| vout |
|---|
PrFwu../e543d.. 24.97 barsTMcF5../9bb8c.. ownership of 15c2f.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMYWv../e459b.. ownership of 52654.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMLkv../6ee3a.. ownership of fd785.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMMZk../11384.. ownership of 81364.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMGR4../670f6.. ownership of fd974.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMSM3../a2f88.. ownership of 42d92.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMQDT../bdbca.. ownership of e5c8e.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMSpr../fe52c.. ownership of c4c94.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMUKD../50047.. ownership of b05a4.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0TMR42../e1d59.. ownership of 2cd40.. as prop with payaddr PrGM6.. rights free controlledby PrGM6.. upto 0PUakf../650dd.. doc published by PrGM6..Definition FalseFalse := ∀ x0 : ο . x0Definition notnot := λ x0 : ο . x0 ⟶ FalseDefinition 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 x4 ⟶ x5) ⟶ x5Definition 5a3b5.. := 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 x5 ⟶ not (x0 x3 x5) ⟶ not (x0 x4 x5) ⟶ x6) ⟶ x6Definition 00e19.. := λ x0 : ι → ι → ο . λ x1 x2 x3 x4 x5 x6 . ∀ x7 : ο . (5a3b5.. 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 x6 ⟶ not (x0 x2 x6) ⟶ not (x0 x3 x6) ⟶ not (x0 x4 x6) ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7Definition 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 x5 ⟶ not (x0 x3 x5) ⟶ x0 x4 x5 ⟶ x6) ⟶ x6Definition 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 x6 ⟶ x0 x2 x6 ⟶ x0 x3 x6 ⟶ not (x0 x4 x6) ⟶ not (x0 x5 x6) ⟶ x7) ⟶ x7Definition 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 x7 ⟶ x0 x2 x7 ⟶ x0 x3 x7 ⟶ not (x0 x4 x7) ⟶ not (x0 x5 x7) ⟶ not (x0 x6 x7) ⟶ x8) ⟶ x8Definition SubqSubq := λ x0 x1 . ∀ x2 . x2 ∈ x0 ⟶ x2 ∈ x1Param atleastpatleastp : ι → ι → οDefinition cdfa5.. := λ x0 x1 . λ x2 : ι → ι → ο . ∀ x3 . x3 ⊆ x1 ⟶ atleastp x0 x3 ⟶ not (∀ x4 . x4 ∈ x3 ⟶ ∀ x5 . x5 ∈ x3 ⟶ (x4 = x5 ⟶ ∀ x6 : ο . x6) ⟶ x2 x4 x5)Param u4 : ιDefinition 86706.. := cdfa5.. u4Definition 35fb6.. := λ x0 . λ x1 : ι → ι → ο . 86706.. x0 (λ x2 x3 . not (x1 x2 x3))Param SetAdjoinSetAdjoin : ι → ι → ιParam UPairUPair : ι → ι → ιDefinition oror := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x2) ⟶ (x1 ⟶ x2) ⟶ x2Known xmxm : ∀ x0 : ο . or x0 (not x0)Known dnegdneg : ∀ x0 : ο . not (not x0) ⟶ x0Param equipequip : ι → ι → οKnown equip_atleastpequip_atleastp : ∀ x0 x1 . equip x0 x1 ⟶ atleastp x0 x1Known 7204a.. : ∀ x0 x1 x2 x3 . (x0 = x1 ⟶ ∀ x4 : ο . x4) ⟶ (x0 = x2 ⟶ ∀ x4 : ο . x4) ⟶ (x1 = x2 ⟶ ∀ x4 : ο . x4) ⟶ (x0 = x3 ⟶ ∀ x4 : ο . x4) ⟶ (x1 = x3 ⟶ ∀ x4 : ο . x4) ⟶ (x2 = x3 ⟶ ∀ x4 : ο . x4) ⟶ equip u4 (SetAdjoin (SetAdjoin (UPair x0 x1) x2) x3)Known 58c12.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 x3 x4 . x0 x1 x2 ⟶ x0 x1 x3 ⟶ x0 x1 x4 ⟶ x0 x2 x3 ⟶ x0 x2 x4 ⟶ x0 x3 x4 ⟶ (∀ x5 . x5 ∈ SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4 ⟶ ∀ x6 . x6 ∈ SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4 ⟶ x0 x5 x6 ⟶ x0 x6 x5) ⟶ ∀ x5 . x5 ∈ SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4 ⟶ ∀ x6 . x6 ∈ SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4 ⟶ (x5 = x6 ⟶ ∀ x7 : ο . x7) ⟶ x0 x5 x6Known c88f0.. : ∀ x0 x1 . x1 ∈ x0 ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ SetAdjoin (SetAdjoin (UPair x1 x2) x3) x4 ⊆ x0Theorem b05a4.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ ∀ x7 . x7 ∈ x1 ⟶ ∀ x8 . x8 ∈ x1 ⟶ ∀ x9 . x9 ∈ x1 ⟶ ∀ x10 . x10 ∈ x1 ⟶ ∀ x11 . x11 ∈ x1 ⟶ ∀ x12 . x12 ∈ x1 ⟶ ∀ x13 . x13 ∈ x1 ⟶ ∀ x14 . x14 ∈ x1 ⟶ (∀ x15 . x15 ∈ x1 ⟶ ∀ x16 . x16 ∈ x1 ⟶ x0 x15 x16 ⟶ x0 x16 x15) ⟶ (x2 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x14 ⟶ ∀ x15 : ο . x15) ⟶ 00e19.. x0 x2 x3 x4 x5 x6 x7 ⟶ 88b7c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x14 ⟶ 86706.. x1 x0 ⟶ 35fb6.. x1 x0 ⟶ (x0 x2 x11 ⟶ x0 x2 x12 ⟶ not (x0 x2 x10) ⟶ not (x0 x2 x9) ⟶ x0 x3 x10 ⟶ not (x0 x3 x9) ⟶ False) ⟶ (x0 x6 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ (x0 x6 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x4 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x4 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ (x0 x2 x14 ⟶ not (x0 x2 x13) ⟶ False) ⟶ (x0 x2 x10 ⟶ not (x0 x2 x9) ⟶ False) ⟶ False...
Definition andand := λ x0 x1 : ο . ∀ x2 : ο . (x0 ⟶ x1 ⟶ x2) ⟶ x2Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0Known 1c461.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2) ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ 88b7c.. x1 x2 x3 x4 x5 x6 x7 x8 ⟶ 88b7c.. x1 x2 x4 x3 x6 x5 x7 x8Known andIandI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1Theorem e5c8e.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ ∀ x7 . x7 ∈ x1 ⟶ ∀ x8 . x8 ∈ x1 ⟶ ∀ x9 . x9 ∈ x1 ⟶ ∀ x10 . x10 ∈ x1 ⟶ ∀ x11 . x11 ∈ x1 ⟶ ∀ x12 . x12 ∈ x1 ⟶ ∀ x13 . x13 ∈ x1 ⟶ ∀ x14 . x14 ∈ x1 ⟶ (∀ x15 . x15 ∈ x1 ⟶ ∀ x16 . x16 ∈ x1 ⟶ x0 x15 x16 ⟶ x0 x16 x15) ⟶ (x2 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x14 ⟶ ∀ x15 : ο . x15) ⟶ 00e19.. x0 x2 x3 x4 x5 x6 x7 ⟶ 88b7c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x14 ⟶ 86706.. x1 x0 ⟶ 35fb6.. x1 x0 ⟶ (x0 x2 x14 ⟶ not (x0 x2 x13) ⟶ False) ⟶ (x0 x6 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ (x0 x6 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x4 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x4 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ False...
Known 06a77.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2) ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ 88b7c.. x1 x2 x3 x4 x5 x6 x7 x8 ⟶ 88b7c.. x1 x2 x3 x4 x5 x6 x8 x7Theorem fd974.. : ∀ x0 . ∀ x1 : ι → ι → ο . (∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ x1 x2 x3 ⟶ x1 x3 x2) ⟶ ∀ x2 . x2 ∈ x0 ⟶ ∀ x3 . x3 ∈ x0 ⟶ ∀ x4 . x4 ∈ x0 ⟶ ∀ x5 . x5 ∈ x0 ⟶ ∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ 88b7c.. x1 x2 x3 x4 x5 x6 x7 x8 ⟶ 88b7c.. x1 x2 x4 x3 x6 x5 x8 x7...
Theorem fd785.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ ∀ x7 . x7 ∈ x1 ⟶ ∀ x8 . x8 ∈ x1 ⟶ ∀ x9 . x9 ∈ x1 ⟶ ∀ x10 . x10 ∈ x1 ⟶ ∀ x11 . x11 ∈ x1 ⟶ ∀ x12 . x12 ∈ x1 ⟶ ∀ x13 . x13 ∈ x1 ⟶ ∀ x14 . x14 ∈ x1 ⟶ (∀ x15 . x15 ∈ x1 ⟶ ∀ x16 . x16 ∈ x1 ⟶ x0 x15 x16 ⟶ x0 x16 x15) ⟶ (x2 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x14 ⟶ ∀ x15 : ο . x15) ⟶ 00e19.. x0 x2 x3 x4 x5 x6 x7 ⟶ 88b7c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x14 ⟶ 86706.. x1 x0 ⟶ 35fb6.. x1 x0 ⟶ (x0 x6 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ (x0 x6 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x4 x8) ⟶ False) ⟶ (x0 x5 x8 ⟶ not (x0 x2 x8) ⟶ False) ⟶ (x0 x4 x8 ⟶ not (x0 x3 x8) ⟶ False) ⟶ False...
Known 8f85a.. : ∀ x0 : ι → ι → ο . ∀ x1 : ι → ι → ι → ι → ι → ι → ι → ο . (∀ x2 x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ ∀ x6 . x6 ∈ x2 ⟶ ∀ x7 . x7 ∈ x2 ⟶ ∀ x8 . x8 ∈ x2 ⟶ ∀ x9 . x9 ∈ x2 ⟶ ∀ x10 . x10 ∈ x2 ⟶ ∀ x11 . x11 ∈ x2 ⟶ ∀ x12 . x12 ∈ x2 ⟶ ∀ x13 . x13 ∈ x2 ⟶ ∀ x14 . x14 ∈ x2 ⟶ ∀ x15 . x15 ∈ x2 ⟶ (∀ x16 . x16 ∈ x2 ⟶ ∀ x17 . x17 ∈ x2 ⟶ x0 x16 x17 ⟶ x0 x17 x16) ⟶ (x3 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x15 ⟶ ∀ x16 : ο . x16) ⟶ 00e19.. x0 x3 x4 x5 x6 x7 x8 ⟶ x1 x9 x10 x11 x12 x13 x14 x15 ⟶ 86706.. x2 x0 ⟶ 35fb6.. x2 x0 ⟶ (x0 x7 x9 ⟶ not (x0 x4 x9) ⟶ False) ⟶ (x0 x7 x9 ⟶ not (x0 x3 x9) ⟶ False) ⟶ (x0 x6 x9 ⟶ not (x0 x5 x9) ⟶ False) ⟶ (x0 x6 x9 ⟶ not (x0 x4 x9) ⟶ False) ⟶ (x0 x6 x9 ⟶ not (x0 x3 x9) ⟶ False) ⟶ (x0 x5 x9 ⟶ not (x0 x4 x9) ⟶ False) ⟶ False) ⟶ ∀ x2 x3 . x3 ∈ x2 ⟶ ∀ x4 . x4 ∈ x2 ⟶ ∀ x5 . x5 ∈ x2 ⟶ ∀ x6 . x6 ∈ x2 ⟶ ∀ x7 . x7 ∈ x2 ⟶ ∀ x8 . x8 ∈ x2 ⟶ ∀ x9 . x9 ∈ x2 ⟶ ∀ x10 . x10 ∈ x2 ⟶ ∀ x11 . x11 ∈ x2 ⟶ ∀ x12 . x12 ∈ x2 ⟶ ∀ x13 . x13 ∈ x2 ⟶ ∀ x14 . x14 ∈ x2 ⟶ ∀ x15 . x15 ∈ x2 ⟶ (∀ x16 . x16 ∈ x2 ⟶ ∀ x17 . x17 ∈ x2 ⟶ x0 x16 x17 ⟶ x0 x17 x16) ⟶ (x3 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x9 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x10 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x11 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x12 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x13 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x14 ⟶ ∀ x16 : ο . x16) ⟶ (x3 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x4 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x5 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x6 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x7 = x15 ⟶ ∀ x16 : ο . x16) ⟶ (x8 = x15 ⟶ ∀ x16 : ο . x16) ⟶ 00e19.. x0 x3 x4 x5 x6 x7 x8 ⟶ x1 x9 x10 x11 x12 x13 x14 x15 ⟶ 86706.. x2 x0 ⟶ 35fb6.. x2 x0 ⟶ FalseTheorem 15c2f.. : ∀ x0 : ι → ι → ο . ∀ x1 x2 . x2 ∈ x1 ⟶ ∀ x3 . x3 ∈ x1 ⟶ ∀ x4 . x4 ∈ x1 ⟶ ∀ x5 . x5 ∈ x1 ⟶ ∀ x6 . x6 ∈ x1 ⟶ ∀ x7 . x7 ∈ x1 ⟶ ∀ x8 . x8 ∈ x1 ⟶ ∀ x9 . x9 ∈ x1 ⟶ ∀ x10 . x10 ∈ x1 ⟶ ∀ x11 . x11 ∈ x1 ⟶ ∀ x12 . x12 ∈ x1 ⟶ ∀ x13 . x13 ∈ x1 ⟶ ∀ x14 . x14 ∈ x1 ⟶ (∀ x15 . x15 ∈ x1 ⟶ ∀ x16 . x16 ∈ x1 ⟶ x0 x15 x16 ⟶ x0 x16 x15) ⟶ (x2 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x8 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x9 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x10 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x11 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x12 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x13 ⟶ ∀ x15 : ο . x15) ⟶ (x2 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x3 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x4 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x5 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x6 = x14 ⟶ ∀ x15 : ο . x15) ⟶ (x7 = x14 ⟶ ∀ x15 : ο . x15) ⟶ 00e19.. x0 x2 x3 x4 x5 x6 x7 ⟶ 88b7c.. (λ x15 x16 . not (x0 x15 x16)) x8 x9 x10 x11 x12 x13 x14 ⟶ 86706.. x1 x0 ⟶ 35fb6.. x1 x0 ⟶ False...
|
|