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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, 58403.. x2 x4 x5 x6 x7 x8∀ x9 : ο . (∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x03d300.. x2 x10 x11 x12 x3 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x08310d.. x2 x10 x11 x12 x13 x14 x3x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x09ab39.. x2 x3 x10 x11 x12 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x01e330.. x2 x3 x10 x11 x12 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x0af3c4.. x2 x10 x11 x12 x3 x13 x14x9)(∀ x10 . x10x0∀ x11 . x11x0∀ x12 . x12x0∀ x13 . x13x0∀ x14 . x14x085e71.. x2 x3 x10 x11 x12 x13 x14x9)x9 leaving 2 subgoals.
Apply H4 with x4.
The subproof is completed by applying H5.
Assume H10: x4x1.
Assume H11: nIn x4 (Sing x3).
Apply setminusE with x1, Sing x3, x5, ...∀ x9 : ο . ...............(∀ x10 . ...∀ x11 . ...∀ x12 . ...∀ x13 . x13x0∀ x14 . x14x085e71.. x2 x3 x10 x11 x12 x13 x14x9)x9 leaving 2 subgoals.
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