# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(X1,h4s_binaryu_u_ieees_roundingu_u_case(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardpositive),s(X1,X5),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,X4),file('i/f/binary_ieee/rounding__case__def_c1', ch4s_binaryu_u_ieees_roundingu_u_caseu_u_defu_c1)).
fof(3, axiom,![X1]:![X7]:![X2]:![X3]:![X4]:![X5]:?[X8]:((p(s(t_bool,X8))<=>s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,X7)))=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(X1,h4s_binaryu_u_ieees_roundingu_u_case(s(t_h4s_binaryu_u_ieees_rounding,X7),s(X1,X5),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,X7))),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(X1,X5),s(X1,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,X7))),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(X1,X4),s(X1,h4s_bools_cond(s(t_bool,X8),s(X1,X3),s(X1,X2)))))))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_roundingu_u_CASE0)).
fof(6, axiom,s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardpositive)))=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/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_rounding2numu_u_thmu_c1)).
fof(8, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X10),s(X1,X9)))=s(X1,X10),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(9, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X10),s(X1,X9)))=s(X1,X9),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(11, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(24, axiom,![X16]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_num2rounding(s(t_h4s_nums_num,X16)))))=s(t_h4s_nums_num,X16)),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_rounding2numu_u_num2rounding)).
fof(25, axiom,![X24]:![X25]:s(t_bool,h4s_primu_u_recs_u_3c(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,X25)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X25))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_distribu_c22)).
fof(26, axiom,![X24]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X24)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X24))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_distribu_c21)).
fof(27, axiom,![X24]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_ltu_c2)).
fof(28, axiom,![X24]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X25))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X24)))))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_ltu_c5)).
fof(31, axiom,![X24]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X24)))))=s(t_bool,t),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_ltu_c1)).
fof(32, axiom,![X26]:?[X16]:(s(t_h4s_binaryu_u_ieees_rounding,X26)=s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_num2rounding(s(t_h4s_nums_num,X16)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_num2roundingu_u_ONTO)).
fof(34, axiom,![X16]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>?[X26]:s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,X26)))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_rounding2numu_u_ONTO)).
fof(36, axiom,![X24]:![X25]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X24))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X25)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X25))),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_numerals_numeralu_u_ltu_c3)).
fof(51, axiom,s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtiestoeven)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/binary_ieee/rounding__case__def_c1', ah4s_binaryu_u_ieees_rounding2numu_u_thmu_c0)).
# SZS output end CNFRefutation
