# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(8, axiom,![X7]:![X8]:(s(t_h4s_options_option(X7),X8)=s(t_h4s_options_option(X7),h4s_options_none)|?[X6]:s(t_h4s_options_option(X7),X8)=s(t_h4s_options_option(X7),h4s_options_some(s(X7,X6)))),file('i/f/alist/ALOOKUP__APPEND', ah4s_options_optionu_u_nchotomy)).
fof(9, axiom,![X7]:![X9]:![X10]:![X4]:s(X9,h4s_options_optionu_u_case(s(t_h4s_options_option(X7),h4s_options_none),s(X9,X10),s(t_fun(X7,X9),X4)))=s(X9,X10),file('i/f/alist/ALOOKUP__APPEND', ah4s_options_optionu_u_caseu_u_defu_c0)).
fof(10, axiom,![X9]:![X7]:![X6]:![X10]:![X4]:s(X9,h4s_options_optionu_u_case(s(t_h4s_options_option(X7),h4s_options_some(s(X7,X6))),s(X9,X10),s(t_fun(X7,X9),X4)))=s(X9,happ(s(t_fun(X7,X9),X4),s(X7,X6))),file('i/f/alist/ALOOKUP__APPEND', ah4s_options_optionu_u_caseu_u_defu_c1)).
fof(12, axiom,![X7]:![X9]:![X10]:![X12]:![X13]:![X14]:(s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X13),s(X7,X14)))=s(t_h4s_options_option(X9),h4s_options_some(s(X9,X10)))=>s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X13),s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X12))),s(X7,X14)))=s(t_h4s_options_option(X9),h4s_options_some(s(X9,X10)))),file('i/f/alist/ALOOKUP__APPEND', ah4s_alists_ALOOKUPu_u_prefixu_c0)).
fof(13, axiom,![X9]:![X7]:![X12]:![X13]:![X14]:(s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X13),s(X7,X14)))=s(t_h4s_options_option(X9),h4s_options_none)=>s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X13),s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X12))),s(X7,X14)))=s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X12),s(X7,X14)))),file('i/f/alist/ALOOKUP__APPEND', ah4s_alists_ALOOKUPu_u_prefixu_c1)).
fof(14, conjecture,![X7]:![X9]:![X15]:(![X10]:s(t_h4s_options_option(X9),happ(s(t_fun(X9,t_h4s_options_option(X9)),X15),s(X9,X10)))=s(t_h4s_options_option(X9),h4s_options_some(s(X9,X10)))=>![X16]:![X17]:![X14]:s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X17),s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X16))),s(X7,X14)))=s(t_h4s_options_option(X9),h4s_options_optionu_u_case(s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X17),s(X7,X14))),s(t_h4s_options_option(X9),h4s_alists_alookup(s(t_h4s_lists_list(t_h4s_pairs_prod(X7,X9)),X16),s(X7,X14))),s(t_fun(X9,t_h4s_options_option(X9)),X15)))),file('i/f/alist/ALOOKUP__APPEND', ch4s_alists_ALOOKUPu_u_APPEND)).
# SZS output end CNFRefutation
