# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/ZERO__LESS__EQ', ch4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/ZERO__LESS__EQ', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/ZERO__LESS__EQ', aHLu_FALSITY)).
fof(9, 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/ZERO__LESS__EQ', ah4s_primu_u_recs_LESSu_u_0)).
fof(10, axiom,![X1]:![X5]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/ZERO__LESS__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(11, 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/ZERO__LESS__EQ', ah4s_arithmetics_numu_u_CASES)).
fof(12, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/arithmetic/ZERO__LESS__EQ', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
