# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2)))))=>s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2))))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))))))),file('i/f/pred_set/CARD__UNION__EQN', ch4s_predu_u_sets_CARDu_u_UNIONu_u_EQN)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/pred_set/CARD__UNION__EQN', aHLu_TRUTH)).
fof(9, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)<=>p(s(t_bool,X2))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X11]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_arithmetics_ADDu_u_SYM)).
fof(17, axiom,![X13]:![X11]:![X12]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X13))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(18, axiom,![X13]:![X11]:![X12]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X13))))=>(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X13)<=>s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X11))))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_arithmetics_ADDu_u_EQu_u_SUB)).
fof(20, axiom,![X1]:![X3]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X3))))=>![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X1,t_bool),X2))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2))))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),X2)))))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X3))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(X1,t_bool),X2))))))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_predu_u_sets_CARDu_u_UNION)).
fof(22, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/CARD__UNION__EQN', aHLu_FALSITY)).
fof(23, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/pred_set/CARD__UNION__EQN', aHLu_BOOLu_CASES)).
fof(27, axiom,![X11]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(28, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/pred_set/CARD__UNION__EQN', ah4s_numerals_numeralu_u_distribu_c1)).
fof(30, axiom,![X11]:![X12]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X12))))),file('i/f/pred_set/CARD__UNION__EQN', ah4s_arithmetics_NOTu_u_LEQ)).
fof(32, axiom,![X11]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/pred_set/CARD__UNION__EQN', ah4s_numerals_numeralu_u_lteu_c1)).
# SZS output end CNFRefutation
