Theorem. (
t22_bcialg_1)
∀k1_xboole_0 : set, ∀v1_funct_2 : set → set → set → prop, ∀k1_relset_1 : set → set → set, ∀v2_struct_0 : set → prop, ∀m1_bcialg_1 : set → set → prop, ∀k1_realset1 : set → set → set, ∀r1_tarski : set → set → prop, ∀l2_bcialg_1 : set → prop, ∀v7_bcialg_1 : set → prop, ∀v5_bcialg_1 : set → prop, ∀v4_bcialg_1 : set → prop, ∀v3_bcialg_1 : set → prop, ∀k4_struct_0 : set → set, ∀k5_relat_1 : set → set → set, ∀r2_hidden : set → set → prop, ∀k9_xtuple_0 : set → set, ∀v3_card_1 : set → set → prop, ∀v1_funct_1 : set → prop, ∀v1_card_1 : set → prop, ∀esk6_1 : set → set, ∀v13_struct_0 : set → set → prop, ∀l1_struct_0 : set → prop, ∀v7_struct_0 : set → prop, ∀esk14_1 : set → set, ∀esk13_1 : set → set, ∀esk8_1 : set → set, ∀esk18_1 : set → set, ∀v1_zfmisc_1 : set → prop, ∀esk21_1 : set → set, ∀v2_relat_1 : set → prop, ∀v7_ordinal1 : set → prop, ∀v3_ordinal1 : set → prop, ∀esk17_0 : set, ∀esk7_1 : set → set, ∀esk2_0 : set, ∀esk5_0 : set, ∀esk10_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀o_0_0_xboole_0 : set, ∀esk16_0 : set, ∀esk12_0 : set, ∀esk11_0 : set, ∀esk1_0 : set, ∀esk20_1 : set → set, ∀esk15_1 : set → set, ∀v8_struct_0 : set → prop, ∀esk22_1 : set → set, ∀u2_struct_0 : set → set, ∀np__1 : set, ∀l2_struct_0 : set → prop, ∀esk9_1 : set → set, ∀v9_struct_0 : set → set → prop, ∀v3_relat_1 : set → prop, ∀esk19_1 : set → set, ∀v1_finset_1 : set → prop, ∀v1_xboole_0 : set → prop, ∀v1_relat_1 : set → prop, ∀v4_relat_1 : set → set → prop, ∀m1_subset_1 : set → set → prop, ∀u1_struct_0 : set → set, ∀k2_zfmisc_1 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀u1_bcialg_1 : set → set, ∀l1_bcialg_1 : set → prop, (∀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 X1 → False) → (∀X2 X1 X3, (X3 = k1_xboole_0 → False) → ((k1_relset_1 X2 X1) = X2 → False) → v1_funct_2 X1 X2 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X3 X2 X1, (X1 = k1_xboole_0 → False) → X3 = k1_xboole_0 → v1_funct_2 X1 X2 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v2_struct_0 X1 → False) → (m1_bcialg_1 X1 X2 → False) → (k4_struct_0 X1) = (k4_struct_0 X2) → (k1_realset1 (u1_bcialg_1 X2) (u1_struct_0 X1)) = (u1_bcialg_1 X1) → v3_bcialg_1 X2 → v3_bcialg_1 X1 → v4_bcialg_1 X2 → v4_bcialg_1 X1 → v5_bcialg_1 X2 → v5_bcialg_1 X1 → v7_bcialg_1 X2 → v7_bcialg_1 X1 → l2_bcialg_1 X2 → l2_bcialg_1 X1 → r1_tarski (u1_struct_0 X1) (u1_struct_0 X2) → False) → (∀X1 X2 X3, (X3 = k1_xboole_0 → False) → (v1_funct_2 X2 X1 X3 → False) → (k1_relset_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → False) → (∀X1 X2 X3, (v1_funct_2 X1 X2 X3 → False) → X3 = k1_xboole_0 → X1 = k1_xboole_0 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X2, ((k1_realset1 (u1_bcialg_1 X2) (u1_struct_0 X1)) = (u1_bcialg_1 X1) → False) → (v2_struct_0 X2 → False) → (v2_struct_0 X1 → False) → v3_bcialg_1 X2 → v3_bcialg_1 X1 → v4_bcialg_1 X2 → v4_bcialg_1 X1 → v5_bcialg_1 X2 → v5_bcialg_1 X1 → v7_bcialg_1 X2 → v7_bcialg_1 X1 → l2_bcialg_1 X2 → l2_bcialg_1 X1 → m1_bcialg_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v2_struct_0 X1 → False) → (r1_tarski (u1_struct_0 X1) (u1_struct_0 X2) → False) → v3_bcialg_1 X2 → v3_bcialg_1 X1 → v4_bcialg_1 X2 → v4_bcialg_1 X1 → v5_bcialg_1 X2 → v5_bcialg_1 X1 → v7_bcialg_1 X2 → v7_bcialg_1 X1 → l2_bcialg_1 X2 → l2_bcialg_1 X1 → m1_bcialg_1 X1 X2 → False) → (∀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 X1 → False) → (∀X1 X2, ((k4_struct_0 X1) = (k4_struct_0 X2) → False) → (v2_struct_0 X2 → False) → (v2_struct_0 X1 → False) → v3_bcialg_1 X2 → v3_bcialg_1 X1 → v4_bcialg_1 X2 → v4_bcialg_1 X1 → v5_bcialg_1 X2 → v5_bcialg_1 X1 → v7_bcialg_1 X2 → v7_bcialg_1 X1 → l2_bcialg_1 X2 → l2_bcialg_1 X1 → m1_bcialg_1 X1 X2 → False) → (∀X1 X3 X2, (v4_relat_1 X3 X2 → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 (k1_relset_1 X2 X1) (k1_zfmisc_1 X2) → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → v2_struct_0 X1 → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X2 X3 X1, (v4_relat_1 (k5_relat_1 X1 X2) X2 → False) → v1_relat_1 X1 → v4_relat_1 X1 X3 → False) → (∀X2 X3 X1, (v4_relat_1 (k5_relat_1 X1 X2) X3 → False) → v1_relat_1 X1 → v4_relat_1 X1 X3 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (l2_bcialg_1 X1 → False) → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v7_bcialg_1 X1 → False) → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v5_bcialg_1 X1 → False) → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v4_bcialg_1 X1 → False) → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v3_bcialg_1 X1 → False) → v3_bcialg_1 X2 → v4_bcialg_1 X2 → v5_bcialg_1 X2 → v7_bcialg_1 X2 → l2_bcialg_1 X2 → m1_bcialg_1 X1 X2 → False) → (∀X2 X1, (v3_card_1 (k9_xtuple_0 X2) X1 → False) → v1_card_1 X1 → v1_relat_1 X2 → v1_funct_1 X2 → v3_card_1 X2 X1 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, ((k5_relat_1 (k5_relat_1 X1 X2) X2) = (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, ((k5_relat_1 X1 (k2_zfmisc_1 X2 X2)) = (k1_realset1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (m1_bcialg_1 (esk6_1 X1) X1 → False) → v3_bcialg_1 X1 → v4_bcialg_1 X1 → v5_bcialg_1 X1 → v7_bcialg_1 X1 → l2_bcialg_1 X1 → False) → (∀X2 X3 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v4_relat_1 X1 X3 → False) → (∀X1 X2, (v3_card_1 (u1_struct_0 X2) X1 → False) → l1_struct_0 X2 → v1_card_1 X1 → v13_struct_0 X2 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_finset_1 X1 → False) → v1_finset_1 (k2_zfmisc_1 X1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_finset_1 X1 → False) → v1_finset_1 (k2_zfmisc_1 X2 X1) → False) → (∀X2 X1, ((k5_relat_1 X1 X2) = X1 → False) → v1_relat_1 X1 → r1_tarski (k9_xtuple_0 X1) X2 → False) → (∀X1, (v7_struct_0 X1 → False) → (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (m1_subset_1 (esk13_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X2 X1, ((k1_relset_1 X2 X1) = (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, ((k5_relat_1 X1 X2) = X1 → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X2 X1, (v3_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v3_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v3_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k5_relat_1 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k5_relat_1 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X1 → False) → (∀X1, (v7_struct_0 X1 → False) → l2_struct_0 X1 → v9_struct_0 (esk9_1 X1) X1 → False) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 X2 → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X1, (v7_struct_0 X1 → False) → (m1_subset_1 (esk9_1 X1) (u1_struct_0 X1) → False) → l2_struct_0 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, v2_struct_0 X1 → l1_struct_0 X1 → v13_struct_0 X1 np__1 → False) → (∀X1, (m1_subset_1 (esk8_1 X1) (u1_struct_0 X1) → False) → l2_struct_0 X1 → False) → (∀X1, (m1_subset_1 (u2_struct_0 X1) (u1_struct_0 X1) → False) → l2_struct_0 X1 → False) → (∀X1, (m1_subset_1 (k4_struct_0 X1) (u1_struct_0 X1) → False) → l2_struct_0 X1 → False) → (∀X1, (v7_struct_0 X1 → False) → l1_struct_0 X1 → v13_struct_0 X1 np__1 → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v13_struct_0 X1 k1_xboole_0 → False) → (∀X1, (v2_struct_0 X1 → False) → (v13_struct_0 X1 np__1 → False) → l1_struct_0 X1 → v7_struct_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v8_struct_0 X1 → False) → l1_struct_0 X1 → v1_finset_1 (u1_struct_0 X1) → False) → (∀X1, (v7_struct_0 X1 → False) → l1_struct_0 X1 → v1_zfmisc_1 (esk14_1 X1) → False) → (∀X1, (v7_struct_0 X1 → False) → l1_struct_0 X1 → v1_zfmisc_1 (u1_struct_0 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k9_xtuple_0 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (esk19_1 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (esk13_1 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (u1_struct_0 X1) → False) → (∀X1, ((k5_relat_1 X1 (k9_xtuple_0 X1)) = X1 → False) → v1_relat_1 X1 → False) → (∀X1, (v9_struct_0 (esk8_1 X1) X1 → False) → l2_struct_0 X1 → False) → (∀X1, (v9_struct_0 (k4_struct_0 X1) X1 → False) → l2_struct_0 X1 → False) → (∀X1, (v13_struct_0 (esk15_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v3_card_1 (esk21_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v3_card_1 (esk20_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, v1_xboole_0 X1 → v3_card_1 X1 np__1 → False) → (∀X1, (v13_struct_0 X1 k1_xboole_0 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v1_finset_1 (u1_struct_0 X1) → False) → l1_struct_0 X1 → v8_struct_0 X1 → False) → (∀X1, (v1_zfmisc_1 (k9_xtuple_0 X1) → False) → v1_zfmisc_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v1_zfmisc_1 (u1_struct_0 X1) → False) → l1_struct_0 X1 → v7_struct_0 X1 → False) → (∀X1, (v1_xboole_0 (u1_struct_0 X1) → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v3_card_1 X1 np__1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v3_card_1 X1 k1_xboole_0 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_card_1 X1 np__1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_card_1 (esk22_1 X1) np__1 → False) → False) → (∀X1, (v2_struct_0 X1 → False) → (v1_zfmisc_1 (esk13_1 X1) → False) → l1_struct_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (esk18_1 X1) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (k1_zfmisc_1 X1) → False) → (∀X1, (v3_card_1 X1 k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, (v8_struct_0 X1 → False) → l1_struct_0 X1 → v7_struct_0 X1 → False) → (∀X1, (v8_struct_0 X1 → False) → l1_struct_0 X1 → v7_struct_0 X1 → False) → (∀X1, (v8_struct_0 X1 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v8_struct_0 X1 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v2_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v3_ordinal1 X1 → v1_finset_1 X1 → False) → (∀X1, (v7_struct_0 X1 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v7_struct_0 X1 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v7_struct_0 X1 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v1_funct_1 (esk21_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (v1_funct_1 (u1_bcialg_1 X1) → False) → l1_bcialg_1 X1 → False) → (∀X1, (v1_relat_1 (esk21_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (l1_struct_0 (esk15_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (v1_xboole_0 (k9_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, ((k4_struct_0 X1) = (u2_struct_0 X1) → False) → l2_struct_0 X1 → False) → (∀X1, (l1_bcialg_1 X1 → False) → l2_bcialg_1 X1 → False) → (∀X1, (l2_struct_0 X1 → False) → l2_bcialg_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_card_1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l1_bcialg_1 X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l2_struct_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (m1_bcialg_1 esk1_0 esk1_0 → False) → (v1_finset_1 esk17_0 → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 np__1 → False) → (v2_struct_0 esk12_0 → False) → (v2_struct_0 esk1_0 → False) → (∀X1 X2, (v1_relat_1 (k2_zfmisc_1 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk7_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((l1_bcialg_1 esk2_0 → False) → False) → ((l2_struct_0 esk12_0 → False) → False) → ((l2_struct_0 esk5_0 → False) → False) → ((v2_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk11_0 → False) → False) → ((v1_card_1 esk10_0 → False) → False) → ((v7_struct_0 esk12_0 → False) → False) → ((l1_struct_0 esk3_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((l2_bcialg_1 esk4_0 → False) → False) → ((l2_bcialg_1 esk1_0 → False) → False) → ((v7_bcialg_1 esk1_0 → False) → False) → ((v5_bcialg_1 esk1_0 → False) → False) → ((v4_bcialg_1 esk1_0 → False) → False) → ((v3_bcialg_1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False