# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_bit1(s(t_h4s_nums_num,X1))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(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_bit2(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,X1))))))))))),file('i/f/arithmetic/MODEQ__NUMERAL_c1', ch4s_arithmetics_MODEQu_u_NUMERALu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__NUMERAL_c1', aHLu_TRUTH)).
fof(7, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/MODEQ__NUMERAL_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, 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_c1', ah4s_primu_u_recs_LESSu_u_0)).
fof(11, 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))))=>![X12]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),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,X12),s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/MODEQ__NUMERAL_c1', ah4s_arithmetics_MODu_u_MOD)).
fof(13, axiom,![X1]:![X13]:![X14]:(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,X14),s(t_h4s_nums_num,X13))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__NUMERAL_c1', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(14, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X5),file('i/f/arithmetic/MODEQ__NUMERAL_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(15, 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_c1', ah4s_arithmetics_BIT10)).
fof(17, 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_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(18, 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_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(19, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__NUMERAL_c1', aHLu_BOOLu_CASES)).
fof(20, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__NUMERAL_c1', aHLu_FALSITY)).
# SZS output end CNFRefutation
