Theorem. (l13_parsp_1)
∀k6_algstr_0 : setsetsetset, ∀v1_vectsp_1 : setprop, ∀l3_algstr_0 : setprop, ∀k4_struct_0 : setset, ∀v7_struct_0 : setprop, ∀v9_struct_0 : setsetprop, ∀esk24_1 : setset, ∀l2_struct_0 : setprop, ∀esk23_1 : setset, ∀k1_xboole_0 : set, ∀l4_algstr_0 : setprop, ∀v3_vectsp_1 : setprop, ∀v6_vectsp_1 : setprop, ∀v1_group_1 : setprop, ∀v8_struct_0 : setprop, ∀v1_finset_1 : setprop, ∀l5_algstr_0 : setprop, ∀esk28_0 : set, ∀esk29_0 : set, ∀esk26_0 : set, ∀esk21_1 : setset, ∀esk19_0 : set, ∀esk13_0 : set, ∀esk15_0 : set, ∀esk18_0 : set, ∀esk12_0 : set, ∀esk20_0 : set, ∀esk17_0 : set, ∀esk11_0 : set, ∀esk14_0 : set, ∀esk16_0 : set, ∀esk25_0 : set, ∀esk22_0 : set, ∀esk27_0 : set, ∀esk30_0 : set, ∀esk1_0 : set, ∀esk5_0 : set, ∀esk2_0 : set, ∀esk7_0 : set, ∀esk4_0 : set, ∀esk3_0 : set, ∀esk6_0 : set, ∀l3_struct_0 : setprop, ∀l4_struct_0 : setprop, ∀v1_zfmisc_1 : setprop, ∀u2_struct_0 : setset, ∀l1_struct_0 : setprop, ∀np__1 : set, ∀v13_struct_0 : setsetprop, ∀v1_xboole_0 : setprop, ∀r2_hidden : setsetprop, ∀v2_vectsp_1 : setprop, ∀l2_algstr_0 : setprop, ∀l1_algstr_0 : setprop, ∀k1_algstr_0 : setsetsetset, ∀esk8_1 : setset, ∀esk10_1 : setset, ∀esk9_1 : setset, ∀v2_struct_0 : setprop, ∀v13_algstr_0 : setprop, ∀v3_group_1 : setprop, ∀v4_vectsp_1 : setprop, ∀v2_rlvect_1 : setprop, ∀v4_rlvect_1 : setprop, ∀m1_subset_1 : setsetprop, ∀u1_struct_0 : setset, ∀l6_algstr_0 : setprop, ∀v3_rlvect_1 : setprop, ∀v5_vectsp_1 : setprop, ∀v5_group_1 : setprop, ∀v33_algstr_0 : setprop, ∀v6_struct_0 : setprop, ∀k3_rlvect_1 : setsetsetset, ∀k4_algstr_0 : setsetset, ∀k5_algstr_0 : setsetsetset, ∀k8_group_1 : setsetsetset, (∀X4 X3 X2 X5 X1, ((k3_rlvect_1 X1 (k8_group_1 X1 X2 X4) (k3_rlvect_1 X1 (k4_algstr_0 X1 (k8_group_1 X1 X2 X5)) (k4_algstr_0 X1 (k8_group_1 X1 X3 (k5_algstr_0 X1 X4 X5))))) = (k8_group_1 X1 (k5_algstr_0 X1 X2 X3) (k5_algstr_0 X1 X4 X5))False)(v2_struct_0 X1False)(v6_struct_0 X1False)v13_algstr_0 X1v33_algstr_0 X1v3_group_1 X1v5_group_1 X1v4_vectsp_1 X1v5_vectsp_1 X1v2_rlvect_1 X1v3_rlvect_1 X1v4_rlvect_1 X1l6_algstr_0 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 X3 X2 X5 X1, ((k3_rlvect_1 X1 (k3_rlvect_1 X1 X2 (k3_rlvect_1 X1 X3 X4)) X5) = (k3_rlvect_1 X1 (k3_rlvect_1 X1 X2 X3) (k3_rlvect_1 X1 X4 X5))False)(v2_struct_0 X1False)(v6_struct_0 X1False)v13_algstr_0 X1v33_algstr_0 X1v3_group_1 X1v5_group_1 X1v4_vectsp_1 X1v5_vectsp_1 X1v2_rlvect_1 X1v3_rlvect_1 X1v4_rlvect_1 X1l6_algstr_0 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)(∀X1, (v3_rlvect_1 X1False)(k1_algstr_0 X1 (k1_algstr_0 X1 (esk8_1 X1) (esk9_1 X1)) (esk10_1 X1)) = (k1_algstr_0 X1 (esk8_1 X1) (k1_algstr_0 X1 (esk9_1 X1) (esk10_1 X1)))l1_algstr_0 X1False)(∀X2 X3 X4 X1, ((k5_algstr_0 X1 (k6_algstr_0 X1 X2 X3) (k6_algstr_0 X1 X2 X4)) = (k6_algstr_0 X1 X2 (k5_algstr_0 X1 X3 X4))False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l6_algstr_0 X1v1_vectsp_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)False)(∀X4 X3 X2 X1, ((k5_algstr_0 X1 (k1_algstr_0 X1 X3 X2) (k1_algstr_0 X1 X4 X2)) = (k5_algstr_0 X1 X3 X4)False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 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, ((k1_algstr_0 X1 (k1_algstr_0 X1 X2 X3) X4) = (k1_algstr_0 X1 X2 (k1_algstr_0 X1 X3 X4))False)v3_rlvect_1 X1l1_algstr_0 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 X1, ((k4_algstr_0 X1 (k1_algstr_0 X1 (k4_algstr_0 X1 X3) (k4_algstr_0 X1 X2))) = (k1_algstr_0 X1 X2 X3)False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k1_algstr_0 X1 (k4_algstr_0 X1 X3) (k4_algstr_0 X1 X2)) = (k4_algstr_0 X1 (k1_algstr_0 X1 X2 X3))False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, ((k6_algstr_0 X1 (k4_algstr_0 X1 X2) X3) = (k4_algstr_0 X1 (k6_algstr_0 X1 X2 X3))False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l6_algstr_0 X1v2_vectsp_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k1_algstr_0 X1 X3 (k4_algstr_0 X1 X2)) = (k4_algstr_0 X1 (k5_algstr_0 X1 X2 X3))False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k4_algstr_0 X1 (k5_algstr_0 X1 X2 X3)) = (k5_algstr_0 X1 X3 X2)False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (v2_struct_0 X1False)(m1_subset_1 (k8_group_1 X1 X2 X3) (u1_struct_0 X1)False)v5_group_1 X1l3_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k1_algstr_0 X1 X2 (k4_algstr_0 X1 X3)) = (k5_algstr_0 X1 X2 X3)False)l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, (m1_subset_1 (k3_rlvect_1 X1 X2 X3) (u1_struct_0 X1)False)v2_rlvect_1 X1l1_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k6_algstr_0 X1 X2 X3) (u1_struct_0 X1)False)l3_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k1_algstr_0 X1 X2 X3) (u1_struct_0 X1)False)l1_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k5_algstr_0 X1 X2 X3) (u1_struct_0 X1)False)l2_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k6_algstr_0 X1 X2 X3) = (k8_group_1 X1 X2 X3)False)(v2_struct_0 X1False)v5_group_1 X1l3_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k8_group_1 X1 X2 X3) = (k8_group_1 X1 X3 X2)False)(v2_struct_0 X1False)v5_group_1 X1l3_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, ((k3_rlvect_1 X1 X2 X3) = (k1_algstr_0 X1 X2 X3)False)v2_rlvect_1 X1l1_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, ((k3_rlvect_1 X1 X2 X3) = (k3_rlvect_1 X1 X3 X2)False)v2_rlvect_1 X1l1_algstr_0 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k4_algstr_0 X1 (k4_algstr_0 X1 X2)) = X2False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (m1_subset_1 (k4_algstr_0 X1 X2) (u1_struct_0 X1)False)l2_algstr_0 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, ((k4_algstr_0 X1 (k4_struct_0 X1)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v13_algstr_0 X1v3_rlvect_1 X1v4_rlvect_1 X1l2_algstr_0 X1False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1, (v7_struct_0 X1False)l2_struct_0 X1v9_struct_0 (esk24_1 X1) X1False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk24_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (v3_rlvect_1 X1False)(m1_subset_1 (esk10_1 X1) (u1_struct_0 X1)False)l1_algstr_0 X1False)(∀X1, (v3_rlvect_1 X1False)(m1_subset_1 (esk9_1 X1) (u1_struct_0 X1)False)l1_algstr_0 X1False)(∀X1, (v3_rlvect_1 X1False)(m1_subset_1 (esk8_1 X1) (u1_struct_0 X1)False)l1_algstr_0 X1False)(∀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, (m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (m1_subset_1 (u2_struct_0 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (m1_subset_1 (k4_struct_0 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀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, (v2_struct_0 X1False)(v1_group_1 X1False)l4_algstr_0 X1v3_vectsp_1 X1v6_vectsp_1 X1False)(∀X1, (v2_struct_0 X1False)(v3_vectsp_1 X1False)v5_group_1 X1l4_algstr_0 X1v6_vectsp_1 X1False)(∀X1, (v2_struct_0 X1False)(v5_vectsp_1 X1False)l6_algstr_0 X1v1_vectsp_1 X1v2_vectsp_1 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 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v9_struct_0 (esk23_1 X1) X1False)l2_struct_0 X1False)(∀X1, (v9_struct_0 (k4_struct_0 X1) X1False)l2_struct_0 X1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_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)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_group_1 X1False)v4_vectsp_1 X1l4_algstr_0 X1False)(∀X1, (v2_struct_0 X1False)(v6_vectsp_1 X1False)v4_vectsp_1 X1l4_algstr_0 X1False)(∀X1, (v2_struct_0 X1False)(v3_vectsp_1 X1False)v4_vectsp_1 X1l4_algstr_0 X1False)(∀X1, (v2_struct_0 X1False)(v2_vectsp_1 X1False)v5_vectsp_1 X1l6_algstr_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_vectsp_1 X1False)v5_vectsp_1 X1l6_algstr_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, (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)(∀X1, (v6_struct_0 X1False)v7_struct_0 X1l4_struct_0 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, ((u2_struct_0 X1) = (k4_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (l5_algstr_0 X1False)l6_algstr_0 X1False)(∀X1, (l3_struct_0 X1False)l4_algstr_0 X1False)(∀X1, (l3_struct_0 X1False)l4_struct_0 X1False)(∀X1, (l2_struct_0 X1False)l2_algstr_0 X1False)(∀X1, (l2_struct_0 X1False)l4_struct_0 X1False)(∀X1, (l2_algstr_0 X1False)l6_algstr_0 X1False)(∀X1, (l3_algstr_0 X1False)l4_algstr_0 X1False)(∀X1, (l1_algstr_0 X1False)l2_algstr_0 X1False)(∀X1, (l4_algstr_0 X1False)l5_algstr_0 X1False)(∀X1, (l4_struct_0 X1False)l5_algstr_0 X1False)(∀X1, (l1_struct_0 X1False)l3_struct_0 X1False)(∀X1, (l1_struct_0 X1False)l2_struct_0 X1False)(∀X1, (l1_struct_0 X1False)l3_algstr_0 X1False)(∀X1, (l1_struct_0 X1False)l1_algstr_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)((k5_algstr_0 esk1_0 (k8_group_1 esk1_0 (k5_algstr_0 esk1_0 esk3_0 esk2_0) (k5_algstr_0 esk1_0 esk7_0 esk5_0)) (k8_group_1 esk1_0 (k5_algstr_0 esk1_0 esk3_0 esk6_0) (k5_algstr_0 esk1_0 esk7_0 esk4_0))) = (k4_struct_0 esk1_0)False)(v1_xboole_0 esk28_0False)(v1_xboole_0 np__1False)(v6_struct_0 esk1_0False)(v2_struct_0 esk30_0False)(v2_struct_0 esk29_0False)(v2_struct_0 esk27_0False)(v2_struct_0 esk26_0False)(v2_struct_0 esk22_0False)(v2_struct_0 esk1_0False)(((k5_algstr_0 esk1_0 (k8_group_1 esk1_0 (k5_algstr_0 esk1_0 esk2_0 esk3_0) (k5_algstr_0 esk1_0 esk4_0 esk5_0)) (k8_group_1 esk1_0 (k5_algstr_0 esk1_0 esk2_0 esk6_0) (k5_algstr_0 esk1_0 esk4_0 esk7_0))) = (k4_struct_0 esk1_0)False)False)(∀X1, (m1_subset_1 (esk21_1 X1) X1False)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)((v1_xboole_0 esk25_0False)False)((v1_xboole_0 k1_xboole_0False)False)((l5_algstr_0 esk27_0False)False)((l5_algstr_0 esk19_0False)False)((l3_struct_0 esk16_0False)False)((l2_struct_0 esk26_0False)False)((l2_struct_0 esk14_0False)False)((l2_algstr_0 esk13_0False)False)((l3_algstr_0 esk29_0False)False)((l3_algstr_0 esk15_0False)False)((l1_algstr_0 esk11_0False)False)((v1_group_1 esk30_0False)False)((l4_algstr_0 esk30_0False)False)((l4_algstr_0 esk22_0False)False)((l4_algstr_0 esk17_0False)False)((l4_struct_0 esk18_0False)False)((v7_struct_0 esk26_0False)False)((l1_struct_0 esk12_0False)False)((l6_algstr_0 esk20_0False)False)((l6_algstr_0 esk1_0False)False)((v4_rlvect_1 esk1_0False)False)((v3_rlvect_1 esk1_0False)False)((v2_rlvect_1 esk1_0False)False)((v5_vectsp_1 esk1_0False)False)((v4_vectsp_1 esk27_0False)False)((v4_vectsp_1 esk22_0False)False)((v4_vectsp_1 esk1_0False)False)((v5_group_1 esk30_0False)False)((v5_group_1 esk29_0False)False)((v5_group_1 esk1_0False)False)((v3_group_1 esk30_0False)False)((v3_group_1 esk29_0False)False)((v3_group_1 esk1_0False)False)((v33_algstr_0 esk1_0False)False)((v13_algstr_0 esk1_0False)False)False
Proof:
The rest of the proof is missing.