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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιιο be given.
Assume H0: ∀ x2 . x2x0∀ x3 . x3x0x1 x2 x3x1 x3 x2.
Let x2 of type ι be given.
Assume H1: x2x0.
Let x3 of type ι be given.
Assume H2: x3x0.
Let x4 of type ι be given.
Assume H3: x4x0.
Let x5 of type ι be given.
Assume H4: x5x0.
Let x6 of type ι be given.
Assume H5: x6x0.
Let x7 of type ι be given.
Assume H6: x7x0.
Let x8 of type ι be given.
Assume H7: x8x0.
Assume H8: 18ba2.. x1 x2 x3 x4 x5 x6 x7 x8.
Let x9 of type ο be given.
Assume H9: f831d.. x1 x2 x3 x4 x5 x6 x8(x2 = x7∀ x10 : ο . x10)(x3 = x7∀ x10 : ο . x10)(x4 = x7∀ x10 : ο . x10)(x5 = x7∀ x10 : ο . x10)(x6 = x7∀ x10 : ο . x10)(x8 = x7∀ x10 : ο . x10)x1 x2 x7x1 x3 x7x1 x4 x7x1 x5 x7not (x1 x6 x7)not (x1 x8 x7)x9.
Claim L10: ...
...
Apply H8 with x9.
Assume H11: f831d.. x1 x2 x3 x4 x5 x6 x7.
Apply H11 with (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)x1 x2 x8x1 x3 x8x1 x4 x8x1 x5 x8not (x1 x6 x8)not (x1 x7 x8)x9.
Assume H12: c5756.. x1 x2 x3 x4 x5 x6.
Apply H12 with ...(...∀ x10 : ο . x10)(x4 = x7∀ x10 : ο . x10)(x5 = x7∀ x10 : ο . x10)(x6 = x7∀ x10 : ο . x10)x1 x2 x7x1 x3 x7x1 x4 x7x1 x5 x7not (x1 x6 x7)(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)x1 x2 x8x1 x3 x8x1 x4 x8x1 x5 x8not (x1 x6 x8)not (x1 x7 x8)x9.
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