ext_certificates : 1320
ext_lines_equal_own_noLC_indices : True
ext_vertex_set_ok : 1320
ext_contains_S : 1320
ext_Sprime_accepted_as_4sphere : 1320
ext_Sprime_fvectors : {'10,45,100,105,42': 1050, '10,44,96,100,40': 218, '10,43,92,95,38': 43, '10,42,88,90,36': 8, '10,41,84,85,34': 1}
finder_cert_file_records : 1320
finder_cert_file_keys : ['B1', 'B2', 'd', 'idx', 'iters', 'lazy', 'n', 'n_lc_edges', 'status', 'time', 'unproved', 'verify_ok']
lemma42_spheres_with_stacked_link : 1318
lemma42_T_is_3sphere_on_V-v : 1318
lemma42_Sigma_is_4sphere_containing_S : 1318
lemma42_(sphere,vertex)_first_hits_checked_bd_cap_vset : 1318
table1
    ('A10', {'n': 10, 'facets': 35, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '10,45,70,35', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 10, 'vertex_transitive': True})
    ('A11', {'n': 11, 'facets': 44, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '11,55,88,44', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 11, 'vertex_transitive': True})
    ('Z13_0', {'n': 13, 'facets': 65, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '13,78,130,65', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 13, 'vertex_transitive': True})
    ('Z13_1', {'n': 13, 'facets': 65, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '13,78,130,65', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 13, 'vertex_transitive': True})
    ('Z14_0', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_1', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_2', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_3', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_4', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_5', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 14, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_6', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_7', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
    ('Z14_8', {'n': 14, 'facets': 77, 'orbit_sizes_ok': True, 'equals_json': True, 'cyclic': True, 'sphere': True, 'f': '14,91,154,77', 'neighborly': True, 'LC_edges': 0, 'missing4': 0, 'stacked_links': 0, 'stacked_agree': True, 'aut': 14, 'vertex_transitive': True})
A10_isomorphic_to_list_entry_35806 : True
reflection_is_automorphism : {'A10': False, 'A11': False, 'Z13_0': False, 'Z13_1': False, 'Z14_0': False, 'Z14_1': False, 'Z14_2': False, 'Z14_3': False, 'Z14_4': False, 'Z14_5': False, 'Z14_6': False, 'Z14_7': False, 'Z14_8': False}
special_certificates
    {'sphere': 'A10', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '10,45,100,105,42'}
    {'sphere': 'A10', 'kind': 'extension', 'cover': [0, 1], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '10,45,100,105,42'}
    {'sphere': 'A10', 'kind': 'extension', 'cover': [0, 5], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '10,45,100,105,42'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 2], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 3], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 4], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 5], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 6], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 7], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 1, 8], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 2, 4], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 2, 5], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 2, 6], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 2, 7], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 2, 8], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 3, 6], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'A11', 'kind': 'extension', 'cover': [0, 3, 7], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '11,55,130,140,56'}
    {'sphere': 'Z13_0', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '13,78,202,225,90'}
    {'sphere': 'Z13_1', 'kind': 'extension', 'cover': [0, 1, 11], 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '13,78,202,225,90'}
    {'sphere': 'Z14_2', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '14,91,244,275,110'}
    {'sphere': 'Z14_4', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '14,91,244,275,110'}
    {'sphere': 'Z14_0', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '14,91,244,275,110'}
    {'sphere': 'Z14_7', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '14,91,244,275,110'}
    {'sphere': 'Z14_8', 'kind': 'extension', 'cover': None, 'V_ok': True, 'contains': True, 'cover_ok': True, 'sphere4': True, 'f': '14,91,244,275,110'}
    {'sphere': 'Z14_5', 'kind': 'completion', 'v': 0, 'T_vertexset_ok': True, 'T_sphere3': True, 'prop41_iii': True, 'Sigma_sphere4': True, 'Sigma_contains_S': True}
    {'sphere': 'n10_line_27137', 'kind': 'completion', 'v': 0, 'T_vertexset_ok': True, 'T_sphere3': True, 'prop41_iii': True, 'Sigma_sphere4': True, 'Sigma_contains_S': True}
special_certificates_all_ok : True
A11_rotation_classes_of_3sets : 15
A11_classes_with_cover_certificate : 14
A11_classes_without : [(0, 1, 9)]
