# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X1)))=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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>(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)))|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_nmr(s(t_h4s_fracs_frac,X1)))))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ch4s_fracs_FRACu_u_SGNu_u_NOTu_u_NEG)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/frac/FRAC__SGN__NOT__NEG', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/frac/FRAC__SGN__NOT__NEG', aHLu_FALSITY)).
fof(7, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(30, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(34, axiom,![X13]:![X3]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X13))))=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,X3)))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_GT)).
fof(42, axiom,![X13]:![X3]:(~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X13)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),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/frac/FRAC__SGN__NOT__NEG', ah4s_intu_u_ariths_notu_u_less)).
fof(52, axiom,![X1]:(s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X1)))=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)))))))<=>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_nmr(s(t_h4s_fracs_frac,X1))))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_fracs_FRACu_u_SGNu_u_POS)).
fof(56, axiom,![X12]:![X18]: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,X12))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X18))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(57, axiom,![X3]:(s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X3)))=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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c0)).
fof(58, axiom,![X3]:![X24]:((((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X3)))=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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))=>p(s(t_bool,X24)))&(((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X3)))=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,X3)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>p(s(t_bool,X24)))&((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X3)))=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)))))))&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,X3)))))=>p(s(t_bool,X24)))))=>p(s(t_bool,X24))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_intExtensions_INTu_u_SGNu_u_CASES0)).
fof(60, axiom,![X13]:![X3]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X13))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,X3)))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_intu_u_le0)).
fof(64, axiom,![X13]:![X3]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X13)))))=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,X13))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_ADDR)).
fof(65, axiom,![X1]:s(t_h4s_integers_int,h4s_fracs_fracu_u_sgn(s(t_h4s_fracs_frac,X1)))=s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,h4s_fracs_fracu_u_nmr(s(t_h4s_fracs_frac,X1))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_fracs_fracu_u_sgnu_u_def)).
fof(70, axiom,![X26]:s(t_h4s_integers_int,h4s_fracs_fracu_u_dnm(s(t_h4s_fracs_frac,X26)))=s(t_h4s_integers_int,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,X26))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_fracs_fracu_u_dnmu_u_def)).
fof(71, axiom,![X19]:s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,X19)))))=s(t_h4s_fracs_frac,X19),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_fracs_fracu_u_biju_c0)).
fof(72, axiom,![X7]:(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_pairs_snd(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),X7))))))<=>s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_fracs_repu_u_frac(s(t_h4s_fracs_frac,h4s_fracs_absu_u_frac(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),X7)))))=s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),X7)),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_fracs_fracu_u_biju_c1)).
fof(73, axiom,![X12]:![X18]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))=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,X18)))))<=>(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(74, axiom,![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),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,X3),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(75, axiom,![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X3))),s(t_h4s_integers_int,X3)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_ADDu_u_LINV)).
fof(78, axiom,![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X3)))))=s(t_h4s_integers_int,X3),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_NEGNEG)).
# SZS output end CNFRefutation
