# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),h4s_lists_nil))),file('i/f/list/SET__TO__LIST__SING', ch4s_lists_SETu_u_TOu_u_LISTu_u_SING)).
fof(8, axiom,![X1]:![X12]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X12))))=>?[X13]:((p(s(t_bool,X13))<=>s(t_fun(X1,t_bool),X12)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))&s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),X12)))=s(t_h4s_lists_list(X1),h4s_bools_cond(s(t_bool,X13),s(t_h4s_lists_list(X1),h4s_lists_nil),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,h4s_predu_u_sets_choice(s(t_fun(X1,t_bool),X12))))),s(t_h4s_lists_list(X1),h4s_lists_setu_u_tou_u_list(s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X12))))))))))),file('i/f/list/SET__TO__LIST__SING', ah4s_lists_SETu_u_TOu_u_LISTu_u_THM)).
fof(10, axiom,![X1]:![X2]:![X12]:~(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X12)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_NOTu_u_INSERTu_u_EMPTY)).
fof(11, axiom,![X1]:![X2]:![X12]:s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X12)))))=s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X12))),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_FINITEu_u_INSERT)).
fof(12, axiom,![X1]:p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_FINITEu_u_EMPTY)).
fof(13, axiom,![X14]:![X15]:((p(s(t_bool,X15))=>p(s(t_bool,X14)))=>((p(s(t_bool,X14))=>p(s(t_bool,X15)))=>s(t_bool,X15)=s(t_bool,X14))),file('i/f/list/SET__TO__LIST__SING', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X1]:![X21]:![X3]:![X22]:![X2]:![X10]:![X11]:((s(t_bool,X11)=s(t_bool,X10)&((p(s(t_bool,X10))=>s(X1,X2)=s(X1,X22))&(~(p(s(t_bool,X10)))=>s(X1,X3)=s(X1,X21))))=>s(X1,h4s_bools_cond(s(t_bool,X11),s(X1,X2),s(X1,X3)))=s(X1,h4s_bools_cond(s(t_bool,X10),s(X1,X22),s(X1,X21)))),file('i/f/list/SET__TO__LIST__SING', ah4s_bools_CONDu_u_CONG)).
fof(19, axiom,![X1]:![X14]:![X15]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X15),s(X1,X14)))=s(X1,X15),file('i/f/list/SET__TO__LIST__SING', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(20, axiom,![X1]:![X14]:![X15]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X15),s(X1,X14)))=s(X1,X14),file('i/f/list/SET__TO__LIST__SING', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(21, axiom,![X1]:![X2]:s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_RESTu_u_SING)).
fof(22, axiom,![X1]:![X12]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X12))))=>p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_rest(s(t_fun(X1,t_bool),X12))))))),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_FINITEu_u_REST)).
fof(23, axiom,![X1]:![X2]:s(X1,h4s_predu_u_sets_choice(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=s(X1,X2),file('i/f/list/SET__TO__LIST__SING', ah4s_predu_u_sets_CHOICEu_u_SING)).
# SZS output end CNFRefutation
