# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(s(t_h4s_nums_num,h4s_nums_0)))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/COUNT__ZERO', ch4s_predu_u_sets_COUNTu_u_ZERO)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/COUNT__ZERO', aHLu_FALSITY)).
fof(7, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/pred_set/COUNT__ZERO', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(9, axiom,![X7]:![X8]:![X9]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))),file('i/f/pred_set/COUNT__ZERO', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(10, axiom,![X4]:![X5]:~(p(s(t_bool,h4s_bools_in(s(X4,X5),s(t_fun(X4,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/COUNT__ZERO', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(12, axiom,![X4]:![X3]:![X14]:(s(t_fun(X4,t_bool),X14)=s(t_fun(X4,t_bool),X3)<=>![X5]:s(t_bool,h4s_bools_in(s(X4,X5),s(t_fun(X4,t_bool),X14)))=s(t_bool,h4s_bools_in(s(X4,X5),s(t_fun(X4,t_bool),X3)))),file('i/f/pred_set/COUNT__ZERO', ah4s_predu_u_sets_EXTENSION)).
fof(13, axiom,![X8]:![X9]:s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X9),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_count(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),file('i/f/pred_set/COUNT__ZERO', ah4s_predu_u_sets_INu_u_COUNT)).
fof(14, axiom,p(s(t_bool,t)),file('i/f/pred_set/COUNT__ZERO', aHLu_TRUTH)).
fof(15, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/COUNT__ZERO', aHLu_BOOLu_CASES)).
fof(18, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/pred_set/COUNT__ZERO', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8)))),file('i/f/pred_set/COUNT__ZERO', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(20, axiom,![X7]:![X8]:![X9]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),file('i/f/pred_set/COUNT__ZERO', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(21, axiom,![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X8),file('i/f/pred_set/COUNT__ZERO', ah4s_numerals_numeralu_u_distribu_c1)).
fof(22, axiom,![X8]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/pred_set/COUNT__ZERO', ah4s_numerals_numeralu_u_distribu_c27)).
fof(23, axiom,![X8]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/pred_set/COUNT__ZERO', ah4s_numerals_numeralu_u_lteu_c1)).
fof(24, axiom,![X8]:![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X8))),file('i/f/pred_set/COUNT__ZERO', ah4s_arithmetics_LESSu_u_EQ)).
fof(25, axiom,![X8]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X8))),file('i/f/pred_set/COUNT__ZERO', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
# SZS output end CNFRefutation
