Theorem. (
t52_interva1)
∀r1_tarski : set → set → prop, ∀v1_xboole_0 : set → prop, ∀m1_interva1 : set → set → prop, ∀k2_interva1 : set → set → set → set, ∀k4_subset_1 : set → set → set → set, ∀k6_interva1 : set → set → set, ∀k5_interva1 : set → set → set, ∀k4_interva1 : set → set → set → set, ∀k1_interva1 : set → set → set → set, ∀k1_xboole_0 : set, ∀k9_interva1 : set → set → set → set, ∀k4_setfam_1 : set → set → set, ∀esk15_1 : set → set, ∀esk9_1 : set → set, ∀esk14_1 : set → set, ∀esk7_1 : set → set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk6_1 : set → set, ∀esk12_1 : set → set, ∀esk13_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk10_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀esk3_2 : set → set → set, ∀esk16_2 : set → set → set, ∀k2_setfam_1 : set → set → set, ∀k10_interva1 : set → set → set, ∀k3_subset_1 : set → set → set, ∀esk4_3 : set → set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk5_3 : set → set → set → set, ∀k4_xboole_0 : set → set → set, ∀a_3_0_interva1 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀esk8_4 : set → set → set → set → set, ∀m1_subset_1 : set → set → prop, (∀X3 X1 X4 X2, (m1_subset_1 (esk8_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 (esk8_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 (esk8_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, ((k2_interva1 X1 (k4_subset_1 X1 (k5_interva1 X1 X2) (k5_interva1 X1 X3)) (k4_subset_1 X1 (k6_interva1 X1 X2) (k6_interva1 X1 X3))) = (k4_interva1 X1 X2 X3) → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → False) → (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X2 → False) → r2_hidden (esk5_3 X1 X2 X3) X3 → r2_hidden (esk5_3 X1 X2 X3) X1 → False) → (∀X3 X1 X4 X2, ((esk8_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) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk4_3 X1 X2 X3) X3 → r2_hidden (esk4_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk4_3 X1 X2 X3) X3 → r2_hidden (esk4_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk4_3 X1 X2 X3) X3 → False) → (r2_hidden (esk4_3 X1 X2 X3) X2 → False) → (r2_hidden (esk4_3 X1 X2 X3) X1 → False) → False) → (∀X4 X3 X5 X1 X2, (X1 = X2 → False) → ((k1_interva1 X3 X1 X4) = k1_xboole_0 → False) → (k1_interva1 X3 X1 X4) = (k1_interva1 X3 X2 X5) → m1_subset_1 X5 (k1_zfmisc_1 X3) → m1_subset_1 X4 (k1_zfmisc_1 X3) → m1_subset_1 X2 (k1_zfmisc_1 X3) → m1_subset_1 X1 (k1_zfmisc_1 X3) → False) → (∀X4 X3 X5 X1 X2, (X1 = X2 → False) → ((k1_interva1 X3 X4 X1) = k1_xboole_0 → False) → (k1_interva1 X3 X4 X1) = (k1_interva1 X3 X5 X2) → m1_subset_1 X5 (k1_zfmisc_1 X3) → m1_subset_1 X4 (k1_zfmisc_1 X3) → m1_subset_1 X2 (k1_zfmisc_1 X3) → m1_subset_1 X1 (k1_zfmisc_1 X3) → False) → (∀X2 X3 X1, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → r2_hidden (esk5_3 X1 X2 X3) 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) → (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X1 → False) → False) → (∀X1 X2, ((k2_interva1 X1 (k3_subset_1 X1 (k6_interva1 X1 X2)) (k3_subset_1 X1 (k5_interva1 X1 X2))) = (k10_interva1 X1 X2) → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X2 X1 → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → v1_xboole_0 (k9_interva1 X1 X2 X3) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → v1_xboole_0 (k4_interva1 X1 X2 X3) → False) → (∀X1 X2, ((k9_interva1 X1 (k2_interva1 X1 X1 X1) X2) = (k10_interva1 X1 X2) → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X2 X1 → 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) → (∀X1 X3 X2, (r1_tarski X3 X2 → False) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 X1) → r1_tarski (k3_subset_1 X1 X2) (k3_subset_1 X1 X3) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_interva1 (k9_interva1 X1 X2 X3) X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_interva1 (k4_interva1 X1 X2 X3) X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k1_interva1 X1 X1 X1) → 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 X1 X2, (r1_tarski (k3_subset_1 X3 X2) (k3_subset_1 X3 X1) → False) → r1_tarski X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → m1_subset_1 X1 (k1_zfmisc_1 X3) → False) → (∀X1 X2, ((k2_interva1 X1 (k5_interva1 X1 X2) (k6_interva1 X1 X2)) = X2 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X2 X1 → 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) → (∀X2 X1 X3, ((k9_interva1 X1 X2 X3) = (k4_setfam_1 X2 X3) → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → False) → (∀X2 X1 X3, ((k4_interva1 X1 X2 X3) = (k2_setfam_1 X2 X3) → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X3 X1 → m1_interva1 X2 X1 → 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) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk16_2 X3 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (r1_tarski (k5_interva1 X1 X2) (k6_interva1 X1 X2) → False) → m1_interva1 X2 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_interva1 X2 X1 → v1_xboole_0 (k10_interva1 X1 X2) → 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (k6_interva1 X1 X2) (k1_zfmisc_1 X1) → False) → m1_interva1 X2 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (k5_interva1 X1 X2) (k1_zfmisc_1 X1) → False) → m1_interva1 X2 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk3_2 X1 X2) X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X2 = (k2_xboole_0 X3 X4) → r2_hidden X1 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, ((k3_subset_1 X2 (k3_subset_1 X2 X1)) = X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_interva1 (k10_interva1 X1 X2) X1 → False) → m1_interva1 X2 X1 → 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) → (∀X2 X1, (r2_hidden (esk16_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) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k4_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X2 X4) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X4 X2) → r2_hidden X1 X2 → False) → (∀X2 X1, ((k3_subset_1 X2 X1) = (k4_xboole_0 X2 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → 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) → (∀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 (esk3_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, (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, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → 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, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk15_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_interva1 (esk9_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk10_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk9_1 X1) → 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) → (r2_hidden esk1_0 (k4_interva1 esk1_0 esk2_0 (k10_interva1 esk1_0 esk2_0)) → False) → (∀X1, v1_subset_1 (esk14_1 X1) X1 → False) → (∀X1, v1_subset_1 X1 X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 esk2_0 → False) → (v1_xboole_0 esk1_0 → 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 (esk14_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk7_1 X1) X1 → False) → False) → (∀X1, (m1_interva1 (esk6_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 X1 (k1_zfmisc_1 X1) → False) → False) → (∀X1, ((k2_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, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k4_xboole_0 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → ((m1_interva1 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk12_1 X1) → False) → False) → ((v1_xboole_0 esk11_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