Theorem. (l137_bcialg_1)
∀esk3_1 : setset, ∀esk2_1 : setset, ∀v15_bcialg_1 : setprop, ∀esk27_1 : setset, ∀esk28_1 : setset, ∀k2_bcialg_1 : setsetset, ∀k1_binop_1 : setsetsetset, ∀esk5_1 : setset, ∀esk6_1 : setset, ∀r2_hidden : setsetprop, ∀v3_card_1 : setsetprop, ∀v13_struct_0 : setsetprop, ∀v1_card_1 : setprop, ∀l1_struct_0 : setprop, ∀esk23_1 : setset, ∀r1_tarski : setsetprop, ∀v9_struct_0 : setsetprop, ∀esk13_1 : setset, ∀l2_struct_0 : setprop, ∀esk12_1 : setset, ∀k1_xboole_0 : set, ∀esk22_1 : setset, ∀v8_struct_0 : setprop, ∀esk19_1 : setset, ∀esk24_1 : setset, ∀v2_relat_1 : setprop, ∀v7_ordinal1 : setprop, ∀v3_ordinal1 : setprop, ∀esk1_0 : set, ∀esk15_0 : set, ∀esk16_0 : set, ∀esk10_0 : set, ∀esk20_0 : set, ∀o_0_0_xboole_0 : set, ∀esk9_0 : set, ∀esk8_0 : set, ∀esk14_0 : set, ∀esk7_0 : set, ∀esk11_1 : setset, ∀esk21_0 : set, ∀v3_relat_1 : setprop, ∀esk25_1 : setset, ∀v1_zfmisc_1 : setprop, ∀esk26_1 : setset, ∀u2_struct_0 : setset, ∀np__1 : set, ∀v1_relat_1 : setprop, ∀esk17_1 : setset, ∀esk18_1 : setset, ∀v7_struct_0 : setprop, ∀v1_finset_1 : setprop, ∀v1_xboole_0 : setprop, ∀esk4_1 : setset, ∀u1_bcialg_1 : setset, ∀l1_bcialg_1 : setprop, ∀v1_funct_1 : setprop, ∀k1_zfmisc_1 : setset, ∀v1_funct_2 : setsetsetprop, ∀k2_zfmisc_1 : setsetset, ∀k5_binop_1 : setsetsetsetset, ∀v16_bcialg_1 : setprop, ∀epred1_1 : setprop, ∀esk31_1 : setset, ∀esk30_1 : setset, ∀esk29_1 : setset, ∀v2_struct_0 : setprop, ∀v4_bcialg_1 : setprop, ∀v7_bcialg_1 : setprop, ∀m1_subset_1 : setsetprop, ∀u1_struct_0 : setset, ∀l2_bcialg_1 : setprop, ∀v5_bcialg_1 : setprop, ∀v3_bcialg_1 : setprop, ∀k1_bcialg_1 : setsetsetset, ∀k4_struct_0 : setset, (∀X3 X2 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3)) (k1_bcialg_1 X1 X3 X2)) (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X3 (k1_bcialg_1 X1 X3 X2))))) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)(v15_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk2_1 X1) (k1_bcialg_1 X1 (esk2_1 X1) (esk3_1 X1))) (k1_bcialg_1 X1 (esk3_1 X1) (esk2_1 X1))) = (k1_bcialg_1 X1 (esk2_1 X1) (k1_bcialg_1 X1 (esk2_1 X1) (k1_bcialg_1 X1 (esk3_1 X1) (k1_bcialg_1 X1 (esk3_1 X1) (esk2_1 X1)))))v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1))) (esk30_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1)) (k1_bcialg_1 X1 (esk29_1 X1) (esk31_1 X1))) (k1_bcialg_1 X1 (esk31_1 X1) (esk30_1 X1))) = (k4_struct_0 X1)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1))) (esk30_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1)) (k1_bcialg_1 X1 (esk29_1 X1) (esk31_1 X1))) (k1_bcialg_1 X1 (esk31_1 X1) (esk30_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1))) (esk30_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1)) (k1_bcialg_1 X1 (esk29_1 X1) (esk31_1 X1))) (k1_bcialg_1 X1 (esk31_1 X1) (esk30_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1))) (esk30_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk29_1 X1) (esk30_1 X1)) (k1_bcialg_1 X1 (esk29_1 X1) (esk31_1 X1))) (k1_bcialg_1 X1 (esk31_1 X1) (esk30_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X3 (k1_bcialg_1 X1 X3 X2)) (k1_bcialg_1 X1 X3 X2)) (k1_bcialg_1 X1 X2 X3)) = (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3)) (k1_bcialg_1 X1 X3 X2))False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1v16_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3)) (k1_bcialg_1 X1 X3 X2)) = (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X3 (k1_bcialg_1 X1 X3 X2))))False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1v15_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X4 X3 X1, (m1_subset_1 (k5_binop_1 X2 X1 X3 X4) X2False)v1_funct_1 X1m1_subset_1 X4 X2m1_subset_1 X3 X2v1_funct_2 X1 (k2_zfmisc_1 X2 X2) X2m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X2) X2))False)(∀X1, (v2_struct_0 X1False)(v16_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk27_1 X1) (esk28_1 X1)) (esk28_1 X1)) (k2_bcialg_1 X1 (esk28_1 X1))) = (k1_bcialg_1 X1 (esk27_1 X1) (esk28_1 X1))v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X4 X3 X2 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X2 X4)) (k1_bcialg_1 X1 X4 X3)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1epred1_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X4 X3 X1, ((k5_binop_1 X2 X1 X3 X4) = (k1_binop_1 X1 X3 X4)False)v1_funct_1 X1m1_subset_1 X4 X2m1_subset_1 X3 X2v1_funct_2 X1 (k2_zfmisc_1 X2 X2) X2m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X2) X2))False)(∀X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) X3) (k2_bcialg_1 X1 X3)) = (k1_bcialg_1 X1 X2 X3)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1v16_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, ((k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3))) = (k1_bcialg_1 X1 X2 X3)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3)) X3) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1epred1_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X4 X2 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X2 X4)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)(k1_bcialg_1 X1 X4 X3) = (k4_struct_0 X1)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X4 X3)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)(k1_bcialg_1 X1 X2 X4) = (k4_struct_0 X1)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X4 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) X4) = (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X4) X3)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k5_binop_1 (u1_struct_0 X1) (u1_bcialg_1 X1) X2 X3) = (k1_bcialg_1 X1 X2 X3)False)l1_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X4 X1, ((k1_bcialg_1 X1 X2 X4) = (k4_struct_0 X1)False)(v2_struct_0 X1False)(k1_bcialg_1 X1 X3 X4) = (k4_struct_0 X1)(k1_bcialg_1 X1 X2 X3) = (k4_struct_0 X1)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (m1_subset_1 (u1_bcialg_1 X1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1)) (u1_struct_0 X1)))False)l1_bcialg_1 X1False)(∀X1 X2 X3, (X2 = X3False)(v2_struct_0 X1False)(k1_bcialg_1 X1 X3 X2) = (k4_struct_0 X1)(k1_bcialg_1 X1 X2 X3) = (k4_struct_0 X1)v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k1_bcialg_1 X1 X2 X3) (u1_struct_0 X1)False)l1_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k1_bcialg_1 X1 X2 (k4_struct_0 X1)) = X2False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)(v5_bcialg_1 X1False)(k1_bcialg_1 X1 (esk4_1 X1) (esk4_1 X1)) = (k4_struct_0 X1)l2_bcialg_1 X1False)(∀X1, (v1_funct_2 (u1_bcialg_1 X1) (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1)) (u1_struct_0 X1)False)l1_bcialg_1 X1False)(∀X2 X1, ((k1_bcialg_1 X1 (k4_struct_0 X1) X2) = (k2_bcialg_1 X1 X2)False)(v2_struct_0 X1False)l2_bcialg_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k1_bcialg_1 X1 X2 X2) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v5_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(m1_subset_1 (k2_bcialg_1 X1 X2) (u1_struct_0 X1)False)l2_bcialg_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, ((k1_bcialg_1 X1 (esk6_1 X1) (esk5_1 X1)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)(v7_bcialg_1 X1False)l2_bcialg_1 X1False)(∀X1, ((k1_bcialg_1 X1 (esk5_1 X1) (esk6_1 X1)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)(v7_bcialg_1 X1False)l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v16_bcialg_1 X1False)(m1_subset_1 (esk28_1 X1) (u1_struct_0 X1)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v16_bcialg_1 X1False)(m1_subset_1 (esk27_1 X1) (u1_struct_0 X1)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v15_bcialg_1 X1False)(m1_subset_1 (esk3_1 X1) (u1_struct_0 X1)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v15_bcialg_1 X1False)(m1_subset_1 (esk2_1 X1) (u1_struct_0 X1)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X1 X2, (v3_card_1 (u1_struct_0 X2) X1False)l1_struct_0 X2v1_card_1 X1v13_struct_0 X2 X1False)(∀X1 X2, (v1_xboole_0 X2False)(v1_finset_1 X1False)v1_finset_1 (k2_zfmisc_1 X1 X2)False)(∀X1 X2, (v1_xboole_0 X2False)(v1_finset_1 X1False)v1_finset_1 (k2_zfmisc_1 X2 X1)False)(∀X1, (m1_subset_1 (esk31_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (m1_subset_1 (esk30_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (m1_subset_1 (esk29_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk31_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk30_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk29_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk31_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk30_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk29_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk31_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk30_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk29_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1, (v7_struct_0 X1False)l2_struct_0 X1v9_struct_0 (esk13_1 X1) X1False)(∀X1 X2, (v1_relat_1 X2False)v1_relat_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1, (v2_struct_0 X1False)(v7_bcialg_1 X1False)(m1_subset_1 (esk6_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v7_bcialg_1 X1False)(m1_subset_1 (esk5_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v5_bcialg_1 X1False)(m1_subset_1 (esk4_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk13_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, v2_struct_0 X1l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (m1_subset_1 (esk12_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (m1_subset_1 (u2_struct_0 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (m1_subset_1 (k4_struct_0 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 k1_xboole_0False)(∀X1, (v2_struct_0 X1False)(v13_struct_0 X1 np__1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_finset_1 X1False)(m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk26_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v2_struct_0 X1False)(v7_bcialg_1 X1False)(esk6_1 X1) = (esk5_1 X1)l2_bcialg_1 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v1_finset_1 (u1_struct_0 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (esk18_1 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk23_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk17_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v9_struct_0 (esk12_1 X1) X1False)l2_struct_0 X1False)(∀X1, (v9_struct_0 (k4_struct_0 X1) X1False)l2_struct_0 X1False)(∀X1, (v13_struct_0 (esk19_1 X1) X1False)v1_card_1 X1False)(∀X1, (v3_card_1 (esk25_1 X1) X1False)v1_card_1 X1False)(∀X1, (v3_card_1 (esk24_1 X1) X1False)v1_card_1 X1False)(∀X1, v1_xboole_0 X1v3_card_1 X1 np__1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_finset_1 (u1_struct_0 X1)False)l1_struct_0 X1v8_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u1_struct_0 X1)False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_xboole_0 (u1_struct_0 X1)False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_zfmisc_1 X1False)v3_card_1 X1 np__1False)(∀X1, (v1_xboole_0 X1False)v3_card_1 X1 k1_xboole_0False)(∀X1, (v1_xboole_0 X1False)(v3_card_1 X1 np__1False)v1_zfmisc_1 X1False)(∀X1, (v1_xboole_0 X1False)(v3_card_1 (esk26_1 X1) np__1False)False)(∀X1, (v2_struct_0 X1False)(v1_zfmisc_1 (esk17_1 X1)False)l1_struct_0 X1False)(∀X1, (v1_finset_1 X1False)v1_finset_1 (esk22_1 X1)False)(∀X1, (v1_finset_1 X1False)v1_finset_1 (k1_zfmisc_1 X1)False)(∀X1, (v3_card_1 X1 k1_xboole_0False)v1_xboole_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v2_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X1, (v3_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X1, (v7_ordinal1 X1False)v3_ordinal1 X1v1_finset_1 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_funct_1 (esk25_1 X1)False)v1_card_1 X1False)(∀X1, (v1_funct_1 (u1_bcialg_1 X1)False)l1_bcialg_1 X1False)(∀X1, (v1_relat_1 (esk25_1 X1)False)v1_card_1 X1False)(∀X1, (l1_struct_0 (esk19_1 X1)False)v1_card_1 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v2_struct_0 X1False)(epred1_1 X1False)l2_bcialg_1 X1False)(∀X1, ((k4_struct_0 X1) = (u2_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (l2_struct_0 X1False)l2_bcialg_1 X1False)(∀X1, (l1_bcialg_1 X1False)l2_bcialg_1 X1False)(∀X1, (v1_finset_1 X1False)v7_ordinal1 X1False)(∀X1, (v1_relat_1 X1False)v1_xboole_0 X1False)(∀X1, (v3_ordinal1 X1False)v1_card_1 X1False)(∀X1, (v1_card_1 X1False)v7_ordinal1 X1False)(∀X1, (v1_card_1 X1False)v1_xboole_0 X1False)(∀X1, (l1_struct_0 X1False)l2_struct_0 X1False)(∀X1, (l1_struct_0 X1False)l1_bcialg_1 X1False)(v15_bcialg_1 esk1_0v16_bcialg_1 esk1_0False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)((v15_bcialg_1 esk1_0False)(v16_bcialg_1 esk1_0False)False)(v1_finset_1 esk21_0False)(v1_xboole_0 esk15_0False)(v1_xboole_0 np__1False)(v2_struct_0 esk16_0False)(v2_struct_0 esk1_0False)(∀X1 X2, (v1_relat_1 (k2_zfmisc_1 X1 X2)False)False)(∀X1, (m1_subset_1 (esk11_1 X1) X1False)False)(∀X1, (r1_tarski X1 X1False)False)((l2_struct_0 esk16_0False)False)((l2_struct_0 esk10_0False)False)((l1_bcialg_1 esk7_0False)False)((v2_relat_1 esk20_0False)False)((v1_relat_1 esk20_0False)False)((v1_relat_1 esk15_0False)False)((v1_card_1 esk14_0False)False)((v7_struct_0 esk16_0False)False)((l1_struct_0 esk8_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((l2_bcialg_1 esk9_0False)False)((l2_bcialg_1 esk1_0False)False)((v7_bcialg_1 esk1_0False)False)((v5_bcialg_1 esk1_0False)False)((v4_bcialg_1 esk1_0False)False)((v3_bcialg_1 esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.