# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2))))&(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X1))))))),file('i/f/pred_set/SUBSET__MAX__SET', ch4s_predu_u_sets_SUBSETu_u_MAXu_u_SET)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SUBSET__MAX__SET', aHLu_FALSITY)).
fof(11, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(26, axiom,![X14]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(30, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_numerals_numeralu_u_lteu_c1)).
fof(31, axiom,![X17]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X17))))=>((~(s(t_fun(t_h4s_nums_num,t_bool),X17)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))=>(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X17))),s(t_fun(t_h4s_nums_num,t_bool),X17))))&![X16]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X16),s(t_fun(t_h4s_nums_num,t_bool),X17))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X17)))))))))&(s(t_fun(t_h4s_nums_num,t_bool),X17)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)=>s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X17)))=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_predu_u_sets_MAXu_u_SETu_u_DEF)).
fof(32, axiom,s(t_h4s_nums_num,h4s_predu_u_sets_maxu_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_predu_u_sets_MAXu_u_SETu_u_REWRITESu_c0)).
fof(38, axiom,![X6]:![X17]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X6,t_bool),X17),s(t_fun(X6,t_bool),h4s_predu_u_sets_empty))))<=>s(t_fun(X6,t_bool),X17)=s(t_fun(X6,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_predu_u_sets_SUBSETu_u_EMPTY)).
fof(40, axiom,![X6]:![X5]:![X17]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X6,t_bool),X17),s(t_fun(X6,t_bool),X5))))<=>![X7]:(p(s(t_bool,h4s_bools_in(s(X6,X7),s(t_fun(X6,t_bool),X17))))=>p(s(t_bool,h4s_bools_in(s(X6,X7),s(t_fun(X6,t_bool),X5)))))),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(41, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/SUBSET__MAX__SET', aHLu_BOOLu_CASES)).
fof(46, axiom,p(s(t_bool,t)),file('i/f/pred_set/SUBSET__MAX__SET', aHLu_TRUTH)).
fof(48, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/pred_set/SUBSET__MAX__SET', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
