# 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_nums_0))))&![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))))),file('i/f/arithmetic/FORALL__NUM', ch4s_arithmetics_FORALLu_u_NUM)).
fof(2, axiom,![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,h4s_nums_0))))&![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_nums_suc(s(t_h4s_nums_num,X2))))))))=>![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),X1),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/FORALL__NUM', ah4s_nums_INDUCTION)).
# SZS output end CNFRefutation
