Theorem. (
l12_projdes1)
∀esk7_5 : set → set → set → set → set → set, ∀v3_collsp : set → prop, ∀r1_projdes1 : set → set → set → set → set → prop, ∀v3_anproj_2 : set → prop, ∀v4_collsp : set → prop, ∀v2_collsp : set → prop, ∀v7_anproj_2 : set → prop, ∀esk10_1 : set → set, ∀l1_struct_0 : set → prop, ∀esk4_0 : set, ∀esk25_0 : set, ∀esk24_1 : set → set, ∀esk23_0 : set, ∀esk22_0 : set, ∀esk2_0 : set, ∀esk6_0 : set, ∀esk5_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk11_1 : set → set, ∀esk12_1 : set → set, ∀esk18_1 : set → set, ∀esk15_1 : set → set, ∀esk14_1 : set → set, ∀esk13_1 : set → set, ∀esk19_1 : set → set, ∀esk17_1 : set → set, ∀esk21_1 : set → set, ∀esk20_1 : set → set, ∀esk8_1 : set → set, ∀esk9_1 : set → set, ∀esk16_6 : set → set → set → set → set → set → set, ∀r1_collsp : set → set → set → set → prop, ∀l1_collsp : set → prop, ∀m1_subset_1 : set → set → prop, ∀u1_struct_0 : set → set, ∀v2_anproj_2 : set → prop, ∀v2_struct_0 : set → prop, (∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X3 (esk16_6 X1 X2 X4 X3 X5 X6) → False) → v2_anproj_2 X1 → l1_collsp 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 X4 X3 X6 → r1_collsp X1 X2 X4 X5 → False) → (∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X3 (esk16_6 X1 X4 X5 X6 X2 X3) → False) → v2_anproj_2 X1 → l1_collsp 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 X6 X3 → r1_collsp X1 X4 X5 X2 → False) → (∀X6 X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (m1_subset_1 (esk16_6 X1 X2 X3 X4 X5 X6) (u1_struct_0 X1) → False) → v2_anproj_2 X1 → l1_collsp 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 X3 X4 X6 → r1_collsp X1 X2 X3 X5 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 (esk7_5 X1 X2 X3 X4 X5) → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 X5 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 (esk7_5 X1 X4 X5 X2 X3) → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 X5 X2 X3 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (m1_subset_1 (esk7_5 X1 X2 X3 X4 X5) (u1_struct_0 X1) → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 X5 → False) → (∀X1 X3 X6 X5 X4 X2, (v2_struct_0 X2 → False) → (v7_anproj_2 X2 → False) → (r1_projdes1 X2 X3 X4 X5 X6 → False) → v2_collsp X2 → v3_collsp X2 → v4_collsp X2 → v2_anproj_2 X2 → v3_anproj_2 X2 → l1_collsp X2 → m1_subset_1 X6 (u1_struct_0 X2) → m1_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) → r1_collsp X2 X5 X6 X1 → r1_collsp X2 X3 X4 X1 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_projdes1 X1 X2 X3 X4 X5 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_projdes1 X1 X3 X4 X5 X2 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_projdes1 X1 X4 X5 X2 X3 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 → False) → (∀X4 X2 X3 X5 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_projdes1 X1 X5 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 → False) → (∀X1 X4 X5 X6 X2 X3, (X2 = X3 → False) → (v2_struct_0 X1 → False) → (r1_collsp X1 X4 X5 X6 → False) → v3_collsp X1 → l1_collsp 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 X6 → r1_collsp X1 X2 X3 X5 → r1_collsp X1 X2 X3 X4 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_collsp X1 → False) → l1_collsp X1 → r1_collsp X1 (esk8_1 X1) (esk8_1 X1) (esk9_1 X1) → r1_collsp X1 (esk8_1 X1) (esk9_1 X1) (esk8_1 X1) → r1_collsp X1 (esk8_1 X1) (esk9_1 X1) (esk9_1 X1) → False) → (∀X1 X4 X5 X2 X3, (X2 = X3 → False) → (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X4 X5 → False) → v2_collsp X1 → v3_collsp X1 → l1_collsp 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 X5 → r1_collsp X1 X2 X3 X4 → False) → (∀X1 X2, (v2_struct_0 X2 → False) → (v2_anproj_2 X2 → False) → l1_collsp X2 → m1_subset_1 X1 (u1_struct_0 X2) → r1_collsp X2 (esk17_1 X2) (esk19_1 X2) X1 → r1_collsp X2 (esk20_1 X2) (esk21_1 X2) X1 → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X4 X3 → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X2 X4 → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X2 → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X2 X3 → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (v7_anproj_2 X1 → False) → (r1_collsp X1 X2 X3 X4 → False) → v2_collsp X1 → v3_collsp X1 → v4_collsp X1 → v2_anproj_2 X1 → v3_anproj_2 X1 → l1_collsp 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 X2 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → l1_collsp X1 → r1_collsp X1 (esk13_1 X1) (esk14_1 X1) (esk15_1 X1) → False) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X2 X3 → False) → v2_collsp X1 → l1_collsp 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) → (∀X3 X2 X4 X1, (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X3 X2 → False) → v2_collsp X1 → l1_collsp 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) → (∀X2 X3 X4 X1, (v2_struct_0 X1 → False) → (r1_collsp X1 X2 X3 X3 → False) → v2_collsp X1 → l1_collsp 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) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (r1_collsp X1 (esk18_1 X1) (esk19_1 X1) (esk21_1 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (r1_collsp X1 (esk17_1 X1) (esk18_1 X1) (esk20_1 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (r1_collsp X1 (esk11_1 X1) (esk12_1 X1) (esk15_1 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (r1_collsp X1 (esk11_1 X1) (esk12_1 X1) (esk14_1 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (r1_collsp X1 (esk11_1 X1) (esk12_1 X1) (esk13_1 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (m1_subset_1 (esk21_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (m1_subset_1 (esk20_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (m1_subset_1 (esk19_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (m1_subset_1 (esk18_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_anproj_2 X1 → False) → (m1_subset_1 (esk17_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (m1_subset_1 (esk15_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (m1_subset_1 (esk14_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (m1_subset_1 (esk13_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (m1_subset_1 (esk12_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (m1_subset_1 (esk11_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_collsp X1 → False) → (m1_subset_1 (esk10_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_collsp X1 → False) → (m1_subset_1 (esk9_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v2_collsp X1 → False) → (m1_subset_1 (esk8_1 X1) (u1_struct_0 X1) → False) → l1_collsp X1 → False) → (∀X1, (v2_struct_0 X1 → False) → (v3_collsp X1 → False) → (esk12_1 X1) = (esk11_1 X1) → l1_collsp X1 → False) → (∀X1, (l1_struct_0 X1 → False) → l1_collsp X1 → False) → (r1_projdes1 esk1_0 esk2_0 esk3_0 esk5_0 esk6_0 → False) → (r1_collsp esk1_0 esk2_0 esk3_0 esk4_0 → False) → (v7_anproj_2 esk1_0 → False) → (v2_struct_0 esk25_0 → False) → (v2_struct_0 esk1_0 → False) → ((r1_projdes1 esk1_0 esk2_0 esk3_0 esk4_0 esk6_0 → False) → False) → ((r1_projdes1 esk1_0 esk2_0 esk3_0 esk4_0 esk5_0 → False) → False) → (∀X1, (m1_subset_1 (esk24_1 X1) X1 → 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 esk23_0 → False) → False) → ((l1_collsp esk25_0 → False) → False) → ((l1_collsp esk22_0 → False) → False) → ((l1_collsp esk1_0 → False) → False) → ((v3_anproj_2 esk25_0 → False) → False) → ((v3_anproj_2 esk1_0 → False) → False) → ((v2_anproj_2 esk25_0 → False) → False) → ((v2_anproj_2 esk1_0 → False) → False) → ((v4_collsp esk25_0 → False) → False) → ((v4_collsp esk1_0 → False) → False) → ((v3_collsp esk25_0 → False) → False) → ((v3_collsp esk1_0 → False) → False) → ((v2_collsp esk25_0 → False) → False) → ((v2_collsp esk1_0 → False) → False) → False