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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.
Let x9 of type ι be given.
Assume H8: x9x0.
Let x10 of type ι be given.
Assume H9: x10x0.
Assume H10: 654b9.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
Let x11 of type ο be given.
Assume H11: af16d.. x1 x2 x7 x4 x10 x6 x3 x8 x9(x2 = x5∀ x12 : ο . x12)(x7 = x5∀ x12 : ο . x12)(x4 = x5∀ x12 : ο . x12)(x10 = x5∀ x12 : ο . x12)(x6 = x5∀ x12 : ο . x12)(x3 = x5∀ x12 : ο . x12)(x8 = x5∀ x12 : ο . x12)(x9 = x5∀ x12 : ο . x12)not (x1 x2 x5)x1 x7 x5not (x1 x4 x5)not (x1 x10 x5)x1 x6 x5not (x1 x3 x5)x1 x8 x5x1 x9 x5x11.
Claim L12: ...
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Apply H10 with x11.
Assume H13: af16d.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Apply H13 with (x2 = x10∀ x12 : ο . x12)(x3 = x10∀ x12 : ο . x12)(x4 = x10∀ x12 : ο . x12)(x5 = x10∀ x12 : ο . x12)(x6 = x10∀ x12 : ο . x12)(x7 = x10∀ x12 : ο . x12)(x8 = x10∀ x12 : ο . x12)(x9 = x10∀ x12 : ο . x12)not (x1 x2 x10)x1 x3 x10not (x1 x4 x10)not (x1 x5 x10)x1 x6 x10not (x1 x7 x10)x1 x8 x10x1 x9 x10x11.
Assume H14: 36d58.. x1 x2 x3 x4 x5 x6 x7 x8.
Apply H14 with ...............................................................(...∀ x12 : ο . x12)not (x1 x2 x10)x1 x3 x10not (x1 x4 x10)not (x1 x5 x10)x1 x6 x10not (x1 x7 x10)x1 x8 x10x1 x9 x10x11.
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