# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_measures_positive(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_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_probabilitys_prob),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_bool),h4s_predu_u_sets_empty)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))&![X3]:(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_probabilitys_events),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_reals_realu_u_lte(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,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_probabilitys_prob),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_bool),X3))))))))),file('i/f/probability/POSITIVE__PROB', ch4s_probabilitys_POSITIVEu_u_PROB)).
fof(33, axiom,![X1]:![X25]:(p(s(t_bool,h4s_measures_positive(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))),X25))))<=>(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))),X25))),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))&![X3]:(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))),X25))))))=>p(s(t_bool,h4s_reals_realu_u_lte(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,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))),X25))),s(t_fun(X1,t_bool),X3))))))))),file('i/f/probability/POSITIVE__PROB', ah4s_measures_positiveu_u_def)).
fof(44, 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/POSITIVE__PROB', ah4s_probabilitys_eventsu_u_def)).
fof(45, 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/POSITIVE__PROB', ah4s_probabilitys_probu_u_def)).
fof(91, axiom,p(s(t_bool,t)),file('i/f/probability/POSITIVE__PROB', aHLu_TRUTH)).
fof(92, axiom,![X15]:(s(t_bool,X15)=s(t_bool,t)|s(t_bool,X15)=s(t_bool,f)),file('i/f/probability/POSITIVE__PROB', aHLu_BOOLu_CASES)).
fof(98, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/probability/POSITIVE__PROB', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
