# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/util_prob/lg__2', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/lg__2', 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/util_prob/lg__2', aHLu_BOOLu_CASES)).
fof(5, axiom,![X6]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_utilu_u_probs_logr(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,X6))),file('i/f/util_prob/lg__2', ah4s_utilu_u_probs_lgu_u_def)).
fof(7, 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))))&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,X6)))))=>(~(s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(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,X6)=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/util_prob/lg__2', ah4s_utilu_u_probs_lgu_u_nonzero)).
fof(11, axiom,![X6]:![X9]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_logr(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X9))))),file('i/f/util_prob/lg__2', ah4s_utilu_u_probs_logru_u_def)).
fof(12, axiom,s(t_h4s_realaxs_real,h4s_transcs_ln(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,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/lg__2', ah4s_transcs_LNu_u_1)).
fof(25, axiom,s(t_h4s_realaxs_real,h4s_reals_u_2f(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_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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_DIVu_u_REFL2)).
fof(37, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X6),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_ADDu_u_RID)).
fof(46, axiom,![X7]:![X6]:s(t_h4s_realaxs_real,h4s_reals_u_2f(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_inv(s(t_h4s_realaxs_real,X7))))),file('i/f/util_prob/lg__2', ah4s_reals_realu_u_div)).
fof(61, axiom,![X6]:(s(t_h4s_realaxs_real,h4s_realaxs_inv(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,X6)=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/lg__2', ah4s_reals_REALu_u_INVu_u_EQu_u_0)).
fof(73, axiom,![X6]: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,X6)))=s(t_h4s_realaxs_real,X6),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(77, axiom,![X10]:![X11]: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,X11))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_OFu_u_NUMu_u_LE)).
fof(91, axiom,![X10]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10)))),file('i/f/util_prob/lg__2', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(101, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,X6))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_DOUBLE)).
fof(110, 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_reals_u_2f(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_DIVu_u_REFL)).
fof(118, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_MULu_u_RZERO)).
fof(119, axiom,![X17]:![X7]:![X6]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X17)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X17)))<=>s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X7)),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_EQu_u_RADD)).
fof(120, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),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/util_prob/lg__2', ah4s_reals_REALu_u_MULu_u_RID)).
fof(133, conjecture,s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/util_prob/lg__2', ch4s_utilu_u_probs_lgu_u_2)).
# SZS output end CNFRefutation
