# 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),X2),s(t_h4s_nums_num,X1))))=>(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))))))&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),X2))),s(t_h4s_nums_num,X1)))))),file('i/f/while/FULL__LEAST__INTRO', ch4s_whiles_FULLu_u_LEASTu_u_INTRO)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/while/FULL__LEAST__INTRO', aHLu_FALSITY)).
fof(17, axiom,![X9]:![X10]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))))),file('i/f/while/FULL__LEAST__INTRO', ah4s_arithmetics_NOTu_u_LESS)).
fof(18, axiom,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X1))))=>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/FULL__LEAST__INTRO', ah4s_whiles_LEASTu_u_INTRO)).
fof(19, axiom,![X10]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),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,X10)))))),file('i/f/while/FULL__LEAST__INTRO', ah4s_whiles_LESSu_u_LEAST)).
fof(21, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/while/FULL__LEAST__INTRO', aHLu_BOOLu_CASES)).
fof(22, axiom,p(s(t_bool,t)),file('i/f/while/FULL__LEAST__INTRO', aHLu_TRUTH)).
fof(24, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/while/FULL__LEAST__INTRO', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
