# 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,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(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', aHLu_TRUTH)).
fof(10, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(12, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(13, axiom,![X1]:~(p(s(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(14, axiom,![X1]:p(s(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(15, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/NOT__ZERO__LT__ZERO', aHLu_BOOLu_CASES)).
fof(17, axiom,![X7]:(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X7)=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)).
# SZS output end CNFRefutation
