# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((?[X3]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X3))))&![X3]:((![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X4))))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X3)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X3))))))=>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),X2))))))),file('i/f/while/LEAST__ELIM', ch4s_whiles_LEASTu_u_ELIM)).
fof(22, axiom,![X18]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X18))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X2))))))),file('i/f/while/LEAST__ELIM', ah4s_whiles_LEASTu_u_INTRO)).
fof(23, axiom,![X4]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X2))))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X4)))))),file('i/f/while/LEAST__ELIM', ah4s_whiles_LESSu_u_LEAST)).
# SZS output end CNFRefutation
