Theorem. (
t9_connsp_1)
∀v3_pre_topc : set → set → prop, ∀v2_pre_topc : set → prop, ∀k7_subset_1 : set → set → set → set, ∀k2_struct_0 : set → set, ∀l1_struct_0 : set → prop, ∀r2_hidden : set → set → prop, ∀esk16_1 : set → set, ∀esk15_1 : set → set, ∀esk1_0 : set, ∀esk3_0 : set, ∀v3_relat_1 : set → prop, ∀esk8_0 : set, ∀esk6_1 : set → set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk4_0 : set, ∀esk10_0 : set, ∀esk5_0 : set, ∀esk12_1 : set → set, ∀esk13_0 : set, ∀esk14_1 : set → set, ∀v2_relat_1 : set → prop, ∀esk2_0 : set, ∀esk9_1 : set → set, ∀k1_xboole_0 : set, ∀v1_relat_1 : set → prop, ∀k1_struct_0 : set → set, ∀esk7_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀k4_xboole_0 : set → set → set, ∀k3_xboole_0 : set → set → set, ∀k3_subset_1 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀r1_connsp_1 : set → set → set → prop, ∀v4_pre_topc : set → set → prop, ∀r1_tarski : set → set → prop, ∀k9_subset_1 : set → set → set → set, ∀k2_pre_topc : set → set → set, ∀u1_struct_0 : set → set, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀l1_pre_topc : set → prop, (∀X2 X3 X1, (r1_tarski (k2_pre_topc X1 (k9_subset_1 (u1_struct_0 X1) X2 X3)) (k9_subset_1 (u1_struct_0 X1) (k2_pre_topc X1 X2) (k2_pre_topc X1 X3)) → False) → l1_pre_topc X1 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, (v3_pre_topc X2 X1 → False) → (k2_pre_topc X1 (k7_subset_1 (u1_struct_0 X1) (k2_struct_0 X1) X2)) = (k7_subset_1 (u1_struct_0 X1) (k2_struct_0 X1) X2) → l1_pre_topc X1 → v2_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, (v4_pre_topc X2 X1 → False) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → v3_pre_topc (k7_subset_1 (u1_struct_0 X1) (k2_struct_0 X1) X2) X1 → False) → (∀X1 X2, ((k2_pre_topc X2 (k7_subset_1 (u1_struct_0 X2) (k2_struct_0 X2) X1)) = (k7_subset_1 (u1_struct_0 X2) (k2_struct_0 X2) X1) → False) → l1_pre_topc X2 → v3_pre_topc X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X2 X3 X1, (r1_connsp_1 X1 X2 X3 → False) → l1_pre_topc X1 → r1_xboole_0 X2 (k2_pre_topc X1 X3) → r1_xboole_0 (k2_pre_topc X1 X2) X3 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, ((k7_subset_1 (u1_struct_0 X1) (k2_struct_0 X1) (k7_subset_1 (u1_struct_0 X1) (k2_struct_0 X1) X2)) = X2 → False) → l1_struct_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X3 X1, (r1_connsp_1 X1 X3 X2 → False) → l1_pre_topc X1 → r1_connsp_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X3 X1, (r1_xboole_0 (k2_pre_topc X1 X2) X3 → False) → l1_pre_topc X1 → r1_connsp_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X1 X3 X2, (r1_xboole_0 X1 (k2_pre_topc X2 X3) → False) → l1_pre_topc X2 → r1_connsp_1 X2 X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2)) → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X1 X2, (v3_pre_topc (k7_subset_1 (u1_struct_0 X2) (k2_struct_0 X2) X1) X2 → False) → l1_pre_topc X2 → v4_pre_topc X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X1 (k3_subset_1 X2 X3)) = (k7_subset_1 X2 X1 X3) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_subset_1 (k9_subset_1 X2 X3 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_subset_1 (k7_subset_1 X2 X1 X3) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X1 X3) = (k9_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (m1_subset_1 (k2_pre_topc X1 X2) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, ((k2_pre_topc X1 (k2_pre_topc X1 X2)) = (k2_pre_topc X1 X2) → False) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X4 X3 X2 X1, (r1_tarski (k3_xboole_0 X1 X3) (k3_xboole_0 X2 X4) → False) → r1_tarski X3 X4 → r1_tarski X1 X2 → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X1) = (k3_xboole_0 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k7_subset_1 X2 X1 X3) = (k4_xboole_0 X1 X3) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X3) = X3 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (v4_pre_topc X2 X1 → False) → l1_pre_topc X1 → v1_xboole_0 X2 → v2_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, (m1_subset_1 (k3_subset_1 X2 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, ((k3_subset_1 X2 (k3_subset_1 X2 X1)) = X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, v1_xboole_0 X1 → v1_subset_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, ((k3_subset_1 X2 X1) = (k4_xboole_0 X2 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1, (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → v2_pre_topc X1 → False) → (∀X1, (m1_subset_1 (esk7_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → v2_pre_topc X1 → False) → (∀X1, l1_struct_0 X1 → v1_subset_1 (k2_struct_0 X1) (u1_struct_0 X1) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1, (m1_subset_1 (k2_struct_0 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X1, (m1_subset_1 (k1_struct_0 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 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_relat_1 (k4_xboole_0 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k3_xboole_0 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (r1_xboole_0 X1 X2 → False) → (k3_xboole_0 X1 X2) = k1_xboole_0 → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = k1_xboole_0 → False) → r1_xboole_0 X1 X2 → False) → (∀X1, (v3_pre_topc (esk7_1 X1) X1 → False) → l1_pre_topc X1 → v2_pre_topc X1 → False) → (∀X1, (v4_pre_topc (esk16_1 X1) X1 → False) → l1_pre_topc X1 → v2_pre_topc X1 → False) → (∀X1, (v4_pre_topc (k2_struct_0 X1) X1 → False) → l1_pre_topc X1 → v2_pre_topc X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk9_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk15_1 X1) X1 → False) → False) → ((v4_pre_topc esk3_0 esk1_0 → False) → (v3_pre_topc esk3_0 esk1_0 → False) → False) → ((v4_pre_topc esk3_0 esk1_0 → False) → (v3_pre_topc esk2_0 esk1_0 → False) → False) → ((v4_pre_topc esk2_0 esk1_0 → False) → (v3_pre_topc esk3_0 esk1_0 → False) → False) → ((v4_pre_topc esk2_0 esk1_0 → False) → (v3_pre_topc esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk9_1 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, (v1_xboole_0 (k1_struct_0 X1) → False) → l1_struct_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, ((k2_struct_0 X1) = (u1_struct_0 X1) → False) → l1_struct_0 X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l1_pre_topc X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, ((k1_struct_0 X1) = k1_xboole_0 → False) → l1_struct_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_connsp_1 esk1_0 (k7_subset_1 (u1_struct_0 esk1_0) esk2_0 esk3_0) (k7_subset_1 (u1_struct_0 esk1_0) esk3_0 esk2_0) → False) → (∀X1, v1_subset_1 (esk14_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 esk8_0 → False) → (∀X1 X2, (r1_tarski (k3_xboole_0 X1 X2) X1 → False) → False) → (∀X2 X1, (r1_xboole_0 (k4_xboole_0 X1 X2) X2 → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 X1) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 (u1_struct_0 esk1_0)) → False) → False) → ((m1_subset_1 esk2_0 (k1_zfmisc_1 (u1_struct_0 esk1_0)) → False) → False) → (∀X1, (m1_subset_1 (esk6_1 X1) X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k4_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k4_xboole_0 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → (∀X1, (v1_xboole_0 (esk12_1 X1) → False) → False) → ((l1_struct_0 esk5_0 → False) → False) → ((v2_relat_1 esk11_0 → False) → False) → ((v1_relat_1 esk11_0 → False) → False) → ((v1_relat_1 esk8_0 → False) → False) → ((v1_xboole_0 esk10_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((l1_pre_topc esk4_0 → False) → False) → ((l1_pre_topc esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False