# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_cross(s(t_fun(X1,t_bool),X3),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/CROSS__EMPTY_c0', ch4s_predu_u_sets_CROSSu_u_EMPTYu_c0)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/pred_set/CROSS__EMPTY_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(4, axiom,![X1]:![X7]:~(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/CROSS__EMPTY_c0', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(5, axiom,![X1]:![X6]:![X8]:(s(t_fun(X1,t_bool),X8)=s(t_fun(X1,t_bool),X6)<=>![X7]:s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X8)))=s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X6)))),file('i/f/pred_set/CROSS__EMPTY_c0', ah4s_predu_u_sets_EXTENSION)).
fof(6, axiom,![X1]:![X2]:![X7]:![X9]:![X3]:(p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(X1,X2),X7),s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_cross(s(t_fun(X1,t_bool),X3),s(t_fun(X2,t_bool),X9))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,h4s_pairs_fst(s(t_h4s_pairs_prod(X1,X2),X7))),s(t_fun(X1,t_bool),X3))))&p(s(t_bool,h4s_bools_in(s(X2,h4s_pairs_snd(s(t_h4s_pairs_prod(X1,X2),X7))),s(t_fun(X2,t_bool),X9)))))),file('i/f/pred_set/CROSS__EMPTY_c0', ah4s_predu_u_sets_INu_u_CROSS)).
# SZS output end CNFRefutation
