# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_fun(t_h4s_nums_num,t_bool),X1)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))=>(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_minu_u_set),s(t_fun(t_h4s_nums_num,t_bool),X1))),s(t_fun(t_h4s_nums_num,t_bool),X1))))&![X2]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_minu_u_set),s(t_fun(t_h4s_nums_num,t_bool),X1))),s(t_h4s_nums_num,X2))))))),file('i/f/pred_set/MIN__SET__LEM', ch4s_predu_u_sets_MINu_u_SETu_u_LEM)).
fof(28, axiom,![X2]:![X8]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X8),s(t_h4s_nums_num,X2))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X8),s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_whiles_least),s(t_fun(t_h4s_nums_num,t_bool),X8))))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_whiles_least),s(t_fun(t_h4s_nums_num,t_bool),X8))),s(t_h4s_nums_num,X2)))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_whiles_FULLu_u_LEASTu_u_INTRO)).
fof(29, axiom,s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_minu_u_set)=s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_whiles_least),file('i/f/pred_set/MIN__SET__LEM', ah4s_predu_u_sets_MINu_u_SETu_u_DEF)).
fof(31, axiom,![X5]:![X2]:![X21]:s(t_bool,h4s_bools_in(s(X5,X2),s(t_fun(X5,t_bool),X21)))=s(t_bool,happ(s(t_fun(X5,t_bool),X21),s(X5,X2))),file('i/f/pred_set/MIN__SET__LEM', ah4s_bools_INu_u_DEF)).
fof(32, axiom,![X5]:![X1]:(?[X2]:p(s(t_bool,h4s_bools_in(s(X5,X2),s(t_fun(X5,t_bool),X1))))<=>~(s(t_fun(X5,t_bool),X1)=s(t_fun(X5,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/MIN__SET__LEM', ah4s_predu_u_sets_MEMBERu_u_NOTu_u_EMPTY)).
fof(35, axiom,p(s(t_bool,t)),file('i/f/pred_set/MIN__SET__LEM', aHLu_TRUTH)).
fof(38, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/pred_set/MIN__SET__LEM', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
