# 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,p(s(t_bool,t)),file('i/f/arithmetic/FORALL__NUM', aHLu_TRUTH)).
fof(18, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/FORALL__NUM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/arithmetic/FORALL__NUM', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(47, axiom,![X21]:(s(t_h4s_nums_num,X21)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X21)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/FORALL__NUM', ah4s_arithmetics_numu_u_CASES)).
# SZS output end CNFRefutation
