# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_finiteu_u_maps_submap(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X3))))))))<=>(s(t_h4s_options_option(X2),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_options_none)|s(t_h4s_options_option(X2),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X3))))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', ch4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_FLOOKUP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', aHLu_TRUTH)).
fof(7, axiom,![X1]:![X4]:![X9]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X9),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_none)<=>~(p(s(t_bool,X9)))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0)).
fof(8, axiom,![X1]:![X3]:![X4]:![X9]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X9),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X3)))<=>(p(s(t_bool,X9))&s(X1,X4)=s(X1,X3))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2)).
fof(9, axiom,![X1]:![X2]:![X4]:![X5]:s(t_h4s_options_option(X2),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5))))),s(t_h4s_options_option(X2),h4s_options_some(s(X2,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(X1,X4))))),s(t_h4s_options_option(X2),h4s_options_none))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(10, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_finiteu_u_maps_submap(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_finiteu_u_maps_fupdate(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X3))))))))<=>(~(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5)))))))|(s(X2,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5),s(X1,X4)))=s(X2,X3)&p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5))))))))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', ah4s_finiteu_u_maps_SUBMAPu_u_FUPDATEu_u_EQN)).
fof(11, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f0)),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', aHLu_BOOLu_CASES)).
fof(13, axiom,~(p(s(t_bool,f0))),file('i/f/finite_map/SUBMAP__FUPDATE__FLOOKUP', aHLu_FALSITY)).
# SZS output end CNFRefutation
