# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(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)),X5))),s(X1,X4)))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,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)),X5))),s(X1,X4)))=s(X2,X3)),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', ch4s_alists_ALOOKUPu_u_SOMEu_u_FAPPLYu_u_alistu_u_tou_u_fmap)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', aHLu_TRUTH)).
fof(10, axiom,![X1]:![X12]:![X10]:(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X12)))<=>s(X1,X10)=s(X1,X12)),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', ah4s_options_SOMEu_u_11)).
fof(11, axiom,![X1]:![X2]:![X10]:![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,X10)))=s(t_h4s_options_option(X2),h4s_bools_cond(s(t_bool,h4s_bools_in(s(X1,X10),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,X10))))),s(t_h4s_options_option(X2),h4s_options_none))),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', ah4s_finiteu_u_maps_FLOOKUPu_u_DEF)).
fof(12, axiom,![X1]:![X2]:![X5]: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)),X5)))))=s(t_fun(X1,t_h4s_options_option(X2)),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X1,X2)),X5))),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', ah4s_alists_ALOOKUPu_u_EQu_u_FLOOKUPu_c0)).
fof(13, axiom,![X1]:![X12]:![X10]:![X18]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X18),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X12)))<=>(p(s(t_bool,X18))&s(X1,X10)=s(X1,X12))),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c2)).
fof(14, axiom,~(p(s(t_bool,f))),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', aHLu_FALSITY)).
fof(15, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)|s(t_bool,X11)=s(t_bool,f)),file('i/f/alist/ALOOKUP__SOME__FAPPLY__alist__to__fmap', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
