# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/probability/INDEP__REFL', aHLu_TRUTH)).
fof(22, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/probability/INDEP__REFL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(39, axiom,![X10]:![X20]:s(t_fun(X10,t_bool),h4s_predu_u_sets_inter(s(t_fun(X10,t_bool),X20),s(t_fun(X10,t_bool),X20)))=s(t_fun(X10,t_bool),X20),file('i/f/probability/INDEP__REFL', ah4s_predu_u_sets_INTERu_u_IDEMPOT)).
fof(40, axiom,![X17]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X17),s(t_h4s_realaxs_real,X17)))=s(t_h4s_realaxs_real,X17)<=>(s(t_h4s_realaxs_real,X17)=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,X17)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),file('i/f/probability/INDEP__REFL', ah4s_utilu_u_probs_REALu_u_MULu_u_IDEMPOT)).
fof(41, axiom,![X10]:![X19]:![X21]:![X22]:(p(s(t_bool,h4s_probabilitys_indep(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X22),s(t_fun(X10,t_bool),X21))))<=>(p(s(t_bool,h4s_bools_in(s(t_fun(X10,t_bool),X22),s(t_fun(t_fun(X10,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19))))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X10,t_bool),X21),s(t_fun(t_fun(X10,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19))))))&s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),h4s_predu_u_sets_inter(s(t_fun(X10,t_bool),X22),s(t_fun(X10,t_bool),X21)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X22))),s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X21)))))))),file('i/f/probability/INDEP__REFL', ah4s_probabilitys_indepu_u_def)).
fof(42, conjecture,![X10]:![X19]:![X22]:((p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19))))&p(s(t_bool,h4s_bools_in(s(t_fun(X10,t_bool),X22),s(t_fun(t_fun(X10,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19)))))))=>(p(s(t_bool,h4s_probabilitys_indep(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X22),s(t_fun(X10,t_bool),X22))))<=>(s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X22)))=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,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X10,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X10,t_bool),t_bool),t_fun(t_fun(X10,t_bool),t_h4s_realaxs_real))),X19),s(t_fun(X10,t_bool),X22)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/probability/INDEP__REFL', ch4s_probabilitys_INDEPu_u_REFL)).
# SZS output end CNFRefutation
