# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/numeral/TWO__EXP__THM_c2', ch4s_numerals_TWOu_u_EXPu_u_THMu_c2)).
fof(6, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(22, axiom,![X1]:s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),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/numeral/TWO__EXP__THM_c2', ah4s_numerals_texpu_u_help0)).
fof(23, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(33, 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,X1))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),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)))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_DIVMODu_u_ID)).
fof(40, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_ALTu_u_ZERO)).
fof(44, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_numerals_numeralu_u_sucu_c0)).
fof(45, axiom,![X1]:![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X1))))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(46, axiom,![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X23),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(48, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_BIT10)).
fof(53, axiom,![X23]:(s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_numu_u_CASES)).
fof(55, axiom,![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
fof(63, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_numerals_numeralu_u_sucu_c1)).
fof(66, axiom,![X1]:![X23]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X1))))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_arithmetics_EXP0u_c1)).
fof(69, axiom,~(p(s(t_bool,f))),file('i/f/numeral/TWO__EXP__THM_c2', aHLu_FALSITY)).
fof(75, 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/numeral/TWO__EXP__THM_c2', ah4s_primu_u_recs_LESSu_u_0)).
fof(80, axiom,![X10]:(s(t_bool,f)=s(t_bool,X10)<=>~(p(s(t_bool,X10)))),file('i/f/numeral/TWO__EXP__THM_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
