# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/extreal/REAL__LT__LMUL__0__NEG', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', 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/extreal/REAL__LT__LMUL__0__NEG', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X6]:(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,X6))))=>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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))))=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,X7)))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LTu_u_LMULu_u_0)).
fof(8, axiom,![X7]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_MULu_u_SYM)).
fof(9, axiom,s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_0)).
fof(11, axiom,![X7]:![X6]:((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,X6))))&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,X7)))))=>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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LTu_u_MUL)).
fof(13, axiom,![X6]: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_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_GT0)).
fof(14, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,X6),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGNEG)).
fof(16, axiom,![X6]:(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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X6))))))<=>~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_POASQ)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(26, axiom,![X7]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))=>~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X7))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(27, axiom,![X6]:(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,X6))))=>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_realaxs_inv(s(t_h4s_realaxs_real,X6))))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_INVu_u_POS)).
fof(31, axiom,![X18]:![X7]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X18)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,X18))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_MULu_u_ASSOC)).
fof(33, axiom,![X7]:![X6]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6)))))<=>s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X7)),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(35, axiom,![X7]:![X6]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))=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,X6)=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,X7)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_ENTIRE)).
fof(37, axiom,![X7]:![X6]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(43, axiom,![X7]:![X6]:(~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))))<=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NOTu_u_LT)).
fof(45, axiom,![X7]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(50, axiom,![X6]:(~(s(t_h4s_realaxs_real,X6)=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_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_INV)).
fof(51, axiom,![X6]:s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_bools_cond(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,X6))),s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_abs0)).
fof(53, axiom,![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=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,X6))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_LE0)).
fof(54, axiom,![X7]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_RMUL)).
fof(55, axiom,![X8]:![X16]:![X17]:s(X8,h4s_bools_cond(s(t_bool,f),s(X8,X17),s(X8,X16)))=s(X8,X16),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(79, axiom,![X7]:![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X7)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_LEu_u_NEG)).
fof(81, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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))))))))),s(t_h4s_realaxs_real,X6))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_MINUS1)).
fof(82, axiom,s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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/extreal/REAL__LT__LMUL__0__NEG', ah4s_reals_REALu_u_NEGu_u_0)).
fof(109, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(133, conjecture,![X7]:![X6]:((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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/extreal/REAL__LT__LMUL__0__NEG', ch4s_extreals_REALu_u_LTu_u_LMULu_u_0u_u_NEG)).
# SZS output end CNFRefutation
