# 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', ch4s_whiles_LEASTu_u_EXISTS)).
fof(21, axiom,![X16]:![X15]:![X19]:(p(s(t_bool,happ(s(t_fun(X16,t_bool),X19),s(X16,X15))))=>p(s(t_bool,happ(s(t_fun(X16,t_bool),X19),s(X16,h4s_mins_u_40(s(t_fun(X16,t_bool),X19))))))),file('i/f/while/LEAST__EXISTS', ah4s_bools_SELECTu_u_AX)).
fof(23, axiom,![X15]:![X19]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X19),s(t_h4s_nums_num,X15))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X19),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X19))))))),file('i/f/while/LEAST__EXISTS', ah4s_whiles_LEASTu_u_INTRO)).
fof(24, axiom,![X20]:![X19]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),X19))))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X19),s(t_h4s_nums_num,X20)))))),file('i/f/while/LEAST__EXISTS', ah4s_whiles_LESSu_u_LEAST)).
fof(26, axiom,![X16]:![X15]:s(t_bool,d_exists(s(t_fun(X16,t_bool),X15)))=s(t_bool,happ(s(t_fun(X16,t_bool),X15),s(X16,h4s_mins_u_40(s(t_fun(X16,t_bool),X15))))),file('i/f/while/LEAST__EXISTS', ah4s_bools_EXISTSu_u_DEF)).
fof(27, axiom,p(s(t_bool,t)),file('i/f/while/LEAST__EXISTS', aHLu_TRUTH)).
fof(29, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/while/LEAST__EXISTS', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
