# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),X1),s(t_h4s_realaxs_real,X2))))=>?[X3]:?[X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),X1),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))))))&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,X2)))))),file('i/f/real/SUP__LEMMA2', ch4s_reals_SUPu_u_LEMMA2)).
fof(12, axiom,![X5]:![X2]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X5))))=>~(s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X5))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(14, axiom,![X5]:![X2]:(s(t_h4s_realaxs_real,X2)=s(t_h4s_realaxs_real,X5)|(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X5))))|p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X2)))))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_LTu_u_TOTAL)).
fof(25, axiom,![X17]:(~(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X17)))=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,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X17))))))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_LTu_u_NZ)).
fof(29, axiom,![X5]:![X2]:~((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X5))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X2)))))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_LTu_u_ANTISYM)).
fof(43, axiom,![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),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,X2),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(44, axiom,![X8]:![X5]:![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X8)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X5))),s(t_h4s_realaxs_real,X8))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_ADDu_u_ASSOC)).
fof(46, axiom,![X5]:![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X5)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X2))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(50, 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_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/real/SUP__LEMMA2', ah4s_reals_REALu_u_LTu_u_01)).
fof(57, axiom,![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real/SUP__LEMMA2', ah4s_reals_REALu_u_ADDu_u_LINV)).
fof(73, axiom,![X2]:s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X2),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/real/SUP__LEMMA2', ah4s_reals_pow0u_c0)).
fof(74, 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/real/SUP__LEMMA2', ah4s_reals_REALu_u_0)).
# SZS output end CNFRefutation
