# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(?[X3]:p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2))))<=>~(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ch4s_predu_u_sets_MEMBERu_u_NOTu_u_EMPTY)).
fof(3, axiom,![X1]:![X3]:![X8]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X8)))=s(t_bool,happ(s(t_fun(X1,t_bool),X8),s(X1,X3))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_predu_u_sets_SPECIFICATION)).
fof(4, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(6, axiom,![X1]:![X12]:![X2]:(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X12)<=>![X3]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X2)))=s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X12)))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(38, axiom,![X1]:![X3]:s(t_bool,happ(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(X1,X3)))=s(t_bool,f),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_predu_u_sets_EMPTYu_u_DEF)).
fof(40, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/MEMBER__NOT__EMPTY', aHLu_FALSITY)).
fof(46, axiom,(p(s(t_bool,f))<=>![X12]:p(s(t_bool,X12))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_bools_Fu_u_DEF)).
fof(47, axiom,![X12]:(s(t_bool,f)=s(t_bool,X12)<=>~(p(s(t_bool,X12)))),file('i/f/pred_set/MEMBER__NOT__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
