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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.
Let x11 of type ι be given.
Assume H10: x11x0.
Assume H11: 9eb9c.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11.
Let x12 of type ο be given.
Assume H12: d92ce.. x1 x3 x2 x9 x6 x5 x11 x10 x4 x8(x3 = x7∀ x13 : ο . x13)(x2 = x7∀ x13 : ο . x13)(x9 = x7∀ x13 : ο . x13)(x6 = x7∀ x13 : ο . x13)(x5 = x7∀ x13 : ο . x13)(x11 = x7∀ x13 : ο . x13)(x10 = x7∀ x13 : ο . x13)(x4 = x7∀ x13 : ο . x13)(x8 = x7∀ x13 : ο . x13)x1 x3 x7not (x1 x2 x7)not (x1 x9 x7)not (x1 x6 x7)x1 x5 x7x1 x11 x7not (x1 x10 x7)x1 x4 x7not (x1 x8 x7)x12.
Claim L13: ...
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Apply H11 with x12.
Assume H14: d92ce.. x1 x2 x3 x4 x5 x6 x7 x8 x9 x10.
Apply H14 with (x2 = x11∀ x13 : ο . x13)(x3 = x11∀ x13 : ο . x13)(x4 = x11∀ x13 : ο . x13)(x5 = x11∀ x13 : ο . x13)(x6 = x11∀ x13 : ο . x13)(x7 = x11∀ x13 : ο . x13)(x8 = x11∀ x13 : ο . x13)(x9 = x11∀ x13 : ο . x13)(x10 = x11∀ x13 : ο . x13)x1 x2 x11not (x1 x3 x11)not (x1 x4 x11)not (x1 x5 x11)x1 x6 x11x1 x7 x11not (x1 x8 x11)x1 x9 x11not (x1 x10 x11)x12.
Assume H15: fa72d.. x1 x2 x3 x4 x5 x6 x7 x8 x9.
Apply H15 with ................................................................................................x1 ... ...not (x1 x10 x11)x12.
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