRk../572f7.. ownership of 5bbcd.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUi1../66a99.. ownership of 63f8a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPHr../0628a.. ownership of 33c84.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUSZ../fd34c.. ownership of 9da57.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVg1../e30a1.. ownership of 5d52e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdCP../4f55d.. ownership of 39d15.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXw3../4c28f.. ownership of a9d5c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRnn../5b10e.. ownership of e0314.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJN2../895b3.. ownership of 6a6e1.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMby1../48b74.. ownership of 472f9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVMV../1cf7e.. ownership of 90a45.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMKY../47d79.. ownership of 5bcaf.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJyf../43c0a.. ownership of d3e5c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMP7b../37204.. ownership of bd9b5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMaSo../f83be.. ownership of c1fa7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPsT../a546f.. ownership of b531a.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMddN../7b26c.. ownership of 3b516.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQJF../cab39.. ownership of 9d73b.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc9Q../d01e5.. ownership of c690d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFbr../30a53.. ownership of 77d26.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMYgR../6f331.. ownership of dd093.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUCz../e987f.. ownership of 9315d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFBT../a29d2.. ownership of 8a85e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc7k../89493.. ownership of e8415.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMMdF../6c861.. ownership of b667c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZbJ../32fe1.. ownership of d9462.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHMR../9b917.. ownership of 92f24.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXL6../d9ca2.. ownership of 657ef.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdng../f9f96.. ownership of e4d19.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLzH../e0543.. ownership of cb931.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY45../a1bf6.. ownership of ec8af.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXUb../298e6.. ownership of 7afff.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMT1Q../acf7c.. ownership of a1e82.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGzL../22416.. ownership of 99fb9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNP5../a53a8.. ownership of 90f6d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQRG../36354.. ownership of 7a0ec.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUyr../711c9.. ownership of 64950.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGxo../cf186.. ownership of 8cc3c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHAn../bd542.. ownership of 05100.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXwg../78699.. ownership of af815.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXfH../24948.. ownership of 0af08.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXxJ../daa5f.. ownership of f3baa.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQtf../d2feb.. ownership of fc755.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdpj../54d14.. ownership of 3cabe.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQx3../8a728.. ownership of fdf84.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPfz../f1f7d.. ownership of 68b13.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc8q../c6394.. ownership of 453db.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNXr../c032f.. ownership of 3cd3c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQVm../646c6.. ownership of 9e11e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMLq5../3a6d2.. ownership of 9888f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGx2../c04c5.. ownership of fbc04.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMGCm../7135a.. ownership of 1b59f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQ1d../e110b.. ownership of bc384.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMN1H../7857c.. ownership of 27862.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVXt../7b3fe.. ownership of 72b39.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMQQY../2d2a6.. ownership of d6106.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJDS../107ad.. ownership of 3946d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNxP../1a826.. ownership of d7c0d.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMUbq../67f4a.. ownership of 66b87.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMRGJ../1c080.. ownership of 67ee8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPWb../b7ab8.. ownership of 1e5e6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPt8../09563.. ownership of 0c961.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMHn3../d68ab.. ownership of 97dd6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMY6B../b4a65.. ownership of f2088.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTgF../d334a.. ownership of e88aa.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMTzt../a1499.. ownership of 25ca3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSMn../66532.. ownership of f8cb3.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWFg../0a485.. ownership of 4a50e.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMZr8../094db.. ownership of c72c4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMd7u../67ec5.. ownership of e36e8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPyx../efadb.. ownership of 96c22.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMPHh../f8e71.. ownership of 61af4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWng../0bb2a.. ownership of 1153f.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXUf../76a39.. ownership of 302e5.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWeA../1973b.. ownership of c0f24.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMW2p../71178.. ownership of 67794.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMbYr../67d34.. ownership of 6b978.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMFYw../b5981.. ownership of ffdc7.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVe5../64ec1.. ownership of 541d9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMJMj../22272.. ownership of 1f2c4.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMSvy../38386.. ownership of 93a56.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML6R../176c9.. ownership of 5b8fe.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMakR../c0738.. ownership of 93d41.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMdy8../96154.. ownership of edc3c.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMWYW../128e4.. ownership of 46449.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMS2p../17618.. ownership of 48ac8.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMKeS../1cd9c.. ownership of 1ffeb.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TML4h../b1329.. ownership of 62f06.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMXdu../ac8b7.. ownership of b4bb9.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMc6i../1e650.. ownership of 934b2.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMV3N../ca59b.. ownership of 18289.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMVWp../8be77.. ownership of bb8e6.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
TMNrg../a65eb.. ownership of 9f625.. as obj with payaddr PrGxv.. rights free controlledby PrGxv.. upto 0
PUWQ4../fe90b.. doc published by PrGxv..
Param True : ο
Definition bb8e6.. := λ x0 : ι → ι → ο . True
Definition bb8e6.. := λ x0 : ι → ι → ο . True
Definition 1f2c4.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim1 (λ x0 . x0)))))))))))
Param 32d20.. : ι
Definition 32d20.. := 32d20..
Param and : οοο
Definition 934b2.. := λ x0 : ι → ι → ο . and (bb8e6.. x0) (x0 1f2c4.. 32d20..)
Param d478c.. : (ιιο) → (ιιο) → ιο
Conjecture a1ac9.. : ∀ x0 x1 : ι → ι → ο . bb8e6.. x0bb8e6.. x1d478c.. x0 x1 32d20..
Definition 62f06.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x0 x0))))) (prim1 (λ x0 . x0))))))))))))
Param 91fd5.. : ιιι
Definition 48ac8.. := 91fd5.. 1f2c4.. (91fd5.. 1f2c4.. 1f2c4..)
Definition edc3c.. := λ x0 : ι → ι → ο . and (934b2.. x0) (x0 62f06.. 48ac8..)
Conjecture 75198.. : ∀ x0 x1 : ι → ι → ο . 934b2.. x0bb8e6.. x1d478c.. x0 x1 48ac8..
Definition 5b8fe.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim1 (λ x0 . x0)))))))))))
Definition 1f2c4.. := 1f2c4..
Definition ffdc7.. := λ x0 : ι → ι → ο . and (edc3c.. x0) (x0 5b8fe.. 1f2c4..)
Conjecture f6498.. : ∀ x0 x1 : ι → ι → ο . edc3c.. x0bb8e6.. x1d478c.. x0 x1 1f2c4..
Definition 67794.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim1 (λ x0 . x0))))))))))
Definition 302e5.. := 91fd5.. 1f2c4.. 32d20..
Definition 61af4.. := λ x0 : ι → ι → ο . and (ffdc7.. x0) (x0 67794.. 302e5..)
Conjecture 51037.. : ∀ x0 x1 : ι → ι → ο . ffdc7.. x0bb8e6.. x1d478c.. x0 x1 302e5..
Definition e36e8.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim1 (λ x0 . x0))))))))))))
Definition 32d20.. := 32d20..
Definition 4a50e.. := λ x0 : ι → ι → ο . and (61af4.. x0) (x0 e36e8.. 32d20..)
Conjecture 3b7e7.. : ∀ x0 x1 : ι → ι → ο . 61af4.. x0bb8e6.. x1d478c.. x0 x1 32d20..
Definition 25ca3.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim1 (λ x0 . x0))))))))
Definition f2088.. := 91fd5.. 1f2c4.. e36e8..
Definition 0c961.. := λ x0 : ι → ι → ο . and (4a50e.. x0) (x0 25ca3.. f2088..)
Conjecture 3fadb.. : ∀ x0 x1 : ι → ι → ο . 4a50e.. x0bb8e6.. x1d478c.. x0 x1 f2088..
Definition 67ee8.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim1 (λ x0 . x0)))))))))))
Definition d7c0d.. := 91fd5.. e36e8.. 32d20..
Definition d6106.. := λ x0 : ι → ι → ο . and (0c961.. x0) (x0 67ee8.. d7c0d..)
Conjecture ddcd3.. : ∀ x0 x1 : ι → ι → ο . 0c961.. x0bb8e6.. x1d478c.. x0 x1 d7c0d..
Definition 27862.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x1)) (prim0 (prim0 x0 x1) (prim0 x0 x0))))) (prim1 (λ x0 . x0))))))))))))))
Definition 1b59f.. := 91fd5.. (91fd5.. 1f2c4.. e36e8..) e36e8..
Definition 9888f.. := λ x0 : ι → ι → ο . and (d6106.. x0) (x0 27862.. 1b59f..)
Conjecture fa148.. : ∀ x0 x1 : ι → ι → ο . d6106.. x0bb8e6.. x1d478c.. x0 x1 1b59f..
Definition 3cd3c.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim1 (λ x0 . x0))))))))))
Param 57d6a.. : ιιι
Definition 68b13.. := 91fd5.. (57d6a.. 67794.. 5b8fe..) 32d20..
Definition 3cabe.. := λ x0 : ι → ι → ο . and (9888f.. x0) (x0 3cd3c.. 68b13..)
Conjecture 57580.. : ∀ x0 x1 : ι → ι → ο . 9888f.. x0bb8e6.. x1d478c.. x0 x1 68b13..
Definition f3baa.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim1 (λ x0 . x0)))))))))))
Definition af815.. := 91fd5.. (57d6a.. 67794.. 5b8fe..) (91fd5.. (57d6a.. 67794.. 5b8fe..) (57d6a.. 67794.. 5b8fe..))
Definition 8cc3c.. := λ x0 : ι → ι → ο . and (3cabe.. x0) (x0 f3baa.. af815..)
Conjecture 4ef9d.. : ∀ x0 x1 : ι → ι → ο . 3cabe.. x0bb8e6.. x1d478c.. x0 x1 af815..
Definition 7a0ec.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim1 (λ x0 . x0)))))))))))))
Param d7cf0.. : ι(ιι) → ι
Definition 99fb9.. := d7cf0.. 1f2c4.. (λ x0 . 91fd5.. (91fd5.. (57d6a.. 67794.. x0) (57d6a.. 67794.. 5b8fe..)) (57d6a.. 67794.. 5b8fe..))
Definition 7afff.. := λ x0 : ι → ι → ο . and (8cc3c.. x0) (x0 7a0ec.. 99fb9..)
Conjecture 26e08.. : ∀ x0 x1 : ι → ι → ο . 8cc3c.. x0bb8e6.. x1d478c.. x0 x1 99fb9..
Definition cb931.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x1 x1) (prim0 x1 x1))))) (prim1 (λ x0 . x0))))))))))))))
Definition 657ef.. := 91fd5.. (91fd5.. 1f2c4.. (57d6a.. 67794.. 5b8fe..)) (57d6a.. 67794.. 5b8fe..)
Definition d9462.. := λ x0 : ι → ι → ο . and (7afff.. x0) (x0 cb931.. 657ef..)
Conjecture 64c5c.. : ∀ x0 x1 : ι → ι → ο . 7afff.. x0bb8e6.. x1d478c.. x0 x1 657ef..
Param bcddf.. : ι(ιι) → ι
Param 236c6.. : ι
Definition e8415.. := λ x0 : ι → ι → ο . and (bb8e6.. x0) (x0 67794.. (bcddf.. 236c6.. (λ x1 . 57d6a.. 67ee8.. (57d6a.. 25ca3.. x1))))
Definition 9315d.. := λ x0 : ι → ι → ο . and (e8415.. x0) (∀ x1 x2 . x0 (57d6a.. 67ee8.. (57d6a.. 25ca3.. (57d6a.. (57d6a.. 62f06.. x1) x2))) (91fd5.. (57d6a.. 67794.. x1) (57d6a.. 67794.. x2)))
Definition 77d26.. := λ x0 : ι → ι → ο . and (9315d.. x0) (∀ x1 . x0 (57d6a.. 67ee8.. (57d6a.. 27862.. x1)) (d7cf0.. 1f2c4.. (λ x2 . 57d6a.. 67ee8.. (57d6a.. x1 x2))))
Definition 9d73b.. := λ x0 : ι → ι → ο . and (77d26.. x0) (∀ x1 x2 . x0 (57d6a.. 3cd3c.. (57d6a.. (57d6a.. 7a0ec.. x1) x2)) (d7cf0.. (57d6a.. 67794.. x1) (λ x3 . 57d6a.. 3cd3c.. (57d6a.. x2 x3))))
Definition b531a.. := λ x0 : ι → ι → ο . and (9d73b.. x0) (∀ x1 x2 . x0 (57d6a.. 3cd3c.. (57d6a.. (57d6a.. f3baa.. x1) x2)) (91fd5.. (57d6a.. 3cd3c.. x1) (57d6a.. 3cd3c.. x2)))
Definition bd9b5.. := λ x0 : ι → ι → ο . and (b531a.. x0) (∀ x1 . x0 (57d6a.. 3cd3c.. (57d6a.. cb931.. x1)) (d7cf0.. 1f2c4.. (λ x2 . 57d6a.. 3cd3c.. (57d6a.. x1 x2))))
Definition 5bcaf.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x0 x1) (prim0 x0 x1))))) (prim1 (λ x0 . x0))))))))))))))
Definition 472f9.. := 57d6a.. 67ee8.. (57d6a.. 27862.. (bcddf.. 1f2c4.. (λ x0 . 57d6a.. 25ca3.. (57d6a.. (57d6a.. 62f06.. x0) (57d6a.. (57d6a.. 62f06.. x0) 5b8fe..)))))
Definition e0314.. := bcddf.. 1f2c4.. (λ x0 . bcddf.. (57d6a.. 67794.. x0) (λ x1 . bcddf.. (57d6a.. 67794.. x0) (λ x2 . 57d6a.. (57d6a.. 7a0ec.. (57d6a.. (57d6a.. 62f06.. x0) 5b8fe..)) (bcddf.. 236c6.. (λ x3 . 57d6a.. (57d6a.. f3baa.. (57d6a.. x3 x1)) (57d6a.. x3 x2))))))
Definition 39d15.. := λ x0 : ι → ι → ο . and (d9462.. x0) (x0 5bcaf.. 472f9..)
Conjecture 235b5.. : ∀ x0 x1 : ι → ι → ο . d9462.. x0bd9b5.. x1d478c.. x0 x1 472f9..
Param 6fe8d.. : (ιιο) → (ιιο) → (ιιο) → ιιο
Param 5c39b.. : ιιο
Conjecture d3a4f.. : ∀ x0 x1 : ι → ι → ο . d9462.. x0bd9b5.. x16fe8d.. x0 x1 5c39b.. e0314.. 472f9..
Definition 9da57.. := λ x0 : ι → ι → ο . and (bd9b5.. x0) (x0 5bcaf.. e0314..)
Definition 63f8a.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim1 (λ x0 . x0)))))))))))
Definition 7e7e4.. := 57d6a.. 3cd3c.. (57d6a.. cb931.. (bcddf.. 236c6.. (λ x0 . 57d6a.. (57d6a.. 7a0ec.. x0) (bcddf.. (57d6a.. 67794.. x0) (λ x1 . 57d6a.. (57d6a.. (57d6a.. 5bcaf.. x0) x1) x1)))))
Definition ed937.. := bcddf.. 1f2c4.. (λ x0 . bcddf.. (57d6a.. 67794.. x0) (λ x1 . bcddf.. (57d6a.. 67794.. (57d6a.. (57d6a.. 62f06.. x0) 5b8fe..)) (λ x2 . bcddf.. (57d6a.. 3cd3c.. (57d6a.. x2 x1)) (λ x3 . x3))))
Definition 5920d.. := λ x0 : ι → ι → ο . and (39d15.. x0) (x0 63f8a.. 7e7e4..)
Conjecture 4daf7.. : ∀ x0 x1 : ι → ι → ο . 39d15.. x09da57.. x1d478c.. x0 x1 7e7e4..
Conjecture ad088.. : ∀ x0 x1 : ι → ι → ο . 39d15.. x09da57.. x16fe8d.. x0 x1 5c39b.. ed937.. 7e7e4..
Definition 29aed.. := λ x0 : ι → ι → ο . and (9da57.. x0) (x0 63f8a.. ed937..)
Definition de260.. := prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x1 x1) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x1 x0)) (prim0 (prim0 x0 x0) (prim0 x0 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x1 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x0) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x1 x1) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x0) (prim0 x0 x1))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x1)) (prim0 (prim0 x0 x1) (prim0 x1 x0))))) (prim0 (prim1 (λ x0 . prim1 (λ x1 . prim0 (prim0 (prim0 x1 x0) (prim0 x0 x0)) (prim0 (prim0 x0 x1) (prim0 x0 x1))))) (prim1 (λ x0 . x0))))))))))))))))))
Definition 21cd8.. := 57d6a.. 3cd3c.. (57d6a.. cb931.. (bcddf.. 1f2c4.. (λ x0 . 57d6a.. (57d6a.. 7a0ec.. x0) (bcddf.. (57d6a.. 67794.. x0) (λ x1 . 57d6a.. (57d6a.. 7a0ec.. x0) (bcddf.. (57d6a.. 67794.. x0) (λ x2 . 57d6a.. (57d6a.. f3baa.. (57d6a.. (57d6a.. (57d6a.. 5bcaf.. x0) x1) x2)) (57d6a.. (57d6a.. (57d6a.. 5bcaf.. x0) x2) x1))))))))
Definition 5d0c6.. := λ x0 : ι → ι → ο . and (5920d.. x0) (x0 de260.. 21cd8..)
Conjecture fcb0d.. : ∀ x0 x1 : ι → ι → ο . 5920d.. x029aed.. x1d478c.. x0 x1 21cd8..
Definition 5d0c6.. := 5d0c6..
Definition 29aed.. := 29aed..