# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))<=>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)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ch4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(8, axiom,![X1]:~(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)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(12, axiom,![X1]: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)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_primu_u_recs_LESSu_u_0)).
fof(42, axiom,![X5]:(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_arithmetics_numu_u_CASES)).
fof(58, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
