# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', aHLu_FALSITY)).
fof(6, axiom,![X6]:![X8]:((((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=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,X6),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,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,X6)=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,X6)))=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,X6)))))=>p(s(t_bool,X8)))))=>p(s(t_bool,X8))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_intExtensions_INTu_u_SGNu_u_CASES0)).
fof(9, axiom,![X6]:(s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=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,X6),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_c2', ah4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c0)).
fof(10, axiom,![X6]:(s(t_h4s_integers_int,h4s_intextensions_sgn(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,X6)=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_c2', ah4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c1)).
fof(12, axiom,![X10]:![X6]:s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X6))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_intu_u_gt0)).
fof(15, 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/intExtension/INT__SGN__CLAUSES_c2', ah4s_numerals_numeralu_u_distribu_c17)).
fof(18, 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/intExtension/INT__SGN__CLAUSES_c2', ah4s_numerals_numeralu_u_equ_c1)).
fof(21, 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/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(32, axiom,![X11]: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_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,X11)))))))))=s(t_bool,f),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_INTu_u_LTu_u_REDUCEu_c3)).
fof(43, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(87, axiom,![X10]:![X6]:(s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X10)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10))))|p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X6)))))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(111, axiom,![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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>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)))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_INTu_u_NEGu_u_EQ0)).
fof(122, axiom,![X11]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_numerals_numeralu_u_distribu_c27)).
fof(123, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_numerals_numeralu_u_distribu_c1)).
fof(124, axiom,![X11]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_nums_num,X11))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(126, axiom,![X10]:![X6]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10))))=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X6)))))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_integers_INTu_u_LTu_u_GT)).
fof(127, axiom,![X11]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_nums_0)),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(128, axiom,![X11]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(133, conjecture,![X6]:(s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=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_gt(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))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c2', ch4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
