# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2))))))=>p(s(t_bool,h4s_arithmetics_modeq(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_arithmetics_bit1(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))))))))))),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ch4s_arithmetics_MODEQu_u_NUMERALu_c3)).
fof(34, axiom,![X1]:![X21]:![X22]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(44, 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))))=>![X32]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X32),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X32),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_MODu_u_MOD)).
fof(48, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(49, 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/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_BIT20)).
fof(51, axiom,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_nums_suc(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/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_TWO)).
fof(52, 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/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_BIT10)).
fof(54, 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/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_ONE)).
fof(55, 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/arithmetic/MODEQ__NUMERAL_c3', ah4s_primu_u_recs_LESSu_u_0)).
fof(56, 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/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(59, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(60, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),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,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(61, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/MODEQ__NUMERAL_c3', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
