# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X1))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_cos),s(t_h4s_realaxs_real,X1))))))),file('i/f/transc/COS__POS__PI2__LE', ch4s_transcs_COSu_u_POSu_u_PI2u_u_LE)).
fof(2, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/transc/COS__POS__PI2__LE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X12]:![X1]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X12))))<=>(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X12))))&~(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X12)))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_LTu_u_LE)).
fof(12, axiom,p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_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/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_LEu_u_01)).
fof(14, axiom,![X12]:![X1]:(~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X12)))))<=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X1))))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_NOTu_u_LT)).
fof(16, axiom,![X13]:![X12]:![X1]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X12))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X13)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X13))))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_LTEu_u_TRANS)).
fof(24, axiom,s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_cos),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/transc/COS__POS__PI2__LE', ah4s_transcs_COSu_u_PI2)).
fof(28, axiom,![X1]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_realaxs_real,X1))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_cos),s(t_h4s_realaxs_real,X1))))))),file('i/f/transc/COS__POS__PI2__LE', ah4s_transcs_COSu_u_POSu_u_PI)).
fof(29, axiom,p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))),file('i/f/transc/COS__POS__PI2__LE', ah4s_transcs_PI2u_u_BOUNDSu_c0)).
fof(36, axiom,![X1]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X1))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_NEGu_u_LT0)).
fof(37, axiom,![X12]:![X1]:(s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X12)|(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X12))))|p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X1)))))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_LTu_u_TOTAL)).
fof(43, axiom,s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),h4s_transcs_cos),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_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/transc/COS__POS__PI2__LE', ah4s_transcs_COSu_u_0)).
fof(50, axiom,![X1]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_MULu_u_RZERO)).
fof(63, axiom,![X1]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/transc/COS__POS__PI2__LE', ah4s_reals_REALu_u_NEGu_u_EQ0)).
# SZS output end CNFRefutation
