# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(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,h4s_rats_ratu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__AINV__0', ch4s_rats_RATu_u_AINVu_u_0)).
fof(20, 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,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0))),file('i/f/rat/RAT__AINV__0', ah4s_rats_ratu_u_00)).
fof(23, 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__AINV__0', ah4s_fracs_FRACu_u_DNMPOS)).
fof(25, axiom,![X19]: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_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,X19)))))))))=s(t_bool,t),file('i/f/rat/RAT__AINV__0', ah4s_integers_INTu_u_LTu_u_REDUCEu_c0)).
fof(26, axiom,![X18]:![X15]:(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,X18))))=>s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X18)))))))=s(t_h4s_integers_int,X15)),file('i/f/rat/RAT__AINV__0', ah4s_fracs_NMR)).
fof(28, axiom,![X18]:![X15]:(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,X18))))=>s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X18)))))))=s(t_h4s_integers_int,X18)),file('i/f/rat/RAT__AINV__0', ah4s_fracs_DNM)).
fof(29, axiom,![X19]:![X20]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X19)))=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,X20)))))<=>(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__AINV__0', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(33, axiom,![X21]:s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,X21)))))=s(t_h4s_rats_rat,h4s_rats_absu_u_rat(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,X21))))),file('i/f/rat/RAT__AINV__0', ah4s_rats_RATu_u_AINVu_u_CALCULATE)).
fof(38, axiom,p(s(t_bool,t)),file('i/f/rat/RAT__AINV__0', aHLu_TRUTH)).
fof(65, axiom,s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0)=s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(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_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__AINV__0', ah4s_fracs_fracu_u_0u_u_def)).
fof(67, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_1)=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__AINV__0', ah4s_integerRings_intu_u_rewritesu_c15)).
fof(72, axiom,![X19]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/rat/RAT__AINV__0', ah4s_integerRings_intu_u_rewritesu_c18)).
fof(76, axiom,![X19]:![X20]: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,X19))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X20)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20))),file('i/f/rat/RAT__AINV__0', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(80, axiom,![X21]:s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,X21)))=s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X21))))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X21))))))),file('i/f/rat/RAT__AINV__0', ah4s_fracs_fracu_u_ainvu_u_def)).
fof(81, axiom,![X17]:s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X17))),s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X17)))))))=s(t_h4s_fracs_frac,X17),file('i/f/rat/RAT__AINV__0', ah4s_fracs_FRAC)).
fof(91, axiom,![X7]:![X1]:![X2]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X2),s(X7,X1)))=s(X7,X1),file('i/f/rat/RAT__AINV__0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(94, axiom,![X19]:![X20]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20))))),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/rat/RAT__AINV__0', ah4s_integerRings_intu_u_rewritesu_c30)).
# SZS output end CNFRefutation
