# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((?[X3]:p(s(t_bool,h4s_bools_in(s(t_h4s_realaxs_real,X3),s(t_fun(t_h4s_realaxs_real,t_bool),X1))))&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)))))=>?[X3]:(p(s(t_bool,h4s_bools_in(s(t_h4s_realaxs_real,X3),s(t_fun(t_h4s_realaxs_real,t_bool),X1))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_inf(s(t_fun(t_h4s_realaxs_real,t_bool),X1))),s(t_h4s_realaxs_real,X2)))))))),file('i/f/util_prob/INF__CLOSE', ch4s_utilu_u_probs_INFu_u_CLOSE)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/util_prob/INF__CLOSE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X13]:![X12]:![X3]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X12))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X13)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X13))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_LTu_u_LADD)).
fof(16, axiom,![X12]:![X3]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),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,X3)))))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_realu_u_lt)).
fof(17, axiom,![X12]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X12)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X3))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(18, axiom,![X13]:![X12]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X13)))))=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,X3),s(t_h4s_realaxs_real,X12))),s(t_h4s_realaxs_real,X13))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_ADDu_u_ASSOC)).
fof(19, axiom,![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X3)))=s(t_h4s_realaxs_real,X3),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(20, axiom,![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),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,X3),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(22, axiom,![X13]:![X1]:((?[X3]:p(s(t_bool,h4s_bools_in(s(t_h4s_realaxs_real,X3),s(t_fun(t_h4s_realaxs_real,t_bool),X1))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_inf(s(t_fun(t_h4s_realaxs_real,t_bool),X1))),s(t_h4s_realaxs_real,X13)))))=>?[X3]:(p(s(t_bool,h4s_bools_in(s(t_h4s_realaxs_real,X3),s(t_fun(t_h4s_realaxs_real,t_bool),X1))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X13)))))),file('i/f/util_prob/INF__CLOSE', ah4s_utilu_u_probs_INFu_u_GREATER)).
fof(24, axiom,![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_ADDu_u_RINV)).
fof(28, axiom,![X12]:![X3]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),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,X3)))))<=>s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,X12)),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(29, axiom,![X12]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X3))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X12)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X3))),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_LEu_u_NEG2)).
fof(31, axiom,![X3]: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,X3)))))=s(t_h4s_realaxs_real,X3),file('i/f/util_prob/INF__CLOSE', ah4s_reals_REALu_u_NEGu_u_NEG)).
# SZS output end CNFRefutation
