# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(9, axiom,![X8]:![X7]:![X9]:![X6]:s(X7,h4s_pairs_fst(s(t_h4s_pairs_prod(X7,X8),h4s_pairs_u_2c(s(X7,X6),s(X8,X9)))))=s(X7,X6),file('i/f/path/pconcat__thm_c1', ah4s_pairs_FST0)).
fof(10, axiom,![X7]:![X8]:![X9]:![X6]:s(X8,h4s_pairs_snd(s(t_h4s_pairs_prod(X7,X8),h4s_pairs_u_2c(s(X7,X6),s(X8,X9)))))=s(X8,X9),file('i/f/path/pconcat__thm_c1', ah4s_pairs_SND0)).
fof(12, axiom,![X7]:![X6]:![X1]:![X16]:s(t_h4s_llists_llist(X7),h4s_llists_lappend(s(t_h4s_llists_llist(X7),h4s_llists_lcons(s(X7,X16),s(t_h4s_llists_llist(X7),X1))),s(t_h4s_llists_llist(X7),X6)))=s(t_h4s_llists_llist(X7),h4s_llists_lcons(s(X7,X16),s(t_h4s_llists_llist(X7),h4s_llists_lappend(s(t_h4s_llists_llist(X7),X1),s(t_h4s_llists_llist(X7),X6))))),file('i/f/path/pconcat__thm_c1', ah4s_llists_LAPPEND0u_c1)).
fof(13, axiom,![X8]:![X7]:![X17]:s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_paths_frompath(s(t_h4s_paths_path(X7,X8),h4s_paths_topath(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),X17)))))=s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),X17),file('i/f/path/pconcat__thm_c1', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(15, axiom,![X7]:![X8]:![X19]:s(X7,h4s_paths_first(s(t_h4s_paths_path(X7,X8),X19)))=s(X7,h4s_pairs_fst(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_paths_frompath(s(t_h4s_paths_path(X7,X8),X19))))),file('i/f/path/pconcat__thm_c1', ah4s_paths_firstu_u_def)).
fof(16, axiom,![X7]:![X8]:![X6]:![X17]:![X19]:s(t_h4s_paths_path(X7,X8),h4s_paths_pcons(s(X7,X6),s(X8,X17),s(t_h4s_paths_path(X7,X8),X19)))=s(t_h4s_paths_path(X7,X8),h4s_paths_topath(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_pairs_u_2c(s(X7,X6),s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_llists_lcons(s(t_h4s_pairs_prod(X8,X7),h4s_pairs_u_2c(s(X8,X17),s(X7,h4s_paths_first(s(t_h4s_paths_path(X7,X8),X19))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_pairs_snd(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_paths_frompath(s(t_h4s_paths_path(X7,X8),X19))))))))))),file('i/f/path/pconcat__thm_c1', ah4s_paths_pconsu_u_def)).
fof(17, axiom,![X8]:![X7]:![X6]:![X17]:![X19]:s(X7,h4s_paths_first(s(t_h4s_paths_path(X7,X8),h4s_paths_pcons(s(X7,X6),s(X8,X17),s(t_h4s_paths_path(X7,X8),X19)))))=s(X7,X6),file('i/f/path/pconcat__thm_c1', ah4s_paths_firstu_u_thmu_c1)).
fof(18, axiom,![X7]:![X8]:![X20]:![X21]:![X22]:s(t_h4s_paths_path(X7,X8),h4s_paths_pconcat(s(t_h4s_paths_path(X7,X8),X21),s(X8,X22),s(t_h4s_paths_path(X7,X8),X20)))=s(t_h4s_paths_path(X7,X8),h4s_paths_topath(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_pairs_u_2c(s(X7,h4s_paths_first(s(t_h4s_paths_path(X7,X8),X21))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_llists_lappend(s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_pairs_snd(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_paths_frompath(s(t_h4s_paths_path(X7,X8),X21))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_llists_lcons(s(t_h4s_pairs_prod(X8,X7),h4s_pairs_u_2c(s(X8,X22),s(X7,h4s_paths_first(s(t_h4s_paths_path(X7,X8),X20))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7)),h4s_pairs_snd(s(t_h4s_pairs_prod(X7,t_h4s_llists_llist(t_h4s_pairs_prod(X8,X7))),h4s_paths_frompath(s(t_h4s_paths_path(X7,X8),X20))))))))))))),file('i/f/path/pconcat__thm_c1', ah4s_paths_pconcatu_u_def)).
fof(19, conjecture,![X23]:![X24]:![X6]:![X17]:![X20]:![X19]:![X22]:s(t_h4s_paths_path(X23,X24),h4s_paths_pconcat(s(t_h4s_paths_path(X23,X24),h4s_paths_pcons(s(X23,X6),s(X24,X17),s(t_h4s_paths_path(X23,X24),X19))),s(X24,X22),s(t_h4s_paths_path(X23,X24),X20)))=s(t_h4s_paths_path(X23,X24),h4s_paths_pcons(s(X23,X6),s(X24,X17),s(t_h4s_paths_path(X23,X24),h4s_paths_pconcat(s(t_h4s_paths_path(X23,X24),X19),s(X24,X22),s(t_h4s_paths_path(X23,X24),X20))))),file('i/f/path/pconcat__thm_c1', ch4s_paths_pconcatu_u_thmu_c1)).
# SZS output end CNFRefutation
