# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),h4s_predu_u_sets_univ))))<=>(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ))))&p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)))))),file('i/f/pred_set/countable__Usum', ch4s_predu_u_sets_countableu_u_Usum)).
fof(7, axiom,![X1]:![X3]:![X12]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X12),s(t_fun(X1,t_bool),X3))))))<=>(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X12))))&p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_unionu_u_countableu_u_IFF)).
fof(8, axiom,![X2]:![X1]:![X12]:![X13]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X2),X13),s(t_fun(X1,t_bool),X12),s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X13),s(t_fun(X1,t_bool),X12))))))=>s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X13),s(t_fun(X1,t_bool),X12)))))=s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X12)))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_inju_u_imageu_u_countableu_u_IFF)).
fof(9, axiom,![X1]:![X4]:p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_INu_u_UNIV)).
fof(10, axiom,![X1]:![X2]:s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),h4s_predu_u_sets_univ)=s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),h4s_predu_u_sets_image(s(t_fun(X1,t_h4s_sums_sum(X1,X2)),h4s_sums_inl),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ))),s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),h4s_predu_u_sets_image(s(t_fun(X2,t_h4s_sums_sum(X1,X2)),h4s_sums_inr),s(t_fun(X2,t_bool),h4s_predu_u_sets_univ))))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_SUMu_u_UNIV)).
fof(11, axiom,![X2]:![X1]:![X9]:![X12]:![X13]:(p(s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X13),s(t_fun(X1,t_bool),X12))))))<=>?[X4]:(s(X2,X9)=s(X2,happ(s(t_fun(X1,X2),X13),s(X1,X4)))&p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X12)))))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_INu_u_IMAGE)).
fof(12, axiom,![X1]:![X2]:![X3]:![X12]:(![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X12))))=>p(s(t_bool,h4s_bools_in(s(t_h4s_sums_sum(X1,X2),happ(s(t_fun(X1,t_h4s_sums_sum(X1,X2)),h4s_sums_inl),s(X1,X4))),s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3)))))=>p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,t_h4s_sums_sum(X1,X2)),h4s_sums_inl),s(t_fun(X1,t_bool),X12),s(t_fun(t_h4s_sums_sum(X1,X2),t_bool),X3))))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_INJu_u_INL)).
fof(13, axiom,![X2]:![X1]:![X3]:![X12]:(![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X12))))=>p(s(t_bool,h4s_bools_in(s(t_h4s_sums_sum(X2,X1),happ(s(t_fun(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(X1,X4))),s(t_fun(t_h4s_sums_sum(X2,X1),t_bool),X3)))))=>p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,t_h4s_sums_sum(X2,X1)),h4s_sums_inr),s(t_fun(X1,t_bool),X12),s(t_fun(t_h4s_sums_sum(X2,X1),t_bool),X3))))),file('i/f/pred_set/countable__Usum', ah4s_predu_u_sets_INJu_u_INR)).
# SZS output end CNFRefutation
