# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,X1),s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_rats_rat,X1),file('i/f/rat/RAT__ADD__RID', ch4s_rats_RATu_u_ADDu_u_RID)).
fof(6, axiom,![X8]:![X6]: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,h4s_fracs_fracu_u_add(s(t_h4s_fracs_frac,X6),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,X8)))))))))=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,h4s_fracs_fracu_u_add(s(t_h4s_fracs_frac,X6),s(t_h4s_fracs_frac,X8))))),file('i/f/rat/RAT__ADD__RID', ah4s_rats_RATu_u_ADDu_u_CONGu_c1)).
fof(7, 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__ADD__RID', ah4s_rats_ratu_u_QUOTIENT)).
fof(8, axiom,![X9]:![X10]:s(t_h4s_rats_rat,h4s_rats_ratu_u_add(s(t_h4s_rats_rat,X10),s(t_h4s_rats_rat,X9)))=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,h4s_fracs_fracu_u_add(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,X10))),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,X9))))))),file('i/f/rat/RAT__ADD__RID', ah4s_rats_ratu_u_addu_u_def)).
fof(9, axiom,s(t_h4s_rats_rat,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))=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,h4s_fracs_fracu_u_0))),file('i/f/rat/RAT__ADD__RID', ah4s_rats_ratu_u_00)).
fof(11, axiom,![X11]:![X7]:![X12]:![X13]:![X14]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X7,t_fun(X7,t_bool)),X14),s(t_fun(X7,X11),X13),s(t_fun(X11,X7),X12))))<=>(![X1]:s(X11,happ(s(t_fun(X7,X11),X13),s(X7,happ(s(t_fun(X11,X7),X12),s(X11,X1)))))=s(X11,X1)&(![X1]:p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X14),s(X7,happ(s(t_fun(X11,X7),X12),s(X11,X1))))),s(X7,happ(s(t_fun(X11,X7),X12),s(X11,X1))))))&![X15]:![X16]:(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X14),s(X7,X15))),s(X7,X16))))<=>(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X14),s(X7,X15))),s(X7,X15))))&(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X14),s(X7,X16))),s(X7,X16))))&s(X11,happ(s(t_fun(X7,X11),X13),s(X7,X15)))=s(X11,happ(s(t_fun(X7,X11),X13),s(X7,X16))))))))),file('i/f/rat/RAT__ADD__RID', ah4s_quotients_QUOTIENTu_u_def)).
fof(13, axiom,![X1]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_add(s(t_h4s_fracs_frac,X1),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0)))=s(t_h4s_fracs_frac,X1),file('i/f/rat/RAT__ADD__RID', ah4s_fracs_FRACu_u_ADDu_u_RID)).
# SZS output end CNFRefutation
