# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),h4s_paths_pmap(s(t_fun(X3,X2),X7),s(t_fun(X4,X1),X6),s(t_h4s_paths_path(X3,X4),X5)))))=s(X2,happ(s(t_fun(X3,X2),X7),s(X3,h4s_paths_first(s(t_h4s_paths_path(X3,X4),X5))))),file('i/f/path/first__pmap', ch4s_paths_firstu_u_pmap)).
fof(10, axiom,![X3]:![X4]:![X5]:s(X3,h4s_paths_first(s(t_h4s_paths_path(X3,X4),X5)))=s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X4),X5))))),file('i/f/path/first__pmap', ah4s_paths_firstu_u_def)).
fof(14, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:s(t_h4s_paths_path(X2,X1),h4s_paths_pmap(s(t_fun(X3,X2),X7),s(t_fun(X4,X1),X6),s(t_h4s_paths_path(X3,X4),X5)))=s(t_h4s_paths_path(X2,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),happ(s(t_fun(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2)))),h4s_pairs_u_23u_23(s(t_fun(X3,X2),X7),s(t_fun(t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3)),t_h4s_llists_llist(t_h4s_pairs_prod(X1,X2))),h4s_llists_lmap(s(t_fun(t_h4s_pairs_prod(X4,X3),t_h4s_pairs_prod(X1,X2)),h4s_pairs_u_23u_23(s(t_fun(X4,X1),X6),s(t_fun(X3,X2),X7))))))),s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X4),X5))))))),file('i/f/path/first__pmap', ah4s_paths_pmapu_u_def)).
fof(35, axiom,![X4]:![X3]:![X8]:![X9]:s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,X9),s(X4,X8)))))=s(X3,X9),file('i/f/path/first__pmap', ah4s_pairs_FST0)).
fof(36, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:![X6]:![X7]:s(t_h4s_pairs_prod(X2,X1),happ(s(t_fun(t_h4s_pairs_prod(X3,X4),t_h4s_pairs_prod(X2,X1)),h4s_pairs_u_23u_23(s(t_fun(X3,X2),X7),s(t_fun(X4,X1),X6))),s(t_h4s_pairs_prod(X3,X4),X5)))=s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,happ(s(t_fun(X3,X2),X7),s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,X4),X5))))),s(X1,happ(s(t_fun(X4,X1),X6),s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X4),X5))))))),file('i/f/path/first__pmap', ah4s_pairs_PAIRu_u_MAP)).
fof(38, axiom,![X4]:![X3]:![X14]:s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X4),h4s_paths_topath(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),X14)))))=s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X3))),X14),file('i/f/path/first__pmap', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
# SZS output end CNFRefutation
