# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,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),X4))))))))<=>s(t_h4s_options_option(X2),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X4),s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X3)))))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X3)))))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ch4s_alists_MEMu_u_fmapu_u_tou_u_alistu_u_FLOOKUP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', aHLu_TRUTH)).
fof(8, axiom,![X1]:![X2]:![X5]:?[X12]:?[X13]:s(t_h4s_pairs_prod(X1,X2),X5)=s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X12),s(X2,X13))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_pairs_ABSu_u_PAIRu_u_THM)).
fof(9, axiom,![X1]:![X6]:![X5]:![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,X5))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6)))<=>(p(s(t_bool,X14))&s(X1,X5)=s(X1,X6))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2)).
fof(10, axiom,![X1]:![X2]:![X5]:![X15]:s(t_h4s_options_option(X2),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X15),s(X1,X5)))=s(t_h4s_options_option(X2),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X15))))),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),X15),s(X1,X5))))),s(t_h4s_options_option(X2),h4s_options_none))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(12, axiom,![X1]:![X2]:![X6]:![X5]:s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X5),s(X2,X6)))))=s(X2,X6),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_pairs_SND0)).
fof(13, axiom,![X2]:![X1]:![X6]:![X5]:s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X5),s(X2,X6)))))=s(X1,X5),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_pairs_FST0)).
fof(14, axiom,![X1]:![X2]:![X6]:![X5]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X5),s(X2,X6))),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),X4))))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X4))))))&s(X2,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X4),s(X1,X5)))=s(X2,X6))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_alists_MEMu_u_fmapu_u_tou_u_alist)).
fof(15, axiom,~(p(s(t_bool,f))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', aHLu_FALSITY)).
fof(16, axiom,![X1]:![X16]:![X6]:![X17]:![X5]:![X18]:![X14]:((s(t_bool,X14)=s(t_bool,X18)&((p(s(t_bool,X18))=>s(X1,X5)=s(X1,X17))&(~(p(s(t_bool,X18)))=>s(X1,X6)=s(X1,X16))))=>s(X1,h4s_bools_cond(s(t_bool,X14),s(X1,X5),s(X1,X6)))=s(X1,h4s_bools_cond(s(t_bool,X18),s(X1,X17),s(X1,X16)))),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', ah4s_bools_CONDu_u_CONG)).
fof(18, axiom,![X22]:(s(t_bool,X22)=s(t_bool,t)|s(t_bool,X22)=s(t_bool,f)),file('i/f/alist/MEM__fmap__to__alist__FLOOKUP', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
