# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral/numeral__mult_c0', ch4s_numerals_numeralu_u_multu_c0)).
fof(5, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,X5)))=s(t_h4s_nums_num,X5),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_MULTu_u_CLAUSESu_c2)).
fof(8, axiom,![X3]:![X4]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),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__mult_c0', ah4s_arithmetics_LEu_u_LT1)).
fof(9, 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__mult_c0', ah4s_arithmetics_ONE)).
fof(11, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_MULTu_c1)).
fof(13, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_MULTu_u_0)).
fof(14, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),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,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_MULTu_u_SUC)).
fof(21, axiom,![X1]:![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,h4s_nums_0),s(t_h4s_nums_num,X5))))&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__mult_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_MULT)).
fof(22, 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/numeral__mult_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(23, 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__mult_c0', ah4s_arithmetics_BIT10)).
fof(47, axiom,![X1]:![X5]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),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,X5))))),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_NOTu_u_LESS)).
fof(51, axiom,![X1]:![X5]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))))),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(52, 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,X1),s(t_h4s_nums_num,X5))))),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(53, axiom,![X1]:~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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__mult_c0', ah4s_arithmetics_NOTu_u_SUCu_u_LESSu_u_EQu_u_0)).
fof(56, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X5),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(58, 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__mult_c0', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(59, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X5),file('i/f/numeral/numeral__mult_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(61, 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/numeral/numeral__mult_c0', ah4s_arithmetics_numu_u_CASES)).
# SZS output end CNFRefutation
