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Proofgold Asset

asset id
d9d95f0bc7264c87c02681204a51d5b8fafa3e09b52b74e47bfb6bfd498d6ccb
asset hash
827f2f2c47ca2b10eca8117815df4931c869200a034e9d4ffc941fea4ffbb7e8
bday / block
22406
tx
a4c53..
preasset
doc published by PrBTh..
Known 30edc..equip_tra : ∀ x0 x1 x2 . equip x0 x1equip x1 x2equip x0 x2
Known 637fd..equip_sym : ∀ x0 x1 . equip x0 x1equip x1 x0
Theorem 86c40.. : ∀ x0 x1 x2 . equip x1 x0equip x2 x0equip x1 x2 (proof)
Known 82600.. : ∀ x0 . equip x0 0x0 = 0
Known d0de4..Empty_eq : ∀ x0 . (∀ x1 . nIn x1 x0)x0 = 0
Known 9d2e6..nIn_I2 : ∀ x0 x1 . (In x0 x1False)nIn x0 x1
Known 2901c..EmptyE : ∀ x0 . In x0 0False
Known 681fa..proj0_setprod : ∀ x0 x1 x2 . In x2 (setprod x0 x1)In (proj0 x2) x0
Known 54d4b..equip_ref : ∀ x0 . equip x0 x0
Theorem 12ef8.. : ∀ x0 x1 . equip x0 0equip (setprod x0 x1) 0 (proof)
Known 1cfb6..proj1_setprod : ∀ x0 x1 x2 . In x2 (setprod x0 x1)In (proj1 x2) x1
Theorem 9f38c.. : ∀ x0 x1 . equip x1 0equip (setprod x0 x1) 0 (proof)
Known FalseEFalseE : False∀ x0 : ο . x0
Param 69aae..exp_nat : ιιι
Known a84bb.. : ∀ x0 x1 x2 x3 . equip x0 x3equip x1 (ordsucc x3)equip_mod x0 x1 x2
Known 02169..add_nat_0R : ∀ x0 . add_nat x0 0 = x0
Known 9e914.. : ∀ x0 x1 . nat_p x1add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))))))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1))))))))))))))))
Known a2e43.. : ∀ x0 . nat_p x0nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0))))))))))))))))
Known 3fe1c..add_nat_com : ∀ x0 . nat_p x0∀ x1 . nat_p x1add_nat x0 x1 = add_nat x1 x0
Known 63495.. : ∀ x0 . add_nat x0 1 = ordsucc x0
Known 2b177.. : ∀ x0 x1 . nat_p x1add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x1)))))))) = ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1))))))))
Known 9b388..mul_nat_1R : ∀ x0 . mul_nat x0 1 = x0
Known 0ac77.. : ∀ x0 x1 . nat_p x1add_nat x0 (ordsucc (ordsucc x1)) = ordsucc (ordsucc (add_nat x0 x1))
Known 7bb3f.. : ∀ x0 x1 . nat_p x1add_nat x0 (ordsucc (ordsucc (ordsucc (ordsucc x1)))) = ordsucc (ordsucc (ordsucc (ordsucc (add_nat x0 x1))))
Known d6dd4.. : ∀ x0 . nat_p x0∀ x1 . nat_p x1∀ x2 x3 . equip x2 x0equip x3 x1equip (binrep x2 x3) (add_nat x0 (69aae.. 2 x1))
Known a62e2.. : ∀ x0 . equip x0 4equip (Power x0) 16
Known 74cfe.. : ∀ x0 . nat_p x0nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0))))))))))))))))))))))))))))))))
Known 5af12.. : ∀ x0 . add_nat x0 2 = ordsucc (ordsucc x0)
Known b2788.. : ∀ x0 . nat_p x0nat_p (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc (ordsucc x0))))))))
Known fddcf.. : 69aae.. 2 2 = 4
Known c83a0.. : ∀ x0 . nat_p x0nat_p (ordsucc (ordsucc (ordsucc (ordsucc x0))))
Known a1573.. : ∀ x0 . equip x0 2equip (Power x0) 4
Known 2b6ba.. : nat_p 4
Known 37c59..exp_nat_1 : ∀ x0 . 69aae.. x0 1 = x0
Known 02b3e.. : ∀ x0 . equip x0 3equip (Power x0) 8
Known f4890..exp_nat_S : ∀ x0 x1 . nat_p x169aae.. x0 (ordsucc x1) = mul_nat x0 (69aae.. x0 x1)
Known c7c31..nat_1 : nat_p 1
Known fad70..mul_nat_0R : ∀ x0 . mul_nat x0 0 = 0
Known 94de7..exp_nat_0 : ∀ x0 . 69aae.. x0 0 = 1
Known e6b7d.. : ∀ x0 . equip x0 1equip (Power x0) 2
Known 224e2.. : ∀ x0 . equip x0 0equip (Power x0) 1
Known 36841..nat_2 : nat_p 2
Known 08405..nat_0 : nat_p 0
Known 9814f.. : nat_p 3
Known 4c6ff.. : ∀ x0 . nat_p x0∀ x1 . nat_p x1∀ x2 x3 . equip x2 x0equip x3 x1equip (setexp x2 x3) (69aae.. x0 x1)
Known 912b9..equip_setprod_mul_nat_2 : ∀ x0 . nat_p x0∀ x1 . nat_p x1∀ x2 x3 . equip x2 x0equip x3 x1equip (setprod x2 x3) (mul_nat x0 x1)
Known 56707..equip_setsum_add_nat_2 : ∀ x0 . nat_p x0∀ x1 . nat_p x1∀ x2 x3 . equip x2 x0equip x3 x1equip (setsum x2 x3) (add_nat x0 x1)
Theorem f6980.. : (∀ x0 x1 x2 . equip_mod (setsum (setsum (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (Power (Power 0))) x2))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 x2))) (setsum (setprod (Power (Power (Power 0))) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) x1)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) x2)) (setsum (setprod (Power (Power 0)) (setexp x0 (binrep (Power (Power 0)) 0))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2))) (setsum (setprod (binrep (Power (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setexp x1 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) x2))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setexp x1 (Power (Power 0))))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (Power (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod x1 (setexp x2 (Power (Power 0)))))) (setsum (setprod (setexp x0 (Power (Power 0))) (setprod x1 x2)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod (setexp x0 (Power (Power 0))) x1)) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (Power (Power 0))) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) x2)) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setexp x0 (Power (Power 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (Power (Power (Power 0))) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod x0 (setexp x1 (binrep (Power (Power 0)) 0)))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod x0 (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod x0 (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod x0 (setexp x1 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x0 (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod x0 (setprod x1 (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod x0 (setprod x1 x2))) (setsum (setprod x0 x1) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x0 (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod x0 (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod x0 x2)) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) x0) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setexp x1 (binrep (Power (Power 0)) 0))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0))))) (setsum (setprod (Power (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) x2)) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setexp x1 (Power (Power 0)))) (setsum (setprod (Power (Power (Power 0))) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x1 (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) (setprod x1 x2)) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) x1) (setsum (setexp x2 (binrep (Power (Power 0)) 0)) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) x2) (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) (Power (Power (Power (Power 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2))) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x1 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (Power (Power 0))) x2))) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x1 (Power (Power 0))))) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setprod x1 x2))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) x1)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod (setexp x0 (binrep (Power (Power 0)) 0)) x2)) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2))) (setsum (setprod (binrep (Power (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setexp x1 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod (setexp x0 (Power (Power 0))) (setprod (setexp x1 (Power (Power 0))) x2))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) (setexp x1 (Power (Power 0))))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x0 (Power (Power 0))) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) (setprod (setexp x0 (Power (Power 0))) (setprod x1 (setexp x2 (Power (Power 0)))))) (setsum (setprod (Power (Power 0)) (setprod (setexp x0 (Power (Power 0))) (setprod x1 x2))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setprod (setexp x0 (Power (Power 0))) x1)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod (setexp x0 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod (setexp x0 (Power (Power 0))) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod (setexp x0 (Power (Power 0))) x2)) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod x0 (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2))) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) (setprod x0 (setexp x1 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod x0 (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x0 (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0)))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod x0 (setprod (setexp x1 (Power (Power 0))) x2))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod x0 (setexp x1 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x0 (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0))))) (setsum (setprod x0 (setprod x1 (setexp x2 (Power (Power 0))))) (setsum (setprod (Power (Power 0)) (setprod x0 (setprod x1 x2))) (setsum (setprod (Power (Power (Power 0))) (setprod x0 x1)) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod x0 (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (Power (Power 0))) 0) (setprod x0 (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod x0 x2)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) x0) (setsum (setprod (Power (binrep (Power (Power 0)) 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) 0) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) (setexp x2 (Power (Power 0))))) (setsum (setprod (Power (Power 0)) (setprod (setexp x1 (binrep (Power (Power 0)) 0)) x2)) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) 0) (setexp x1 (binrep (Power (Power 0)) 0))) (setsum (setprod (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) (setprod (setexp x1 (Power (Power 0))) (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (Power 0)) 0) (setprod (setexp x1 (Power (Power 0))) x2)) (setsum (setprod (Power (Power (Power 0))) (setexp x1 (Power (Power 0)))) (setsum (setprod (Power (Power 0)) (setprod x1 (setexp x2 (binrep (Power (Power 0)) 0)))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x1 (setexp x2 (Power (Power 0))))) (setsum (setprod (binrep (Power (binrep (Power (Power 0)) 0)) (Power (Power 0))) (setprod x1 x2)) (setsum (setprod (binrep (Power (Power (Power 0))) (Power 0)) x1) (setsum (setprod (binrep (binrep (Power (Power (Power 0))) (Power 0)) 0) (setexp x2 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0)) (Power (Power 0))) (Power 0))) (binrep (binrep (Power (binrep (Power (Power (Power 0))) 0)) (binrep (Power (Power 0)) 0)) 0)) (binrep (Power (binrep (Power (Power (Power 0))) 0)) (binrep (Power (Power 0)) 0))) (binrep (Power (binrep (Power (Power (Power 0))) 0)) (Power (Power 0)))) (binrep (binrep (Power (binrep (Power (Power (Power 0))) 0)) (Power 0)) 0)) (binrep (Power (binrep (Power (Power (Power 0))) 0)) (Power 0))) (binrep (Power (Power (Power (Power 0)))) (binrep (Power (Power 0)) 0))) (binrep (binrep (binrep (Power (Power (Power (Power 0)))) (Power (Power 0))) (Power 0)) 0)) (binrep (Power (Power (Power (Power 0)))) 0)) (Power (Power (Power (Power 0))))) (binrep (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0)) 0)) (binrep (Power (binrep (Power (Power 0)) 0)) (Power 0))) (binrep (Power (Power (Power 0))) (Power 0))) (binrep (Power (Power (Power 0))) 0)) (Power (Power (Power 0))))False)∀ x0 : ο . x0 (proof)