# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_probabilitys_indep(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))),X5),s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))&s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))=>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))),X5))),s(t_fun(X1,t_bool),X2)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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))),X5))),s(t_fun(X1,t_bool),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_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))),X5))),s(t_fun(X1,t_bool),X3)))))),file('i/f/probability/PROB__INDEP', ch4s_probabilitys_PROBu_u_INDEP)).
fof(13, axiom,![X13]:![X14]:((p(s(t_bool,X14))=>p(s(t_bool,X13)))=>((p(s(t_bool,X13))=>p(s(t_bool,X14)))=>s(t_bool,X14)=s(t_bool,X13))),file('i/f/probability/PROB__INDEP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(40, axiom,![X1]:![X5]:![X25]:![X26]:(p(s(t_bool,h4s_probabilitys_indep(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))),X5),s(t_fun(X1,t_bool),X26),s(t_fun(X1,t_bool),X25))))<=>(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X26),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))),X5))))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X25),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))),X5))))))&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))),X5))),s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X26),s(t_fun(X1,t_bool),X25)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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))),X5))),s(t_fun(X1,t_bool),X26))),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))),X5))),s(t_fun(X1,t_bool),X25)))))))),file('i/f/probability/PROB__INDEP', ah4s_probabilitys_indepu_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_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/PROB__INDEP', ah4s_probabilitys_probu_u_def)).
fof(57, axiom,![X1]:![X3]:![X4]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X4)))),file('i/f/probability/PROB__INDEP', ah4s_predu_u_sets_INTERu_u_SUBSETu_c0)).
# SZS output end CNFRefutation
