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Proofgold Signed Transaction

vin
PrJx3../86721..
PUN4t../5cd69..
vout
PrJx3../fc7d8.. 5.79 bars
TMRVW../a62ad.. ownership of 167dc.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
TMUbt../92b15.. ownership of 52d50.. as prop with payaddr Pr4zB.. rightscost 0.00 controlledby Pr4zB.. upto 0
PUTEr../ac717.. doc published by Pr4zB..
Param 4402e.. : ι(ιιο) → ο
Param cf2df.. : ι(ιιο) → ο
Definition SubqSubq := λ x0 x1 . ∀ x2 . x2x0x2x1
Param setminussetminus : ιιι
Param SingSing : ιι
Definition FalseFalse := ∀ x0 : ο . x0
Definition notnot := λ x0 : ο . x0False
Definition 2f869.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2∀ x6 : ο . x6)(x1 = x3∀ x6 : ο . x6)(x2 = x3∀ x6 : ο . x6)(x1 = x4∀ x6 : ο . x6)(x2 = x4∀ x6 : ο . x6)(x3 = x4∀ x6 : ο . x6)not (x0 x1 x2)not (x0 x1 x3)not (x0 x2 x3)not (x0 x1 x4)not (x0 x2 x4)x0 x3 x4x5)x5
Definition 87c36.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (2f869.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)x0 x2 x5not (x0 x3 x5)x0 x4 x5x6)x6
Definition f201d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (87c36.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6not (x0 x2 x6)x0 x3 x6not (x0 x4 x6)x0 x5 x6x7)x7
Definition 2452c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f201d.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7x0 x2 x7not (x0 x3 x7)x0 x4 x7not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition 983a2.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 6647d.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 4a35f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)x0 x3 x8not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 4f557.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8not (x0 x2 x8)x0 x3 x8not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition cbd9e.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)x0 x2 x8x0 x3 x8not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition e643b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8x0 x2 x8x0 x3 x8not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 180f5.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 . ∀ x5 : ο . ((x1 = x2∀ x6 : ο . x6)(x1 = x3∀ x6 : ο . x6)(x2 = x3∀ x6 : ο . x6)(x1 = x4∀ x6 : ο . x6)(x2 = x4∀ x6 : ο . x6)(x3 = x4∀ x6 : ο . x6)not (x0 x1 x2)not (x0 x1 x3)not (x0 x2 x3)not (x0 x1 x4)x0 x2 x4x0 x3 x4x5)x5
Definition 45422.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 . ∀ x6 : ο . (180f5.. x0 x1 x2 x3 x4(x1 = x5∀ x7 : ο . x7)(x2 = x5∀ x7 : ο . x7)(x3 = x5∀ x7 : ο . x7)(x4 = x5∀ x7 : ο . x7)not (x0 x1 x5)x0 x2 x5x0 x3 x5not (x0 x4 x5)x6)x6
Definition 85e71.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (45422.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6not (x0 x2 x6)not (x0 x3 x6)x0 x4 x6x0 x5 x6x7)x7
Definition 843b8.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (85e71.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7x0 x2 x7x0 x3 x7not (x0 x4 x7)not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition 70e9a.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (843b8.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition ec99f.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition 6ea2b.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)x0 x1 x8not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)not (x0 x7 x8)x9)x9
Definition cb643.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)x0 x7 x8x9)x9
Definition 6caef.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)x0 x3 x8not (x0 x4 x8)not (x0 x5 x8)not (x0 x6 x8)x0 x7 x8x9)x9
Definition f6f09.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (87c36.. x0 x1 x2 x3 x4 x5(x1 = x6∀ x8 : ο . x8)(x2 = x6∀ x8 : ο . x8)(x3 = x6∀ x8 : ο . x8)(x4 = x6∀ x8 : ο . x8)(x5 = x6∀ x8 : ο . x8)x0 x1 x6x0 x2 x6x0 x3 x6not (x0 x4 x6)not (x0 x5 x6)x7)x7
Definition 88b7c.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 . ∀ x8 : ο . (f6f09.. x0 x1 x2 x3 x4 x5 x6(x1 = x7∀ x9 : ο . x9)(x2 = x7∀ x9 : ο . x9)(x3 = x7∀ x9 : ο . x9)(x4 = x7∀ x9 : ο . x9)(x5 = x7∀ x9 : ο . x9)(x6 = x7∀ x9 : ο . x9)x0 x1 x7x0 x2 x7x0 x3 x7not (x0 x4 x7)not (x0 x5 x7)not (x0 x6 x7)x8)x8
Definition 7a491.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (88b7c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)x0 x7 x8x9)x9
Definition 04e02.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (843b8.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)x0 x7 x8x9)x9
Definition 737dc.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)x0 x5 x8not (x0 x6 x8)x0 x7 x8x9)x9
Definition 70e38.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 x7 x8 . ∀ x9 : ο . (2452c.. x0 x1 x2 x3 x4 x5 x6 x7(x1 = x8∀ x10 : ο . x10)(x2 = x8∀ x10 : ο . x10)(x3 = x8∀ x10 : ο . x10)(x4 = x8∀ x10 : ο . x10)(x5 = x8∀ x10 : ο . x10)(x6 = x8∀ x10 : ο . x10)(x7 = x8∀ x10 : ο . x10)not (x0 x1 x8)not (x0 x2 x8)not (x0 x3 x8)not (x0 x4 x8)not (x0 x5 x8)x0 x6 x8x0 x7 x8x9)x9
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0x1x2)x2
Definition nInnIn := λ x0 x1 . not (x0x1)
Known setminusEsetminusE : ∀ x0 x1 x2 . x2setminus x0 x1and (x2x0) (nIn x2 x1)
Known 84110.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x02452c.. x2 x4 x5 x6 x7 x8 x9 x10∀ x11 : ο . (not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)x2 x5 x3x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3x2 x5 x3x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3x2 x5 x3not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x11)(x2 x4 x3not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)x2 x9 x3not (x2 x10 x3)x11)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)x2 x9 x3not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)x2 x9 x3not (x2 x10 x3)x11)(not (x2 x4 x3)x2 x5 x3not (x2 x6 x3)x2 x7 x3not (x2 x8 x3)x2 x9 x3not (x2 x10 x3)x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)x2 x10 x3x11)(not (x2 x4 x3)not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)not (x2 x8 x3)not (x2 x9 x3)x2 x10 x3x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)x2 x10 x3x11)(not (x2 x4 x3)not (x2 x5 x3)x2 x6 x3not (x2 x7 x3)x2 x8 x3not (x2 x9 x3)x2 x10 x3x11)(not (x2 x4 x3)not (x2 x5 x3)not (x2 x6 x3)not (x2 x7 x3)not (x2 x8 x3)x2 x9 x3x2 x10 x3x11)x11
Known c75bf.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2)∀ x2 . x2x0∀ x3 . x3x0∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x02452c.. x1 x2 x3 x4 x5 x6 x7 x82452c.. x1 x2 x4 x3 x6 x5 x8 x7
Known neq_i_symneq_i_sym : ∀ x0 x1 . (x0 = x1∀ x2 : ο . x2)x1 = x0∀ x2 : ο . x2
Known Subq_traSubq_tra : ∀ x0 x1 x2 . x0x1x1x2x0x2
Known setminus_Subqsetminus_Subq : ∀ x0 x1 . setminus x0 x1x0
Known SingISingI : ∀ x0 . x0Sing x0
Theorem 167dc.. : ∀ x0 x1 . ∀ x2 : ι → ι → ο . (∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3)4402e.. x1 x2cf2df.. x1 x2∀ x3 . x3x1x0setminus x1 (Sing x3)∀ x4 . x4x0∀ x5 . x5x0∀ x6 . x6x0∀ x7 . x7x0∀ x8 . x8x0∀ x9 . x9x0∀ x10 . x10x02452c.. x2 x4 x5 x6 x7 x8 x9 x10∀ x11 : ο . (∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0983a2.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x06647d.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x04a35f.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x04f557.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0cbd9e.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0e643b.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x070e9a.. x2 x12 x13 x3 x14 x15 x16 x17 x18x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0ec99f.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x06ea2b.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0cb643.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x06caef.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x07a491.. x2 x3 x12 x13 x14 x15 x16 x17 x18x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x004e02.. x2 x12 x13 x3 x14 x15 x16 x17 x18x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0737dc.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)(∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x070e38.. x2 x12 x13 x14 x15 x16 x17 x18 x3x11)x11 (proof)