# 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,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__THM', ch4s_arithmetics_FORALLu_u_NUMu_u_THM)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/FORALL__NUM__THM', aHLu_FALSITY)).
fof(23, 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__THM', ah4s_nums_INDUCTION)).
fof(24, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/FORALL__NUM__THM', aHLu_BOOLu_CASES)).
fof(26, axiom,p(s(t_bool,t)),file('i/f/arithmetic/FORALL__NUM__THM', aHLu_TRUTH)).
fof(28, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/FORALL__NUM__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
