# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,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,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ch4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c1)).
fof(6, axiom,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_nums_0)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_integers_INTu_u_NEGu_u_0)).
fof(9, axiom,![X1]:?[X7]:((p(s(t_bool,X7))<=>s(t_h4s_integers_int,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_intextensions_sgn(s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,X7),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,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_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/intExtension/INT__SGN__CLAUSES_c1', ah4s_intExtensions_SGNu_u_def)).
fof(10, axiom,![X1]:![X8]:((((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,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)))))))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))=>p(s(t_bool,X8)))&(((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,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,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>p(s(t_bool,X8)))&((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,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,X1)))))=>p(s(t_bool,X8)))))=>p(s(t_bool,X8))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_intExtensions_INTu_u_SGNu_u_CASES0)).
fof(13, axiom,![X1]:(~(s(t_h4s_integers_int,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_intextensions_sgn(s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_intExtensions_INTu_u_NOT0u_u_SGNNOT0)).
fof(18, axiom,![X2]:![X9]:![X10]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X10),s(X2,X9)))=s(X2,X10),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(20, axiom,![X14]:![X15]:![X16]:![X6]:(s(t_bool,X6)=s(t_bool,h4s_bools_cond(s(t_bool,X16),s(t_bool,X15),s(t_bool,X14)))<=>((p(s(t_bool,X6))|(p(s(t_bool,X16))|~(p(s(t_bool,X14)))))&((p(s(t_bool,X6))|(~(p(s(t_bool,X15)))|~(p(s(t_bool,X16)))))&((p(s(t_bool,X6))|(~(p(s(t_bool,X15)))|~(p(s(t_bool,X14)))))&((~(p(s(t_bool,X16)))|(p(s(t_bool,X15))|~(p(s(t_bool,X6)))))&(p(s(t_bool,X16))|(p(s(t_bool,X14))|~(p(s(t_bool,X6)))))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_sats_dcu_u_cond)).
fof(28, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
# SZS output end CNFRefutation
