# 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_c1', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/intExtension/INT__SGN__CLAUSES_c1', aHLu_BOOLu_CASES)).
fof(13, axiom,![X1]:(s(t_bool,t)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(15, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(16, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(17, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(18, 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_c1', ah4s_numerals_numeralu_u_distribu_c17)).
fof(19, 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_c1', ah4s_numerals_numeralu_u_equ_c1)).
fof(20, axiom,![X11]:![X12]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X11)))<=>s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X11)),file('i/f/intExtension/INT__SGN__CLAUSES_c1', ah4s_integers_INTu_u_INJ)).
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_c1', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(22, axiom,![X6]:?[X13]:((p(s(t_bool,X13))<=>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,X13),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/intExtension/INT__SGN__CLAUSES_c1', ah4s_intExtensions_SGNu_u_def)).
fof(23, 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_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_c1', ch4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
