Theorem. (t60_cat_3)
∀k1_xboole_0 : set, ∀v9_cat_1 : setsetsetsetprop, ∀m1_cat_1 : setsetsetsetprop, ∀k5_cat_1 : setsetsetsetsetsetset, ∀k4_cat_1 : setsetset, ∀esk8_4 : setsetsetsetset, ∀esk6_4 : setsetsetsetset, ∀esk7_4 : setsetsetsetset, ∀esk9_5 : setsetsetsetsetset, ∀k3_graph_1 : setsetset, ∀esk18_4 : setsetsetsetset, ∀a_3_0_cat_1 : setsetsetset, ∀esk11_3 : setsetsetset, ∀k10_cat_3 : setsetsetset, ∀v10_cat_1 : setsetprop, ∀esk26_2 : setsetset, ∀k1_graph_1 : setsetset, ∀v7_struct_0 : setprop, ∀esk21_1 : setset, ∀l1_struct_0 : setprop, ∀esk20_1 : setset, ∀v13_struct_0 : setsetprop, ∀np__1 : set, ∀v15_struct_0 : setprop, ∀v1_zfmisc_1 : setprop, ∀l5_struct_0 : setprop, ∀v14_struct_0 : setprop, ∀esk24_0 : set, ∀esk22_0 : set, ∀esk19_0 : set, ∀esk13_0 : set, ∀esk15_0 : set, ∀esk12_0 : set, ∀esk14_0 : set, ∀esk17_1 : setset, ∀esk4_0 : set, ∀esk23_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀v1_finset_1 : setprop, ∀v8_struct_0 : setprop, ∀r1_tarski : setsetprop, ∀esk25_1 : setset, ∀k2_graph_1 : setsetset, ∀l1_graph_1 : setprop, ∀k1_zfmisc_1 : setset, ∀v1_xboole_0 : setprop, ∀esk16_3 : setsetsetset, ∀r1_cat_1 : setsetsetprop, ∀esk10_4 : setsetsetsetset, ∀k1_cat_1 : setsetsetset, ∀v11_struct_0 : setprop, ∀v2_cat_1 : setprop, ∀v4_cat_1 : setprop, ∀v6_cat_1 : setprop, ∀u4_struct_0 : setset, ∀m1_subset_1 : setsetprop, ∀u1_struct_0 : setset, ∀r2_cat_3 : setsetsetsetprop, ∀k4_graph_1 : setsetset, ∀l1_cat_1 : setprop, ∀v5_cat_1 : setprop, ∀v3_cat_1 : setprop, ∀k2_cat_1 : setsetsetset, ∀esk5_7 : setsetsetsetsetsetsetset, ∀r2_hidden : setsetprop, ∀v2_struct_0 : setprop, (∀X6 X4 X2 X3 X5 X7 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden (esk5_7 X1 X2 X3 X4 X5 X6 X7) (k2_cat_1 X1 X5 X2)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X7 (u4_struct_0 X1)m1_subset_1 X6 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_cat_3 X1 X2 X3 X4r2_hidden X7 (k2_cat_1 X1 X5 (k4_graph_1 X1 X4))r2_hidden X6 (k2_cat_1 X1 X5 (k4_graph_1 X1 X3))False)(∀X6 X4 X2 X3 X5 X7 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 (esk5_7 X1 X2 X3 X4 X5 X6 X7) (u4_struct_0 X1)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X7 (u4_struct_0 X1)m1_subset_1 X6 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_cat_3 X1 X2 X3 X4r2_hidden X7 (k2_cat_1 X1 X5 (k4_graph_1 X1 X4))r2_hidden X6 (k2_cat_1 X1 X5 (k4_graph_1 X1 X3))False)(∀X8 X6 X5 X7 X1 X2 X3 X4, ((k1_cat_1 X1 X2 X3) = X4False)(v2_struct_0 X1False)(v11_struct_0 X1False)(esk5_7 X1 X5 X3 X6 X7 X4 X8) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X8 (u4_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_cat_3 X1 X5 X3 X6r2_hidden X2 (k2_cat_1 X1 X7 X5)r2_hidden X8 (k2_cat_1 X1 X7 (k4_graph_1 X1 X6))r2_hidden X4 (k2_cat_1 X1 X7 (k4_graph_1 X1 X3))False)(∀X8 X6 X5 X7 X1 X2 X3 X4, ((k1_cat_1 X1 X2 X3) = X4False)(v2_struct_0 X1False)(v11_struct_0 X1False)(esk5_7 X1 X5 X6 X3 X7 X8 X4) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X8 (u4_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_cat_3 X1 X5 X6 X3r2_hidden X2 (k2_cat_1 X1 X7 X5)r2_hidden X8 (k2_cat_1 X1 X7 (k4_graph_1 X1 X6))r2_hidden X4 (k2_cat_1 X1 X7 (k4_graph_1 X1 X3))False)(∀X4 X3 X7 X8 X2 X5 X6 X1, ((esk5_7 X1 X7 X3 X5 X8 X4 X6) = X2False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k1_cat_1 X1 X2 X5) = X6(k1_cat_1 X1 X2 X3) = X4v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u4_struct_0 X1)m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_cat_3 X1 X7 X3 X5r2_hidden X2 (k2_cat_1 X1 X8 X7)r2_hidden X6 (k2_cat_1 X1 X8 (k4_graph_1 X1 X5))r2_hidden X4 (k2_cat_1 X1 X8 (k4_graph_1 X1 X3))False)(∀X4 X5 X1 X3 X2, ((k2_cat_1 X1 X3 X2) = k1_xboole_0False)((k2_cat_1 X1 X2 X3) = k1_xboole_0False)(v2_struct_0 X1False)(v11_struct_0 X1False)(v9_cat_1 X5 X1 X2 X3False)(k5_cat_1 X1 X3 X2 X3 X4 X5) = (k4_cat_1 X1 X3)(k5_cat_1 X1 X2 X3 X2 X5 X4) = (k4_cat_1 X1 X2)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X5 X1 X2 X3m1_cat_1 X4 X1 X3 X2False)(∀X3 X5 X6 X2 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (k5_cat_1 X1 X2 X3 X4 X5 X6) X1 X2 X4False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X6 X1 X3 X4m1_cat_1 X5 X1 X2 X3False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2(esk9_5 X1 X2 X3 X4 X5) = X5(k1_cat_1 X1 (esk9_5 X1 X2 X3 X4 X5) X4) = (esk8_4 X1 X2 X3 X4)(k1_cat_1 X1 (esk9_5 X1 X2 X3 X4 X5) X3) = (esk7_4 X1 X2 X3 X4)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_hidden X5 (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(∀X2 X4 X3 X1, ((k5_cat_1 X1 X2 X3 X2 (esk10_4 X1 X3 X2 X4) X4) = (k4_cat_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X3 X2v9_cat_1 X4 X1 X3 X2False)(∀X2 X4 X3 X1, ((k5_cat_1 X1 X2 X3 X2 X4 (esk10_4 X1 X2 X3 X4)) = (k4_cat_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X2 X3v9_cat_1 X4 X1 X2 X3False)(∀X2 X5 X6 X1 X3 X4, ((k2_cat_1 X1 X3 X4) = k1_xboole_0False)((k2_cat_1 X1 X2 X3) = k1_xboole_0False)((k5_cat_1 X1 X2 X3 X4 X5 X6) = (k1_cat_1 X1 X5 X6)False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X6 X1 X3 X4m1_cat_1 X5 X1 X2 X3False)(∀X3 X2 X1, ((k5_cat_1 X1 X2 X2 X2 (k4_cat_1 X1 X2) X3) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X3 X1 X2 X2False)(∀X3 X2 X1, ((k5_cat_1 X1 X2 X2 X2 X3 (k4_cat_1 X1 X2)) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X3 X1 X2 X2False)(∀X5 X2 X3 X4 X1, ((esk9_5 X1 X2 X3 X4 X5) = X5False)((k1_cat_1 X1 (esk9_5 X1 X2 X3 X4 X5) X3) = (esk7_4 X1 X2 X3 X4)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_hidden X5 (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(∀X5 X2 X3 X4 X1, ((esk9_5 X1 X2 X3 X4 X5) = X5False)((k1_cat_1 X1 (esk9_5 X1 X2 X3 X4 X5) X4) = (esk8_4 X1 X2 X3 X4)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_hidden X5 (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(r2_hidden (esk9_5 X1 X2 X3 X4 X5) (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_hidden X5 (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk9_5 X1 X2 X3 X4 X5) (u4_struct_0 X1)False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_hidden X5 (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) X2)False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(r2_hidden (esk8_4 X1 X2 X3 X4) (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) (k4_graph_1 X1 X4))False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(r2_hidden (esk7_4 X1 X2 X3 X4) (k2_cat_1 X1 (esk6_4 X1 X2 X3 X4) (k4_graph_1 X1 X3))False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X4 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (esk10_4 X1 X2 X3 X4) X1 X3 X2False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X2 X3v9_cat_1 X4 X1 X2 X3False)(∀X4 X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(k2_cat_1 X1 X2 X3) = k1_xboole_0v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X2 X3v9_cat_1 X4 X1 X2 X3False)(∀X4 X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(k2_cat_1 X1 X2 X3) = k1_xboole_0v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X3 X2v9_cat_1 X4 X1 X3 X2False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk8_4 X1 X2 X3 X4) (u4_struct_0 X1)False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk7_4 X1 X2 X3 X4) (u4_struct_0 X1)False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk6_4 X1 X2 X3 X4) (u1_struct_0 X1)False)(k3_graph_1 X1 X4) = X2(k3_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X3 X1 X2 X5, (X5 = (k4_cat_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k1_cat_1 X1 X5 X4) = X4(k1_cat_1 X1 X5 X3) = X3v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r2_cat_3 X1 X2 X3 X4r2_hidden X5 (k2_cat_1 X1 X2 X2)False)(∀X1 X4 X3 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(r1_cat_1 X2 X3 X4False)v2_cat_1 X2v3_cat_1 X2v4_cat_1 X2v5_cat_1 X2v6_cat_1 X2l1_cat_1 X2m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)m1_cat_1 X1 X2 X3 X4v9_cat_1 X1 X2 X3 X4False)(∀X4 X1 X3 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(m1_subset_1 (esk18_4 X1 X2 X3 X4) (u4_struct_0 X2)False)l1_cat_1 X2m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)r2_hidden X1 (a_3_0_cat_1 X2 X3 X4)False)(∀X4 X2 X3 X1, ((k3_graph_1 X1 (esk18_4 X2 X1 X3 X4)) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)r2_hidden X2 (a_3_0_cat_1 X1 X3 X4)False)(∀X4 X2 X3 X1, ((k4_graph_1 X1 (esk18_4 X2 X1 X3 X4)) = X4False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)r2_hidden X2 (a_3_0_cat_1 X1 X3 X4)False)(∀X1 X2 X3 X4, ((k2_cat_1 X2 X3 X4) = k1_xboole_0False)(v2_struct_0 X2False)(v11_struct_0 X2False)(r2_hidden X1 (k2_cat_1 X2 X3 X4)False)l1_cat_1 X2m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u4_struct_0 X2)m1_cat_1 X1 X2 X3 X4False)(∀X1 X2 X3 X4, ((k2_cat_1 X2 X3 X4) = k1_xboole_0False)(v2_struct_0 X2False)(v11_struct_0 X2False)(m1_cat_1 X1 X2 X3 X4False)l1_cat_1 X2m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u4_struct_0 X2)r2_hidden X1 (k2_cat_1 X2 X3 X4)False)(∀X2 X4 X3 X1, ((k1_cat_1 X1 (k1_cat_1 X1 X2 X3) X4) = (k1_cat_1 X1 X2 (k1_cat_1 X1 X3 X4))False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k3_graph_1 X1 X4) = (k4_graph_1 X1 X3)(k3_graph_1 X1 X3) = (k4_graph_1 X1 X2)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v9_cat_1 (esk11_3 X1 X2 X3) X1 X2 X3False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1r1_cat_1 X1 X2 X3m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (esk11_3 X1 X2 X3) X1 X2 X3False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1r1_cat_1 X1 X2 X3m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X2 X1 X3, ((k3_graph_1 X1 X2) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_cat_3 X1 X3 X2 X4False)(∀X4 X2 X1 X3, ((k3_graph_1 X1 X2) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_cat_3 X1 X3 X4 X2False)(∀X4 X1 X3 X2, ((esk18_4 X1 X2 X3 X4) = X1False)(v2_struct_0 X2False)(v11_struct_0 X2False)l1_cat_1 X2m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X3 (u1_struct_0 X2)r2_hidden X1 (a_3_0_cat_1 X2 X3 X4)False)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 X4 (u4_struct_0 X1)False)l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m1_cat_1 X4 X1 X2 X3False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (k10_cat_3 X1 X2 X3) X1 X2 X3False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (esk16_3 X1 X2 X3) X1 X2 X3False)l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 X2 X1 (k3_graph_1 X1 X2) (k4_graph_1 X1 X2)False)l1_cat_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_cat_1 (k4_cat_1 X1 X2) X1 X2 X2False)v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X2 X1 X3, ((k3_graph_1 X1 X2) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_hidden X2 (k2_cat_1 X1 X3 X4)False)(∀X4 X2 X1 X3, ((k4_graph_1 X1 X2) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)r2_hidden X2 (k2_cat_1 X1 X4 X3)False)(∀X3 X2 X1, ((k3_graph_1 X1 (k1_cat_1 X1 X2 X3)) = (k3_graph_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k3_graph_1 X1 X3) = (k4_graph_1 X1 X2)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)False)(∀X3 X2 X1, ((k4_graph_1 X1 (k1_cat_1 X1 X2 X3)) = (k4_graph_1 X1 X3)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k3_graph_1 X1 X3) = (k4_graph_1 X1 X2)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)False)(∀X1 X5 X4 X3 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(r2_hidden X3 (a_3_0_cat_1 X2 X4 X5)False)X1 = X3(k4_graph_1 X2 X1) = X5(k3_graph_1 X2 X1) = X4l1_cat_1 X2m1_subset_1 X5 (u1_struct_0 X2)m1_subset_1 X4 (u1_struct_0 X2)m1_subset_1 X1 (u4_struct_0 X2)False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden X2 (k2_cat_1 X1 X3 X4)False)(k4_graph_1 X1 X2) = X4(k3_graph_1 X1 X2) = X3l1_cat_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)False)(∀X3 X4 X2 X1, ((k10_cat_3 X1 X3 X2) = X4False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k4_graph_1 X1 X4) = X2(k3_graph_1 X1 X4) = X3v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v10_cat_1 X2 X1m1_subset_1 X4 (u4_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k3_graph_1 X1 (k10_cat_3 X1 X2 X3)) = X2False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v10_cat_1 X3 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k4_graph_1 X1 (k10_cat_3 X1 X2 X3)) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v10_cat_1 X3 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r1_cat_1 X1 X3 X2False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1r1_cat_1 X1 X2 X3m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden (k4_cat_1 X1 X2) (k2_cat_1 X1 X2 X2)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)v5_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)v1_xboole_0 (k2_cat_1 X1 X2 X2)False)(∀X3 X2 X1, ((k1_cat_1 X1 X3 (k4_cat_1 X1 X2)) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k4_graph_1 X1 X3) = X2v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 (k2_cat_1 X1 X2 X3) (k1_zfmisc_1 (u4_struct_0 X1))False)l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(k2_cat_1 X1 (k3_graph_1 X1 X2) (k4_graph_1 X1 X2)) = k1_xboole_0l1_cat_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k1_cat_1 X1 X2 X3) (u4_struct_0 X1)False)l1_cat_1 X1m1_subset_1 X3 (u4_struct_0 X1)m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X3 X1, ((a_3_0_cat_1 X1 X2 X3) = (k2_cat_1 X1 X2 X3)False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r1_cat_1 X1 X2 X2False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k3_graph_1 X1 (k4_cat_1 X1 X2)) = X2False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k4_graph_1 X1 (k4_cat_1 X1 X2)) = X2False)(v2_struct_0 X1False)(v11_struct_0 X1False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk26_2 X3 X2)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 (k3_graph_1 X1 X2) (u1_struct_0 X1)False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 (k4_graph_1 X1 X2) (u1_struct_0 X1)False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, (m1_subset_1 (k2_graph_1 X1 X2) (u1_struct_0 X1)False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, (m1_subset_1 (k1_graph_1 X1 X2) (u1_struct_0 X1)False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, ((k2_graph_1 X1 X2) = (k4_graph_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1, ((k3_graph_1 X1 X2) = (k1_graph_1 X1 X2)False)(v2_struct_0 X1False)(v11_struct_0 X1False)l1_graph_1 X1m1_subset_1 X2 (u4_struct_0 X1)False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1, (r2_hidden (esk26_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)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk25_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk20_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)(∀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, v2_struct_0 X1l1_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, (v15_struct_0 X1False)l5_struct_0 X1v1_zfmisc_1 (u4_struct_0 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (esk21_1 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (u1_struct_0 X1)False)(∀X1, (v11_struct_0 X1False)l5_struct_0 X1v1_xboole_0 (u4_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk25_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk20_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v6_cat_1 X1False)l1_cat_1 X1v15_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v5_cat_1 X1False)l1_cat_1 X1v7_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v4_cat_1 X1False)l1_cat_1 X1v15_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v3_cat_1 X1False)l1_cat_1 X1v7_struct_0 X1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v11_struct_0 X1False)v2_struct_0 X1l5_struct_0 X1v14_struct_0 X1False)(∀X1, (v11_struct_0 X1False)v2_struct_0 X1l5_struct_0 X1v14_struct_0 X1False)(∀X1, (v1_finset_1 (u1_struct_0 X1)False)l1_struct_0 X1v8_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u4_struct_0 X1)False)l5_struct_0 X1v15_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u1_struct_0 X1)False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_xboole_0 (u4_struct_0 X1)False)v11_struct_0 X1l5_struct_0 X1False)(∀X1, (v1_xboole_0 (u1_struct_0 X1)False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_zfmisc_1 (esk20_1 X1)False)l1_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)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v15_struct_0 X1False)v11_struct_0 X1l5_struct_0 X1False)(∀X1, (v14_struct_0 X1False)v11_struct_0 X1l5_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v2_struct_0 X1False)(v14_struct_0 X1False)l5_struct_0 X1False)(∀X1, (l1_graph_1 X1False)l1_cat_1 X1False)(∀X1, (l5_struct_0 X1False)l1_graph_1 X1False)(∀X1, (l1_struct_0 X1False)l5_struct_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(r1_cat_1 esk1_0 esk2_0 (k4_graph_1 esk1_0 esk3_0)False)(v1_xboole_0 esk24_0False)(v1_xboole_0 np__1False)(v15_struct_0 esk22_0False)(v11_struct_0 esk23_0False)(v11_struct_0 esk1_0False)(v2_struct_0 esk23_0False)(v2_struct_0 esk1_0False)((r2_cat_3 esk1_0 esk2_0 esk3_0 esk4_0False)False)((v10_cat_1 (k4_graph_1 esk1_0 esk4_0) esk1_0False)False)(∀X1, (m1_subset_1 (esk17_1 X1) X1False)False)((m1_subset_1 esk4_0 (u4_struct_0 esk1_0)False)False)((m1_subset_1 esk3_0 (u4_struct_0 esk1_0)False)False)((m1_subset_1 esk2_0 (u1_struct_0 esk1_0)False)False)(∀X1, (r1_tarski X1 X1False)False)((v1_xboole_0 esk19_0False)False)((v1_xboole_0 k1_xboole_0False)False)((l1_graph_1 esk13_0False)False)((l5_struct_0 esk22_0False)False)((l5_struct_0 esk15_0False)False)((l1_struct_0 esk14_0False)False)((l1_cat_1 esk23_0False)False)((l1_cat_1 esk12_0False)False)((l1_cat_1 esk1_0False)False)((v6_cat_1 esk1_0False)False)((v5_cat_1 esk1_0False)False)((v4_cat_1 esk1_0False)False)((v3_cat_1 esk1_0False)False)((v2_cat_1 esk1_0False)False)False
Proof:
The rest of the proof is missing.