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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.
Let x9 of type ι be given.
Assume H10: x9x0.
Let x10 of type ι be given.
Assume H11: x10x0.
Let x11 of type ι be given.
Assume H12: x11x0.
Let x12 of type ι be given.
Assume H13: x12x0.
Let x13 of type ι be given.
Assume H14: x13x0.
Apply setminusE with x1, Sing x3, x4, e5a83.. x2 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13∀ x14 : ο . (∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0∀ x21 . x21x0∀ x22 . x22x0∀ x23 . x23x0∀ x24 . x24x092a6c.. x2 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x3x14)(∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0∀ x21 . x21x0∀ x22 . x22x0∀ x23 . x23x0∀ x24 . x24x059ef4.. x2 x15 x3 x16 x17 x18 x19 x20 x21 x22 x23 x24x14)x14 leaving 2 subgoals.
Apply H4 with x4.
The subproof is completed by applying H5.
Assume H15: x4x1.
Assume H16: nIn x4 (Sing x3).
Apply setminusE with x1, Sing x3, x5, ...∀ x14 : ο . (∀ x15 . ...∀ x16 . ...∀ x17 . ...∀ x18 . ...∀ x19 . ...∀ x20 . ...∀ x21 . ...∀ x22 . ...∀ x23 . ...∀ x24 . ...92a6c.. ... ... ... ... ... ... ... ... ... ... ... ...x14)(∀ x15 . x15x0∀ x16 . x16x0∀ x17 . x17x0∀ x18 . x18x0∀ x19 . x19x0∀ x20 . x20x0∀ x21 . x21x0∀ x22 . x22x0∀ x23 . x23x0∀ x24 . x24x059ef4.. x2 x15 x3 x16 x17 x18 x19 x20 x21 x22 x23 x24x14)x14 leaving 2 subgoals.
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