# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,~(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_1)=s(t_h4s_fracs_frac,h4s_fracs_fracu_u_0)),file('i/f/frac/FRAC__1__0', ch4s_fracs_FRACu_u_1u_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/frac/FRAC__1__0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/frac/FRAC__1__0', aHLu_FALSITY)).
fof(4, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/frac/FRAC__1__0', aHLu_BOOLu_CASES)).
fof(9, axiom,![X2]:![X4]:![X5]:![X3]:![X6]:![X7]:(s(t_h4s_pairs_prod(X2,X4),h4s_pairs_u_2c(s(X2,X3),s(X4,X5)))=s(t_h4s_pairs_prod(X2,X4),h4s_pairs_u_2c(s(X2,X7),s(X4,X6)))<=>(s(X2,X3)=s(X2,X7)&s(X4,X5)=s(X4,X6))),file('i/f/frac/FRAC__1__0', ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ)).
fof(10, axiom,![X8]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/frac/FRAC__1__0', ah4s_numerals_numeralu_u_distribu_c17)).
fof(11, axiom,![X8]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/frac/FRAC__1__0', ah4s_numerals_numeralu_u_equ_c1)).
fof(12, axiom,![X8]:![X9]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X9)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))<=>s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,X8)),file('i/f/frac/FRAC__1__0', ah4s_integers_INTu_u_INJ)).
fof(13, 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/frac/FRAC__1__0', ah4s_fracs_fracu_u_0u_u_def)).
fof(14, axiom,s(t_h4s_fracs_frac,h4s_fracs_fracu_u_1)=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_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__1__0', ah4s_fracs_fracu_u_1u_u_def)).
fof(15, axiom,![X10]:![X11]:![X12]:![X13]:(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))))=>(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,X10))))=>(~(s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,X13),s(t_h4s_integers_int,X11)))=s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_integers_int),h4s_pairs_u_2c(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X10))))=>~(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,X13),s(t_h4s_integers_int,X11)))))=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,X12),s(t_h4s_integers_int,X10))))))))),file('i/f/frac/FRAC__1__0', ah4s_fracs_FRACu_u_NOTu_u_EQ)).
fof(16, axiom,![X8]: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,X8)))))))))=s(t_bool,t),file('i/f/frac/FRAC__1__0', ah4s_integers_INTu_u_LTu_u_REDUCEu_c0)).
# SZS output end CNFRefutation
