# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_llists_tolist(s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2)))))=s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_options_optionu_u_map(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),h4s_lists_cons(s(X1,X3))),s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_llists_tolist(s(t_h4s_llists_llist(X1),X2))))),file('i/f/llist/toList__THM_c1', ch4s_llists_toListu_u_THMu_c1)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/llist/toList__THM_c1', aHLu_TRUTH)).
fof(9, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)<=>p(s(t_bool,X2))),file('i/f/llist/toList__THM_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:![X6]:![X7]:![X10]:s(t_h4s_options_option(X1),h4s_options_optionu_u_map(s(t_fun(X6,X1),X10),s(t_h4s_options_option(X6),h4s_options_some(s(X6,X7)))))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,happ(s(t_fun(X6,X1),X10),s(X6,X7))))),file('i/f/llist/toList__THM_c1', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c0)).
fof(12, axiom,![X6]:![X1]:![X7]:![X10]:(s(t_h4s_options_option(X6),h4s_options_none)=s(t_h4s_options_option(X6),h4s_options_optionu_u_map(s(t_fun(X1,X6),X10),s(t_h4s_options_option(X1),X7)))<=>s(t_h4s_options_option(X1),X7)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/llist/toList__THM_c1', ah4s_options_OPTIONu_u_MAPu_u_EQu_u_NONEu_u_bothu_u_waysu_c1)).
fof(13, axiom,![X11]:![X2]:![X12]:![X3]:s(t_h4s_options_option(t_h4s_lists_list(X11)),h4s_llists_ltake(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,X12))),s(t_h4s_llists_llist(X11),h4s_llists_lcons(s(X11,X3),s(t_h4s_llists_llist(X11),X2)))))=s(t_h4s_options_option(t_h4s_lists_list(X11)),h4s_options_optionu_u_map(s(t_fun(t_h4s_lists_list(X11),t_h4s_lists_list(X11)),h4s_lists_cons(s(X11,X3))),s(t_h4s_options_option(t_h4s_lists_list(X11)),h4s_llists_ltake(s(t_h4s_nums_num,X12),s(t_h4s_llists_llist(X11),X2))))),file('i/f/llist/toList__THM_c1', ah4s_llists_LTAKEu_u_THMu_c2)).
fof(14, axiom,![X1]:![X2]:![X3]:s(t_h4s_options_option(t_h4s_nums_num),h4s_llists_llength(s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2)))))=s(t_h4s_options_option(t_h4s_nums_num),h4s_options_optionu_u_map(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_options_option(t_h4s_nums_num),h4s_llists_llength(s(t_h4s_llists_llist(X1),X2))))),file('i/f/llist/toList__THM_c1', ah4s_llists_LLENGTHu_u_THMu_c1)).
fof(15, axiom,![X6]:![X13]:s(t_h4s_options_option(t_h4s_lists_list(X6)),h4s_llists_tolist(s(t_h4s_llists_llist(X6),X13)))=s(t_h4s_options_option(t_h4s_lists_list(X6)),h4s_bools_cond(s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X6),X13))),s(t_h4s_options_option(t_h4s_lists_list(X6)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_options_the(s(t_h4s_options_option(t_h4s_nums_num),h4s_llists_llength(s(t_h4s_llists_llist(X6),X13))))),s(t_h4s_llists_llist(X6),X13))),s(t_h4s_options_option(t_h4s_lists_list(X6)),h4s_options_none))),file('i/f/llist/toList__THM_c1', ah4s_llists_toList0)).
fof(17, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2)))))=s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X1),X2))),file('i/f/llist/toList__THM_c1', ah4s_llists_LFINITEu_u_THMu_c1)).
fof(19, axiom,![X6]:![X13]:(p(s(t_bool,h4s_llists_lfinite(s(t_h4s_llists_llist(X6),X13))))=>?[X12]:s(t_h4s_options_option(t_h4s_nums_num),h4s_llists_llength(s(t_h4s_llists_llist(X6),X13)))=s(t_h4s_options_option(t_h4s_nums_num),h4s_options_some(s(t_h4s_nums_num,X12)))),file('i/f/llist/toList__THM_c1', ah4s_llists_LFINITEu_u_HASu_u_LENGTH)).
fof(20, axiom,![X6]:![X8]:![X7]:(s(t_h4s_options_option(X6),h4s_options_some(s(X6,X7)))=s(t_h4s_options_option(X6),h4s_options_some(s(X6,X8)))<=>s(X6,X7)=s(X6,X8)),file('i/f/llist/toList__THM_c1', ah4s_options_SOMEu_u_11)).
fof(28, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,t0),s(X6,X5),s(X6,X4)))=s(X6,X5),file('i/f/llist/toList__THM_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(31, axiom,![X6]:![X7]:s(X6,h4s_options_the(s(t_h4s_options_option(X6),h4s_options_some(s(X6,X7)))))=s(X6,X7),file('i/f/llist/toList__THM_c1', ah4s_options_THEu_u_DEF)).
fof(32, axiom,![X6]:![X22]:![X21]:(s(t_h4s_options_option(X6),h4s_bools_cond(s(t_bool,X21),s(t_h4s_options_option(X6),X22),s(t_h4s_options_option(X6),h4s_options_none)))=s(t_h4s_options_option(X6),h4s_options_none)<=>(p(s(t_bool,X21))=>p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X6),X22)))))),file('i/f/llist/toList__THM_c1', ah4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c0)).
# SZS output end CNFRefutation
