# 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_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c9', ch4s_numerals_numeralu_u_distribu_c9)).
fof(2, 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__distrib_c9', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(23, axiom,![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/numeral/numeral__distrib_c9', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(28, 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/numeral__distrib_c9', ah4s_arithmetics_BIT10)).
fof(30, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit2(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_suc(s(t_h4s_nums_num,h4s_nums_0))))))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_BIT20)).
fof(32, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_ALTu_u_ZERO)).
fof(35, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),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__distrib_c9', ah4s_arithmetics_EXP0u_c0)).
fof(36, axiom,![X1]:![X17]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17)))=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,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,X17)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_EXPu_u_EQu_u_1)).
fof(40, axiom,![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_numu_u_CASES)).
fof(41, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numeral/numeral__distrib_c9', ah4s_nums_NOTu_u_SUC)).
fof(42, 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__distrib_c9', ah4s_arithmetics_ONE)).
fof(43, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_MULTu_c0)).
fof(51, axiom,![X1]:![X17]:(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_0)<=>(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,X17)))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_EXPu_u_EQu_u_0)).
fof(54, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_exp(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,X1),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_EXPu_u_1u_c1)).
fof(64, axiom,![X1]:![X17]:(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X1)),file('i/f/numeral/numeral__distrib_c9', ah4s_primu_u_recs_INVu_u_SUCu_u_EQ)).
fof(67, axiom,![X1]:![X17]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_NOTu_u_LESS)).
fof(74, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),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,X17),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_EXP0u_c1)).
fof(75, axiom,![X11]:![X12]:![X1]:s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_EXPu_u_ADD)).
fof(76, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_TIMES2)).
fof(77, axiom,![X4]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,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(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)))))&s(t_h4s_nums_num,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))))))),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_MULTu_u_EQu_u_1)).
fof(78, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),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,X17),file('i/f/numeral/numeral__distrib_c9', ah4s_arithmetics_MULTu_u_RIGHTu_u_1)).
fof(80, 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/numeral__distrib_c9', ah4s_numerals_numeralu_u_sucu_c1)).
# SZS output end CNFRefutation
