Theorem. (
t38_interva1)
∀k3_subset_1 : set → set → set, ∀k9_subset_1 : set → set → set → set, ∀k2_xboole_0 : set → set → set, ∀k3_xboole_0 : set → set → set, ∀k1_setfam_1 : set → set, ∀esk14_1 : set → set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk16_1 : set → set, ∀esk18_0 : set, ∀esk10_1 : set → set, ∀esk15_0 : set, ∀o_0_0_xboole_0 : set, ∀esk17_1 : set → set, ∀esk19_1 : set → set, ∀k1_xboole_0 : set, ∀esk20_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀esk4_2 : set → set → set, ∀k3_tarski : set → set, ∀esk21_2 : set → set → set, ∀esk11_2 : set → set → set, ∀m2_subset_1 : set → set → set → prop, ∀k4_subset_1 : set → set → set → set, ∀esk13_3 : set → set → set → set, ∀esk7_3 : set → set → set → set, ∀esk8_3 : set → set → set → set, ∀esk9_3 : set → set → set → set, ∀esk6_4 : set → set → set → set → set, ∀esk5_4 : set → set → set → set → set, ∀k4_xboole_0 : set → set → set, ∀k4_setfam_1 : set → set → set, ∀v1_interva1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀a_3_1_interva1 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀esk12_4 : set → set → set → set → set, ∀k7_interva1 : set → set → set, ∀k8_interva1 : set → set → set, ∀k7_subset_1 : set → set → set → set, ∀r1_tarski : set → set → prop, ∀v1_xboole_0 : set → prop, (∀X2 X4 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (r1_tarski (k7_subset_1 X1 (k7_interva1 X1 X2) (k8_interva1 X1 X3)) (esk12_4 X4 X1 X2 X3) → False) → v1_interva1 X3 X1 → v1_interva1 X2 X1 → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → r2_hidden X4 (a_3_1_interva1 X1 X2 X3) → False) → (∀X3 X1 X2 X4, (v1_xboole_0 X4 → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (r1_tarski (esk12_4 X1 X2 X3 X4) (k7_subset_1 X2 (k8_interva1 X2 X3) (k7_interva1 X2 X4)) → False) → v1_interva1 X4 X2 → v1_interva1 X3 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → r2_hidden X1 (a_3_1_interva1 X2 X3 X4) → False) → (∀X3 X2 X4 X1, ((k4_xboole_0 (esk5_4 X2 X3 X4 X1) (esk6_4 X2 X3 X4 X1)) = X1 → False) → X4 = (k4_setfam_1 X2 X3) → r2_hidden X1 X4 → False) → (∀X4 X3 X1 X2 X5, (v1_xboole_0 X5 → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X2 → False) → (r2_hidden X3 (a_3_1_interva1 X2 X4 X5) → False) → X1 = X3 → v1_interva1 X5 X2 → v1_interva1 X4 X2 → m1_subset_1 X1 (k1_zfmisc_1 X2) → m1_subset_1 X5 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → r1_tarski X1 (k7_subset_1 X2 (k8_interva1 X2 X4) (k7_interva1 X2 X5)) → r1_tarski (k7_subset_1 X2 (k7_interva1 X2 X4) (k8_interva1 X2 X5)) X1 → False) → (∀X3 X1 X2 X4, (v1_xboole_0 X4 → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 (esk12_4 X1 X2 X3 X4) (k1_zfmisc_1 X2) → False) → v1_interva1 X4 X2 → v1_interva1 X3 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → r2_hidden X1 (a_3_1_interva1 X2 X3 X4) → False) → (∀X3 X1 X2 X4, ((esk12_4 X1 X2 X3 X4) = X1 → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → v1_interva1 X4 X2 → v1_interva1 X3 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → r2_hidden X1 (a_3_1_interva1 X2 X3 X4) → False) → (∀X2 X1 X3 X4, (r2_hidden (esk6_4 X1 X2 X3 X4) X2 → False) → X3 = (k4_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk5_4 X1 X2 X3 X4) X1 → False) → X3 = (k4_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X3 X2 X1, (X3 = (k4_setfam_1 X1 X2) → False) → ((k4_xboole_0 (esk8_3 X1 X2 X3) (esk9_3 X1 X2 X3)) = (esk7_3 X1 X2 X3) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → False) → (∀X5 X4 X1 X2 X3, (X3 = (k4_setfam_1 X1 X2) → False) → (esk7_3 X1 X2 X3) = (k4_xboole_0 X4 X5) → r2_hidden X5 X2 → r2_hidden X4 X1 → r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (∀X2 X1 X3, (X1 = (k7_interva1 X2 X3) → False) → (v1_xboole_0 X3 → False) → v1_interva1 X3 X2 → r2_hidden X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → r1_tarski X1 (esk13_3 X2 X3 X1) → False) → (∀X2 X3 X1, (X3 = (k4_setfam_1 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk9_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k4_setfam_1 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X1 X3 X2, (X3 = (k7_interva1 X1 X2) → False) → (v1_xboole_0 X2 → False) → (r2_hidden (esk13_3 X1 X2 X3) X2 → False) → v1_interva1 X2 X1 → r2_hidden X3 X2 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X3 X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X3 X2 → False) → v1_interva1 X2 X1 → r1_tarski X3 (k8_interva1 X1 X2) → r1_tarski (k7_interva1 X1 X2) X3 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → 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 (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) → (∀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) → (∀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) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k4_setfam_1 X2 X3) (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (m2_subset_1 (k8_interva1 X2 X1) (k1_zfmisc_1 X2) X1 → False) → v1_interva1 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (m2_subset_1 (k7_interva1 X2 X1) (k1_zfmisc_1 X2) X1 → False) → v1_interva1 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X4 X1 X2 X3, (v1_xboole_0 X3 → False) → (r1_tarski X1 X4 → False) → X1 = (k7_interva1 X2 X3) → v1_interva1 X3 X2 → r2_hidden X4 X3 → r2_hidden X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (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, (m1_subset_1 (k9_subset_1 X2 X3 X1) (k1_zfmisc_1 X2) → False) → 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 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 X3 X1 → False) → m2_subset_1 X3 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 X1 X3 → False) → m2_subset_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 X2) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → (r1_tarski (k7_interva1 X1 X2) X3 → False) → v1_interva1 X2 X1 → r2_hidden X3 X2 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (r1_tarski X1 (k8_interva1 X2 X3) → False) → v1_interva1 X3 X2 → r2_hidden X1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (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, ((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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk11_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 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) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m2_subset_1 X1 X3 X2 → False) → m1_subset_1 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X4 X3 X2 X1, (r1_tarski (k4_xboole_0 X1 X4) (k4_xboole_0 X2 X3) → False) → r1_tarski X3 X4 → r1_tarski X1 X2 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk21_2 X3 X2) → False) → (∀X4 X2 X1 X3 X5 X6, (r2_hidden X5 X6 → False) → X6 = (k4_setfam_1 X2 X4) → X5 = (k4_xboole_0 X1 X3) → r2_hidden X3 X4 → r2_hidden X1 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 X1) = (k3_xboole_0 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, ((k8_interva1 X2 X1) = (k3_tarski X1) → False) → (v1_xboole_0 X1 → False) → v1_interva1 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1, ((k7_interva1 X2 X1) = (k1_setfam_1 X1) → False) → (v1_xboole_0 X1 → False) → v1_interva1 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (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, (m1_subset_1 (k3_subset_1 X2 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk4_2 X1 X2) 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, (r2_hidden (esk21_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) → (∀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) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk4_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 (esk20_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk14_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 (esk20_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk14_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) → ((a_3_1_interva1 esk1_0 esk2_0 esk3_0) = (k4_setfam_1 esk2_0 esk3_0) → False) → (∀X1, v1_subset_1 (esk19_1 X1) X1 → False) → (∀X1, v1_xboole_0 (esk16_1 X1) → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk3_0 → False) → (v1_xboole_0 esk2_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, ((k3_xboole_0 (k2_xboole_0 X1 X2) (k2_xboole_0 X1 X3)) = (k2_xboole_0 X1 (k3_xboole_0 X2 X3)) → False) → False) → (∀X2 X3 X1, ((k3_xboole_0 (k3_xboole_0 X1 X2) X3) = (k3_xboole_0 X1 (k3_xboole_0 X2 X3)) → False) → False) → (∀X1 X2, (m1_subset_1 (k4_xboole_0 X1 X2) (k1_zfmisc_1 X1) → 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) → (∀X1, (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 (k1_zfmisc_1 X1)) → 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) → (∀X1, (r1_tarski (k1_setfam_1 X1) (k3_tarski X1) → False) → False) → (∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0)) → False) → False) → ((m1_subset_1 esk2_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0)) → False) → False) → (∀X1, (m1_subset_1 (esk10_1 X1) X1 → False) → False) → (∀X1, (v1_interva1 (esk16_1 X1) X1 → 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, ((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) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((v1_interva1 esk3_0 esk1_0 → False) → False) → ((v1_interva1 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk17_1 X1) → False) → False) → ((v1_xboole_0 esk15_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