# 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),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3))))<=>s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2))=>![X2]:s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,X2)),file('i/f/while/LEAST__EQ_c0', ch4s_whiles_LEASTu_u_EQu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/while/LEAST__EQ_c0', aHLu_TRUTH)).
fof(10, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/while/LEAST__EQ_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X20]:![X21]:((?[X3]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X21),s(t_h4s_nums_num,X3))))&![X3]:((![X22]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X3))))=>~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X21),s(t_h4s_nums_num,X22))))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X21),s(t_h4s_nums_num,X3)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X20),s(t_h4s_nums_num,X3))))))=>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),X21))))))),file('i/f/while/LEAST__EQ_c0', ah4s_whiles_LEASTu_u_ELIM)).
# SZS output end CNFRefutation
