# 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__NEG__0__NEG', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/REAL__LT__LMUL__NEG__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__NEG__0__NEG', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X6]:((p(s(t_bool,h4s_realaxs_realu_u_lt(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))))))&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,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__NEG__0__NEG', ah4s_extreals_REALu_u_LTu_u_RMULu_u_NEGu_u_0)).
fof(8, 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__NEG__0__NEG', ah4s_reals_REALu_u_NEGu_u_GT0)).
fof(9, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/extreal/REAL__LT__LMUL__NEG__0__NEG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(35, axiom,![X6]:s(t_bool,h4s_realaxs_realu_u_lt(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_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))),file('i/f/extreal/REAL__LT__LMUL__NEG__0__NEG', ah4s_reals_REALu_u_NEGu_u_LT0)).
fof(38, 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__NEG__0__NEG', ah4s_reals_REALu_u_NEGu_u_RMUL)).
fof(41, 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,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X7))),file('i/f/extreal/REAL__LT__LMUL__NEG__0__NEG', ah4s_reals_REALu_u_NEGu_u_LMUL)).
fof(46, 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__NEG__0__NEG', ah4s_reals_REALu_u_NOTu_u_LT)).
fof(47, 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__NEG__0__NEG', ah4s_reals_REALu_u_MULu_u_SYM)).
fof(55, 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__NEG__0__NEG', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(60, 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__NEG__0__NEG', ah4s_reals_REALu_u_0)).
fof(66, axiom,![X8]:![X26]:![X27]:s(X8,h4s_bools_cond(s(t_bool,f),s(X8,X27),s(X8,X26)))=s(X8,X26),file('i/f/extreal/REAL__LT__LMUL__NEG__0__NEG', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(67, 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__NEG__0__NEG', ah4s_reals_abs0)).
fof(71, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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))),file('i/f/extreal/REAL__LT__LMUL__NEG__0__NEG', ah4s_reals_REALu_u_MULu_u_LZERO)).
fof(98, 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__NEG__0__NEG', ah4s_reals_REALu_u_NEGu_u_0)).
fof(119, 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__NEG__0__NEG', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(123, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/extreal/REAL__LT__LMUL__NEG__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_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))))))&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,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__NEG__0__NEG', ch4s_extreals_REALu_u_LTu_u_LMULu_u_NEGu_u_0u_u_NEG)).
# SZS output end CNFRefutation
