Theorem. (
t17_pre_topc)
∀k2_pre_topc : set → set → set, ∀u1_struct_0 : set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀esk17_3 : set → set → set → set, ∀l1_pre_topc : set → prop, ∀r1_tarski : set → set → prop, ∀l1_struct_0 : set → prop, ∀esk10_1 : set → set, ∀esk8_1 : set → set, ∀k1_xboole_0 : set, ∀esk14_1 : set → set, ∀esk13_0 : set, ∀esk12_1 : set → set, ∀esk11_0 : set, ∀esk6_0 : set, ∀esk7_0 : set, ∀esk9_1 : set → set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk15_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀esk18_2 : set → set → set, ∀v4_pre_topc : set → set → prop, ∀m1_pre_topc : set → set → prop, ∀k9_subset_1 : set → set → set → set, ∀k2_struct_0 : set → set, ∀esk16_3 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀esk5_3 : set → set → set → set, ∀k3_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk5_3 X1 X2 X3) X3 → r2_hidden (esk5_3 X1 X2 X3) X2 → r2_hidden (esk5_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (r2_hidden X1 (k2_pre_topc X2 X3) → False) → l1_pre_topc X2 → r2_hidden X1 (u1_struct_0 X2) → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2)) → r2_hidden X1 (esk17_3 X2 X3 X1) → False) → (∀X3 X1 X2, ((k9_subset_1 (u1_struct_0 X1) (esk16_3 X2 X1 X3) (k2_struct_0 X1)) = X3 → False) → l1_pre_topc X2 → m1_pre_topc X1 X2 → v4_pre_topc X3 X1 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X1 X2 X4 X3, (v4_pre_topc X4 X3 → False) → (k9_subset_1 (u1_struct_0 X3) X1 (k2_struct_0 X3)) = X4 → l1_pre_topc X2 → m1_pre_topc X3 X2 → v4_pre_topc X1 X2 → m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X2 X3 X1, (r2_hidden X3 (k2_pre_topc X1 X2) → False) → (m1_subset_1 (esk17_3 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → r2_hidden X3 (u1_struct_0 X1) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X2 X3 X1 X4, (r2_hidden X1 X4 → False) → l1_pre_topc X2 → r1_tarski X3 X4 → v4_pre_topc X4 X2 → r2_hidden X1 (u1_struct_0 X2) → r2_hidden X1 (k2_pre_topc X2 X3) → m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X2 → False) → False) → (∀X2 X3 X1, (r2_hidden X3 (k2_pre_topc X1 X2) → False) → (v4_pre_topc (esk17_3 X1 X2 X3) X1 → False) → l1_pre_topc X1 → r2_hidden X3 (u1_struct_0 X1) → m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → (∀X1 X3 X2, (r2_hidden X3 (k2_pre_topc X2 X1) → False) → (r1_tarski X1 (esk17_3 X2 X1 X3) → False) → l1_pre_topc X2 → r2_hidden X3 (u1_struct_0 X2) → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X3 X2 X1, (m1_subset_1 (esk16_3 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → m1_pre_topc X2 X1 → v4_pre_topc X3 X2 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X3 X2 X1, (v4_pre_topc (esk16_3 X1 X2 X3) X1 → False) → l1_pre_topc X1 → m1_pre_topc X2 X1 → v4_pre_topc X3 X2 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 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, ((k9_subset_1 X2 X1 X3) = (k9_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (X1 = X2 → False) → r2_hidden (esk18_2 X1 X2) X2 → r2_hidden (esk18_2 X1 X2) X1 → 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 X3 X1, (m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_pre_topc X1 → m1_pre_topc X2 X1 → m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2)) → 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) → (∀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, ((k9_subset_1 X2 X3 X3) = X3 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (r1_tarski X1 (k3_xboole_0 X2 X3) → False) → r1_tarski X1 X3 → r1_tarski X1 X2 → 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) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk18_2 X1 X2) X2 → False) → (r2_hidden (esk18_2 X1 X2) X1 → False) → 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) → (∀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) → (∀X2 X1 X3, (r1_tarski X1 X3 → False) → r1_tarski X2 X3 → 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, 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) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → 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, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (l1_pre_topc X2 → False) → l1_pre_topc X1 → m1_pre_topc X2 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 (esk10_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (m1_pre_topc (esk8_1 X1) X1 → False) → l1_pre_topc X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk15_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk10_1 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, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k9_subset_1 (u1_struct_0 esk2_0) (k2_pre_topc esk1_0 esk3_0) (k2_struct_0 esk2_0)) = (k2_pre_topc esk2_0 esk4_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) → (∀X1 X2, (r1_tarski (k3_xboole_0 X1 X2) X1 → 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 esk4_0 (k1_zfmisc_1 (u1_struct_0 esk2_0)) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 (u1_struct_0 esk1_0)) → False) → False) → (∀X1, (m1_subset_1 (esk9_1 X1) X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((m1_pre_topc esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk12_1 X1) → False) → False) → ((l1_struct_0 esk7_0 → False) → False) → ((v1_xboole_0 esk11_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((l1_pre_topc esk6_0 → False) → False) → ((l1_pre_topc esk1_0 → False) → False) → ((esk4_0 = esk3_0 → False) → False) → False