Theorem. (
t40_interva1)
∀k4_setfam_1 : set → set → set, ∀m2_subset_1 : set → set → set → prop, ∀k4_xboole_0 : set → set → set, ∀k1_setfam_1 : set → set, ∀v1_subset_1 : set → set → prop, ∀esk16_1 : set → set, ∀esk9_1 : set → set, ∀k1_xboole_0 : set, ∀esk15_1 : set → set, ∀esk4_1 : set → set, ∀o_0_0_xboole_0 : set, ∀esk11_0 : set, ∀esk5_1 : set → set, ∀esk13_1 : set → set, ∀esk14_0 : set, ∀esk12_1 : set → set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk10_1 : set → set, ∀k3_tarski : set → set, ∀esk17_2 : set → set → set, ∀esk6_2 : set → set → set, ∀k5_interva1 : set → set → set, ∀k6_interva1 : set → set → set, ∀k1_interva1 : set → set → set → set, ∀m1_interva1 : set → set → prop, ∀k9_interva1 : set → set → set → set, ∀k2_interva1 : set → set → set → set, ∀a_3_0_interva1 : set → set → set → set, ∀esk7_4 : set → set → 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, ∀esk8_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)) (esk8_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 (esk8_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) → (∀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 (esk8_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 X4 X2, (m1_subset_1 (esk7_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 (esk7_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 (esk7_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) → (∀X3 X1 X2 X4, ((esk8_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) → (∀X3 X1 X4 X2, ((esk7_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 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) → (∀X4 X2 X1 X3, ((k8_interva1 X1 X2) = X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → X2 = (k2_interva1 X1 X4 X3) → v1_interva1 X2 X1 → m1_subset_1 X4 (k1_zfmisc_1 X1) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X4 X2 X1 X3, ((k7_interva1 X1 X2) = X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → X2 = (k2_interva1 X1 X3 X4) → v1_interva1 X2 X1 → m1_subset_1 X4 (k1_zfmisc_1 X1) → m1_subset_1 X3 (k1_zfmisc_1 X1) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 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, ((a_3_1_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) → 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)) → 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_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) → (∀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) → (∀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, ((k1_interva1 X2 X1 X3) = (k2_interva1 X2 X1 X3) → False) → m1_subset_1 X3 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → 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) → (∀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) → (∀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 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) → (∀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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk6_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk17_2 X3 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, ((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) → (∀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 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → m1_interva1 X1 X2 → False) → (∀X2 X1, (r2_hidden (esk17_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, (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) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (v1_interva1 X1 X2 → False) → m1_interva1 X1 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 (esk16_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 (esk16_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) → ((k2_interva1 esk1_0 (k7_subset_1 esk1_0 (k5_interva1 esk1_0 esk2_0) (k6_interva1 esk1_0 esk3_0)) (k7_subset_1 esk1_0 (k6_interva1 esk1_0 esk2_0) (k5_interva1 esk1_0 esk3_0))) = (k9_interva1 esk1_0 esk2_0 esk3_0) → False) → (∀X1, v1_subset_1 (esk15_1 X1) X1 → False) → (∀X1, v1_xboole_0 (esk12_1 X1) → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk3_0 → False) → (v1_xboole_0 esk2_0 → False) → (v1_xboole_0 esk1_0 → False) → (∀X1, (m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → False) → (∀X1, (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk13_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_interva1 (esk12_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 (esk5_1 X1) X1 → False) → False) → (∀X1, (m1_interva1 (esk4_1 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) → ((m1_interva1 esk3_0 esk1_0 → False) → False) → ((m1_interva1 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk13_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