Theorem. (t45_yellow_4)
∀k12_lattice3 : setsetsetset, ∀v2_lattice3 : setprop, ∀r1_orders_2 : setsetsetprop, ∀esk18_4 : setsetsetsetset, ∀v5_orders_2 : setprop, ∀k2_xboole_0 : setsetset, ∀esk8_3 : setsetsetset, ∀v12_waybel_0 : setsetprop, ∀k4_subset_1 : setsetsetset, ∀v2_waybel_0 : setsetprop, ∀r1_tarski : setsetprop, ∀esk7_2 : setsetset, ∀esk17_1 : setset, ∀v13_struct_0 : setsetprop, ∀np__1 : set, ∀k1_xboole_0 : set, ∀v1_zfmisc_1 : setprop, ∀o_0_0_xboole_0 : set, ∀esk9_0 : set, ∀esk10_0 : set, ∀esk11_1 : setset, ∀esk2_0 : set, ∀esk4_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀v1_finset_1 : setprop, ∀v8_struct_0 : setprop, ∀esk14_1 : setset, ∀esk15_1 : setset, ∀l1_struct_0 : setprop, ∀esk16_1 : setset, ∀v7_struct_0 : setprop, ∀v1_waybel_0 : setsetprop, ∀esk19_2 : setsetset, ∀esk5_2 : setsetset, ∀esk6_2 : setsetset, ∀k4_yellow_4 : setsetsetset, ∀v1_xboole_0 : setprop, ∀k3_yellow_4 : setsetsetset, ∀v2_struct_0 : setprop, ∀m1_subset_1 : setsetprop, ∀k1_zfmisc_1 : setset, ∀u1_struct_0 : setset, ∀a_3_18_yellow_4 : setsetsetset, ∀r2_hidden : setsetprop, ∀l1_orders_2 : setprop, ∀k11_lattice3 : setsetsetset, ∀esk13_4 : setsetsetsetset, ∀esk12_4 : setsetsetsetset, (∀X3 X1 X4 X2, ((k11_lattice3 X2 (esk12_4 X1 X2 X3 X4) (esk13_4 X1 X2 X3 X4)) = X1False)(v2_struct_0 X2False)l1_orders_2 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))r2_hidden X1 (a_3_18_yellow_4 X2 X3 X4)False)(∀X4 X3 X2 X1, (X4 = (k12_lattice3 X1 X2 X3)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1r1_orders_2 X1 X4 X3r1_orders_2 X1 X4 X2m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_orders_2 X1 (esk18_4 X1 X2 X3 X4) X4False)(∀X4 X3 X2 X1, (X4 = (k12_lattice3 X1 X2 X3)False)(r1_orders_2 X1 (esk18_4 X1 X2 X3 X4) X2False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1r1_orders_2 X1 X4 X3r1_orders_2 X1 X4 X2m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X3 X2 X1, (X4 = (k12_lattice3 X1 X2 X3)False)(r1_orders_2 X1 (esk18_4 X1 X2 X3 X4) X3False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1r1_orders_2 X1 X4 X3r1_orders_2 X1 X4 X2m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X3 X2 X1, (X4 = (k12_lattice3 X1 X2 X3)False)(m1_subset_1 (esk18_4 X1 X2 X3 X4) (u1_struct_0 X1)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1r1_orders_2 X1 X4 X3r1_orders_2 X1 X4 X2m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X1 X4 X2, (v2_struct_0 X2False)(m1_subset_1 (esk13_4 X1 X2 X3 X4) (u1_struct_0 X2)False)l1_orders_2 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))r2_hidden X1 (a_3_18_yellow_4 X2 X3 X4)False)(∀X3 X1 X4 X2, (v2_struct_0 X2False)(m1_subset_1 (esk12_4 X1 X2 X3 X4) (u1_struct_0 X2)False)l1_orders_2 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))r2_hidden X1 (a_3_18_yellow_4 X2 X3 X4)False)(∀X3 X1 X4 X2, (v2_struct_0 X2False)(r2_hidden (esk13_4 X1 X2 X3 X4) X4False)l1_orders_2 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))r2_hidden X1 (a_3_18_yellow_4 X2 X3 X4)False)(∀X3 X1 X4 X2, (v2_struct_0 X2False)(r2_hidden (esk12_4 X1 X2 X3 X4) X3False)l1_orders_2 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))r2_hidden X1 (a_3_18_yellow_4 X2 X3 X4)False)(∀X3 X4 X5 X1 X2, (r1_orders_2 X2 X1 X5False)X5 = (k12_lattice3 X2 X3 X4)v5_orders_2 X2v2_lattice3 X2l1_orders_2 X2r1_orders_2 X2 X1 X4r1_orders_2 X2 X1 X3m1_subset_1 X5 (u1_struct_0 X2)m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u1_struct_0 X2)False)(∀X4 X5 X6 X3 X1 X2, (v2_struct_0 X2False)(r2_hidden X4 (a_3_18_yellow_4 X2 X5 X6)False)X4 = (k11_lattice3 X2 X1 X3)l1_orders_2 X2r2_hidden X3 X6r2_hidden X1 X5m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u1_struct_0 X2)m1_subset_1 X6 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X5 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk8_3 X1 X2 X3) X3r2_hidden (esk8_3 X1 X2 X3) X1False)(∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk8_3 X1 X2 X3) X3r2_hidden (esk8_3 X1 X2 X3) X2False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)(r2_hidden (esk8_3 X1 X2 X3) X3False)(r2_hidden (esk8_3 X1 X2 X3) X2False)(r2_hidden (esk8_3 X1 X2 X3) X1False)False)(∀X3 X2 X1, (v2_struct_0 X1False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)l1_orders_2 X1v1_xboole_0 (k3_yellow_4 X1 X2 X3)m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X3 X4 X1, (r2_hidden X4 X1False)l1_orders_2 X2v12_waybel_0 X1 X2r2_hidden X3 X1r1_orders_2 X2 X4 X3m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X2 X3 X1, (m1_subset_1 (k4_yellow_4 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1))False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X4 X3 X2 X1, (r1_orders_2 X1 X2 X3False)X2 = (k12_lattice3 X1 X3 X4)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X3 X2 X1, (r1_orders_2 X1 X2 X3False)X2 = (k12_lattice3 X1 X4 X3)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, (v2_struct_0 X1False)(m1_subset_1 (k3_yellow_4 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_orders_2 X1m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X3 X1, ((k4_yellow_4 X1 X2 X3) = (k3_yellow_4 X1 X2 X3)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X3 X1, ((k4_yellow_4 X1 X2 X3) = (k4_yellow_4 X1 X3 X2)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X3 X2 X1, ((k3_yellow_4 X1 X2 X3) = (a_3_18_yellow_4 X1 X2 X3)False)(v2_struct_0 X1False)l1_orders_2 X1m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X3 X1, (m1_subset_1 (k12_lattice3 X1 X2 X3) (u1_struct_0 X1)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k11_lattice3 X1 X2 X3) (u1_struct_0 X1)False)l1_orders_2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k12_lattice3 X1 X2 X3) = (k11_lattice3 X1 X2 X3)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k12_lattice3 X1 X2 X3) = (k12_lattice3 X1 X3 X2)False)v5_orders_2 X1v2_lattice3 X1l1_orders_2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)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)(∀X2 X1, (v12_waybel_0 X2 X1False)(r1_orders_2 X1 (esk6_2 X1 X2) (esk5_2 X1 X2)False)l1_orders_2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))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 X1, (v12_waybel_0 X2 X1False)l1_orders_2 X1r2_hidden (esk6_2 X1 X2) X2m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 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)(∀X3 X2 X1, ((k4_subset_1 X2 X1 X1) = X1False)m1_subset_1 X3 (k1_zfmisc_1 X2)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, (v12_waybel_0 X2 X1False)(m1_subset_1 (esk6_2 X1 X2) (u1_struct_0 X1)False)l1_orders_2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (v12_waybel_0 X2 X1False)(m1_subset_1 (esk5_2 X1 X2) (u1_struct_0 X1)False)l1_orders_2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (v12_waybel_0 X2 X1False)(r2_hidden (esk5_2 X1 X2) X2False)l1_orders_2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk19_2 X3 X2)False)(∀X1 X2, (v2_waybel_0 X1 X2False)l1_orders_2 X2v1_xboole_0 X1m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X1 X2, (v1_waybel_0 X1 X2False)l1_orders_2 X2v1_xboole_0 X1m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk7_2 X1 X2) X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)(r2_hidden X1 X3False)X2 = (k2_xboole_0 X3 X4)r2_hidden X1 X2False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1, (r2_hidden (esk19_2 X1 X2) X2False)r2_hidden X1 X2False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X4 X1 X3, (r2_hidden X1 X3False)X3 = (k2_xboole_0 X2 X4)r2_hidden X1 X2False)(∀X2 X4 X1 X3, (r2_hidden X1 X3False)X3 = (k2_xboole_0 X4 X2)r2_hidden X1 X2False)(∀X1 X3 X2, (r2_hidden X3 X2False)r1_tarski X1 X2r2_hidden X3 X1False)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk7_2 X1 X2) X1False)False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X1, (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_orders_2 X1False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, l1_struct_0 X1v2_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 k1_xboole_0False)(∀X1, (v2_struct_0 X1False)(v13_struct_0 X1 np__1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v1_finset_1 (u1_struct_0 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (esk16_1 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk17_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk15_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v2_waybel_0 (esk14_1 X1) X1False)l1_orders_2 X1False)(∀X1, (v1_waybel_0 (esk14_1 X1) X1False)l1_orders_2 X1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v1_finset_1 (u1_struct_0 X1)False)l1_struct_0 X1v8_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u1_struct_0 X1)False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_xboole_0 (u1_struct_0 X1)False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_zfmisc_1 (esk15_1 X1)False)l1_struct_0 X1False)(∀X1, v2_lattice3 X1l1_orders_2 X1v2_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v2_struct_0 X1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v2_struct_0 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (l1_struct_0 X1False)l1_orders_2 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(r1_tarski (k4_yellow_4 esk1_0 (k4_subset_1 (u1_struct_0 esk1_0) esk2_0 esk3_0) (k4_subset_1 (u1_struct_0 esk1_0) esk2_0 esk4_0)) (k4_subset_1 (u1_struct_0 esk1_0) esk2_0 (k4_yellow_4 esk1_0 esk3_0 esk4_0))False)(v1_xboole_0 np__1False)(∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1)False)False)((m1_subset_1 esk4_0 (k1_zfmisc_1 (u1_struct_0 esk1_0))False)False)((m1_subset_1 esk3_0 (k1_zfmisc_1 (u1_struct_0 esk1_0))False)False)((m1_subset_1 esk2_0 (k1_zfmisc_1 (u1_struct_0 esk1_0))False)False)(∀X1, (m1_subset_1 (esk11_1 X1) X1False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1False)False)((v12_waybel_0 esk2_0 esk1_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((l1_struct_0 esk10_0False)False)((l1_orders_2 esk9_0False)False)((l1_orders_2 esk1_0False)False)((v2_lattice3 esk1_0False)False)((v5_orders_2 esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.