# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(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))),X2))))=>(p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3))))<=>(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_h4s_extreals_extreal),X3),s(t_fun(t_fun(X1,t_h4s_extreals_extreal),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_measures_mu_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))),X2))),s(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))),X2))))),s(t_h4s_pairs_prod(t_fun(t_h4s_extreals_extreal,t_bool),t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool)),h4s_measures_borel))))))&(p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X3))))))&p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_minus(s(t_fun(X1,t_h4s_extreals_extreal),X3)))))))))),file('i/f/lebesgue/integrable__plus__minus', ch4s_lebesgues_integrableu_u_plusu_u_minus)).
fof(25, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3))))<=>(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_h4s_extreals_extreal),X3),s(t_fun(t_fun(X1,t_h4s_extreals_extreal),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_measures_mu_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))),X2))),s(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))),X2))))),s(t_h4s_pairs_prod(t_fun(t_h4s_extreals_extreal,t_bool),t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool)),h4s_measures_borel))))))&(~(s(t_h4s_extreals_extreal,h4s_lebesgues_posu_u_fnu_u_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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X3)))))=s(t_h4s_extreals_extreal,h4s_extreals_posinf))&~(s(t_h4s_extreals_extreal,h4s_lebesgues_posu_u_fnu_u_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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_minus(s(t_fun(X1,t_h4s_extreals_extreal),X3)))))=s(t_h4s_extreals_extreal,h4s_extreals_posinf))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_lebesgues_integrableu_u_def)).
fof(26, axiom,![X1]:![X2]:![X3]:((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))),X2))))&p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3)))))=>p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X3))))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_lebesgues_integrableu_u_fnu_u_plus)).
fof(27, axiom,![X1]:![X2]:![X3]:((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))),X2))))&p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3)))))=>p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_minus(s(t_fun(X1,t_h4s_extreals_extreal),X3))))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_lebesgues_integrableu_u_fnu_u_minus)).
fof(28, axiom,![X1]:![X2]:![X3]:((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))),X2))))&![X10]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X3),s(X1,X10)))))))=>(p(s(t_bool,h4s_lebesgues_integrable(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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3))))<=>(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_h4s_extreals_extreal),X3),s(t_fun(t_fun(X1,t_h4s_extreals_extreal),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_measures_mu_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))),X2))),s(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))),X2))))),s(t_h4s_pairs_prod(t_fun(t_h4s_extreals_extreal,t_bool),t_fun(t_fun(t_h4s_extreals_extreal,t_bool),t_bool)),h4s_measures_borel))))))&~(s(t_h4s_extreals_extreal,h4s_lebesgues_posu_u_fnu_u_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))),X2),s(t_fun(X1,t_h4s_extreals_extreal),X3)))=s(t_h4s_extreals_extreal,h4s_extreals_posinf))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_lebesgues_integrableu_u_pos)).
fof(31, axiom,![X1]:![X10]:![X21]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_minus(s(t_fun(X1,t_h4s_extreals_extreal),X21))),s(X1,X10)))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_measures_FNu_u_MINUSu_u_POS)).
fof(37, axiom,![X1]:![X10]:![X21]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X21))),s(X1,X10)))))),file('i/f/lebesgue/integrable__plus__minus', ah4s_measures_FNu_u_PLUSu_u_POS)).
# SZS output end CNFRefutation
