# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/finite_map/FLOOKUP__o__f', aHLu_TRUTH)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f0)),file('i/f/finite_map/FLOOKUP__o__f', aHLu_BOOLu_CASES)).
fof(12, 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__o__f', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(13, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f0),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/finite_map/FLOOKUP__o__f', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(18, axiom,![X9]:![X16]:![X17]:![X4]:s(X16,h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_options_none),s(X16,X17),s(t_fun(X9,X16),X4)))=s(X16,X17),file('i/f/finite_map/FLOOKUP__o__f', ah4s_options_optionu_u_caseu_u_defu_c0)).
fof(19, axiom,![X16]:![X9]:![X6]:![X17]:![X4]:s(X16,h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_options_some(s(X9,X6))),s(X16,X17),s(t_fun(X9,X16),X4)))=s(X16,happ(s(t_fun(X9,X16),X4),s(X9,X6))),file('i/f/finite_map/FLOOKUP__o__f', ah4s_options_optionu_u_caseu_u_defu_c1)).
fof(21, axiom,![X9]:![X16]:![X6]:![X4]:s(t_h4s_options_option(X16),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X9,X16),X4),s(X9,X6)))=s(t_h4s_options_option(X16),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,X16),X4))))),s(t_h4s_options_option(X16),h4s_options_some(s(X16,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X16),X4),s(X9,X6))))),s(t_h4s_options_option(X16),h4s_options_none))),file('i/f/finite_map/FLOOKUP__o__f', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(22, axiom,![X18]:![X9]:![X16]:![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_ou_u_f(s(t_fun(X16,X18),X4),s(t_h4s_finiteu_u_maps_fmap(X9,X16),X5)))))=s(t_fun(X9,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X9,X16),X5))),file('i/f/finite_map/FLOOKUP__o__f', ah4s_finiteu_u_maps_FDOMu_u_ou_u_f)).
fof(23, axiom,![X18]:![X16]:![X9]:![X6]:![X5]:![X4]:(p(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,X16),X5))))))=>s(X18,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X18),h4s_finiteu_u_maps_ou_u_f(s(t_fun(X16,X18),X4),s(t_h4s_finiteu_u_maps_fmap(X9,X16),X5))),s(X9,X6)))=s(X18,happ(s(t_fun(X16,X18),X4),s(X16,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X9,X16),X5),s(X9,X6)))))),file('i/f/finite_map/FLOOKUP__o__f', ah4s_finiteu_u_maps_ou_u_fu_u_FAPPLY)).
fof(24, conjecture,![X16]:![X18]:![X9]:![X19]:(![X4]:![X17]:s(t_h4s_options_option(X9),happ(s(t_fun(X18,t_h4s_options_option(X9)),happ(s(t_fun(t_fun(X18,X9),t_fun(X18,t_h4s_options_option(X9))),X19),s(t_fun(X18,X9),X4))),s(X18,X17)))=s(t_h4s_options_option(X9),h4s_options_some(s(X9,happ(s(t_fun(X18,X9),X4),s(X18,X17)))))=>![X20]:![X21]:![X4]:s(t_h4s_options_option(X9),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X16,X9),h4s_finiteu_u_maps_ou_u_f(s(t_fun(X18,X9),X4),s(t_h4s_finiteu_u_maps_fmap(X16,X18),X21))),s(X16,X20)))=s(t_h4s_options_option(X9),h4s_options_optionu_u_case(s(t_h4s_options_option(X18),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X16,X18),X21),s(X16,X20))),s(t_h4s_options_option(X9),h4s_options_none),s(t_fun(X18,t_h4s_options_option(X9)),happ(s(t_fun(t_fun(X18,X9),t_fun(X18,t_h4s_options_option(X9))),X19),s(t_fun(X18,X9),X4)))))),file('i/f/finite_map/FLOOKUP__o__f', ch4s_finiteu_u_maps_FLOOKUPu_u_ou_u_f)).
# SZS output end CNFRefutation
