# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X3))))),s(X1,X2)))=s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X3))))))),s(X1,happ(s(t_fun(X1,X1),X4),s(X1,X2))))),file('i/f/numeral/numeral__funpow_c1', ch4s_numerals_numeralu_u_funpowu_c1)).
fof(35, axiom,![X1]:![X2]:![X4]:s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),s(t_h4s_nums_num,h4s_nums_0),s(X1,X2)))=s(X1,X2),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_FUNPOW0u_c0)).
fof(36, axiom,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3))),s(X1,X2)))=s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),s(t_h4s_nums_num,X3),s(X1,happ(s(t_fun(X1,X1),X4),s(X1,X2))))),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_FUNPOW0u_c1)).
fof(37, axiom,![X1]:![X2]:![X4]:s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X4),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(X1,X2)))=s(X1,happ(s(t_fun(X1,X1),X4),s(X1,X2))),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_FUNPOWu_u_1)).
fof(46, axiom,![X25]:s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25)))))=s(t_h4s_nums_num,X25),file('i/f/numeral/numeral__funpow_c1', ah4s_primu_u_recs_PRE0u_c1)).
fof(47, axiom,s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__funpow_c1', ah4s_primu_u_recs_PRE0u_c0)).
fof(48, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X2),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(50, axiom,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_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_ONE)).
fof(54, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X3)))))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__funpow_c1', ah4s_numerals_numeralu_u_distribu_c9)).
fof(60, axiom,![X25]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_nums_0)))=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/numeral__funpow_c1', ah4s_arithmetics_EXP0u_c0)).
fof(62, axiom,![X25]:(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_0)|?[X3]:s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X3)))),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_numu_u_CASES)).
fof(80, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__funpow_c1', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
