# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))),s(X1,X2))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))|p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/UNION__applied', ch4s_predu_u_sets_UNIONu_u_applied)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/pred_set/UNION__applied', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/UNION__applied', aHLu_FALSITY)).
fof(4, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X4))))|p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3)))))),file('i/f/pred_set/UNION__applied', ah4s_predu_u_sets_INu_u_UNION)).
fof(5, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/UNION__applied', aHLu_BOOLu_CASES)).
fof(7, axiom,![X1]:![X2]:![X9]:s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X9)))=s(t_bool,happ(s(t_fun(X1,t_bool),X9),s(X1,X2))),file('i/f/pred_set/UNION__applied', ah4s_bools_INu_u_DEF)).
# SZS output end CNFRefutation
