# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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))))<=>?[X2]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))&![X3]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X3),s(t_fun(t_h4s_nums_num,t_bool),X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))))),file('i/f/pred_set/NUM__SET__WOP', ch4s_predu_u_sets_NUMu_u_SETu_u_WOP)).
fof(25, axiom,![X8]:![X20]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X20),s(t_h4s_nums_num,X8))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X20),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X20))))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X20))),s(t_h4s_nums_num,X8)))))),file('i/f/pred_set/NUM__SET__WOP', ah4s_whiles_FULLu_u_LEASTu_u_INTRO)).
fof(33, axiom,![X6]:![X8]:![X21]:s(t_bool,h4s_bools_in(s(X6,X8),s(t_fun(X6,t_bool),X21)))=s(t_bool,happ(s(t_fun(X6,t_bool),X21),s(X6,X8))),file('i/f/pred_set/NUM__SET__WOP', ah4s_bools_INu_u_DEF)).
fof(40, axiom,![X6]:![X20]:(~(?[X8]:p(s(t_bool,happ(s(t_fun(X6,t_bool),X20),s(X6,X8)))))<=>![X8]:~(p(s(t_bool,happ(s(t_fun(X6,t_bool),X20),s(X6,X8)))))),file('i/f/pred_set/NUM__SET__WOP', ah4s_bools_NOTu_u_EXISTSu_u_THM)).
# SZS output end CNFRefutation
