# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/finite_map/FLOOKUP__DRESTRICT', aHLu_TRUTH)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/finite_map/FLOOKUP__DRESTRICT', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(16, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(17, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(24, axiom,![X9]:![X6]:![X1]:![X18]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_predu_u_sets_inter(s(t_fun(X9,t_bool),X18),s(t_fun(X9,t_bool),X1))))))<=>(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X18))))&p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1)))))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_predu_u_sets_INu_u_INTER)).
fof(25, axiom,![X19]:![X9]:![X20]:![X4]:s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X19),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4),s(t_fun(X9,t_bool),X20)))))=s(t_fun(X9,t_bool),h4s_predu_u_sets_inter(s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4))),s(t_fun(X9,t_bool),X20))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c0)).
fof(26, axiom,![X19]:![X9]:![X6]:![X20]:![X4]:s(X19,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X19),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4),s(t_fun(X9,t_bool),X20))),s(X9,X6)))=s(X19,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_predu_u_sets_inter(s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4))),s(t_fun(X9,t_bool),X20))))),s(X19,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4),s(X9,X6))),s(X19,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X19),h4s_finiteu_u_maps_fempty),s(X9,X6))))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_finiteu_u_maps_DRESTRICTu_u_DEFu_c1)).
fof(27, axiom,![X9]:![X19]:![X6]:![X4]:s(t_h4s_options_option(X19),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4),s(X9,X6)))=s(t_h4s_options_option(X19),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4))))),s(t_h4s_options_option(X19),h4s_options_some(s(X19,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X4),s(X9,X6))))),s(t_h4s_options_option(X19),h4s_options_none))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(28, conjecture,![X9]:![X19]:![X18]:![X21]:![X22]:s(t_h4s_options_option(X19),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X9,X19),h4s_finiteu_u_maps_drestrict(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X22),s(t_fun(X9,t_bool),X18))),s(X9,X21)))=s(t_h4s_options_option(X19),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X9,X21),s(t_fun(X9,t_bool),X18))),s(t_h4s_options_option(X19),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X9,X19),X22),s(X9,X21))),s(t_h4s_options_option(X19),h4s_options_none))),file('i/f/finite_map/FLOOKUP__DRESTRICT', ch4s_finiteu_u_maps_FLOOKUPu_u_DRESTRICT)).
# SZS output end CNFRefutation
