# 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(19, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(21, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(35, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/frac/FRAC__SGN__NOT__NEG', aHLu_BOOLu_CASES)).
fof(37, axiom,![X13]:![X6]:(s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X13)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),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,X6)))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(38, axiom,![X13]:![X6]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),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,X6)))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_GT)).
fof(39, axiom,![X14]:![X15]: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,X14))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(40, axiom,![X6]:?[X16]:((p(s(t_bool,X16))<=>s(t_h4s_integers_int,X6)=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_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,X16),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_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),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_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_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_intExtensions_SGNu_u_def)).
fof(41, 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(42, axiom,![X14]:![X15]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X15)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))<=>s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,X14)),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_INJ)).
fof(43, axiom,![X13]:![X6]:(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X13)))<=>s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X13)),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c1)).
fof(44, axiom,![X14]:![X15]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))=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,X15)))))<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X15)=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(45, axiom,![X14]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(46, axiom,![X14]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_numerals_numeralu_u_distribu_c17)).
fof(47, axiom,![X14]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_numerals_numeralu_u_equ_c1)).
fof(48, axiom,![X5]:![X2]:![X3]:s(X5,h4s_bools_cond(s(t_bool,t),s(X5,X3),s(X5,X2)))=s(X5,X3),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(49, axiom,![X5]:![X2]:![X3]:s(X5,h4s_bools_cond(s(t_bool,f),s(X5,X3),s(X5,X2)))=s(X5,X2),file('i/f/frac/FRAC__SGN__NOT__NEG', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
