# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(?[X4]:s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X4)))|?[X4]:?[X5]:?[X6]:s(t_h4s_paths_path(X1,X2),X3)=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X4),s(X2,X5),s(t_h4s_paths_path(X1,X2),X6)))),file('i/f/path/path__cases', ch4s_paths_pathu_u_cases)).
fof(3, axiom,![X1]:![X2]:![X4]:![X5]:![X3]:s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,X4),s(X2,X5),s(t_h4s_paths_path(X1,X2),X3)))=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_pairs_u_2c(s(X1,X4),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lcons(s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X5),s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X3))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_pairs_snd(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),X3))))))))))),file('i/f/path/path__cases', ah4s_paths_pconsu_u_def)).
fof(4, axiom,![X2]:![X1]:![X4]:s(t_h4s_paths_path(X1,X2),h4s_paths_stoppedu_u_at(s(X1,X4)))=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_pairs_u_2c(s(X1,X4),s(t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1)),h4s_llists_lnil))))),file('i/f/path/path__cases', ah4s_paths_stoppedu_u_atu_u_def)).
fof(6, axiom,![X2]:![X1]:![X9]:?[X5]:s(t_h4s_paths_path(X1,X2),X9)=s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X5))),file('i/f/path/path__cases', ah4s_paths_toPathu_u_onto)).
fof(8, axiom,![X1]:![X2]:![X4]:?[X6]:?[X5]:s(t_h4s_pairs_prod(X1,X2),X4)=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X6),s(X2,X5))),file('i/f/path/path__cases', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(11, axiom,![X1]:![X14]:(s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lnil)|?[X15]:?[X16]:s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X15),s(t_h4s_llists_llist(X1),X16)))),file('i/f/path/path__cases', ah4s_llists_llistu_u_CASES)).
fof(12, axiom,![X1]:![X2]:![X7]:![X4]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X7)))))=s(X2,X7),file('i/f/path/path__cases', ah4s_pairs_SND0)).
fof(13, axiom,![X2]:![X1]:![X5]:s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),h4s_paths_topath(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X5)))))=s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),X5),file('i/f/path/path__cases', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(14, axiom,![X1]:![X2]:![X3]:s(X1,h4s_paths_first(s(t_h4s_paths_path(X1,X2),X3)))=s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,t_h4s_llists_llist(t_h4s_pairs_prod(X2,X1))),h4s_paths_frompath(s(t_h4s_paths_path(X1,X2),X3))))),file('i/f/path/path__cases', ah4s_paths_firstu_u_def)).
fof(42, axiom,![X2]:![X1]:![X7]:![X4]:s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X7)))))=s(X1,X4),file('i/f/path/path__cases', ah4s_pairs_FST0)).
# SZS output end CNFRefutation
