# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((s(X2,X3)=s(X2,happ(s(t_fun(t_h4s_pairs_prod(X2,X1),X2),h4s_pairs_fst),s(t_h4s_pairs_prod(X2,X1),X4)))|s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X6),s(X2,X3)))=s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(X2,X3))))=>s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X6),s(t_h4s_pairs_prod(X2,X1),X4))),s(X2,X3)))=s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X5),s(t_h4s_pairs_prod(X2,X1),X4))),s(X2,X3)))),file('i/f/finite_map/FUPDATE__SAME__APPLY', ch4s_finiteu_u_maps_FUPDATEu_u_SAMEu_u_APPLY)).
fof(2, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(29, axiom,![X1]:![X2]:![X9]:![X3]:![X25]:![X26]:(~(s(X2,X26)=s(X2,X3))=>s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X25),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X9))))),s(X2,X26)))=s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X25),s(X2,X26)))),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_finiteu_u_maps_NOTu_u_EQu_u_FAPPLY)).
fof(30, axiom,![X1]:![X2]:![X3]:![X25]:![X27]:![X26]:?[X28]:((p(s(t_bool,X28))<=>s(X2,X3)=s(X2,X26))&s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X25),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X26),s(X1,X27))))),s(X2,X3)))=s(X1,h4s_bools_cond(s(t_bool,X28),s(X1,X27),s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X25),s(X2,X3)))))),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_finiteu_u_maps_FAPPLYu_u_FUPDATEu_u_THM)).
fof(31, axiom,![X2]:![X1]:![X9]:![X3]:![X25]:s(X1,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X2,X1),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X2,X1),X25),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X9))))),s(X2,X3)))=s(X1,X9),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_finiteu_u_maps_FAPPLYu_u_FUPDATE)).
fof(34, axiom,![X2]:![X1]:![X3]:?[X17]:?[X16]:s(t_h4s_pairs_prod(X2,X1),X3)=s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X17),s(X1,X16))),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(43, axiom,![X1]:![X2]:![X9]:![X3]:s(X2,happ(s(t_fun(t_h4s_pairs_prod(X2,X1),X2),h4s_pairs_fst),s(t_h4s_pairs_prod(X2,X1),h4s_pairs_u_2c(s(X2,X3),s(X1,X9)))))=s(X2,X3),file('i/f/finite_map/FUPDATE__SAME__APPLY', ah4s_pairs_FST0)).
# SZS output end CNFRefutation
