# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X3))),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5))))))))<=>s(t_h4s_options_option(X2),happ(s(t_fun(X1,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/alist/MEM__pair__fmap__to__alist__FLOOKUP', ch4s_alists_MEMu_u_pairu_u_fmapu_u_tou_u_alistu_u_FLOOKUP)).
fof(5, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(35, axiom,![X1]:![X2]:![X4]:![X8]:s(t_h4s_options_option(X2),happ(s(t_fun(X1,t_h4s_options_option(X2)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X8))),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),X8))))),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),X8),s(X1,X4))))),s(t_h4s_options_option(X2),h4s_options_none))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(37, axiom,![X1]:![X2]:![X4]:![X23]:![X8]:(s(t_h4s_options_option(X2),happ(s(t_fun(X1,t_h4s_options_option(X2)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X8))),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X23)))<=>(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),X8))))))&s(X2,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X8),s(X1,X4)))=s(X2,X23))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_finiteu_u_maps_flookupu_u_thmu_c1)).
fof(39, axiom,![X1]:![X4]:![X14]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X14),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,X14)))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0)).
fof(40, axiom,![X1]:![X4]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_options_NOTu_u_NONEu_u_SOME)).
fof(43, axiom,![X1]:![X2]:![X4]:![X8]:(s(t_h4s_options_option(X2),happ(s(t_fun(X1,t_h4s_options_option(X2)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X8))),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_options_none)<=>~(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),X8)))))))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_finiteu_u_maps_flookupu_u_thmu_c0)).
fof(48, axiom,~(p(s(t_bool,f))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', aHLu_FALSITY)).
fof(59, axiom,![X18]:(s(t_bool,f)=s(t_bool,X18)<=>~(p(s(t_bool,X18)))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(62, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X4),s(X2,X3))),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),h4s_alists_fmapu_u_tou_u_alist(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X5))))))))<=>(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))),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_alists_MEMu_u_fmapu_u_tou_u_alist)).
fof(79, axiom,![X1]:![X11]:![X12]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X12),s(X1,X11)))=s(X1,X12),file('i/f/alist/MEM__pair__fmap__to__alist__FLOOKUP', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
# SZS output end CNFRefutation
