# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:![X9]:s(t_h4s_paths_path(X1,X2),h4s_paths_pmap(s(t_fun(X3,X1),X9),s(t_fun(X4,X2),X8),s(t_h4s_paths_path(X3,X4),h4s_paths_pcons(s(X3,X5),s(X4,X6),s(t_h4s_paths_path(X3,X4),X7)))))=s(t_h4s_paths_path(X1,X2),h4s_paths_pcons(s(X1,happ(s(t_fun(X3,X1),X9),s(X3,X5))),s(X2,happ(s(t_fun(X4,X2),X8),s(X4,X6))),s(t_h4s_paths_path(X1,X2),h4s_paths_pmap(s(t_fun(X3,X1),X9),s(t_fun(X4,X2),X8),s(t_h4s_paths_path(X3,X4),X7))))),file('i/f/path/pmap__thm_c1', ch4s_paths_pmapu_u_thmu_c1)).
fof(2, axiom,![X3]:![X1]:![X5]:![X6]:![X7]:s(t_h4s_paths_path(X3,X1),h4s_paths_pcons(s(X3,X5),s(X1,X6),s(t_h4s_paths_path(X3,X1),X7)))=s(t_h4s_paths_path(X3,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),h4s_pairs_u_2c(s(X3,X5),s(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3)),h4s_llists_lcons(s(t_h4s_pairs_prod(X1,X3),h4s_pairs_u_2c(s(X1,X6),s(X3,h4s_paths_first(s(t_h4s_paths_path(X3,X1),X7))))),s(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3)),h4s_pairs_snd(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X1),X7))))))))))),file('i/f/path/pmap__thm_c1', ah4s_paths_pconsu_u_def)).
fof(3, axiom,![X4]:![X2]:![X3]:![X1]:![X7]:![X8]:![X9]:s(t_h4s_paths_path(X2,X4),h4s_paths_pmap(s(t_fun(X3,X2),X9),s(t_fun(X1,X4),X8),s(t_h4s_paths_path(X3,X1),X7)))=s(t_h4s_paths_path(X2,X4),h4s_paths_topath(s(t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X2))),happ(s(t_fun(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),t_h4s_pairs_prod(X2,t_h4s_llists_llist(t_h4s_pairs_prod(X4,X2)))),h4s_pairs_u_23u_23(s(t_fun(X3,X2),X9),s(t_fun(t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3)),t_h4s_llists_llist(t_h4s_pairs_prod(X4,X2))),h4s_llists_lmap(s(t_fun(t_h4s_pairs_prod(X1,X3),t_h4s_pairs_prod(X4,X2)),h4s_pairs_u_23u_23(s(t_fun(X1,X4),X8),s(t_fun(X3,X2),X9))))))),s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X1),X7))))))),file('i/f/path/pmap__thm_c1', ah4s_paths_pmapu_u_def)).
fof(5, axiom,![X1]:![X3]:![X6]:s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X1),h4s_paths_topath(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),X6)))))=s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),X6),file('i/f/path/pmap__thm_c1', ah4s_paths_pathu_u_repu_u_bijectionsu_u_thmu_c1)).
fof(8, axiom,![X1]:![X3]:![X4]:![X2]:![X13]:![X5]:![X8]:![X9]:s(t_h4s_pairs_prod(X1,X4),happ(s(t_fun(t_h4s_pairs_prod(X3,X2),t_h4s_pairs_prod(X1,X4)),h4s_pairs_u_23u_23(s(t_fun(X3,X1),X9),s(t_fun(X2,X4),X8))),s(t_h4s_pairs_prod(X3,X2),h4s_pairs_u_2c(s(X3,X5),s(X2,X13)))))=s(t_h4s_pairs_prod(X1,X4),h4s_pairs_u_2c(s(X1,happ(s(t_fun(X3,X1),X9),s(X3,X5))),s(X4,happ(s(t_fun(X2,X4),X8),s(X2,X13))))),file('i/f/path/pmap__thm_c1', ah4s_pairs_PAIRu_u_MAPu_u_THM)).
fof(10, axiom,![X2]:![X4]:![X3]:![X1]:![X7]:![X8]:![X9]:s(X4,h4s_pairs_snd(s(t_h4s_pairs_prod(X2,X4),happ(s(t_fun(t_h4s_pairs_prod(X3,X1),t_h4s_pairs_prod(X2,X4)),h4s_pairs_u_23u_23(s(t_fun(X3,X2),X9),s(t_fun(X1,X4),X8))),s(t_h4s_pairs_prod(X3,X1),X7)))))=s(X4,happ(s(t_fun(X1,X4),X8),s(X1,h4s_pairs_snd(s(t_h4s_pairs_prod(X3,X1),X7))))),file('i/f/path/pmap__thm_c1', ah4s_pairs_SNDu_u_PAIRu_u_MAP)).
fof(11, axiom,![X3]:![X1]:![X7]:s(X3,h4s_paths_first(s(t_h4s_paths_path(X3,X1),X7)))=s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,t_h4s_llists_llist(t_h4s_pairs_prod(X1,X3))),h4s_paths_frompath(s(t_h4s_paths_path(X3,X1),X7))))),file('i/f/path/pmap__thm_c1', ah4s_paths_firstu_u_def)).
fof(12, axiom,![X1]:![X3]:![X20]:![X21]:![X9]:s(t_h4s_llists_llist(X1),happ(s(t_fun(t_h4s_llists_llist(X3),t_h4s_llists_llist(X1)),h4s_llists_lmap(s(t_fun(X3,X1),X9))),s(t_h4s_llists_llist(X3),h4s_llists_lcons(s(X3,X21),s(t_h4s_llists_llist(X3),X20)))))=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,happ(s(t_fun(X3,X1),X9),s(X3,X21))),s(t_h4s_llists_llist(X1),happ(s(t_fun(t_h4s_llists_llist(X3),t_h4s_llists_llist(X1)),h4s_llists_lmap(s(t_fun(X3,X1),X9))),s(t_h4s_llists_llist(X3),X20))))),file('i/f/path/pmap__thm_c1', ah4s_llists_LMAP0u_c1)).
fof(13, axiom,![X4]:![X2]:![X3]:![X1]:![X7]:![X8]:![X9]:s(X2,h4s_pairs_fst(s(t_h4s_pairs_prod(X2,X4),happ(s(t_fun(t_h4s_pairs_prod(X3,X1),t_h4s_pairs_prod(X2,X4)),h4s_pairs_u_23u_23(s(t_fun(X3,X2),X9),s(t_fun(X1,X4),X8))),s(t_h4s_pairs_prod(X3,X1),X7)))))=s(X2,happ(s(t_fun(X3,X2),X9),s(X3,h4s_pairs_fst(s(t_h4s_pairs_prod(X3,X1),X7))))),file('i/f/path/pmap__thm_c1', ah4s_pairs_FSTu_u_PAIRu_u_MAP)).
# SZS output end CNFRefutation
