Theorem. (
t25_connsp_3)
∀k4_xboole_0 : set → set → set, ∀esk11_3 : set → set → set → set, ∀esk4_2 : set → set → set, ∀k7_subset_1 : set → set → set → set, ∀esk7_3 : set → set → set → set, ∀esk9_2 : set → set → set, ∀v2_struct_0 : set → prop, ∀v1_xboole_0 : set → prop, ∀v2_connsp_1 : set → set → prop, ∀r1_tarski : set → set → prop, ∀esk6_2 : set → set → set, ∀v7_struct_0 : set → prop, ∀esk19_1 : set → set, ∀l1_struct_0 : set → prop, ∀esk18_1 : set → set, ∀esk24_1 : set → set, ∀esk17_1 : set → set, ∀v8_struct_0 : set → prop, ∀v1_finset_1 : set → prop, ∀esk14_1 : set → set, ∀v6_pre_topc : set → prop, ∀esk21_1 : set → set, ∀esk20_1 : set → set, ∀o_0_0_xboole_0 : set, ∀esk12_0 : set, ∀esk13_0 : set, ∀esk15_1 : set → set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk23_1 : set → set, ∀esk26_1 : set → set, ∀np__1 : set, ∀v13_struct_0 : set → set → prop, ∀k1_xboole_0 : set, ∀v1_zfmisc_1 : set → prop, ∀esk16_1 : set → set, ∀esk22_1 : set → set, ∀esk25_1 : set → set, ∀esk27_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀v4_pre_topc : set → set → prop, ∀esk8_2 : set → set → set, ∀k3_tarski : set → set, ∀k9_subset_1 : set → set → set → set, ∀r1_xboole_0 : set → set → prop, ∀v2_pre_topc : set → prop, ∀u1_struct_0 : set → set, ∀k5_setfam_1 : set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v3_connsp_1 : set → set → prop, ∀esk5_3 : set → set → set → set, ∀l1_pre_topc : set → prop, ∀m1_connsp_3 : set → set → prop, ∀r2_hidden : set → set → prop, ∀esk10_3 : set → set → set → set, ∀k3_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk10_3 X1 X2 X3) X3 → r2_hidden (esk10_3 X1 X2 X3) X2 → r2_hidden (esk10_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X2 → False) → r2_hidden (esk11_3 X1 X2 X3) X3 → r2_hidden (esk11_3 X1 X2 X3) X1 → False) → (∀X3 X2 X1, (m1_connsp_3 X2 X1 → False) → X2 = (k5_setfam_1 (u1_struct_0 X1) X3) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → v3_connsp_1 (esk5_3 X1 X2 X3) X1 → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1))) → False) → (∀X3 X2 X1, (m1_connsp_3 X2 X1 → False) → (m1_subset_1 (esk5_3 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → X2 = (k5_setfam_1 (u1_struct_0 X1) X3) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1))) → False) → (∀X2 X3 X1, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → r2_hidden (esk11_3 X1 X2 X3) X2 → False) → (∀X3 X2 X1, (m1_connsp_3 X2 X1 → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → X2 = (k5_setfam_1 (u1_struct_0 X1) X3) → l1_pre_topc X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1))) → False) → (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (esk11_3 X1 X2 X3) X1 → False) → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X2 → False) → False) → (∀X3 X1 X2, (v3_connsp_1 X1 X2 → False) → l1_pre_topc X2 → m1_connsp_3 X3 X2 → r2_hidden X1 (esk4_2 X2 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 X3, (X2 = X3 → False) → (r1_xboole_0 X2 X3 → False) → v2_pre_topc X1 → l1_pre_topc X1 → v3_connsp_1 X3 X1 → v3_connsp_1 X2 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, (m1_subset_1 (esk4_2 X1 X2) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1))) → False) → l1_pre_topc X1 → m1_connsp_3 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → 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, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk8_2 X1 X2) X3 → r2_hidden (esk8_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk7_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk7_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → 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) → (∀X1 X2, ((k5_setfam_1 (u1_struct_0 X2) (esk4_2 X2 X1)) = X1 → False) → l1_pre_topc X2 → m1_connsp_3 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk8_2 X1 X2) X2 → False) → (r2_hidden (esk8_2 X1 X2) (esk9_2 X1 X2) → False) → False) → (∀X2 X1, (v4_pre_topc X2 X1 → False) → v2_pre_topc X1 → l1_pre_topc X1 → v3_connsp_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → 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) → (∀X2 X1, (v2_struct_0 X1 → False) → v2_pre_topc X1 → l1_pre_topc X1 → v1_xboole_0 X2 → v3_connsp_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, (m1_subset_1 (k5_setfam_1 X2 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1, (v2_connsp_1 X2 X1 → False) → l1_pre_topc X1 → v3_connsp_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → 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) → v2_pre_topc X1 → l1_pre_topc X1 → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk8_2 X1 X2) X2 → False) → (r2_hidden (esk9_2 X1 X2) X1 → False) → False) → (∀X2 X3 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_xboole_0 X2 X3) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X2 X1, (v2_connsp_1 X2 X1 → False) → l1_pre_topc X1 → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk6_2 X1 X2) X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X4 = (k4_xboole_0 X2 X3) → r2_hidden X1 X2 → False) → (∀X2 X1, ((k5_setfam_1 X2 X1) = (k3_tarski X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 (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) → (∀X4 X3 X2 X1, X3 = (k4_xboole_0 X4 X2) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → r2_hidden X1 X2 → False) → (∀X2 X1, (m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → m1_connsp_3 X2 X1 → 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) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k4_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X4 X2) → r2_hidden X1 X3 → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r2_hidden X3 X1 → r1_tarski X1 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, (v2_struct_0 X1 → False) → (m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → v2_pre_topc X1 → l1_pre_topc X1 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) X1 → False) → False) → (∀X1, (m1_subset_1 (esk25_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → v2_pre_topc X1 → l1_pre_topc X1 → False) → (∀X1, (v7_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 (esk22_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_struct_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → r1_tarski X2 X1 → r1_tarski X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1, (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (v1_zfmisc_1 X2 → False) → v1_zfmisc_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, (r1_tarski X1 (k3_tarski X2) → False) → r2_hidden X1 X2 → 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) → (∀X1, (v2_struct_0 X1 → False) → (v4_pre_topc (esk27_1 X1) X1 → False) → v2_pre_topc X1 → l1_pre_topc 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, (v2_struct_0 X1 → False) → v2_pre_topc X1 → l1_pre_topc X1 → v1_xboole_0 (esk27_1 X1) → False) → (∀X1, (v4_pre_topc (esk25_1 X1) X1 → False) → v2_pre_topc X1 → l1_pre_topc X1 → False) → (∀X1, v2_struct_0 X1 → l1_struct_0 X1 → v13_struct_0 X1 np__1 → 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_zfmisc_1 X1 → False) → (m1_subset_1 (esk26_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk24_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk17_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 (esk19_1 X1) → False) → (∀X1, (v7_struct_0 X1 → False) → l1_struct_0 X1 → v1_zfmisc_1 (u1_struct_0 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (esk22_1 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (esk18_1 X1) → False) → (∀X1, (v2_struct_0 X1 → False) → l1_struct_0 X1 → v1_xboole_0 (u1_struct_0 X1) → False) → (∀X1, (m1_connsp_3 (esk14_1 X1) X1 → False) → l1_pre_topc X1 → False) → (∀X1, (v13_struct_0 X1 k1_xboole_0 → False) → v2_struct_0 X1 → l1_struct_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk23_1 X1) X1 → False) → False) → (∀X1, (v1_finset_1 (u1_struct_0 X1) → False) → l1_struct_0 X1 → v8_struct_0 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, (v2_struct_0 X1 → False) → (v1_zfmisc_1 (esk18_1 X1) → False) → l1_struct_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk26_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk24_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk17_1 X1) → False) → (∀X1, (v6_pre_topc X1 → False) → v2_struct_0 X1 → l1_pre_topc 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, (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) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X1, (v1_xboole_0 (esk16_1 X1) → False) → l1_pre_topc X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_zfmisc_1 (esk24_1 X1) → False) → False) → (∀X1, (l1_struct_0 X1 → False) → l1_pre_topc X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (m1_connsp_3 (k7_subset_1 (u1_struct_0 esk1_0) esk2_0 esk3_0) esk1_0 → False) → (∀X1, v1_subset_1 (esk21_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 np__1 → False) → (v2_struct_0 esk1_0 → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk20_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 (esk15_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) → ((m1_connsp_3 esk3_0 esk1_0 → False) → False) → ((m1_connsp_3 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk20_1 X1) → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((l1_struct_0 esk13_0 → False) → False) → ((l1_pre_topc esk12_0 → False) → False) → ((l1_pre_topc esk1_0 → False) → False) → ((v2_pre_topc esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False