# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((~(s(t_fun(t_h4s_nums_num,t_bool),X2)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))&(~(s(t_fun(t_h4s_nums_num,t_bool),X1)=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))&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_minu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X1))),s(t_h4s_nums_num,h4s_predu_u_sets_minu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X2))))))),file('i/f/pred_set/SUBSET__MIN__SET', ch4s_predu_u_sets_SUBSETu_u_MINu_u_SET)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SUBSET__MIN__SET', aHLu_FALSITY)).
fof(24, axiom,![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_minu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X17))),s(t_fun(t_h4s_nums_num,t_bool),X17))))&![X9]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X9),s(t_fun(t_h4s_nums_num,t_bool),X17))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_predu_u_sets_minu_u_set(s(t_fun(t_h4s_nums_num,t_bool),X17))),s(t_h4s_nums_num,X9))))))),file('i/f/pred_set/SUBSET__MIN__SET', ah4s_predu_u_sets_MINu_u_SETu_u_LEM)).
fof(27, 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))))<=>![X9]:(p(s(t_bool,h4s_bools_in(s(X6,X9),s(t_fun(X6,t_bool),X17))))=>p(s(t_bool,h4s_bools_in(s(X6,X9),s(t_fun(X6,t_bool),X5)))))),file('i/f/pred_set/SUBSET__MIN__SET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(28, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/SUBSET__MIN__SET', aHLu_BOOLu_CASES)).
fof(30, axiom,p(s(t_bool,t)),file('i/f/pred_set/SUBSET__MIN__SET', aHLu_TRUTH)).
fof(32, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/pred_set/SUBSET__MIN__SET', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
