# 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(3, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/pred_set/MIN__SET__LEM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(54, axiom,![X10]:![X25]:![X17]:(?[X2]:(s(X10,X2)=s(X10,X25)&p(s(t_bool,happ(s(t_fun(X10,t_bool),X17),s(X10,X2)))))<=>p(s(t_bool,happ(s(t_fun(X10,t_bool),X17),s(X10,X25))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_bools_UNWINDu_u_THM2)).
fof(60, axiom,![X20]:![X17]:((~(s(t_fun(t_h4s_nums_num,t_bool),X17)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))&![X2]:((![X7]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X7),s(t_fun(t_h4s_nums_num,t_bool),X17))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X7)))))&p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X17)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X20),s(t_h4s_nums_num,X2))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X20),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),X17))))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_predu_u_sets_MINu_u_SETu_u_ELIM)).
fof(61, axiom,![X1]:(?[X22]:p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X22),s(t_fun(t_h4s_nums_num,t_bool),X1))))<=>?[X22]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X22),s(t_fun(t_h4s_nums_num,t_bool),X1))))&![X23]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X23),s(t_fun(t_h4s_nums_num,t_bool),X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X23))))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_predu_u_sets_NUMu_u_SETu_u_WOP)).
fof(63, axiom,![X2]:![X17]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,X2))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),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),X17))))))&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),X17))),s(t_h4s_nums_num,X2)))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_whiles_FULLu_u_LEASTu_u_INTRO)).
fof(69, axiom,![X17]:(?[X22]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,X22))))=>?[X22]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,X22))))&![X23]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X22))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X17),s(t_h4s_nums_num,X23)))))))),file('i/f/pred_set/MIN__SET__LEM', ah4s_arithmetics_WOP)).
fof(73, axiom,![X10]:![X2]:![X17]:s(t_bool,h4s_bools_in(s(X10,X2),s(t_fun(X10,t_bool),X17)))=s(t_bool,happ(s(t_fun(X10,t_bool),X17),s(X10,X2))),file('i/f/pred_set/MIN__SET__LEM', ah4s_predu_u_sets_SPECIFICATION)).
fof(74, 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)).
# SZS output end CNFRefutation
