# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,X1)))))=s(t_h4s_rats_rat,X1),file('i/f/rat/RAT__AINV__AINV', ch4s_rats_RATu_u_AINVu_u_AINV)).
fof(6, axiom,![X8]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,X8)))))=s(t_h4s_fracs_frac,X8),file('i/f/rat/RAT__AINV__AINV', ah4s_fracs_FRACu_u_AINVu_u_AINV)).
fof(7, axiom,![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_ainv(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,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_ainv(s(t_h4s_fracs_frac,X6))))),file('i/f/rat/RAT__AINV__AINV', ah4s_rats_RATu_u_AINVu_u_CONG)).
fof(8, 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__AINV__AINV', ah4s_rats_ratu_u_QUOTIENT)).
fof(9, axiom,![X1]:s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,X1)))=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_ainv(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,X1))))))),file('i/f/rat/RAT__AINV__AINV', ah4s_rats_ratu_u_ainvu_u_def)).
fof(11, axiom,![X9]:![X7]:![X10]:![X11]:![X12]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X7,t_fun(X7,t_bool)),X12),s(t_fun(X7,X9),X11),s(t_fun(X9,X7),X10))))<=>(![X13]:s(X9,happ(s(t_fun(X7,X9),X11),s(X7,happ(s(t_fun(X9,X7),X10),s(X9,X13)))))=s(X9,X13)&(![X13]:p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X12),s(X7,happ(s(t_fun(X9,X7),X10),s(X9,X13))))),s(X7,happ(s(t_fun(X9,X7),X10),s(X9,X13))))))&![X14]:![X15]:(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X12),s(X7,X14))),s(X7,X15))))<=>(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X12),s(X7,X14))),s(X7,X14))))&(p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X12),s(X7,X15))),s(X7,X15))))&s(X9,happ(s(t_fun(X7,X9),X11),s(X7,X14)))=s(X9,happ(s(t_fun(X7,X9),X11),s(X7,X15))))))))),file('i/f/rat/RAT__AINV__AINV', ah4s_quotients_QUOTIENTu_u_def)).
# SZS output end CNFRefutation
