# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3))))=>(~(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3)=s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),h4s_predu_u_sets_empty))=>p(s(t_bool,h4s_bools_in(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_closest(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_realaxs_real),X2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3),s(t_h4s_realaxs_real,X1))),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3)))))),file('i/f/float/CLOSEST__IN__SET', ch4s_floats_CLOSESTu_u_INu_u_SET)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/float/CLOSEST__IN__SET', aHLu_FALSITY)).
fof(32, axiom,![X7]:![X1]:![X2]:![X3]:![X23]:(p(s(t_bool,h4s_ieees_isu_u_closest(s(t_fun(X7,t_h4s_realaxs_real),X2),s(t_fun(X7,t_bool),X3),s(t_h4s_realaxs_real,X1),s(X7,X23))))<=>(p(s(t_bool,h4s_bools_in(s(X7,X23),s(t_fun(X7,t_bool),X3))))&![X24]:(p(s(t_bool,h4s_bools_in(s(X7,X24),s(t_fun(X7,t_bool),X3))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(X7,t_h4s_realaxs_real),X2),s(X7,X23))),s(t_h4s_realaxs_real,X1))))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(X7,t_h4s_realaxs_real),X2),s(X7,X24))),s(t_h4s_realaxs_real,X1))))))))))),file('i/f/float/CLOSEST__IN__SET', ah4s_ieees_isu_u_closest0)).
fof(33, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3))))=>(~(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3)=s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),h4s_predu_u_sets_empty))=>(p(s(t_bool,h4s_ieees_isu_u_closest(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_realaxs_real),X2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3),s(t_h4s_realaxs_real,X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_closest(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_realaxs_real),X2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3),s(t_h4s_realaxs_real,X1))))))&(?[X24]:(p(s(t_bool,h4s_ieees_isu_u_closest(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_realaxs_real),X2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3),s(t_h4s_realaxs_real,X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X24))))&p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),X24)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X4),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_ieees_closest(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_h4s_realaxs_real),X2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_bool),X3),s(t_h4s_realaxs_real,X1)))))))))),file('i/f/float/CLOSEST__IN__SET', ah4s_floats_CLOSESTu_u_ISu_u_EVERYTHING)).
fof(34, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/float/CLOSEST__IN__SET', aHLu_BOOLu_CASES)).
fof(35, axiom,p(s(t_bool,t)),file('i/f/float/CLOSEST__IN__SET', aHLu_TRUTH)).
fof(38, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/float/CLOSEST__IN__SET', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
