# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, 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)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/lg__2', aHLu_TRUTH)).
fof(7, axiom,![X1]:(s(t_bool,t)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/util_prob/lg__2', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(11, axiom,![X10]:![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/util_prob/lg__2', ah4s_numerals_numeralu_u_distribu_c22)).
fof(12, 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/util_prob/lg__2', ah4s_reals_REALu_u_LTu_u_01)).
fof(13, axiom,![X4]:(~(s(t_h4s_realaxs_real,X4)=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,X4),s(t_h4s_realaxs_real,X4)))=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(14, axiom,![X10]:![X11]: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,X10))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/util_prob/lg__2', ah4s_reals_ltu_u_intu_c0)).
fof(15, 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(16, axiom,![X3]:![X4]:((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,X4))))&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,X3)))))=>s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X4))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X3)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3)))),file('i/f/util_prob/lg__2', ah4s_transcs_LNu_u_MONOu_u_LT)).
fof(17, axiom,![X4]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_lg(s(t_h4s_realaxs_real,X4)))=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,X4))),file('i/f/util_prob/lg__2', ah4s_utilu_u_probs_lgu_u_def)).
fof(18, axiom,![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X10))),file('i/f/util_prob/lg__2', ah4s_numerals_numeralu_u_distribu_c21)).
fof(19, axiom,![X10]:![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X11))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))))),file('i/f/util_prob/lg__2', ah4s_numerals_numeralu_u_ltu_c5)).
fof(20, axiom,![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X10)))))=s(t_bool,t),file('i/f/util_prob/lg__2', ah4s_numerals_numeralu_u_ltu_c1)).
fof(21, axiom,![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/util_prob/lg__2', ah4s_numerals_numeralu_u_ltu_c2)).
fof(22, axiom,![X3]:![X4]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X4),s(t_h4s_realaxs_real,X3))))=>~(s(t_h4s_realaxs_real,X4)=s(t_h4s_realaxs_real,X3))),file('i/f/util_prob/lg__2', ah4s_reals_REALu_u_LTu_u_IMPu_u_NE)).
fof(23, axiom,![X4]:![X12]:s(t_h4s_realaxs_real,h4s_utilu_u_probs_logr(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X4)))=s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X4))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,X12))))),file('i/f/util_prob/lg__2', ah4s_utilu_u_probs_logru_u_def)).
fof(24, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/lg__2', aHLu_FALSITY)).
fof(26, 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)).
# SZS output end CNFRefutation
