# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X1))))))&![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X1))))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2)))))))),file('i/f/while/LEAST__EXISTS__IMP', ch4s_whiles_LEASTu_u_EXISTSu_u_IMP)).
fof(7, axiom,![X1]:(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X1))))))&![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X1))))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2)))))))),file('i/f/while/LEAST__EXISTS__IMP', ah4s_whiles_LEASTu_u_EXISTS)).
# SZS output end CNFRefutation
