# 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(X1,X3),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4))))))))=>p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X3),s(X2,h4s_finiteu_u_maps_fapply(s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4))),s(X1,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)),X4))))))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ch4s_alists_alistu_u_tou_u_fmapu_u_FAPPLYu_u_MEM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', aHLu_TRUTH)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:![X2]:![X6]:![X7]: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),X7))),s(X1,X6)))=s(t_h4s_options_option(X2),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_finiteu_u_maps_fdom(s(t_h4s_finiteu_u_maps_fmap(X1,X2),X7))))),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),X7),s(X1,X6))))),s(t_h4s_options_option(X2),h4s_options_none))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(8, axiom,![X1]:![X2]:![X8]:![X9]:![X4]:(s(t_h4s_options_option(X2),happ(s(t_fun(X1,t_h4s_options_option(X2)),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4))),s(X1,X9)))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X8)))=>p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X9),s(X2,X8))),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)),X4))))))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ah4s_alists_ALOOKUPu_u_MEM)).
fof(9, axiom,![X1]:![X2]:![X4]:s(t_fun(X1,t_h4s_options_option(X2)),h4s_finiteu_u_maps_flookup(s(t_h4s_finiteu_u_maps_fmap(X1,X2),h4s_alists_alistu_u_tou_u_fmap(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4)))))=s(t_fun(X1,t_h4s_options_option(X2)),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X4))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ah4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c0)).
fof(10, axiom,![X1]:![X10]:![X6]:![X11]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X11),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10)))<=>(p(s(t_bool,X11))&s(X1,X6)=s(X1,X10))),file('i/f/alist/alist__to__fmap__FAPPLY__MEM', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2)).
# SZS output end CNFRefutation
