# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_probabilitys_probu_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))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X2),s(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))),X4)))))))=>s(t_bool,h4s_reals_realu_u_lte(s(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))),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_probabilitys_pu_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_fun(X1,t_bool),X2))))),s(t_h4s_realaxs_real,X3)))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(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))))))),s(t_h4s_realaxs_real,X3))),s(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))),X4),s(t_fun(X1,t_bool),X2)))))),file('i/f/probability/PROB__COMPL__LE1', ch4s_probabilitys_PROBu_u_COMPLu_u_LE1)).
fof(6, axiom,![X5]:![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X5)))=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,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_LEu_u_LNEG)).
fof(7, axiom,![X5]:![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X5)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X6))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_LEu_u_NEG2)).
fof(9, axiom,![X1]:![X2]:![X4]:((p(s(t_bool,h4s_probabilitys_probu_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))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X2),s(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))),X4)))))))=>s(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))),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_probabilitys_pu_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_fun(X1,t_bool),X2)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(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))))))),s(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))),X4),s(t_fun(X1,t_bool),X2)))))),file('i/f/probability/PROB__COMPL__LE1', ah4s_probabilitys_PROBu_u_COMPL)).
fof(20, axiom,![X5]:![X6]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X5))))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_realu_u_sub0)).
fof(27, axiom,![X5]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X6))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(28, axiom,![X7]:![X5]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X7)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5))),s(t_h4s_realaxs_real,X7))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_ADDu_u_ASSOC)).
fof(29, axiom,![X5]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X5)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X5))))),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_NEGu_u_ADD)).
fof(30, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6)))))=s(t_h4s_realaxs_real,X6),file('i/f/probability/PROB__COMPL__LE1', ah4s_reals_REALu_u_NEGu_u_NEG)).
# SZS output end CNFRefutation
