# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X3),s(t_h4s_fracs_frac,X2))))&p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X2),s(t_h4s_fracs_frac,X1)))))=>p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X3),s(t_h4s_fracs_frac,X1))))),file('i/f/rat/RAT__EQUIV__TRANS', ch4s_rats_RATu_u_EQUIVu_u_TRANS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__EQUIV__TRANS', aHLu_TRUTH)).
fof(5, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, axiom,![X7]:![X8]:(p(s(t_bool,h4s_rats_ratu_u_equiv(s(t_h4s_fracs_frac,X8),s(t_h4s_fracs_frac,X7))))<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X8))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X7)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X7))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X8)))))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_rats_ratu_u_equivu_u_def)).
fof(7, axiom,![X9]:p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X9)))))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_fracs_FRACu_u_DNMPOS)).
fof(8, axiom,![X10]:![X5]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X10)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X5))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_integers_INTu_u_MULu_u_SYM)).
fof(9, axiom,![X11]:![X10]:![X5]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X11)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X10))),s(t_h4s_integers_int,X11))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_integers_INTu_u_MULu_u_ASSOC)).
fof(11, axiom,![X12]:![X2]:![X3]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X12))))=>(s(t_h4s_integers_int,X3)=s(t_h4s_integers_int,X2)<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X12)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X12))))),file('i/f/rat/RAT__EQUIV__TRANS', ah4s_intExtensions_INTu_u_EQu_u_RMULu_u_EXP)).
# SZS output end CNFRefutation
