Theorem. (t76_cat_3)
∀esk19_4 : setsetsetsetset, ∀a_3_0_cat_1 : setsetsetset, ∀esk18_3 : setsetsetset, ∀k8_funcop_1 : setsetsetset, ∀v5_relat_1 : setsetprop, ∀v1_relat_1 : setprop, ∀v4_relat_1 : setsetprop, ∀esk28_2 : setsetset, ∀k2_graph_1 : setsetset, ∀v7_struct_0 : setprop, ∀esk23_1 : setset, ∀l1_struct_0 : setprop, ∀esk22_1 : setset, ∀v13_struct_0 : setsetprop, ∀np__1 : set, ∀v8_struct_0 : setprop, ∀v1_finset_1 : setprop, ∀v14_struct_0 : setprop, ∀esk25_0 : set, ∀esk20_2 : setsetset, ∀esk17_1 : setset, ∀esk21_0 : set, ∀esk14_0 : set, ∀esk12_0 : set, ∀esk15_0 : set, ∀esk13_0 : set, ∀esk24_0 : set, ∀esk26_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀l5_struct_0 : setprop, ∀v1_zfmisc_1 : setprop, ∀v15_struct_0 : setprop, ∀k1_xboole_0 : set, ∀r1_tarski : setsetprop, ∀esk27_1 : setset, ∀k1_graph_1 : setsetset, ∀esk11_2 : setsetset, ∀l1_graph_1 : setprop, ∀k4_cat_1 : setsetset, ∀esk16_3 : setsetsetset, ∀m1_cat_1 : setsetsetsetprop, ∀k1_tarski : setset, ∀k1_cat_3 : setsetsetset, ∀k10_funct_2 : setsetsetsetset, ∀v1_xboole_0 : setprop, ∀k4_graph_1 : setsetset, ∀esk10_4 : setsetsetsetset, ∀k3_graph_1 : setsetset, ∀esk8_5 : setsetsetsetsetset, ∀esk6_4 : setsetsetsetset, ∀esk9_5 : setsetsetsetsetset, ∀esk7_4 : setsetsetsetset, ∀v2_struct_0 : setprop, ∀esk5_7 : setsetsetsetsetsetsetset, ∀u4_struct_0 : setset, ∀k7_partfun1 : setsetsetset, ∀k1_cat_1 : setsetsetset, ∀v3_cat_1 : setprop, ∀v5_cat_1 : setprop, ∀l1_cat_1 : setprop, ∀m1_subset_1 : setsetprop, ∀m2_cat_3 : setsetsetsetprop, ∀k2_cat_1 : setsetsetset, ∀r2_hidden : setsetprop, ∀k2_zfmisc_1 : setsetset, ∀k1_zfmisc_1 : setset, ∀r2_funct_2 : setsetsetsetprop, ∀k2_cat_3 : setsetsetset, ∀v1_funct_2 : setsetsetprop, ∀r3_cat_3 : setsetsetsetprop, ∀u1_struct_0 : setset, ∀v1_funct_1 : setprop, ∀v6_cat_1 : setprop, ∀v4_cat_1 : setprop, ∀v2_cat_1 : setprop, ∀v11_struct_0 : setprop, ∀esk4_6 : setsetsetsetsetsetset, (∀X7 X3 X6 X4 X5 X2 X1, ((esk4_6 X1 X3 X4 X2 X5 X6) = X7False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k1_cat_1 X1 (k7_partfun1 (u4_struct_0 X1) X2 (esk5_7 X1 X3 X4 X2 X5 X6 X7)) X7) = (k7_partfun1 (u4_struct_0 X1) X6 (esk5_7 X1 X3 X4 X2 X5 X6 X7))v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X2m1_subset_1 X7 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)r3_cat_3 X1 X3 X4 X2m2_cat_3 X6 X1 X5 X4v1_funct_2 X2 X4 (u4_struct_0 X1)r2_hidden X7 (k2_cat_1 X1 X3 X5)m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X4 (u4_struct_0 X1)))r2_funct_2 X4 (u1_struct_0 X1) (k2_cat_3 X1 X4 X2) (k2_cat_3 X1 X4 X6)False)(∀X7 X2 X6 X3 X5 X4 X1, ((esk4_6 X1 X2 X3 X4 X5 X6) = X7False)(v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden (esk5_7 X1 X2 X3 X4 X5 X6 X7) X3False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X7 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r3_cat_3 X1 X2 X3 X4m2_cat_3 X6 X1 X5 X3v1_funct_2 X4 X3 (u4_struct_0 X1)r2_hidden X7 (k2_cat_1 X1 X2 X5)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_funct_2 X3 (u1_struct_0 X1) (k2_cat_3 X1 X3 X4) (k2_cat_3 X1 X3 X6)False)(∀X5 X3 X4 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X3 X4 X2False)(esk8_5 X1 X3 X4 X2 X5) = X5(k1_cat_1 X1 (k7_partfun1 (u4_struct_0 X1) X2 (esk9_5 X1 X3 X4 X2 X5)) (esk8_5 X1 X3 X4 X2 X5)) = (k7_partfun1 (u4_struct_0 X1) (esk7_4 X1 X3 X4 X2) (esk9_5 X1 X3 X4 X2 X5))v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X2m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m2_cat_3 X2 X1 X3 X4v1_funct_2 X2 X4 (u4_struct_0 X1)m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X4 (u4_struct_0 X1)))r2_hidden X5 (k2_cat_1 X1 X3 (esk6_4 X1 X3 X4 X2))False)(∀X5 X3 X6 X2 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden (esk4_6 X1 X2 X3 X4 X5 X6) (k2_cat_1 X1 X2 X5)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r3_cat_3 X1 X2 X3 X4m2_cat_3 X6 X1 X5 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_funct_2 X3 (u1_struct_0 X1) (k2_cat_3 X1 X3 X4) (k2_cat_3 X1 X3 X6)False)(∀X5 X3 X6 X2 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m1_subset_1 (esk4_6 X1 X2 X3 X4 X5 X6) (u4_struct_0 X1)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r3_cat_3 X1 X2 X3 X4m2_cat_3 X6 X1 X5 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_funct_2 X3 (u1_struct_0 X1) (k2_cat_3 X1 X3 X4) (k2_cat_3 X1 X3 X6)False)(∀X2 X5 X3 X4 X7 X1 X6 X8, ((k1_cat_1 X1 (k7_partfun1 (u4_struct_0 X1) X4 X8) X7) = (k7_partfun1 (u4_struct_0 X1) X6 X8)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(esk4_6 X1 X2 X3 X4 X5 X6) = X7v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4r2_hidden X8 X3m1_subset_1 X7 (u4_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r3_cat_3 X1 X2 X3 X4m2_cat_3 X6 X1 X5 X3v1_funct_2 X4 X3 (u4_struct_0 X1)r2_hidden X7 (k2_cat_1 X1 X2 X5)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_funct_2 X3 (u1_struct_0 X1) (k2_cat_3 X1 X3 X4) (k2_cat_3 X1 X3 X6)False)(∀X1 X3 X2 X4 X5 X6, ((esk8_5 X3 X5 X2 X4 X6) = X6False)((k1_cat_1 X3 (k7_partfun1 (u4_struct_0 X3) X4 X1) (esk8_5 X3 X5 X2 X4 X6)) = (k7_partfun1 (u4_struct_0 X3) (esk7_4 X3 X5 X2 X4) X1)False)(v2_struct_0 X3False)(v11_struct_0 X3False)(r3_cat_3 X3 X5 X2 X4False)v2_cat_1 X3v3_cat_1 X3v4_cat_1 X3v5_cat_1 X3v6_cat_1 X3l1_cat_1 X3v1_funct_1 X4r2_hidden X1 X2m1_subset_1 X6 (u4_struct_0 X3)m1_subset_1 X5 (u1_struct_0 X3)m2_cat_3 X4 X3 X5 X2v1_funct_2 X4 X2 (u4_struct_0 X3)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u4_struct_0 X3)))r2_hidden X6 (k2_cat_1 X3 X5 (esk6_4 X3 X5 X2 X4))False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X2 X3 X4False)(r2_hidden (esk9_5 X1 X2 X3 X4 X5) X3False)(esk8_5 X1 X2 X3 X4 X5) = X5v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X4 X1 X2 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_hidden X5 (k2_cat_1 X1 X2 (esk6_4 X1 X2 X3 X4))False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X2 X3 X4False)(r2_hidden (esk8_5 X1 X2 X3 X4 X5) (k2_cat_1 X1 X2 (esk6_4 X1 X2 X3 X4))False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X4 X1 X2 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_hidden X5 (k2_cat_1 X1 X2 (esk6_4 X1 X2 X3 X4))False)(∀X5 X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk8_5 X1 X2 X3 X4 X5) (u4_struct_0 X1)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X5 (u4_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X4 X1 X2 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))r2_hidden X5 (k2_cat_1 X1 X2 (esk6_4 X1 X2 X3 X4))False)(∀X2 X3 X4 X1, (X2 = (k2_cat_3 X1 X3 X4)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(k7_partfun1 (u1_struct_0 X1) X2 (esk10_4 X1 X3 X4 X2)) = (k3_graph_1 X1 (k7_partfun1 (u4_struct_0 X1) X4 (esk10_4 X1 X3 X4 X2)))v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4v1_funct_1 X2v1_funct_2 X4 X3 (u4_struct_0 X1)v1_funct_2 X2 X3 (u1_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u1_struct_0 X1)))False)(∀X4 X1 X3 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(r3_cat_3 X2 X4 X1 X3False)(r2_funct_2 X1 (u1_struct_0 X2) (k2_cat_3 X2 X1 X3) (k2_cat_3 X2 X1 (esk7_4 X2 X4 X1 X3))False)v2_cat_1 X2v3_cat_1 X2v4_cat_1 X2v5_cat_1 X2v6_cat_1 X2l1_cat_1 X2v1_funct_1 X3m1_subset_1 X4 (u1_struct_0 X2)m2_cat_3 X3 X2 X4 X1v1_funct_2 X3 X1 (u4_struct_0 X2)m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 (u4_struct_0 X2)))False)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X2 X3 X4False)(m2_cat_3 (esk7_4 X1 X2 X3 X4) X1 (esk6_4 X1 X2 X3 X4) X3False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X4 X1 X2 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))False)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r3_cat_3 X1 X2 X3 X4False)(m1_subset_1 (esk6_4 X1 X2 X3 X4) (u1_struct_0 X1)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X4 X1 X2 X3v1_funct_2 X4 X3 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X1)))False)(∀X3 X2 X4 X1, (X4 = (k2_cat_3 X1 X2 X3)False)(v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden (esk10_4 X1 X2 X3 X4) X2False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X4v1_funct_1 X3v1_funct_2 X4 X2 (u1_struct_0 X1)v1_funct_2 X3 X2 (u4_struct_0 X1)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u1_struct_0 X1)))m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u4_struct_0 X1)))False)(∀X1 X3 X2 X4, (r2_funct_2 X2 X3 X4 X1False)v1_funct_1 X4v1_funct_1 X1v1_funct_2 X4 X2 X3v1_funct_2 X1 X2 X3r2_funct_2 X2 X3 X1 X4m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))False)(∀X3 X4 X1 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(m2_cat_3 X1 X2 X3 X4False)v2_cat_1 X2v3_cat_1 X2v4_cat_1 X2v5_cat_1 X2v6_cat_1 X2l1_cat_1 X2v1_funct_1 X1m1_subset_1 X3 (u1_struct_0 X2)r3_cat_3 X2 X3 X4 X1v1_funct_2 X1 X4 (u4_struct_0 X2)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X4 (u4_struct_0 X2)))False)(∀X3 X1 X2 X4 X5, ((k7_partfun1 (u1_struct_0 X2) X1 X5) = (k3_graph_1 X2 (k7_partfun1 (u4_struct_0 X2) X4 X5))False)(v2_struct_0 X2False)(v11_struct_0 X2False)X1 = (k2_cat_3 X2 X3 X4)v2_cat_1 X2v3_cat_1 X2v4_cat_1 X2v5_cat_1 X2v6_cat_1 X2l1_cat_1 X2v1_funct_1 X4v1_funct_1 X1r2_hidden X5 X3v1_funct_2 X4 X3 (u4_struct_0 X2)v1_funct_2 X1 X3 (u1_struct_0 X2)m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u4_struct_0 X2)))m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 (u1_struct_0 X2)))False)(∀X1 X2 X3 X4, (X3 = X4False)v1_funct_1 X4v1_funct_1 X3v1_funct_2 X4 X1 X2v1_funct_2 X3 X1 X2r2_funct_2 X1 X2 X3 X4m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))False)(∀X4 X1 X3 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(m1_subset_1 (esk19_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, ((k4_graph_1 X1 (esk19_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)(∀X4 X2 X3 X1, ((k3_graph_1 X1 (esk19_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)(∀X1 X4 X3 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k10_funct_2 X1 X2 X3 X4) X2False)v1_funct_1 X3v1_funct_2 X3 X1 X2m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))False)(∀X3 X4 X1 X2, (r2_funct_2 X3 X4 X1 X2False)X1 = X2v1_funct_1 X2v1_funct_1 X1v1_funct_2 X2 X3 X4v1_funct_2 X1 X3 X4m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4))m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4))False)(∀X4 X1 X3 X2, (r2_funct_2 X2 X3 X1 X1False)v1_funct_1 X4v1_funct_1 X1v1_funct_2 X4 X2 X3v1_funct_2 X1 X2 X3m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))False)(∀X4 X1 X3 X5 X2, ((k4_graph_1 X1 (k7_partfun1 (u4_struct_0 X1) X3 X5)) = 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 X1r2_hidden X5 X4m1_subset_1 X2 (u1_struct_0 X1)m2_cat_3 X3 X1 X2 X4False)(∀X4 X2 X1 X3, (v2_struct_0 X3False)(v11_struct_0 X3False)(m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u4_struct_0 X3)))False)v2_cat_1 X3v3_cat_1 X3v4_cat_1 X3v5_cat_1 X3v6_cat_1 X3l1_cat_1 X3m1_subset_1 X4 (u1_struct_0 X3)m2_cat_3 X1 X3 X4 X2False)(∀X4 X2 X1 X3, (v2_struct_0 X3False)(v11_struct_0 X3False)(v1_funct_2 X1 X2 (u4_struct_0 X3)False)v2_cat_1 X3v3_cat_1 X3v4_cat_1 X3v5_cat_1 X3v6_cat_1 X3l1_cat_1 X3m1_subset_1 X4 (u1_struct_0 X3)m2_cat_3 X1 X3 X4 X2False)(∀X4 X1 X3 X2, ((esk19_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)(∀X4 X1 X3 X2, ((k10_funct_2 X1 X2 X3 X4) = (k7_partfun1 X2 X3 X4)False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_funct_1 X3v1_funct_2 X3 X1 X2m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))False)(∀X4 X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m2_cat_3 (k1_cat_3 (u4_struct_0 X1) X4 X3) X1 X2 (k1_tarski X4)False)(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_3 X1 X2 X3) (k1_zfmisc_1 (k2_zfmisc_1 X2 (u1_struct_0 X1)))False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X3v1_funct_2 X3 X2 (u4_struct_0 X1)m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u4_struct_0 X1)))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 X4 X1 X2, (v2_struct_0 X2False)(v11_struct_0 X2False)(v1_funct_1 X1False)v2_cat_1 X2v3_cat_1 X2v4_cat_1 X2v5_cat_1 X2v6_cat_1 X2l1_cat_1 X2m1_subset_1 X3 (u1_struct_0 X2)m2_cat_3 X1 X2 X3 X4False)(∀X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v1_funct_2 (k2_cat_3 X1 X2 X3) X2 (u1_struct_0 X1)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X3v1_funct_2 X3 X2 (u4_struct_0 X1)m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X2 (u4_struct_0 X1)))False)(∀X3 X2 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(m2_cat_3 (esk18_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 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 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(v1_funct_1 (k2_cat_3 X1 X2 X3)False)v2_cat_1 X1v3_cat_1 X1v4_cat_1 X1v5_cat_1 X1v6_cat_1 X1l1_cat_1 X1v1_funct_1 X3v1_funct_2 X3 X2 (u4_struct_0 X1)m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_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, ((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)(∀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)(∀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(k3_graph_1 X2 X1) = X4(k4_graph_1 X2 X1) = X5l1_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)(∀X4 X2 X3 X1, (v2_struct_0 X1False)(v11_struct_0 X1False)(r2_hidden X2 (k2_cat_1 X1 X3 X4)False)(k3_graph_1 X1 X2) = X3(k4_graph_1 X1 X2) = X4l1_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 X2 X1, (v1_xboole_0 X1False)(m1_subset_1 (k1_cat_3 X1 X2 X3) (k1_zfmisc_1 (k2_zfmisc_1 (k1_tarski X2) X1))False)m1_subset_1 X3 X1False)(∀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 (k4_cat_1 X1 X2) X3) = X3False)(v2_struct_0 X1False)(v11_struct_0 X1False)(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 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)(∀X3 X4 X2 X1, ((k7_partfun1 X1 (k8_funcop_1 X1 X4 X2) X3) = X2False)(v1_xboole_0 X1False)m1_subset_1 X2 X1r2_hidden X3 X4False)(∀X3 X2 X1, (v1_xboole_0 X1False)(m1_subset_1 (k8_funcop_1 X1 X2 X3) (k1_zfmisc_1 (k2_zfmisc_1 X2 X1))False)m1_subset_1 X3 X1False)(∀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)(∀X3 X2 X1, (v1_xboole_0 X1False)(v1_funct_2 (k1_cat_3 X1 X2 X3) (k1_tarski X2) X1False)m1_subset_1 X3 X1False)(∀X2 X3 X1, ((k2_cat_1 X1 X2 X3) = (a_3_0_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, (v1_xboole_0 X1False)(v1_funct_2 (k8_funcop_1 X1 X2 X3) X2 X1False)m1_subset_1 X3 X1False)(∀X3 X2 X1, (m1_subset_1 (k7_partfun1 X2 X1 X3) X2False)v1_relat_1 X1v1_funct_1 X1v5_relat_1 X1 X2False)(∀X3 X2 X1, (v1_xboole_0 X1False)(v1_funct_1 (k8_funcop_1 X1 X2 X3)False)m1_subset_1 X3 X1False)(∀X3 X2 X1, (v1_xboole_0 X1False)(v1_funct_1 (k1_cat_3 X1 X2 X3)False)m1_subset_1 X3 X1False)(∀X3 X1 X2, (v5_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2))False)(∀X3 X1 X2, (v4_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))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)(∀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)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X1))False)(∀X3 X2 X1, (v1_relat_1 X1False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk28_2 X3 X2)False)(∀X3 X2 X1, ((k1_cat_3 X1 X3 X2) = (k2_zfmisc_1 (k1_tarski X3) (k1_tarski X2))False)(v1_xboole_0 X1False)m1_subset_1 X2 X1False)(∀X3 X2 X1, ((k8_funcop_1 X1 X3 X2) = (k2_zfmisc_1 X3 (k1_tarski X2))False)(v1_xboole_0 X1False)m1_subset_1 X2 X1False)(∀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, (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, (X2 = (k1_tarski X1)False)(esk11_2 X1 X2) = X1r2_hidden (esk11_2 X1 X2) X2False)(∀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, ((k4_graph_1 X1 X2) = (k2_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 (esk28_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 X1, (X2 = (k1_tarski X1)False)((esk11_2 X1 X2) = X1False)(r2_hidden (esk11_2 X1 X2) X2False)False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk22_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)(∀X2 X1 X3, (X1 = X3False)X2 = (k1_tarski X3)r2_hidden X1 X2False)(∀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 (esk23_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 (esk27_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk22_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)(∀X2 X1 X3, (r2_hidden X1 X3False)X1 = X2X3 = (k1_tarski X2)False)(∀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 (esk22_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)(r3_cat_3 esk2_0 esk3_0 (k1_tarski esk1_0) (k1_cat_3 (u4_struct_0 esk2_0) esk1_0 (k4_cat_1 esk2_0 esk3_0))False)(∀X1, v1_xboole_0 (k1_tarski X1)False)(v1_xboole_0 esk26_0False)(v1_xboole_0 np__1False)(v15_struct_0 esk24_0False)(v11_struct_0 esk25_0False)(v11_struct_0 esk2_0False)(v2_struct_0 esk25_0False)(v2_struct_0 esk2_0False)(∀X2 X1, (m1_subset_1 (k2_zfmisc_1 X1 (k1_tarski X2)) (k1_zfmisc_1 (k2_zfmisc_1 X1 (k1_tarski X2)))False)False)(∀X2 X1, (v1_funct_2 (k2_zfmisc_1 X1 (k1_tarski X2)) X1 (k1_tarski X2)False)False)(∀X2 X1, (m1_subset_1 (esk20_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))False)False)(∀X1 X2, (v1_funct_1 (k2_zfmisc_1 X1 (k1_tarski X2))False)False)(∀X2 X1, (v5_relat_1 (esk20_2 X1 X2) X2False)False)(∀X1 X2, (v4_relat_1 (esk20_2 X1 X2) X1False)False)(∀X1 X2, (v1_xboole_0 (esk20_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk20_2 X1 X2)False)False)(∀X1, (m1_subset_1 (esk17_1 X1) X1False)False)((m1_subset_1 esk3_0 (u1_struct_0 esk2_0)False)False)(∀X1, (r1_tarski X1 X1False)False)((l1_graph_1 esk13_0False)False)((v1_xboole_0 esk21_0False)False)((v1_xboole_0 k1_xboole_0False)False)((l5_struct_0 esk24_0False)False)((l5_struct_0 esk15_0False)False)((l1_struct_0 esk14_0False)False)((l1_cat_1 esk25_0False)False)((l1_cat_1 esk12_0False)False)((l1_cat_1 esk2_0False)False)((v6_cat_1 esk2_0False)False)((v5_cat_1 esk2_0False)False)((v4_cat_1 esk2_0False)False)((v3_cat_1 esk2_0False)False)((v2_cat_1 esk2_0False)False)False
Proof:
The rest of the proof is missing.