# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/numeral_bit/LOG__compute', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/LOG__compute', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/numeral_bit/LOG__compute', aHLu_BOOLu_CASES)).
fof(17, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/numeral_bit/LOG__compute', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/numeral_bit/LOG__compute', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(19, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/numeral_bit/LOG__compute', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(36, axiom,![X21]:![X9]:![X6]:![X22]:s(X9,h4s_combins_fail(s(X9,X6),s(X21,X22)))=s(X9,X6),file('i/f/numeral_bit/LOG__compute', ah4s_combins_FAILu_u_DEF)).
fof(38, axiom,![X23]:![X24]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X23)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X23))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_LESSu_u_EQ)).
fof(39, axiom,![X23]:![X24]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X23)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24))))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_NOTu_u_LESS)).
fof(42, axiom,![X23]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X23)))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(43, axiom,![X20]:![X23]:![X24]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X20)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X20))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(44, axiom,![X23]:![X24]:(~(s(t_h4s_nums_num,X24)=s(t_h4s_nums_num,X23))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X23))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,X24)))))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(45, axiom,![X23]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X23))),file('i/f/numeral_bit/LOG__compute', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(46, axiom,![X23]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X23),file('i/f/numeral_bit/LOG__compute', ah4s_numerals_numeralu_u_distribu_c1)).
fof(47, axiom,![X23]:![X24]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X24)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24))))))),file('i/f/numeral_bit/LOG__compute', ah4s_numerals_numeralu_u_distribu_c2)).
fof(49, axiom,![X23]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X23)))))=s(t_h4s_nums_num,X23),file('i/f/numeral_bit/LOG__compute', ah4s_numerals_numeralu_u_addu_c0)).
fof(50, axiom,![X23]:![X24]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X24)))))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24))))))),file('i/f/numeral_bit/LOG__compute', ah4s_numerals_numeralu_u_addu_c2)).
fof(51, axiom,![X23]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/LOG__compute', ah4s_numerals_numeralu_u_lteu_c1)).
fof(52, axiom,![X23]:![X24]:((p(s(t_bool,h4s_primu_u_recs_u_3c(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,X24))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X23)))))=>s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24)))))))))),file('i/f/numeral_bit/LOG__compute', ah4s_logroots_LOGu_u_RWT)).
fof(53, conjecture,![X23]:![X24]:![X25]:?[X26]:((p(s(t_bool,X26))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),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,X23)=s(t_h4s_nums_num,h4s_nums_0)))&s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X23)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,X26),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_combins_fail(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_bool,X25))),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),h4s_logroots_log),s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X24)))))))))))),file('i/f/numeral_bit/LOG__compute', ch4s_numeralu_u_bits_LOGu_u_compute)).
# SZS output end CNFRefutation
