# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((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))))&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,X1)))))=>s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,X1)))))),file('i/f/util_prob/lg__mul', ch4s_utilu_u_probs_lgu_u_mul)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/lg__mul', aHLu_TRUTH)).
fof(8, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/util_prob/lg__mul', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X10]:![X1]:![X2]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,X2)))))=s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X10))),s(t_h4s_realaxs_real,X2))),file('i/f/util_prob/lg__mul', ah4s_reals_REALu_u_DIVu_u_ADD)).
fof(12, axiom,![X1]:![X2]:((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))))&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,X1)))))=>s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X1)))))),file('i/f/util_prob/lg__mul', ah4s_transcs_LNu_u_MUL)).
fof(13, axiom,![X2]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,X2)))=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,X2))),file('i/f/util_prob/lg__mul', ah4s_utilu_u_probs_lgu_u_def)).
fof(14, axiom,![X2]:![X11]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_logr(s(t_h4s_realaxs_real,X11),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X11))))),file('i/f/util_prob/lg__mul', ah4s_utilu_u_probs_logru_u_def)).
# SZS output end CNFRefutation
