# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)<=>(s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)&s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/EMPTY__UNION', ch4s_predu_u_sets_EMPTYu_u_UNION)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/EMPTY__UNION', aHLu_FALSITY)).
fof(5, axiom,![X2]:(s(t_bool,X2)=s(t_bool,f)<=>~(p(s(t_bool,X2)))),file('i/f/pred_set/EMPTY__UNION', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(7, axiom,![X1]:![X2]:![X3]:(s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),X2)<=>![X8]:s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2)))),file('i/f/pred_set/EMPTY__UNION', ah4s_predu_u_sets_EXTENSION)).
fof(8, axiom,![X1]:![X8]:~(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/EMPTY__UNION', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(10, axiom,![X1]:![X8]:![X2]:![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X3))))|p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/EMPTY__UNION', ah4s_predu_u_sets_INu_u_UNION)).
fof(11, axiom,p(s(t_bool,t0)),file('i/f/pred_set/EMPTY__UNION', aHLu_TRUTH)).
fof(12, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/pred_set/EMPTY__UNION', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
