# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/finite_map/FLOOKUP__FUNION', aHLu_FALSITY)).
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__FUNION', aHLu_BOOLu_CASES)).
fof(6, 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/FLOOKUP__FUNION', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(16, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, 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__FUNION', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(18, 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__FUNION', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(24, axiom,![X9]:![X18]:![X19]:![X4]:s(X18,h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_options_none),s(X18,X19),s(t_fun(X9,X18),X4)))=s(X18,X19),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_options_optionu_u_caseu_u_defu_c0)).
fof(25, axiom,![X18]:![X9]:![X6]:![X19]:![X4]:s(X18,h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_options_some(s(X9,X6))),s(X18,X19),s(t_fun(X9,X18),X4)))=s(X18,happ(s(t_fun(X9,X18),X4),s(X9,X6))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_options_optionu_u_caseu_u_defu_c1)).
fof(28, axiom,![X9]:![X6]:![X1]:![X20]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_predu_u_sets_union(s(t_fun(X9,t_bool),X20),s(t_fun(X9,t_bool),X1))))))<=>(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X20))))|p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),X1)))))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_predu_u_sets_INu_u_UNION)).
fof(29, axiom,![X9]:![X18]:![X5]:![X4]:s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X18),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4),s(t_h4s_finiteu_u_maps_fmap(X9,X18),X5)))))=s(t_fun(X9,t_bool),h4s_predu_u_sets_union(s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4))),s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X5))))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_finiteu_u_maps_FUNIONu_u_DEFu_c0)).
fof(30, axiom,![X18]:![X9]:![X6]:![X5]:![X4]:s(X18,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X18),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4),s(t_h4s_finiteu_u_maps_fmap(X9,X18),X5))),s(X9,X6)))=s(X18,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,X18),X4))))),s(X18,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4),s(X9,X6))),s(X18,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X5),s(X9,X6))))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_finiteu_u_maps_FUNIONu_u_DEFu_c1)).
fof(31, axiom,![X9]:![X18]:![X6]:![X4]:s(t_h4s_options_option(X18),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4),s(X9,X6)))=s(t_h4s_options_option(X18),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,X18),X4))))),s(t_h4s_options_option(X18),h4s_options_some(s(X18,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X18),X4),s(X9,X6))))),s(t_h4s_options_option(X18),h4s_options_none))),file('i/f/finite_map/FLOOKUP__FUNION', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(32, conjecture,![X18]:![X9]:![X21]:(![X19]:s(t_h4s_options_option(X9),happ(s(t_fun(X9,t_h4s_options_option(X9)),X21),s(X9,X19)))=s(t_h4s_options_option(X9),h4s_options_some(s(X9,X19)))=>![X22]:![X23]:![X24]:s(t_h4s_options_option(X9),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X18,X9),h4s_finiteu_u_maps_funion(s(t_h4s_finiteu_u_maps_fmap(X18,X9),X24),s(t_h4s_finiteu_u_maps_fmap(X18,X9),X23))),s(X18,X22)))=s(t_h4s_options_option(X9),h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X18,X9),X24),s(X18,X22))),s(t_h4s_options_option(X9),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X18,X9),X23),s(X18,X22))),s(t_fun(X9,t_h4s_options_option(X9)),X21)))),file('i/f/finite_map/FLOOKUP__FUNION', ch4s_finiteu_u_maps_FLOOKUPu_u_FUNION)).
# SZS output end CNFRefutation
