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Proofgold Proof

pf
Apply ax_c11__ax_c11_b__ax_c11n__ax_c15__ax_c9__ax_c9_b__ax_c9_b1__ax_c9_b2__ax_c9_b3__ax_c14__ax_c16__ax_riotaBAD__df_lsatoms__df_lshyp__df_lcv__df_lfl__df_lkr__df_ldual with ∀ x0 x1 . wn (∀ x2 . wceq (cv x2) (cv x0))wn (∀ x2 . wceq (cv x2) (cv x1))wceq (cv x0) (cv x1)∀ x2 . wceq (cv x0) (cv x1).
Assume H0: ∀ x0 : ι → ι → ο . ∀ x1 x2 . (∀ x3 . wceq (cv x3) (cv x2))(∀ x3 . x0 x3 x2)∀ x3 . x0 x1 x3.
Assume H1: ∀ x0 : ι → ο . (∀ x1 . wceq (cv x1) (cv x1))(∀ x1 . x0 x1)∀ x1 . x0 x1.
Assume H2: ∀ x0 x1 . (∀ x2 . wceq (cv x2) (cv x1))∀ x2 . wceq (cv x2) (cv x0).
Assume H3: ∀ x0 : ι → ο . ∀ x1 x2 . wn (∀ x3 . wceq (cv x3) (cv x1))wceq (cv x2) (cv x1)x0 x2∀ x3 . wceq (cv x3) (cv x1)x0 x3.
Assume H4: ∀ x0 x1 . wn (∀ x2 . wceq (cv x2) (cv x0))wn (∀ x2 . wceq (cv x2) (cv x1))wceq (cv x0) (cv x1)∀ x2 . wceq (cv x0) (cv x1).
Assume H5: ∀ x0 . wn (∀ x1 . wceq (cv x1) (cv x1))wn (∀ x1 . wceq (cv x1) (cv x1))wceq (cv x0) (cv x0)∀ x1 . wceq (cv x1) (cv x1).
Assume H6: ∀ x0 . wn (∀ x1 . wceq (cv x1) (cv x0))wn (∀ x1 . wceq (cv x1) (cv x0))wceq (cv x0) (cv x0)∀ x1 . wceq (cv x0) (cv x0).
Assume H7: ∀ x0 x1 . wn (∀ x2 . wceq (cv x2) (cv x2))wn (∀ x2 . wceq (cv x2) (cv x0))wceq (cv x1) (cv x0)∀ x2 . wceq (cv x2) (cv x0).
Assume H8: ∀ x0 x1 . wn (∀ x2 . wceq (cv x2) (cv x0))wn (∀ x2 . wceq (cv x2) (cv x2))wceq (cv x0) (cv x1)∀ x2 . wceq (cv x0) (cv x2).
Assume H9: ∀ x0 x1 . wn (∀ x2 . wceq (cv x2) ...)wn (∀ x2 . wceq (cv x2) (cv x1))wcel (cv x0) (cv x1)∀ x2 . wcel (cv x0) (cv x1).
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