# 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))))&![X4]: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,X4)))))))=>(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__pos', ch4s_lebesgues_integrableu_u_pos)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/lebesgue/integrable__pos', aHLu_TRUTH)).
fof(11, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/lebesgue/integrable__pos', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(14, axiom,![X15]:~(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,X15)))=s(t_h4s_extreals_extreal,h4s_extreals_posinf)),file('i/f/lebesgue/integrable__pos', ah4s_extreals_numu_u_notu_u_inftyu_c1)).
fof(15, 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__pos', ah4s_lebesgues_integrableu_u_def)).
fof(16, axiom,![X1]:![X7]:(![X4]: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),X7),s(X1,X4))))))=>s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X7)))=s(t_fun(X1,t_h4s_extreals_extreal),X7)),file('i/f/lebesgue/integrable__pos', ah4s_measures_FNu_u_PLUSu_u_POSu_u_ID)).
fof(17, axiom,![X1]:![X7]:(![X4]: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),X7),s(X1,X4))))))=>![X4]: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),X7))),s(X1,X4)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/lebesgue/integrable__pos', ah4s_measures_FNu_u_MINUSu_u_POSu_u_ZERO)).
fof(18, axiom,![X1]:![X16]:(![X4]:s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X16),s(X1,X4)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))=>![X2]:(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))))=>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),X16)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/lebesgue/integrable__pos', ah4s_lebesgues_posu_u_fnu_u_integralu_u_zero)).
fof(19, axiom,~(p(s(t_bool,f0))),file('i/f/lebesgue/integrable__pos', aHLu_FALSITY)).
fof(20, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f0)),file('i/f/lebesgue/integrable__pos', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
