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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.
Assume H9: 8b97c.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Let x10 of type ο be given.
Assume H10: 3819d.. x1 x9 x7 x6 x8 x4 x3 x5(x9 = x2∀ x11 : ο . x11)(x7 = x2∀ x11 : ο . x11)(x6 = x2∀ x11 : ο . x11)(x8 = x2∀ x11 : ο . x11)(x4 = x2∀ x11 : ο . x11)(x3 = x2∀ x11 : ο . x11)(x5 = x2∀ x11 : ο . x11)not (x1 x9 x2)not (x1 x7 x2)not (x1 x6 x2)x1 x8 x2not (x1 x4 x2)not (x1 x3 x2)not (x1 x5 x2)x10.
Claim L11: ...
...
Apply H9 with x10.
Assume H12: 3819d.. x1 x2 x3 x4 x5 x6 x7 x8.
Apply H12 with (x2 = x9∀ x11 : ο . x11)(x3 = x9∀ x11 : ο . x11)(x4 = x9∀ x11 : ο . x11)(x5 = x9∀ x11 : ο . x11)(x6 = x9∀ x11 : ο . x11)(x7 = x9∀ x11 : ο . x11)(x8 = x9∀ x11 : ο . x11)not (x1 x2 x9)not (x1 x3 x9)not (x1 x4 x9)x1 x5 x9not (x1 x6 x9)not (x1 x7 x9)not (x1 x8 x9)x10.
Assume H13: 2de86.. x1 x2 x3 x4 x5 x6 x7.
Apply H13 with ..........................................(... = ...∀ x11 : ο . x11)(x5 = x9∀ x11 : ο . x11)(x6 = x9∀ x11 : ο . x11)(x7 = x9∀ x11 : ο . x11)(x8 = x9∀ x11 : ο . x11)not (x1 x2 x9)not (x1 x3 x9)not (x1 x4 x9)x1 x5 x9not (x1 x6 x9)not (x1 x7 x9)not (x1 x8 x9)x10.
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