Theorem. (
t4_latsum_1)
∀k2_zfmisc_1 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀k3_relat_1 : set → set → set, ∀esk12_3 : set → set → set → set, ∀k3_xboole_0 : set → set → set, ∀esk8_3 : set → set → set → set, ∀esk7_3 : set → set → set → set, ∀r8_relat_2 : set → set → prop, ∀v5_relat_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀v2_waybel_0 : set → set → prop, ∀v4_orders_2 : set → prop, ∀esk20_1 : set → set, ∀k1_xboole_0 : set, ∀esk22_0 : set, ∀esk2_0 : set, ∀esk18_1 : set → set, ∀esk21_0 : set, ∀esk16_0 : set, ∀esk17_0 : set, ∀esk19_2 : set → set → set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk1_0 : set, ∀l1_struct_0 : set → prop, ∀r1_tarski : set → set → prop, ∀v1_waybel_0 : set → set → prop, ∀v4_relat_1 : set → set → prop, ∀g1_orders_2 : set → set → set, ∀esk14_2 : set → set → set, ∀esk13_2 : set → set → set, ∀esk15_2 : set → set → set, ∀esk6_2 : set → set → set, ∀esk5_2 : set → set → set, ∀r1_latsum_1 : set → set → prop, ∀esk10_3 : set → set → set → set, ∀esk11_3 : set → set → set → set, ∀v1_relat_1 : set → prop, ∀k4_tarski : set → set → set, ∀esk9_5 : set → set → set → set → set → set, ∀r2_hidden : set → set → prop, ∀u1_struct_0 : set → set, ∀k2_xboole_0 : set → set → set, ∀u1_orders_2 : set → set, ∀k4_relset_1 : set → set → set → set → set → set → set, ∀v1_orders_2 : set → prop, ∀l1_orders_2 : set → prop, ∀k1_latsum_1 : set → set → set, (∀X1 X2 X3, (X1 = (k1_latsum_1 X2 X3) → False) → (u1_struct_0 X1) = (k2_xboole_0 (u1_struct_0 X2) (u1_struct_0 X3)) → (u1_orders_2 X1) = (k2_xboole_0 (k2_xboole_0 (u1_orders_2 X2) (u1_orders_2 X3)) (k4_relset_1 (u1_struct_0 X2) (u1_struct_0 X2) (u1_struct_0 X3) (u1_struct_0 X3) (u1_orders_2 X2) (u1_orders_2 X3))) → l1_orders_2 X3 → l1_orders_2 X2 → l1_orders_2 X1 → v1_orders_2 X1 → False) → (∀X4 X5 X6 X1 X2 X3, (m1_subset_1 (k4_relset_1 X2 X3 X5 X6 X1 X4) (k1_zfmisc_1 (k2_zfmisc_1 X2 X6)) → False) → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X5 X6)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X2 X3, ((u1_orders_2 X1) = (k2_xboole_0 (k2_xboole_0 (u1_orders_2 X2) (u1_orders_2 X3)) (k4_relset_1 (u1_struct_0 X2) (u1_struct_0 X2) (u1_struct_0 X3) (u1_struct_0 X3) (u1_orders_2 X2) (u1_orders_2 X3))) → False) → X1 = (k1_latsum_1 X2 X3) → l1_orders_2 X3 → l1_orders_2 X2 → l1_orders_2 X1 → v1_orders_2 X1 → False) → (∀X4 X5 X6 X1 X2 X3, ((k4_relset_1 X2 X3 X5 X6 X1 X4) = (k3_relat_1 X1 X4) → False) → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X5 X6)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X2 X1 X5 X4 X3, (r2_hidden (k4_tarski (esk9_5 X1 X2 X3 X4 X5) X5) X2 → False) → X3 = (k3_relat_1 X1 X2) → v1_relat_1 X3 → r2_hidden (k4_tarski X4 X5) X3 → False) → (∀X3 X2 X5 X1 X4, (r2_hidden (k4_tarski X1 (esk9_5 X2 X3 X4 X1 X5)) X2 → False) → X4 = (k3_relat_1 X2 X3) → v1_relat_1 X4 → r2_hidden (k4_tarski X1 X5) X4 → False) → (∀X4 X1 X2 X3, (X3 = (k3_relat_1 X1 X2) → False) → v1_relat_1 X3 → r2_hidden (k4_tarski X4 (esk11_3 X1 X2 X3)) X2 → r2_hidden (k4_tarski (esk10_3 X1 X2 X3) X4) X1 → r2_hidden (k4_tarski (esk10_3 X1 X2 X3) (esk11_3 X1 X2 X3)) X3 → False) → (∀X2 X1 X3, (X3 = (k3_relat_1 X1 X2) → False) → (r2_hidden (k4_tarski (esk10_3 X1 X2 X3) (esk11_3 X1 X2 X3)) X3 → False) → (r2_hidden (k4_tarski (esk12_3 X1 X2 X3) (esk11_3 X1 X2 X3)) X2 → False) → v1_relat_1 X3 → False) → (∀X1 X2 X3, (X3 = (k3_relat_1 X1 X2) → False) → (r2_hidden (k4_tarski (esk10_3 X1 X2 X3) (esk11_3 X1 X2 X3)) X3 → False) → (r2_hidden (k4_tarski (esk10_3 X1 X2 X3) (esk12_3 X1 X2 X3)) X1 → False) → v1_relat_1 X3 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X2 → r2_hidden (esk8_3 X1 X2 X3) X1 → False) → (∀X1 X2, (r1_latsum_1 X1 X2 → False) → l1_orders_2 X2 → l1_orders_2 X1 → r2_hidden (k4_tarski (esk5_2 X1 X2) (esk6_2 X1 X2)) (u1_orders_2 X2) → r2_hidden (k4_tarski (esk5_2 X1 X2) (esk6_2 X1 X2)) (u1_orders_2 X1) → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk7_3 X1 X2 X3) X3 → r2_hidden (esk7_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk7_3 X1 X2 X3) X3 → r2_hidden (esk7_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk7_3 X1 X2 X3) X2 → False) → (r2_hidden (esk7_3 X1 X2 X3) X1 → False) → False) → (∀X3 X2 X1 X4, (r2_hidden (k4_tarski X1 X2) (u1_orders_2 X4) → False) → l1_orders_2 X4 → l1_orders_2 X3 → r1_latsum_1 X3 X4 → r2_hidden (k4_tarski X1 X2) (u1_orders_2 X3) → r2_hidden X2 (k3_xboole_0 (u1_struct_0 X3) (u1_struct_0 X4)) → r2_hidden X1 (k3_xboole_0 (u1_struct_0 X3) (u1_struct_0 X4)) → False) → (∀X3 X2 X1 X4, (r2_hidden (k4_tarski X1 X2) (u1_orders_2 X4) → False) → l1_orders_2 X4 → l1_orders_2 X3 → r1_latsum_1 X4 X3 → r2_hidden (k4_tarski X1 X2) (u1_orders_2 X3) → r2_hidden X2 (k3_xboole_0 (u1_struct_0 X4) (u1_struct_0 X3)) → r2_hidden X1 (k3_xboole_0 (u1_struct_0 X4) (u1_struct_0 X3)) → False) → (∀X2 X1, (r1_latsum_1 X1 X2 → False) → (r2_hidden (k4_tarski (esk5_2 X1 X2) (esk6_2 X1 X2)) (u1_orders_2 X2) → False) → (r2_hidden (k4_tarski (esk5_2 X1 X2) (esk6_2 X1 X2)) (u1_orders_2 X1) → False) → l1_orders_2 X2 → l1_orders_2 X1 → False) → (∀X4 X2 X5 X3 X1, (r2_hidden (k4_tarski X3 X5) X1 → False) → v1_relat_1 X1 → r2_hidden X5 X2 → r2_hidden X4 X2 → r2_hidden X3 X2 → r8_relat_2 X1 X2 → r2_hidden (k4_tarski X4 X5) X1 → r2_hidden (k4_tarski X3 X4) X1 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X2 → False) → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → v1_relat_1 X1 → r2_hidden (k4_tarski (esk13_2 X1 X2) (esk15_2 X1 X2)) X1 → False) → (∀X5 X3 X2 X4 X1 X6, (r2_hidden (k4_tarski X1 X4) X6 → False) → X6 = (k3_relat_1 X3 X5) → v1_relat_1 X6 → r2_hidden (k4_tarski X2 X4) X5 → r2_hidden (k4_tarski X1 X2) X3 → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → (r2_hidden (k4_tarski (esk14_2 X1 X2) (esk15_2 X1 X2)) X1 → False) → v1_relat_1 X1 → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → (r2_hidden (k4_tarski (esk13_2 X1 X2) (esk14_2 X1 X2)) X1 → False) → v1_relat_1 X1 → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (g1_orders_2 X1 X3) = (g1_orders_2 X2 X4) → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X1)) → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (g1_orders_2 X3 X1) = (g1_orders_2 X4 X2) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X3)) → False) → (∀X1 X2, (v1_orders_2 (g1_orders_2 X1 X2) → False) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X1)) → False) → (∀X1 X2, (l1_orders_2 (g1_orders_2 X1 X2) → False) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X1)) → False) → (∀X1, (m1_subset_1 (u1_orders_2 X1) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))) → False) → l1_orders_2 X1 → False) → (∀X3 X1 X2, (v5_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X3 X1 X2, (v4_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X1)) → False) → (∀X2 X1, (r1_latsum_1 X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) (k3_xboole_0 (u1_struct_0 X1) (u1_struct_0 X2)) → False) → l1_orders_2 X2 → l1_orders_2 X1 → False) → (∀X2 X1, (r1_latsum_1 X1 X2 → False) → (r2_hidden (esk5_2 X1 X2) (k3_xboole_0 (u1_struct_0 X1) (u1_struct_0 X2)) → False) → l1_orders_2 X2 → l1_orders_2 X1 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → r2_hidden (k4_tarski X1 X3) (k2_zfmisc_1 X2 X4) → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → r2_hidden (k4_tarski X3 X1) (k2_zfmisc_1 X4 X2) → False) → (∀X3 X2 X1, (v1_relat_1 X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X4 X3 X2 X1, (r2_hidden (k4_tarski X1 X3) (k2_zfmisc_1 X2 X4) → False) → r2_hidden X3 X4 → r2_hidden X1 X2 → False) → (∀X1 X2 X3, (v5_relat_1 (k2_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v5_relat_1 X3 X2 → v5_relat_1 X1 X2 → False) → (∀X1 X2 X3, (v4_relat_1 (k2_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 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 X3, ((u1_struct_0 X1) = (k2_xboole_0 (u1_struct_0 X2) (u1_struct_0 X3)) → False) → X1 = (k1_latsum_1 X2 X3) → l1_orders_2 X3 → l1_orders_2 X2 → l1_orders_2 X1 → v1_orders_2 X1 → False) → (∀X1 X2, (v2_waybel_0 X1 X2 → False) → l1_orders_2 X2 → v1_xboole_0 X1 → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X1 X2, (v1_waybel_0 X1 X2 → False) → l1_orders_2 X2 → v1_xboole_0 X1 → m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2)) → False) → (∀X1 X2 X3, (v5_relat_1 (k3_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v5_relat_1 X1 X2 → False) → (∀X1 X2 X3, (v4_relat_1 (k3_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v4_relat_1 X1 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) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → (r2_hidden (esk15_2 X1 X2) X2 → False) → v1_relat_1 X1 → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → (r2_hidden (esk14_2 X1 X2) X2 → False) → v1_relat_1 X1 → False) → (∀X2 X1, (r8_relat_2 X1 X2 → False) → (r2_hidden (esk13_2 X1 X2) X2 → False) → v1_relat_1 X1 → 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 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) → (∀X1, (v4_orders_2 X1 → False) → l1_orders_2 X1 → r8_relat_2 (u1_orders_2 X1) (u1_struct_0 X1) → 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) → (∀X1, (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 (u1_struct_0 X1)) → False) → l1_orders_2 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v1_orders_2 (k1_latsum_1 X1 X2) → False) → l1_orders_2 X2 → l1_orders_2 X1 → False) → (∀X2 X1, (l1_orders_2 (k1_latsum_1 X1 X2) → False) → l1_orders_2 X2 → l1_orders_2 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1, ((g1_orders_2 (u1_struct_0 X1) (u1_orders_2 X1)) = X1 → False) → l1_orders_2 X1 → v1_orders_2 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X1, (r8_relat_2 (u1_orders_2 X1) (u1_struct_0 X1) → False) → l1_orders_2 X1 → v4_orders_2 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v2_waybel_0 (esk20_1 X1) X1 → False) → l1_orders_2 X1 → False) → (∀X1, (v1_waybel_0 (esk20_1 X1) X1 → False) → l1_orders_2 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l1_orders_2 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r2_hidden (k4_tarski esk3_0 esk4_0) (u1_orders_2 esk1_0) → False) → (v1_xboole_0 esk22_0 → False) → (∀X2 X1, (m1_subset_1 (esk19_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → ((r2_hidden (k4_tarski esk3_0 esk4_0) (u1_orders_2 (k1_latsum_1 esk1_0 esk2_0)) → False) → False) → (∀X2 X1, (v5_relat_1 (esk19_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk19_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_xboole_0 (esk19_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (esk19_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 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) → (∀X1, (m1_subset_1 (esk18_1 X1) X1 → False) → False) → ((r2_hidden esk4_0 (u1_struct_0 esk1_0) → False) → False) → ((r2_hidden esk3_0 (u1_struct_0 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_latsum_1 esk1_0 esk2_0 → False) → False) → ((l1_struct_0 esk17_0 → False) → False) → ((v1_xboole_0 esk21_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v4_orders_2 esk1_0 → False) → False) → ((l1_orders_2 esk16_0 → False) → False) → ((l1_orders_2 esk2_0 → False) → False) → ((l1_orders_2 esk1_0 → False) → False) → False