Theorem. (
t13_interva1)
∀k2_setfam_1 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk7_4 : set → set → set → set → set, ∀esk8_4 : set → set → set → set → set, ∀k8_subset_1 : set → set → set → set, ∀esk23_2 : set → set → set, ∀k3_xboole_0 : set → set → set, ∀v1_subset_1 : set → set → prop, ∀esk22_1 : set → set, ∀k1_xboole_0 : set, ∀esk21_1 : set → set, ∀esk20_0 : set, ∀esk19_1 : set → set, ∀esk13_1 : set → set, ∀o_0_0_xboole_0 : set, ∀esk18_0 : set, ∀esk12_1 : set → set, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk5_0 : set, ∀esk2_0 : set, ∀esk16_1 : set → set, ∀esk17_1 : set → set, ∀esk6_2 : set → set → set, ∀k9_subset_1 : set → set → set → set, ∀k2_interva1 : set → set → set → set, ∀m1_interva1 : set → set → prop, ∀k1_interva1 : set → set → set → set, ∀esk9_3 : set → set → set → set, ∀esk10_3 : set → set → set → set, ∀esk11_3 : set → set → set → set, ∀a_3_0_interva1 : set → set → set → set, ∀esk14_4 : set → set → set → set → set, ∀r1_tarski : set → set → prop, ∀esk15_6 : set → set → set → set → set → set → set, ∀k4_subset_1 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀a_5_1_interva1 : set → set → set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, (∀X6 X4 X1 X3 X5 X2, (v1_xboole_0 X2 → False) → (r1_tarski (esk15_6 X1 X2 X3 X4 X5 X6) (k4_subset_1 X2 X4 X6) → False) → m1_subset_1 X6 (k1_zfmisc_1 X2) → m1_subset_1 X5 (k1_zfmisc_1 X2) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_5_1_interva1 X2 X3 X4 X5 X6) → False) → (∀X6 X3 X4 X2 X5 X1, (v1_xboole_0 X1 → False) → (r1_tarski (k4_subset_1 X1 X2 X3) (esk15_6 X4 X1 X2 X5 X3 X6) → False) → m1_subset_1 X6 (k1_zfmisc_1 X1) → m1_subset_1 X5 (k1_zfmisc_1 X1) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → r2_hidden X4 (a_5_1_interva1 X1 X2 X5 X3 X6) → False) → (∀X6 X4 X1 X3 X5 X2, (v1_xboole_0 X2 → False) → (m1_subset_1 (esk15_6 X1 X2 X3 X4 X5 X6) (k1_zfmisc_1 X2) → False) → m1_subset_1 X6 (k1_zfmisc_1 X2) → m1_subset_1 X5 (k1_zfmisc_1 X2) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_5_1_interva1 X2 X3 X4 X5 X6) → False) → (∀X6 X4 X1 X3 X5 X2, ((esk15_6 X1 X2 X3 X4 X5 X6) = X1 → False) → (v1_xboole_0 X2 → False) → m1_subset_1 X6 (k1_zfmisc_1 X2) → m1_subset_1 X5 (k1_zfmisc_1 X2) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_5_1_interva1 X2 X3 X4 X5 X6) → False) → (∀X3 X6 X5 X7 X4 X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X3 (a_5_1_interva1 X2 X4 X6 X5 X7) → False) → X1 = X3 → m1_subset_1 X7 (k1_zfmisc_1 X2) → m1_subset_1 X6 (k1_zfmisc_1 X2) → m1_subset_1 X5 (k1_zfmisc_1 X2) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → r1_tarski X1 (k4_subset_1 X2 X6 X7) → r1_tarski (k4_subset_1 X2 X4 X5) X1 → False) → (∀X3 X2 X4 X1, ((k2_xboole_0 (esk7_4 X2 X3 X4 X1) (esk8_4 X2 X3 X4 X1)) = X1 → False) → X4 = (k2_setfam_1 X2 X3) → r2_hidden X1 X4 → False) → (∀X3 X1 X4 X2, (m1_subset_1 (esk14_4 X1 X2 X3 X4) (k1_zfmisc_1 X2) → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_interva1 X2 X3 X4) → False) → (∀X3 X1 X4 X2, (r1_tarski (esk14_4 X1 X2 X3 X4) X4 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_interva1 X2 X3 X4) → False) → (∀X1 X2 X4 X3, (r1_tarski X1 (esk14_4 X2 X3 X1 X4) → False) → m1_subset_1 X4 (k1_zfmisc_1 X3) → m1_subset_1 X1 (k1_zfmisc_1 X3) → r2_hidden X2 (a_3_0_interva1 X3 X1 X4) → False) → (∀X2 X1 X3 X4, (r2_hidden (esk8_4 X1 X2 X3 X4) X2 → False) → X3 = (k2_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk7_4 X1 X2 X3 X4) X1 → False) → X3 = (k2_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X3 X1 X4 X2, ((esk14_4 X1 X2 X3 X4) = X1 → False) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 X2) → r2_hidden X1 (a_3_0_interva1 X2 X3 X4) → False) → (∀X3 X2 X1, (X3 = (k2_setfam_1 X1 X2) → False) → ((k2_xboole_0 (esk10_3 X1 X2 X3) (esk11_3 X1 X2 X3)) = (esk9_3 X1 X2 X3) → False) → (r2_hidden (esk9_3 X1 X2 X3) X3 → False) → False) → (∀X5 X4 X1 X2 X3, (X3 = (k2_setfam_1 X1 X2) → False) → (esk9_3 X1 X2 X3) = (k2_xboole_0 X4 X5) → r2_hidden X5 X2 → r2_hidden X4 X1 → r2_hidden (esk9_3 X1 X2 X3) X3 → False) → (∀X3 X4 X1 X2, (r1_tarski X1 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X3) → m1_subset_1 X1 (k1_zfmisc_1 X3) → r2_hidden X2 (k1_interva1 X3 X1 X4) → False) → (∀X3 X4 X1 X2, (r1_tarski X1 X2 → False) → m1_subset_1 X4 (k1_zfmisc_1 X3) → m1_subset_1 X2 (k1_zfmisc_1 X3) → r2_hidden X1 (k1_interva1 X3 X4 X2) → False) → (∀X1 X5 X4 X2 X3, (r2_hidden X3 (a_3_0_interva1 X2 X4 X5) → False) → X1 = X3 → r1_tarski X4 X1 → r1_tarski X1 X5 → m1_subset_1 X5 (k1_zfmisc_1 X2) → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X3 X1, (X3 = (k2_setfam_1 X1 X2) → False) → (r2_hidden (esk9_3 X1 X2 X3) X3 → False) → (r2_hidden (esk11_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k2_setfam_1 X1 X2) → False) → (r2_hidden (esk9_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X1 → False) → False) → (∀X1 X4 X2 X3, (r2_hidden X2 (k1_interva1 X4 X1 X3) → False) → r1_tarski X2 X3 → r1_tarski X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X4) → m1_subset_1 X1 (k1_zfmisc_1 X4) → False) → (∀X3 X2 X1, (m1_subset_1 (k1_interva1 X2 X1 X3) (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_subset_1 (k4_subset_1 X2 X1 X3) (k1_zfmisc_1 X2) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_interva1 (k2_interva1 X2 X1 X3) X2 → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((a_3_0_interva1 X2 X1 X3) = (k1_interva1 X2 X1 X3) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k2_interva1 X2 X1 X3) = (k1_interva1 X2 X1 X3) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k4_subset_1 X2 X1 X3) = (k4_subset_1 X2 X3 X1) → 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 (k8_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) → (∀X3 X2 X1, ((k8_subset_1 X2 X1 X3) = (k8_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k4_subset_1 X2 X1 X3) = (k2_xboole_0 X1 X3) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k4_subset_1 X2 X1 X1) = X1 → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X4 X3 X2 X1, (r1_tarski (k2_xboole_0 X1 X3) (k2_xboole_0 X2 X4) → False) → r1_tarski X3 X4 → r1_tarski X1 X2 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk23_2 X3 X2) → False) → (∀X4 X2 X1 X3 X5 X6, (r2_hidden X5 X6 → False) → X6 = (k2_setfam_1 X2 X4) → X5 = (k2_xboole_0 X1 X3) → r2_hidden X3 X4 → r2_hidden 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, ((k8_subset_1 X2 X1 X3) = (k3_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, ((k8_subset_1 X2 X1 X1) = X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (r1_tarski (k2_xboole_0 X1 X3) X2 → False) → r1_tarski X3 X2 → r1_tarski X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk6_2 X1 X2) 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, (r2_hidden (esk23_2 X1 X2) X2 → False) → r2_hidden X1 X2 → 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) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r1_tarski X1 X2 → r2_hidden X3 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) → (∀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, (m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → m1_interva1 X1 X2 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) X1 → False) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X1 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X2 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) → (∀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, ((k3_xboole_0 X1 X2) = X1 → False) → r1_tarski X1 X2 → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = X2 → False) → r1_tarski X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk22_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, (v1_xboole_0 X1 → False) → (m1_interva1 (esk16_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk22_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk17_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk16_1 X1) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k2_setfam_1 (k2_interva1 esk1_0 esk2_0 esk3_0) (k2_interva1 esk1_0 esk4_0 esk5_0)) = (a_5_1_interva1 esk1_0 esk2_0 esk3_0 esk4_0 esk5_0) → False) → (∀X1, v1_subset_1 (esk21_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk1_0 → False) → (∀X2 X3 X1, ((k2_xboole_0 (k3_xboole_0 X1 X2) (k3_xboole_0 X1 X3)) = (k3_xboole_0 X1 (k2_xboole_0 X2 X3)) → False) → False) → (∀X2 X3 X1, ((k2_xboole_0 (k2_xboole_0 X1 X2) X3) = (k2_xboole_0 X1 (k2_xboole_0 X2 X3)) → False) → False) → (∀X1 X2, (r1_tarski (k3_xboole_0 X1 X2) X1 → False) → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_setfam_1 X1 X2) = (k2_setfam_1 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_interva1 (esk12_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 (esk13_1 X1) X1 → False) → False) → ((m1_subset_1 esk5_0 (k1_zfmisc_1 esk1_0) → False) → False) → ((m1_subset_1 esk4_0 (k1_zfmisc_1 esk1_0) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 esk1_0) → False) → False) → ((m1_subset_1 esk2_0 (k1_zfmisc_1 esk1_0) → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((r1_tarski esk4_0 esk5_0 → False) → False) → ((r1_tarski esk2_0 esk3_0 → False) → False) → (∀X1, (v1_xboole_0 (esk19_1 X1) → False) → False) → ((v1_xboole_0 esk18_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False