# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X2),s(X1,X3)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))=>![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_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))),X4),s(t_fun(X1,t_h4s_extreals_extreal),X2)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/lebesgue/integral__zero', ch4s_lebesgues_integralu_u_zero)).
fof(3, axiom,![X1]:![X4]:![X6]: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))),X4),s(t_fun(X1,t_h4s_extreals_extreal),X6)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sub(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))),X4),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_plus(s(t_fun(X1,t_h4s_extreals_extreal),X6))))),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))),X4),s(t_fun(X1,t_h4s_extreals_extreal),h4s_measures_fnu_u_minus(s(t_fun(X1,t_h4s_extreals_extreal),X6))))))),file('i/f/lebesgue/integral__zero', ah4s_lebesgues_integralu_u_def)).
fof(7, axiom,![X1]:![X2]:(![X3]:s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X2),s(X1,X3)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))=>![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_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))),X4),s(t_fun(X1,t_h4s_extreals_extreal),X2)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/lebesgue/integral__zero', ah4s_lebesgues_posu_u_fnu_u_integralu_u_zero)).
fof(8, axiom,![X12]:![X13]:![X6]:![X14]:(![X3]:s(X13,happ(s(t_fun(X12,X13),X6),s(X12,X3)))=s(X13,happ(s(t_fun(X12,X13),X14),s(X12,X3)))=>s(t_fun(X12,X13),X6)=s(t_fun(X12,X13),X14)),file('i/f/lebesgue/integral__zero', aHLu_EXT)).
fof(9, axiom,![X3]:s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sub(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,X3)))=s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,X3))),file('i/f/lebesgue/integral__zero', ah4s_extreals_subu_u_lzero)).
fof(10, axiom,![X1]:![X6]:![X3]: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),X6))),s(X1,X3)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X6),s(X1,X3))),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,h4s_extreals_extrealu_u_ainv(s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X6),s(X1,X3))))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/lebesgue/integral__zero', ah4s_measures_fnu_u_minusu_u_def)).
fof(11, axiom,![X1]:![X6]:![X3]: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),X6))),s(X1,X3)))=s(t_h4s_extreals_extreal,h4s_bools_cond(s(t_bool,h4s_extreals_extrealu_u_lt(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),X6),s(X1,X3))))),s(t_h4s_extreals_extreal,happ(s(t_fun(X1,t_h4s_extreals_extreal),X6),s(X1,X3))),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/lebesgue/integral__zero', ah4s_measures_fnu_u_plusu_u_def)).
fof(12, axiom,s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_ainv(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,h4s_extreals_extrealu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/lebesgue/integral__zero', ah4s_extreals_negu_u_0)).
fof(13, axiom,![X1]:![X15]:![X16]:s(X1,h4s_bools_cond(s(t_bool,X16),s(X1,X15),s(X1,X15)))=s(X1,X15),file('i/f/lebesgue/integral__zero', ah4s_bools_CONDu_u_ID)).
# SZS output end CNFRefutation
