Theorem. (l29_projdes1)
∀esk18_6 : setsetsetsetsetsetset, ∀esk28_4 : setsetsetsetset, ∀r2_projdes1 : setsetsetsetsetprop, ∀esk16_1 : setset, ∀esk15_1 : setset, ∀esk22_1 : setset, ∀esk23_1 : setset, ∀esk19_1 : setset, ∀esk21_1 : setset, ∀esk13_1 : setset, ∀esk14_1 : setset, ∀esk17_1 : setset, ∀esk1_0 : set, ∀esk11_0 : set, ∀esk10_0 : set, ∀esk9_0 : set, ∀esk27_0 : set, ∀esk7_0 : set, ∀esk4_0 : set, ∀esk5_0 : set, ∀esk2_0 : set, ∀esk25_0 : set, ∀esk24_0 : set, ∀esk26_1 : setset, ∀esk8_0 : set, ∀esk3_0 : set, ∀esk6_0 : set, ∀l1_struct_0 : setprop, ∀esk20_1 : setset, ∀esk12_3 : setsetsetset, ∀epred1_2 : setsetprop, ∀v7_anproj_2 : setprop, ∀r1_projdes1 : setsetsetsetsetprop, ∀v3_collsp : setprop, ∀v2_anproj_2 : setprop, ∀l1_collsp : setprop, ∀m1_subset_1 : setsetprop, ∀u1_struct_0 : setset, ∀v3_anproj_2 : setprop, ∀v4_collsp : setprop, ∀v2_collsp : setprop, ∀r1_collsp : setsetsetsetprop, ∀v2_struct_0 : setprop, (∀X7 X6 X5 X2 X3 X4 X8 X9 X10 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X8 X9 X10False)(r1_collsp X1 X5 X6 X7False)(r1_collsp X1 X2 X3 X4False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X10 (u1_struct_0 X1)m1_subset_1 X9 (u1_struct_0 X1)m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X6 X7 X10r1_projdes1 X1 X5 X6 X7 X9r1_projdes1 X1 X5 X6 X7 X8r1_projdes1 X1 X2 X3 X4 X10r1_projdes1 X1 X2 X3 X4 X9r1_projdes1 X1 X2 X3 X4 X8False)(∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X3 (esk18_6 X1 X2 X4 X3 X5 X6)False)v2_anproj_2 X1l1_collsp X1m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X4 X3 X6r1_collsp X1 X2 X4 X5False)(∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X3 (esk18_6 X1 X4 X5 X6 X2 X3)False)v2_anproj_2 X1l1_collsp X1m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X5 X6 X3r1_collsp X1 X4 X5 X2False)(∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1False)(m1_subset_1 (esk18_6 X1 X2 X3 X4 X5 X6) (u1_struct_0 X1)False)v2_anproj_2 X1l1_collsp X1m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X3 X4 X6r1_collsp X1 X2 X3 X5False)(∀X9 X5 X1 X3 X2 X11 X10 X12 X4 X8 X6 X7, (X6 = X7False)(X5 = X9False)(X5 = X8False)(r1_projdes1 X1 X2 X3 X6 X5False)(r1_projdes1 X1 X2 X3 X4 X6False)epred1_2 X1 X2m1_subset_1 X12 (u1_struct_0 X1)m1_subset_1 X11 (u1_struct_0 X1)m1_subset_1 X10 (u1_struct_0 X1)m1_subset_1 X9 (u1_struct_0 X1)m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)r1_collsp X1 X10 X11 X12r1_collsp X1 X9 X7 X11r1_collsp X1 X8 X7 X10r1_collsp X1 X5 X6 X7r1_collsp X1 X5 X3 X9r1_collsp X1 X5 X2 X8r1_collsp X1 X4 X6 X12r1_collsp X1 X3 X6 X11r1_collsp X1 X2 X6 X10r1_projdes1 X1 X2 X3 X4 X5False)(∀X1 X6 X7 X4 X5 X2 X3, (X2 = X3False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X5 X6 X7 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4r1_projdes1 X1 X5 X6 X7 X3r1_projdes1 X1 X5 X6 X7 X2False)(∀X4 X5 X2 X3 X6 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X6False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X3 X5 X6r1_projdes1 X1 X2 X3 X4 X6False)(∀X1 X11 X10 X9 X5 X6 X4 X7 X8 X2 X3, (X2 = X3False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X9 X10 X11False)(r1_collsp X1 X3 X7 X8False)(r1_projdes1 X1 X2 X5 X6 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X11 (u1_struct_0 X1)m1_subset_1 X10 (u1_struct_0 X1)m1_subset_1 X9 (u1_struct_0 X1)m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X7 X8 X10r1_collsp X1 X5 X6 X10r1_collsp X1 X4 X2 X3r1_collsp X1 X3 X8 X11r1_collsp X1 X3 X7 X9r1_collsp X1 X2 X6 X11r1_collsp X1 X2 X5 X9False)(∀X3 X1 X7 X8 X6 X2 X4 X5, (X4 = X5False)(X3 = X5False)(X2 = X5False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X6 X7 X8 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X5 X8 X4r1_collsp X1 X5 X7 X3r1_collsp X1 X5 X6 X2r1_projdes1 X1 X2 X3 X4 X5False)(∀X1 X3 X4 X5 X2 X6, (X2 = X6False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X5 X2 X6r1_projdes1 X1 X2 X3 X4 X6False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X3 X5 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X4 X3 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X4 X5 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X5 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X5 X4 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X2 X4 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X2 X5 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X4 X2 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X4 X5 X2False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X5 X2 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X3 X5 X4 X2False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X2 X3 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X2 X5 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X3 X2 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X3 X5 X2False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X5 X2 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X4 X5 X3 X2False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X2 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X2 X4 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X3 X2 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X3 X4 X2False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X4 X2 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X5 X4 X3 X2False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_projdes1 X1 X2 X3 X4 (esk28_4 X1 X2 X3 X4)False)(∀X3 X1 X6 X7 X5 X2 X4 X8, (X4 = X8False)(X3 = X8False)(X2 = X8False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X5 X6 X7 X8False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X8 (u1_struct_0 X1)m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X8 X7 X4r1_collsp X1 X8 X6 X3r1_collsp X1 X8 X5 X2r1_collsp X1 X2 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4r2_projdes1 X1 X2 X3 X4 X5False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4r2_projdes1 X1 X2 X4 X5 X3False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4r2_projdes1 X1 X2 X5 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4r2_projdes1 X1 X5 X2 X3 X4False)(∀X3 X5 X4 X2 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X5 X4 X2False)(r1_collsp X1 X5 X3 X4False)(r1_collsp X1 X5 X2 X3False)(r1_collsp X1 X2 X3 X4False)(r2_projdes1 X1 X5 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_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 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X2 X3 X4 X5False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X3 X4 X5 X2False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X4 X5 X2 X3False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4False)(∀X4 X2 X3 X5 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_projdes1 X1 X5 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X3 X4False)(∀X6 X2 X7 X3 X1 X4 X5, (X4 = X5False)(X2 = X6False)(v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)X4 = X7v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X7 (u1_struct_0 X1)m1_subset_1 X6 (u1_struct_0 X1)m1_subset_1 X5 (u1_struct_0 X1)m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X6 X5 X7r1_collsp X1 X2 X4 X5r1_collsp X1 X2 X3 X6False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X1 X2 X4 X5False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X1 X4 X2 X5False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X1 X4 X5 X2False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X4 X1 X2 X5False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X4 X1 X5 X2False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X5 X4 X1 X2 X3, (v2_struct_0 X3False)(v7_anproj_2 X3False)(r1_projdes1 X3 X4 X5 X2 X1False)X1 = X2v2_collsp X3v3_collsp X3v4_collsp X3v2_anproj_2 X3v3_anproj_2 X3l1_collsp X3m1_subset_1 X5 (u1_struct_0 X3)m1_subset_1 X4 (u1_struct_0 X3)m1_subset_1 X2 (u1_struct_0 X3)m1_subset_1 X1 (u1_struct_0 X3)False)(∀X1, (v2_struct_0 X1False)(v2_collsp X1False)l1_collsp X1r1_collsp X1 (esk15_1 X1) (esk15_1 X1) (esk16_1 X1)r1_collsp X1 (esk15_1 X1) (esk16_1 X1) (esk15_1 X1)r1_collsp X1 (esk15_1 X1) (esk16_1 X1) (esk16_1 X1)False)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)(m1_subset_1 (esk28_4 X1 X2 X3 X4) (u1_struct_0 X1)False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp 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)(∀X1 X2, (v2_struct_0 X2False)(v2_anproj_2 X2False)l1_collsp X2m1_subset_1 X1 (u1_struct_0 X2)r1_collsp X2 (esk19_1 X2) (esk21_1 X2) X1r1_collsp X2 (esk22_1 X2) (esk23_1 X2) X1False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X2 X4 X3False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X3 X2 X4False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X3 X4 X2False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X4 X2 X3False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(r1_collsp X1 X2 X3 X4False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_collsp X1 X4 X3 X2False)(∀X1 X2, ((esk13_1 X2) = X1False)((esk14_1 X2) = X1False)(v2_struct_0 X2False)(v3_anproj_2 X2False)l1_collsp X2m1_subset_1 X1 (u1_struct_0 X2)r1_collsp X2 (esk13_1 X2) (esk14_1 X2) X1False)(∀X2 X3 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X3 (esk12_3 X1 X2 X3)False)v3_anproj_2 X1l1_collsp X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X4 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X2 X3False)v2_collsp X1l1_collsp 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 X4 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X3 X2False)v2_collsp X1l1_collsp 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)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(r1_collsp X1 X2 X3 X3False)v2_collsp X1l1_collsp 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)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(r1_collsp X1 (esk20_1 X1) (esk21_1 X1) (esk23_1 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(r1_collsp X1 (esk19_1 X1) (esk20_1 X1) (esk22_1 X1)False)l1_collsp X1False)(∀X2 X3 X1, (v2_struct_0 X1False)(m1_subset_1 (esk12_3 X1 X2 X3) (u1_struct_0 X1)False)v3_anproj_2 X1l1_collsp X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1 X3 X2, (v2_struct_0 X2False)(esk12_3 X2 X1 X3) = X1v3_anproj_2 X2l1_collsp X2m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u1_struct_0 X2)False)(∀X1 X3 X2, (v2_struct_0 X2False)(esk12_3 X2 X3 X1) = X1v3_anproj_2 X2l1_collsp X2m1_subset_1 X3 (u1_struct_0 X2)m1_subset_1 X1 (u1_struct_0 X2)False)(∀X2 X1, (v2_struct_0 X1False)(v7_anproj_2 X1False)(epred1_2 X1 X2False)v2_collsp X1v3_collsp X1v4_collsp X1v2_anproj_2 X1v3_anproj_2 X1l1_collsp X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)(v3_anproj_2 X1False)(m1_subset_1 (esk14_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v3_anproj_2 X1False)(m1_subset_1 (esk13_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(m1_subset_1 (esk22_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(m1_subset_1 (esk21_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(m1_subset_1 (esk20_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_anproj_2 X1False)(m1_subset_1 (esk19_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_collsp X1False)(m1_subset_1 (esk17_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_collsp X1False)(m1_subset_1 (esk16_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (v2_struct_0 X1False)(v2_collsp X1False)(m1_subset_1 (esk15_1 X1) (u1_struct_0 X1)False)l1_collsp X1False)(∀X1, (l1_struct_0 X1False)l1_collsp X1False)(r1_collsp esk1_0 esk9_0 esk10_0 esk11_0False)(v7_anproj_2 esk1_0False)(v2_struct_0 esk27_0False)(v2_struct_0 esk1_0False)(esk7_0 = esk4_0False)(esk6_0 = esk3_0False)(esk5_0 = esk2_0False)(esk4_0 = esk2_0False)(esk3_0 = esk2_0False)((r2_projdes1 esk1_0 esk2_0 esk6_0 esk7_0 esk8_0False)False)((r1_collsp esk1_0 esk7_0 esk8_0 esk10_0False)False)((r1_collsp esk1_0 esk6_0 esk8_0 esk11_0False)False)((r1_collsp esk1_0 esk6_0 esk7_0 esk9_0False)False)((r1_collsp esk1_0 esk4_0 esk5_0 esk10_0False)False)((r1_collsp esk1_0 esk3_0 esk5_0 esk11_0False)False)((r1_collsp esk1_0 esk3_0 esk4_0 esk9_0False)False)((r1_collsp esk1_0 esk2_0 esk8_0 esk5_0False)False)((r1_collsp esk1_0 esk2_0 esk7_0 esk4_0False)False)((r1_collsp esk1_0 esk2_0 esk6_0 esk3_0False)False)(∀X1, (m1_subset_1 (esk26_1 X1) X1False)False)((m1_subset_1 esk11_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk10_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk9_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk8_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk7_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk6_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk5_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk4_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk3_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk2_0 (u1_struct_0 esk1_0)False)False)((l1_struct_0 esk25_0False)False)((l1_collsp esk27_0False)False)((l1_collsp esk24_0False)False)((l1_collsp esk1_0False)False)((v3_anproj_2 esk27_0False)False)((v3_anproj_2 esk1_0False)False)((v2_anproj_2 esk27_0False)False)((v2_anproj_2 esk1_0False)False)((v4_collsp esk27_0False)False)((v4_collsp esk1_0False)False)((v3_collsp esk27_0False)False)((v3_collsp esk1_0False)False)((v2_collsp esk27_0False)False)((v2_collsp esk1_0False)False)False
Proof:
The rest of the proof is missing.