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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιιο be given.
Assume H0: ∀ x3 . x3x1∀ x4 . x4x1x2 x3 x4x2 x4 x3.
Assume H1: 4402e.. x1 x2.
Assume H2: cf2df.. x1 x2.
Let x3 of type ι be given.
Assume H3: x3x1.
Assume H4: x0setminus x1 (Sing x3).
Let x4 of type ι be given.
Assume H5: x4x0.
Let x5 of type ι be given.
Assume H6: x5x0.
Let x6 of type ι be given.
Assume H7: x6x0.
Let x7 of type ι be given.
Assume H8: x7x0.
Let x8 of type ι be given.
Assume H9: x8x0.
Apply setminusE with x1, Sing x3, x4, ...∀ x9 : ο . (∀ x10 . ...∀ x11 . ...∀ x12 . ...∀ x13 . ...∀ x14 . ...51771.. x2 x10 x11 x12 x13 x3 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x04ce91.. x2 x10 x11 x12 x3 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0fba9e.. x2 x3 x10 x11 x12 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x039b60.. x2 x10 x11 x3 x12 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x038251.. x2 x10 x11 x12 x3 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0ba720.. x2 x10 x11 x12 x3 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0247da.. x2 x10 x3 x11 x12 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x00da49.. x2 x10 x11 x12 x13 x3 x14x9)x9 leaving 2 subgoals.
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