# 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))=>?[X2]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/bit/NOT__ZERO__ADD1', ch4s_bits_NOTu_u_ZEROu_u_ADD1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bit/NOT__ZERO__ADD1', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bit/NOT__ZERO__ADD1', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/bit/NOT__ZERO__ADD1', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/bit/NOT__ZERO__ADD1', ah4s_arithmetics_ADDu_c0)).
fof(7, axiom,![X7]:(~(s(t_h4s_nums_num,X7)=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,X7))))),file('i/f/bit/NOT__ZERO__ADD1', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(8, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/bit/NOT__ZERO__ADD1', ah4s_arithmetics_ADD1)).
fof(9, axiom,![X7]:![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X1))))=>?[X2]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/bit/NOT__ZERO__ADD1', ah4s_arithmetics_LESSu_u_ADDu_u_1)).
# SZS output end CNFRefutation
