# 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_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))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ch4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/intExtension/INT__SGN__CLAUSES_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', aHLu_FALSITY)).
fof(12, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(14, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(15, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/intExtension/INT__SGN__CLAUSES_c0', aHLu_BOOLu_CASES)).
fof(17, axiom,![X7]:![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,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(18, axiom,![X1]:?[X9]:((p(s(t_bool,X9))<=>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,X9),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_c0', ah4s_intExtensions_SGNu_u_def)).
fof(20, axiom,![X7]:![X8]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7)))=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,X8)))))<=>(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(21, axiom,![X7]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(22, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_distribu_c17)).
fof(23, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_equ_c1)).
fof(25, 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/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(26, 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/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
