# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1))))=>~(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X1),s(t_h4s_rats_rat,X2)))))),file('i/f/rat/RAT__LES__ANTISYM', ch4s_rats_RATu_u_LESu_u_ANTISYM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__LES__ANTISYM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/rat/RAT__LES__ANTISYM', aHLu_FALSITY)).
fof(12, axiom,![X1]:![X2]:(p(s(t_bool,h4s_rats_ratu_u_les(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1))))<=>s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,X1),s(t_h4s_rats_rat,X2)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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/rat/RAT__LES__ANTISYM', ah4s_rats_ratu_u_lesu_u_def)).
fof(13, axiom,![X12]:s(t_h4s_integers_int,h4s_rats_ratu_u_sgn(s(t_h4s_rats_rat,X12)))=s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X12))))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_rats_ratu_u_sgnu_u_def)).
fof(14, axiom,![X1]:![X2]:s(t_h4s_rats_rat,h4s_rats_ratu_u_sub(s(t_h4s_rats_rat,X2),s(t_h4s_rats_rat,X1)))=s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X2))),s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,X1))))))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_rats_ratu_u_subu_u_def)).
fof(15, axiom,![X13]:s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,h4s_rats_repu_u_rat(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X13)))))))=s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X13))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_rats_RATu_u_SGNu_u_CONG)).
fof(16, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/rat/RAT__LES__ANTISYM', aHLu_BOOLu_CASES)).
fof(17, axiom,![X14]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_numerals_numeralu_u_equ_c1)).
fof(18, axiom,![X14]:![X15]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X15)))))<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(19, axiom,![X14]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/rat/RAT__LES__ANTISYM', ah4s_numerals_numeralu_u_distribu_c17)).
fof(21, axiom,![X16]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,X16)))))))=s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X16))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_fracs_FRACu_u_SGNu_u_NEG)).
fof(22, axiom,![X17]:![X13]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,X17),s(t_h4s_fracs_frac,X13)))))=s(t_h4s_fracs_frac,h4s_fracs_fracu_u_sub(s(t_h4s_fracs_frac,X13),s(t_h4s_fracs_frac,X17))),file('i/f/rat/RAT__LES__ANTISYM', ah4s_fracs_FRACu_u_AINVu_u_SUB)).
# SZS output end CNFRefutation
