# 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_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_nums_0)))|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))))))))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ch4s_fracs_FRACu_u_SGNu_u_IMPu_u_EQGT)).
fof(15, axiom,![X11]:![X12]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X11)))=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,X12)))))<=>(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(28, 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_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_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_nums_0)))|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))))))))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_fracs_FRACu_u_SGNu_u_TOTAL)).
fof(35, axiom,![X11]:![X12]: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,X11))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(37, axiom,![X11]:(~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X11),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_nums_0)))=s(t_h4s_integers_int,X11)|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,X11)))))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_intExtensions_INTu_u_NOTGTu_u_IMPu_u_EQLT)).
fof(38, axiom,![X7]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(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)))))=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,X7))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_integers_INTu_u_NEGu_u_LT0)).
fof(43, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_numerals_numeralu_u_distribu_c17)).
fof(49, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(52, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_numerals_numeralu_u_equ_c1)).
fof(53, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))))=s(t_bool,t),file('i/f/frac/FRAC__SGN__IMP__EQGT', ah4s_numerals_numeralu_u_ltu_c0)).
fof(67, axiom,~(p(s(t_bool,f))),file('i/f/frac/FRAC__SGN__IMP__EQGT', aHLu_FALSITY)).
fof(80, axiom,p(s(t_bool,t)),file('i/f/frac/FRAC__SGN__IMP__EQGT', aHLu_TRUTH)).
# SZS output end CNFRefutation
