# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))&![X3]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),X3))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X4),s(t_fun(X1,t_h4s_nums_num),X3))))))))=>![X3]:(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),X3)))))),file('i/f/bag/FINITE__BAG__INDUCT', ch4s_bags_FINITEu_u_BAGu_u_INDUCT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/FINITE__BAG__INDUCT', aHLu_TRUTH)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/bag/FINITE__BAG__INDUCT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X1]:![X3]:(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X1,t_h4s_nums_num),X3))))<=>![X2]:((p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))&![X17]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),X17))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X4),s(t_fun(X1,t_h4s_nums_num),X17))))))))=>p(s(t_bool,happ(s(t_fun(t_fun(X1,t_h4s_nums_num),t_bool),X2),s(t_fun(X1,t_h4s_nums_num),X3)))))),file('i/f/bag/FINITE__BAG__INDUCT', ah4s_bags_FINITEu_u_BAG0)).
fof(16, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/FINITE__BAG__INDUCT', aHLu_BOOLu_CASES)).
fof(17, axiom,~(p(s(t_bool,f))),file('i/f/bag/FINITE__BAG__INDUCT', aHLu_FALSITY)).
# SZS output end CNFRefutation
