# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,happ(s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat),s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,X1)))))))=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_nmr(s(t_h4s_fracs_frac,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/rat/RAT__NMREQ0__CONG', ch4s_rats_RATu_u_NMREQ0u_u_CONG)).
fof(2, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(15, axiom,![X14]:![X1]:(p(s(t_bool,happ(s(t_fun(t_h4s_fracs_frac,t_bool),happ(s(t_fun(t_h4s_fracs_frac,t_fun(t_h4s_fracs_frac,t_bool)),h4s_rats_ratu_u_equiv),s(t_h4s_fracs_frac,X1))),s(t_h4s_fracs_frac,X14))))<=>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,X1))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X14)))))=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,X14))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X1)))))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_rats_ratu_u_equivu_u_def)).
fof(18, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_fracs_frac,t_fun(t_h4s_fracs_frac,t_bool)),h4s_rats_ratu_u_equiv),s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat)))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_rats_ratu_u_QUOTIENT)).
fof(19, axiom,![X7]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,X7)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(20, axiom,![X17]: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,X17)))))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_fracs_FRACu_u_DNMPOS)).
fof(21, axiom,![X20]:![X5]:![X21]:![X22]:![X23]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X23),s(t_fun(X5,X20),X22),s(t_fun(X20,X5),X21))))<=>(![X24]:s(X20,happ(s(t_fun(X5,X20),X22),s(X5,happ(s(t_fun(X20,X5),X21),s(X20,X24)))))=s(X20,X24)&(![X24]:p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X23),s(X5,happ(s(t_fun(X20,X5),X21),s(X20,X24))))),s(X5,happ(s(t_fun(X20,X5),X21),s(X20,X24))))))&![X11]:![X25]:(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X23),s(X5,X11))),s(X5,X25))))<=>(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X23),s(X5,X11))),s(X5,X11))))&(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X23),s(X5,X25))),s(X5,X25))))&s(X20,happ(s(t_fun(X5,X20),X22),s(X5,X11)))=s(X20,happ(s(t_fun(X5,X20),X22),s(X5,X25))))))))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_quotients_QUOTIENTu_u_def)).
fof(22, axiom,![X26]:![X27]:![X24]:(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,X26))))=>(s(t_h4s_integers_int,X24)=s(t_h4s_integers_int,X27)<=>s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X24),s(t_h4s_integers_int,X26)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X27),s(t_h4s_integers_int,X26))))),file('i/f/rat/RAT__NMREQ0__CONG', ah4s_intExtensions_INTu_u_EQu_u_RMULu_u_EXP)).
# SZS output end CNFRefutation
