# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_univ))))<=>(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)))))),file('i/f/pred_set/INFINITE__PAIR__UNIV', ch4s_predu_u_sets_INFINITEu_u_PAIRu_u_UNIV)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/INFINITE__PAIR__UNIV', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/INFINITE__PAIR__UNIV', aHLu_FALSITY)).
fof(5, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/pred_set/INFINITE__PAIR__UNIV', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X1]:![X2]:![X7]:![X8]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_cross(s(t_fun(X1,t_bool),X8),s(t_fun(X2,t_bool),X7))))))<=>(s(t_fun(X1,t_bool),X8)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)|(s(t_fun(X2,t_bool),X7)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)|(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X8))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X2,t_bool),X7)))))))),file('i/f/pred_set/INFINITE__PAIR__UNIV', ah4s_predu_u_sets_FINITEu_u_CROSSu_u_EQ)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/INFINITE__PAIR__UNIV', aHLu_BOOLu_CASES)).
fof(11, axiom,![X1]:~(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/INFINITE__PAIR__UNIV', ah4s_predu_u_sets_UNIVu_u_NOTu_u_EMPTY)).
fof(12, axiom,![X1]:![X2]:s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_univ)=s(t_fun(t_h4s_pairs_prod(X1,X2),t_bool),h4s_predu_u_sets_cross(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(X2,t_bool),h4s_predu_u_sets_univ))),file('i/f/pred_set/INFINITE__PAIR__UNIV', ah4s_predu_u_sets_CROSSu_u_UNIV)).
# SZS output end CNFRefutation
