# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:((p(s(t_bool,h4s_probabilitys_randomu_u_variable(s(t_fun(X1,X2),X5),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))&p(s(t_bool,h4s_bools_in(s(t_fun(X2,t_bool),X6),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3)))))))=>s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,happ(s(t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real),h4s_probabilitys_distribution(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4),s(t_fun(X1,X2),X5))),s(t_fun(X2,t_bool),X6)))))=s(t_h4s_extreals_extreal,h4s_lebesgues_integral(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real)),h4s_pairs_u_2c(s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real),h4s_probabilitys_distribution(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4),s(t_fun(X1,X2),X5))))))),s(t_fun(X2,t_h4s_extreals_extreal),h4s_measures_indicatoru_u_fn(s(t_fun(X2,t_bool),X6)))))),file('i/f/probability/distribution__lebesgue__thm2', ch4s_probabilitys_distributionu_u_lebesgueu_u_thm2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/probability/distribution__lebesgue__thm2', aHLu_TRUTH)).
fof(10, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)<=>p(s(t_bool,X12))),file('i/f/probability/distribution__lebesgue__thm2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X1]:![X3]:![X19]:((p(s(t_bool,h4s_measures_measureu_u_space(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X19))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X3),s(t_fun(t_fun(X1,t_bool),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_bool)),h4s_measures_measurableu_u_sets),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X19)))))))=>s(t_h4s_extreals_extreal,h4s_lebesgues_integral(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_indicatoru_u_fn(s(t_fun(X1,t_bool),X3)))))=s(t_h4s_extreals_extreal,h4s_extreals_normal(s(t_h4s_realaxs_real,happ(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_measures_measure),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X19))),s(t_fun(X1,t_bool),X3)))))),file('i/f/probability/distribution__lebesgue__thm2', ah4s_lebesgues_integralu_u_indicator)).
fof(16, axiom,![X1]:![X20]:![X21]:![X22]:s(t_fun(t_fun(X1,t_bool),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_bool)),h4s_measures_measurableu_u_sets),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X21),s(t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_pairs_u_2c(s(t_fun(t_fun(X1,t_bool),t_bool),X20),s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),X22)))))))=s(t_fun(t_fun(X1,t_bool),t_bool),X20),file('i/f/probability/distribution__lebesgue__thm2', ah4s_measures_measurableu_u_setsu_u_def)).
fof(17, axiom,![X1]:![X20]:![X21]:![X22]:s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_measures_measure),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X21),s(t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_pairs_u_2c(s(t_fun(t_fun(X1,t_bool),t_bool),X20),s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),X22)))))))=s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),X22),file('i/f/probability/distribution__lebesgue__thm2', ah4s_measures_measureu_u_def)).
fof(18, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_probabilitys_randomu_u_variable(s(t_fun(X1,X2),X5),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))=>p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real)),h4s_pairs_u_2c(s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real),h4s_probabilitys_distribution(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4),s(t_fun(X1,X2),X5))))))))))),file('i/f/probability/distribution__lebesgue__thm2', ah4s_probabilitys_distributionu_u_probu_u_space)).
fof(23, axiom,![X1]:s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_probabilitys_prob)=s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_measures_measure),file('i/f/probability/distribution__lebesgue__thm2', ah4s_probabilitys_probu_u_def)).
fof(24, axiom,![X1]:![X4]:(p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4))))<=>(p(s(t_bool,h4s_measures_measureu_u_space(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4))))&s(t_h4s_realaxs_real,happ(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real)),h4s_measures_measure),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X4))),s(t_fun(X1,t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(X1,t_bool)),h4s_probabilitys_pu_u_space),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),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/probability/distribution__lebesgue__thm2', ah4s_probabilitys_probu_u_spaceu_u_def)).
fof(25, axiom,![X1]:s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_bool)),h4s_probabilitys_events)=s(t_fun(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),t_fun(t_fun(X1,t_bool),t_bool)),h4s_measures_measurableu_u_sets),file('i/f/probability/distribution__lebesgue__thm2', ah4s_probabilitys_eventsu_u_def)).
# SZS output end CNFRefutation
