# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)<=>p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X2))))),file('i/f/pred_set/DISJOINT__EMPTY__REFL', ch4s_predu_u_sets_DISJOINTu_u_EMPTYu_u_REFL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/DISJOINT__EMPTY__REFL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/DISJOINT__EMPTY__REFL', aHLu_FALSITY)).
fof(7, axiom,![X1]:![X3]:![X2]:(p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))))<=>s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/DISJOINT__EMPTY__REFL', ah4s_predu_u_sets_DISJOINTu_u_DEF)).
fof(8, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/DISJOINT__EMPTY__REFL', aHLu_BOOLu_CASES)).
fof(9, axiom,![X1]:![X2]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),X2),file('i/f/pred_set/DISJOINT__EMPTY__REFL', ah4s_predu_u_sets_INTERu_u_IDEMPOT)).
# SZS output end CNFRefutation
